[EVEL•CA ADD

Technical Memorandum 8-81

EXPERIMENTAL QUIET SPROCKET DESIGN AND NOISE REDUCTION

IN TRACKED VEHICLES

0Stephen A. Hammond

Curtis A. AspelundDavid C. Rennison FThomas R. Norris 4

Georges R. Garinther

April 1981AMCMS Code 612716.H700011

(Contract DAAKI1-78-C-0131)

Approved for publc release;distribution unlimited.

U. S. ARMY HUMAN ENGINEERING LABORATORY

".-- Aberdeen Proving Ground, Maryland

81 8 1-4 056

Destroy this report when no longer needed.Do not return it to the originator.

The findings in this report are not to be construed aS-an official Departmentof the Army position unless so designated by other authorized documents.

Use of trade names in this report does not constitute an official endorsementor approval of the use of such commercial products.

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flfl11L&WTAION AGEREAD INSTRUCTIONSREPORT PCff W NPAEBEFORE COMPLETING FORM

I. REPORT NUMBER I _GVT ACCESSION No. 3. REIIN5 CATALOG NUMBER/ / 2. GOP N

* ~~Technical MemorandA 8-81_ý 1,41__________)-___6. *TITLE (and Subiltl.) 'S. ----- -- -xEy..E. PRO CVERED

-EXPERIMENTAL QUIET SPROCKET DESIGN AND NOISE\2/REDUTIO INIRAKEDVEHICLES Fia ,-O-'

6.PERfOCRM f=_ERT NUMBER

S7. AUYNOR(s-) -. i A--,=NTRACT OR GRANT NUMBER(&)

Stephen A. /Hammnd Thomas R./Norris* Curtis A.!Aspelund Georges R t~arinther DAAK11-78-C-0l3l

David C. .. Re~nnis~on/ r)

9. PERFORMNG OR ,GANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PRO7JECT, TASKAREA & WORK UNIT NUMBERS

FMC Corporation, Ordnance Engineering Division,

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US Army Human Engineering Laboratory A rC2 Z81/ ______

Aberdeen Proving Ground. MD 21005 240UME~'IAE

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18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continuo on reverse side it n~e~cssarymid Identity by block number)

Tracked Vehicles Track and Suspension

Noise Reduction Statistical Energy AnalysisMechanical Impedance Measurement Finite Element Modal Analysis\Noise Sources

2&AABSTRACT (Coatfouo am reverse slif 9f ,ecoas"T ad Identlify br bloc~k num~bev)

The noise produced by track-laying vehicles has historically been a problem

in the US Army. Exterior noise provide,, enemy forces with a means of de-

tection at great distances. Interior vehicle noise prevents accurate

person-to-person or electrically-aided communication and is responsible for

excessive hearing loss among exposed personnel.

This program provides the Army with advanced technology to reduce tracked-

vehicle noise. The goals established were a 15 dB(A) reduction in interior - -

ooI ORI 1i7 EDITION OF 7 NO0V 65 IS OBSOLETE(onni)

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ABSTRACT (Continued)

noise to a level meeting the lOOdB(A) limit of MIL-STD-1474B, and a 6 dBreduction in exterior noise, representing a 50% reduction in detectionrange.

The work presently being reported, which is the third phase of the program,involved the design and fabrication of a high compliance prototype idlerand a high compliance experimental sprocket. The idler provided a reductionof 15 dB(A) of idler-contributed noise and the sprocket provided approx-imately 10 dB(A) of sprocket-contributed noise.

This report provides a comparison of the hull namics of the MII3AI andthe AIFV in order to determine the reason for the significantly lower noiselevel of the AIM.

A preliminary finite element analysis was made to determine if this tech-nique could be used to predict the dynamic response of the hull with theultimate aim of providing a method ¶of predicting hull configuration toachieve significant noise reduction.

ST

SECURITY cLASSIFicATION OF THIS PAGErI42en Vet. Entered)

AMCMS Code 612716.H700011 Technical Memorandum 8-81

EXPERIMENTAL QUIET SPROCKET DESIGN AND NOISE REDUCTION

IN TRACKED VEHICLES

Stephen A. HammondaCurtis A. Aspelunda Accession For

Dav•id C. Rennisonb NTIS-GRA&I

Thomas R. Norrisc DTIC TABGeorges R. Garinther Unoxincedo 111

Avaolbb.' > (odco

Dist spcc;a2.

April 1981

"- •trector

U.S. Army Human Engineering Laboratory

aFMC CorporationbTolt Beranek & Newman Inc.CConsultants in Engineering Acoustics

U. S. ARNMY HUMAN ENGINEERING LABORATORYAberdeen Proving Ground, Maryland 21005

Approved for public release;distribution unlimited.

CONTENTS

PageNo

1. EXECUTIVE SUMMARY ......... ..... ........................... I2. OBJECTIVES AND GOALS .......... ... .......................... 5

3. DISCUSSION OF TRACKED VEHICLE INTERIOR NOISE ...... .............. 3

3.1 General Discussion ...... ....... ........................ 33.2 MI13AI Interior Noise Levels ...... ................... ... 13

4. EXPERIMENTAL COMPARISON OF THE HULL DYNAMICS OF THE AIFV ANDMI3AI VEHICLES ......... ... ............................ .. 13

4.1 Conceptual Approach ......... ........................ .. 134.2 Vehicle Structural Characteristics ...... ................ .. 144.3 Power Flow Analysis. . . .................... .21

4.3.1 Review of Concepts ...... ..................... ... 214.3.2 Measured Results ... .... .............. 23

4.3.2.1 Hull Vibration Levels. ............... 234.3.2.2 Interior Noise Levels ................. 234.3.2.3 Hull Radiation Efficiencies.. . . . . . 284.3.2.4 Structural and Acoustic Loss Factor Data ........ 284.3.2.5 Power Flow Calculations .................. .. 35

4.3.3 Discussion ................................... 374.4 Hull Attachment Point Transfer Function Analysis .............. 40

4.4.1 General ...... ..... ....... ................... .. 404.4.2 Noise-to-Force Transfer Functions . . .. . . ....... .. 404.4.3 Hull Inertance Transfer Functions .... ............. .. 42

4.4.3.1 Left/Right Asymmetries - AIFV .............. .. 424.4.3.2 Left/Right Asynmnetries - M113A1 ............. .. 494.4.3.3 Effect of the AIFV Turret ...... ............. 494.4.3.4 AIFV/MI13AI Comparisons .................. .. 56

4.4.4 Discussion ............ ......................... 56

5. FINITE ELEMENT MODAL ANALYSIS OF AN M113AI VEHICLE ..... ........... 63

5.1 General ............ .............................. ... 635.2 Sunminary of Equations for Generalized Structural Vibration

Response and Interior Acoustic Power Radiation ............. .. 645.3 Modeling Procedure ......... ..... ........................ 655.4 Results ............... .............................. 67

5.4.1 Initial Model Configuration ...... ................ .. 675.4.2 Revised Hull Dynamic Model. ........................ .. 905.4.3 Frequency and Space-Averaged Calculations .... ......... 101

5.5 Discussion and Recommendations ....... .................. 109

6. PROTOTYPE COMPLIANT IDLER WHEEL DEVELOPMENT ..... .............. 110

6.1 Background ......... ... ............................ 1100.2 Experimental Idler Wheel ...... ... ..................... 110

6.2.1 Conceptual Approach ......... .................... 1106.2.2 Test Results ..... ....... ....................... . ii

PEPEDING PAGE BLANK-iNOT FIL-iED

6.2.2.1 Compliance . . . . . . . . . . . . . . 1116.2.2.2 Interior Noise Reduction of the Experimental

Idler Wheel ......... .................... 1156.2.2.3 Exterior Noise Reduction of the Experimental

Idler Wheel ................................ 1156.2.2.4 Durability of the Experimental Idler Wheel . . . 118

6.2.3 Further Investigations with the Experimental Idler Wheel.. 1206.2.3.1 Sources of Rapid Noise Level Variations ........ 1206.2.3.2 Shape of Experimental Idler Paddle Contact

Surfaces ........................... 1276.2.3.3 Effects of Combined Axial and Radial Compliance

Changes ............ ................... 1276.2.3.4 Track Guide Scrub Noise .................. .. 1316.2.3.5 Increased Diameter Idler .... ............. .. 131

6.3 Prototype Idler Wheel .......... ....................... 1346.3.1 Design Goals ........ ........................ .. 1346.3.2 Design Criteria ........... ..................... 1346.3.3 Design Concepts ................................... 138

6.3.3.1 Sectional Idler Rim ....... ................ 1386.3.3.2 Thin Flexible Rim/Rubber in Compression ... ..... 1386.3.3.3 Thick Rigid Rim/Rubber in Compression .... ...... 1406.3.3.4 Rim of Rollers ........................... .. 1406.3.3.5 Rigid Rim/Rubber-in-Shear ....... ............ 140

6.3.4 Results .......................................... * 1436.3.4.1 Compliance ..................... ..... ..... 1446.3.4.2 Interior Noise Reduction ...... ............. 1446.3.4.3 Exterior Noise Reduction ...... ............. 1446.3.4.4 Durability ....... ................... .14S6.3.4.5. Conclusions and Recommendations .............. 149

7. EXPERIMENTAL SPROCKET CARRIER DEVELOPMENT ...... ............... 149

7.1 Conceptual Approach ........ ........................ .. 1497.2 Design Goals ........... ........................... .. 1507.3 Design Criteria .......... .......................... .. 1507.4 Design Concepts ..................................- 151

7.4.1 Rubber in Radial Compression and Torsional Shear. ....... 1517.4.1.1 Solid Pair of Rubber Rings .... ............ .. 1527.4.1.2 Directionally Modified Compliance ............. 1527.4.1.3 Three Concentric Ring Pairs. . . . . . . . . . . 1547.4.1.4 Rubber in Radial Compression and Radial Shear ... 154

7.4.2 Compliant Fabric Isolator ..... ................. .. 1547.4.3 Overload Gear with Rubber Separators in Compression . ... 1587.4.4 Rubber in Shear ......... ...................... .. 158

7.4.4.1 Single and Double Pairs of Annuli ............. 1587.4.4.2 Triple Annuli Pairs ....... ................ 161

7.5 Results ............ .............................. 1617.5.1 Compliance ........ ......................... .. 1617.5.2 Interior Noise Redurqtion of the Experimental Sprocket . . . 1617.5.3 Exterior Noise Signature at the Experimental Sprocket . . . 1647.5.4 Experimental Sprocket Clatter ...... ............... 1647.5.5 Durability ........ ......................... .. 172

7.6 Recommendations .......... .......................... 174References ........ ..... ... ................................. 175

iv

Appendices

A. Theory for Hull Vibrational Response and Interior Sound Levels .... 177

B. STARDYNE Input and Output Data for Original Hull Model .... ........ 189

C. STARDYNE Input and Output Data for Revised Hull Model ........... ... 208

V

Figures

3.1 Schematic Diagram of Sources and Paths Responsible forInterior Noise in Tracked Vehicles ...... ................ 9

3.2 Noise Source Spectra at 15 mph At Center of Crew Compartment . 10

3.3 Noise Source Spectra at 25 mph At Center of Crew Compartment . . 10

3.4 Noise Source Spectra at 32 mph At Center of Crew Compartment . . 11

3.5 Track System Source Contributions to M113A1 Crew Area NoiseLevels At Various Speeds ....... .................... .. 11

3.6 Speed Dependence of Production M113A1 Noise At the CrewPosition Operating On Paved Track ..... ... ............... 12

4.1 Comparison of Hull Vertical Sections, TdKen AlongVehicle Length . . . . . . . ........ . . . . . . .... . 15

4.2 Comparison of AIFV/M113A1 Hull Details -- Rear View ......... 16

4.3 Hull Section Views, Looking Forward ................... ... 17

4.4 Comparison of Horizontal Sections of Vehicles, Above Sponsons.. 18

4.5 Comparison of Left and Right Idler Pads for AIFV ............ 19

4.6 Comparison of Left Idler Pad for AIFV and M113 ........... ... 20

4.7 Comparison of Hull Acceleration Levels on Left and RightHand Sides of Tracked Vehicles at 32 km/hr (20 mph):(a) AIFV # SJ005, (b) M113A1 (on blocks [16]) ......... ...... 25

4.8 Comparison of Acceleration Levels on Similar Hull Surfaces onAIFV and M113A1 Tracked Vehicles Underway at 32 km/hr (20 mph) . 26

4.9 Dependence of A-Weighted Interior Sound Level on VehicleSpeed for the Vehicles Tested ....... ................. ... 27

4.10 Crew Position Interior Sound Level Spectra for UnderwayAIFV Vehicles at 32 km/hr (20 mph) ........ .............. 29

4.11 Interior Sound Level Spectra, AIFV NSJ0005, Showing theEffect of Forward Speed ..... ....... .................... 30

4.12 Effect of Forward Speed on Interior Sound Level Spectra

for AIFV NSJO002 ......... ........................ .. 31

4.13 Calculated Radiation Efficiencies for Typical Hull Panels. . . 32

4.14 Structural Loss Factor Data for AIFV (NSJO005) ........... ... 33

vi

Figures (cont.)

4.15 Structural Loss Factor Data for M113A1 (SJ136) .............. 34

4.16 Comparison of Hull Dissipated (L d), Hull Radidted (Lr ), andAcoustic Dissipated (Lwa) Power tevels; AIFV (NSJOOO5Y at 32km/hr (20 mph), Test Track Data ........ ............. .. .36

4.17(a)Major Contributors to the Hull Radiated Power Levels; AIFV(NSJO005) at 32 kin/hr (20 mph), Test Track Data ............. 38

4.17(b)Major Contributors to the Hull Radiated Power Levels, M113A1Vehicle at 32 km/hr (20 mph) supported on Jackstands .......... 39

4.18 Instrumentation for Hull Inertance and Transfer FunctionMeasurements .......... ........................... .. 41

4.19 Nuise-to-Force Transfer Functions for Horizontal Excitation ofIdley Spindle (a) AIFV, (b) M113A1 ...................... 43

4.20 Noise-to-Force Transfer function for Vertical Excitation ofIdler Spindle (a) AIFV, (b) M113A] ...... ................ 44

4.21 Noise-to-Force Transfer Functions for (a) Vertical and (b)Horizontal Excitation of Idler Spindles (Average of Left andRight Idlers Presented; 50N Pink Noise Force Input) ........ 45

4.22 Comparison of Left - and Right-side Horizontal Inertances onAIFV Idler Spindles (Turret on Vehicle) ...... ............ 46

4.23 Comparison of Left - and Right-side Vertical Inertances on AIFVIdler Spindles (Turret on Vehicle) ....... ................ 47

4.24 Corparison of Horizontal and Vertical Left Idler SpindleInertances on AIFV Vehicle (Turret on Vehicle) .............. 48

4.25 Comparison of Left - and Right-side Horizontal Final DriveInertances on AIFV Vehicles (Turret on Vehicle) ........... .. 50

4.26 Comiparison of Left - and Right-side Vertical Final DriveInertances on AIFV Vehicle (Turret on Vehicle) .............. 51

4.27 Comparison of Left - and Right-side Horizontal Inertances onM113Ai Idler Spindles ........ ....................... 52

4.28 Comparison of Left - and Right-side Vertical Inertances onM113AL Idler Spindles ......... ...................... 53

4.29 Comparison of Horizontal and Vertical Left Idler SpindleInertances on M113A1 Vehicle ...... ................... .. 54

4.30 Effect of Turret Mass on Horizontal Idler Inertance Functionof AIFV (Right Side) ....... ....................... .55

vii

77

Figures (cont.)

4.31 Effect of Turret Mass on Vertical Idler Inertance Functionof AIFV (Right Side) ....... ....................... .57

4.32 Effect of Turret Mass on Vertical Final-drive InertanceFunction of AIFV (Right Side) ......... .................. 58

4.33 Comparison of Vertical Inertance Functions for M113A1 andAIFV Vehicles (Left Side) ....... .................... .. 59

4.34 Comparison of Horizontal Inertance Functions for M113A1 andAIFV Vehicles (Left Side) ....... .................... .. 60

4.35 Comparison of AIFV and M113A1 Inertance Functions: FinalDrive Attach ...... ........................... 61

4.36 Roadwheel Attach' Inertance, Measured at Bottom of Attach..... 62

5.1 Isometric View of Node Locations, Initial Hull Model(a) Side Plate (b) Bottom Plate (c) Top Plate .... .......... 68(d) Element Projections . . . . . . . . . . . . . . . . . . .. . 69

5.2 Isometric View of Hull Elements - Initial Hull Model .......... 70

5.3 Idler Pad Static Flexibilities ...... .................. .. 72

5.4 Typical Vibration Mode Shapes for Initial Model of M113A1 Hull(a) 19.6 Hz Antisymmetric (b) 30.3 Hz Symmetric(c) 53.2 Hz Antisymmetric (d) 56.4 Hz Symmetric .......... 75(e) 62.7 Hz Antisymmetric f 66.8 Hz Symmetric(g) 85.9 HzAntisymmetric (h) 93.7 Hz Symmetric .......... 76(i) 111.6 Hz Antisymmetric j 136.6 Hz Symmetric(k) 156 Hz Antisymmetric (1) 176 Hz Symmetric ........... 77(m) 207 Hz Antisymmetric (n) 219.7 Hz Symmetric(o) 222 Hz Antisymmetric ....... .................... .. 78

5.5 Hull Modal Density ........ ... ....................... 80

5.6 (a) Horizontal Idler Response to Horizontal Idler Excitation . . 81b) Vertical Idler Response to Vertical Idler Excitation ..... .82c) Vertical Idler Response to Horizontal Idler Excitation. . . . 83

5.7 Comparison of Measured and Calculated Horizontal and VerticalLeft Idler Spindle Inertances on M113A1 Vehicle .... ......... 84

5.8 (a) Top Plate Response to Idler Force .................. 86(b) Bottom Plate Response tv Idler Force ..... ............ 87

5.q Effect of Variation in Loss Factor on Calculated Horizontal andVertical Left Idler Spindle Inertances on M113A1 Vehicle..... 88

viii

Figures (cont.)

5.10 Effect of Loss Factor Changes on Calculated Bottom PlateTransfer Function (Node 1001) for Vertical Idler Force ......... 89

5.11 Top Plate Transfer Functions for Vertical Idler Force .... ...... 89

5.12 Representative Modes Shapes of Torsion Box Beam ............ .. 91

5.13 (a) Isometric View of Hull Elements - Revised Hull Model . . .. 93(b) Node Map of Revised Hull Model: Projection ............. 94

5.14 Typical Vibration Mode Shapes For Revised Model of M113 Hull(a) 29.5 Hz Symmetric (b) 41.3 Hz Antisymmetric(c) 55.0 Hz Symmetric (d) 62.6 Hz Antisymmetric ......... 97(e) 103.0 Hz Antisymmetric (f) 105.0 Hz Symmetric(g) 172.7 HzSymmetric (h) 213.3 Hz Antisymmetric ........ 98(i) 245.1 Hz Symmetric (j) 273.0 Hz Antisymmetric(k) 296.0 Hz Symmetric . . . . . . . . . . . . . . . . . .. . 99

5.15 Comparison of Measured and Calculated, Horizontal and VerticalInertances for M113AI Left Idler Spindle: Revised Hull Model . . 100

5.16 Acceleration-to-Force Transfer Function for Hull Top Plate:Comparison of Calculations and Measured Data ..... ........... 100

5.17(a)The Effect of Different Idlers and Their Locations onHorizontal Idler Inertance Functions ...... ............... 102

5.17(b)The Effect of Different Idlers and Their Locations on

Vertical Idler Inertance Functions ...... ................ .. 102

5.18 Effect of Ilder Location on Roof Response: Vertical Excitation . 103

5.19 Vertical Idler Inertance (10) of M113 Vehicle ..... .......... 105

5.20 Contribution of Resonant and Nonresonant Modes to Top PlateResponse for Vertical Excitation of Idler (10) ............... 107

5.21 Comparison of Measured and Predicted Noise-to-Force TransferFunction for Vertical Excitation of Idler Spindle on M113A1 . . 108

6.1 Schematic Diagram of the Experimental Compliant Idler Wheel . . . 112

6.2 Experimental Idler Wheel Mounted on Test Stand ............ .. 113

6.3 Experimental Idler Wheel Mounted on Test Stand (Closeup) ....... 114

6.4 Interior Noise Reduction of tpe Experimental Compliant Idler. .. 116

6.5 Interior Noise Spectra at 30 mph Due to Right Idler Wheel Only. . 117

1x

Figures (cont.)

6.6 Exterior Noise of M113A1 Standard Idler Pair Compared toM113A1 Exhaust Noise at 25 Feet to the Left .... .......... .. 119

6.7 2,000 Hz Exterior Noise at 30-mph, 3 Feet from ExperimentalIdler ................ .............................. 121

6.8 250 Hz Interior Noise at 30-mph, Due to Experimental Idler .. . 122

6.9 Spectrum of Sound Level Meter "DC" Output which Correspondsto Interior Noise Level Fluctuations ................... .. 126

6.10 Effect of Metallic Track-Idler Impacts. Conpliant Idler,Rounded Paddle vs Flat Tops ........ ................... .. 128

6.11 Triaxial Vibration Levels on the Experimental Idler Discat 30 mph ................ ...... ...................... 129

6.12 Triaxial Vibration Levels on the Increased ComplianceExperimental Idler at 30 mph. .................. 130

6.13 The Effect of Increased Compliance in the ExperimentalIdler at 30 mph, Interior Noise ...... ................. .. 132

6.14 The Effect of Track Guide Scrubbing on Interior Noise ......... 133

6.15 Interior Noise Reduction Due to a Large Diameter Idler Wheel. .. 13b

6.16 Prototype Idler Wheel Mounted on an M113A1 Vehicle ............ 136

6.17 Schematic Diagram of the Prototype Compliant Idler Wheel. . . .. 137

6.18 Idler Concept: Thin Flexible Rim; Rubber in Comnpression ....... 139

6.19 Idler Concept: Thick Rigid Rim; Rubber in Compression ........ 141

6.20 Idler Concept: Rim Composed of Rollers .... ............. .. 142

6.21 Interior Noise Reduction with the Prototype CompliantIdler Wheel ............. ........................... 145

6.22 Interior Noise Spectra Comparison for the Standard andPrototype Idler Wheels .......... ...................... 14b

6.23 Exterior Noise Spectra of M113AI Standard Idler Pair, Prototype

Idler and M113A1 Exhaust, at 25 feet to the Left of Hull ....... 1477.1 Sprocket Concept: Solid Rubber Ring in Compression.. ........ 153

7.2 Sprocket Concept: Seomented Rubber Ring in Compression with

Circumferential Holes .......... ...................... .. 155

7.3 Sprocket Concept: Three Rubber Ring Pairs in Compression .... 156

X

Figures (cont.)

7.4 Sprocket Concept: Rubber in Both Radial Compression andRadial Shear ...... ................... . . . . . . . . . 157

7.5 Sprocket Concept: Fabric Isolator........ . . . . . . . . . 159

7.6 Sprocket Concept: Overload Gear with Rubber Separators inCompression . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

7.7 Sprocket Concept: Rubber in Shear. The Design Chosen forExperimental Development and Test . . . . . . . . . . . . . . . . 162

7.8 Experimental Sprocket Mounted on Test Stand . . . . . . . . . . . 163

7.9 Noise Reduction in Crew compartment Due to the ExperimentalCompliant Sprocket ...... . . . . . . . . . . . . . . . . . .165

7.10 Noise Reduction in the Driver's Compartment Due to theExperimental Compliant Sprocket . . . . . . . . . . . . . . . . . 166

7.11 Crew Area Noise Spectra of Standard and ExperimentalSprocket Wheels at 30 mph ...... . . . . . . . . . . . . . .167

7.12 Drivers Compartment Noise Spectra of Standard andExperimental Sprocket Wheels at 30 mph. . . . . . . . . . . . . . 168

7.13 Exterior Noise Levels 25 feet to the Right of the VehicleDue to the Left Sprocket Only . . . . . . . . . . . . . . . . . . 169

7.14 Exterior Noise Spectra at 30 mph Due to the Left SprocketOnly. Measured 25 feet to the Right of the Hull. . . . . . . . . 170

xi

1=

Tabl es

4.1 Space-Averaged Mean Square Acceleration Level, 063 re I y, forthe AIFV NSJO005 at 32 km/hr (20 mph) ......... ................ 24

4.2 Loss Factor Data for Hull Structure and Interior AcousticVolume For the AIFV Vehicle ........ ..................... 35

5.1 Idler Attach Pad Flexibility ...... ... .................... .. 71

5.2 Modal Extraction Data: Initial Hull Model ........ ............. 74

5.3 Modal Extraction Data: Revised HjIl Model ...... ............. 96

5.4 Equivalent Beam Properties (5-inch idler spindle) .............. 1Ul

5.5 Normalized Generalized Mass of Structural Lleiments ........... 106

6.1 Variations of Interior Sound Levels ...... ................. .. 124

6.2 Calculated lIterior Noise Modulation Frequencies .............. 125

x1

ACKNOWLEDGEMENT

The Human Engineering Laboratory greatly appreciates the encouragement and fund-

inq provided by the I . S. Army Tank-Automotive Command. The success of this

program would not have been possible without the effort of Don Rees of that

orqan izat ion.

0 1%

xiii

HiF __ _

1. EXECUTIVE SUMMARY jTHIS STUDY SHOWED THAT CONVENTIONAL NOISE REDUCTION TECHNIOUESARE ONLY MARGINALLY EFFECTIVE IN TRACKED VEHICLES. BASED ON ASPECIAL COMPUTER PROGRAM PREDICTION, IT SHOULD BE POSSIBLE TOACHIEVE A 65% NOISE REDUCTION INSIDE AN M113 HULL BY REDESIGN-ING THE IDLER AND SPROCKET AND ISOLATING THE ROADWHEELS. THEADDITIONAL NOISE REDUCTION TO MEET MIL-STD-1474B SHOULD COME =ABOUT THROUGH HULL MODIFICATIONS. FULL SCALE SUSPENSIONHARDWARE HAS DEMONSTRATED THAT THE ABOVE GOAL IS REALISTICALLYACHIEVABLE.

The noise produced by track-laying vehicles has historically been a prob-lem in the U.S. Army. Exterior vehicle noise provides enemy forces witha means of detection at great distances. Interior vehicle noise preventsaccurate person-to-person or electrically aided communication and con-tributes to hearing loss amonq exposed Army personnel.

If the Army is to provide personnel with armored vehicles having maximumeffectiveness, noise must he reduced to the limits prescribed by MIL-STO-1474B. To accomplish this end, a multiphase program has been conductedto develop a thorough understanding of the noise sources, the acousticaland vibratory paths through which energy enters the hull structure,and the mechanisms by which noise arrives at the various crew locations,and emanates from the exterior of the vehicle. Based upon the results ofthese analyses, the redesiqn of major noise-producinq components and theapplication of new materials and coatings will then he under'-aken. Thevehicle chosen to develop this noise reduction technology is theM113A1. The goals set for the program were a 17 dB(A) reduction ininterior noise to a level of 100 d1(A), and a 6 dB reduction iF, exteriornoise representing a 50' reduction in detection ranqe. T~is reportdescribes the third phase of the proqram to reduce the noise cf armoredtrack-laying vehicles to the above goals.

Phase I of the proqram isolated and rank ordered the various ncise sour-ces responsible for overall noise, developed a computer proqram to pre-dict changes 1i.n noise level produced by channes in track and suspension,

systems, and provided an understandinq of the noise producing iiechanismof vehicles such as the MII3AI. This phase found that track-idler inter-action was the major source of noise with the sprocket and roadwheelsheinq the second and third sources, respectively.

"Phase II developed the concepts necessary to reduce suspension system!noise, and produced an experimental idler to verify the noise .-eductioncapability of these concepts. The vibratory power flow of the M1I3]hull was analyzed and experimental damping, absorptive, and harriertreatments were evaluated along with experimental modifications.

The present phase (II) involved desiqning and fabricatino a prototypelquiet idlei and an expcri.ental quipt sorocket. Also the hull dynamicsof the MI13AI and the AIFV (both of similar size and suspension) werecompared to determine the reason for the significantly lower noise levelof the AIFV. A preliminary finite element analvsis was r:iade to mvetermnine

_ I

if this technique could be used to predict the vibrational mode shapesand dynamic response of the M113A1 vehicle with the ultimate aim of pre-dicting the hull configuration required to achieve significant noisereduction.

Based upon the conclusion that the idler is the major noise contributor,a completely new design of the idler wheel was pursued. The designproceeded in two steps, the first being a verification of the conceptthat an increase in complience of the wheel rim would indeed reducenoise. This idler wheel was designed to permit experimental variationsof radial, tangential and axial compliance. The second step was a prac-tical design which incorporated those features determined to be most ap-propriate in the experimental version of the idler. This prototype idlerwheel was designed with the goal of being practical, increasing noise re-duction potential, and being directly interchangeable with the standardidler wheel. It has a solid outer rim mounted on two rubber "doughnuts"acting in shear which, isolate the rim from the axle. The maximum strokeof the rim when contactinq the track is 3/4 inch, with a fail-safe stopin the event of a severe impact upon the idler. Measurements on the teststand indicate that this prototype idler wheel reduces interior idlergenerated noise by 15 dB(A) to a sound level of 95 dB(A) at a speed of 30mph. Limited duirability tests at 30 mph indicate that this idler wheelis both durable and practical.

The idler contribution to the exterior acoustic signature was reduced towell below the level of exhaust noise. If the sprockets and roadwheelscan be quieted as much as the idler, then suspension-related noise wouldno longer lead to vehicle detection, even at high speeds, as the exhaustnoise would then be dominant.

Based upon the corcepts developed for the idler, an experimental sprockethas been developed using a number of rubber "doughnuts" to isolate theaxle from the outer rim. However, a compliant sprocket is significantlymore complicated since it must be capable of transmitting torque throughthe compliant element. Also, it must have fail-safe stops in the tanqen-tial as well as the radial direction. Tests of the experimental sprocketindicate that it is up to IO dB(A) quieter than the noise produced by astandard sprocket. Although noise reduction is less than that providedby the prototype idler and the design is more complex, it is anticipatedthat the second generation sprocket design will be practical and willprovide 12-15 dB(A) noise reduction.

The next subject which was addressed in Phase III was the comparison ofthe noise of the M113A1 with that of the AIFV. A-weighted noise levelsinside the AIFV vehicles and structural vibration levels on the hull ofthe vehicle are on the average, 5 dB lower than for M113A1 vehicles. Al-though the track and suspension or both vehicles are essentially the samethe upper hull shape and idler attachment are different. These differen-ces were investigated using the concepts of statistical energy analysisfor hull generated noise and the attachment transfer function to inves-tigate idler qenerated noise. It was concluded from this analysis thatthe major hull radiating elements are the bottom plates and upper side

-2-

plates at low frequencies for the AIFV vehicle. For the M113A1 vehiclethe top plate is dominant and the side platcs are still important. At

higher frequencies (above 500 Hz), the sponsons dominate the acousticradiation for both vehicles.

Inertance functions are measures of the power accepting and dissipatingcharacteristics of the hull structure. In general, reductions in idlerinertances will lead to reductions in structural response levels, whichin turn will lead to reductions in interior noise levels, provided thatthe acoustic radiation efficiencies of the structural elements are notsignificantly altered.

At frequencies below 250 Hz, the vertical inertance of both M113A1 andAIFV hulls is greater than that in the horizontal direction. This indi-cates that if the horizontal and vertical idler input forces were equal,vertical forces would dominate the hull response. However, test trackdata show the horizontal forces can exceed vertical forces by up to 10 dBfor at least one speed during normal pperation.

Chanqes in idler attachment point configuration have no significant ef-fect on vertical inertances. However, the raised idler location for theAIFV vehicle has a lower horizontal inertance (by about 5 dR) in the fre-quency range 125 Hz to 250 Hz. Therefore, at frequencies above 125 Hz(see Fig. 22, ref. 16), the idler attachment point will, to some extent,affect (by up to 5 dB) the vehicle interior noise levels, at least at aspeed of 30 mph.

It was also concluded that changes in the idler stiffness by up to a fac-tor of ten will have no significant effect on the hull structural re-sponse or vehicle interior noise levels. This is because power flow intothe hull is controlled by relatively flexible hull members with lonqstructural wavelengths. Additionally, the turret mass does not signifi-cantly impact the vehicle inertance functions and hence interior noiselevels.

Appropriate structural modifications were not immediately obvious fromthe statistical energy and attachment transfer function analyses, so afinite element analysis was developed to guide the hull redesignprocess which aims to produce practical hull modifications providing5 to 10 dR(A) noise reduction. In this analysis technique, the M113A1is modeled by a number of individual structural components or elementswhich are interconnected at a number of joints, or nodal points. Thesimplicity of the M113A1 shape lends itself well to this type ofanalysis. This analysis technique provides accurate calculation ofhull resonance frequencies and mode shapes which, in turn, provides anunderstandinq of the hull power flow for noise control purposes.

The initial model which was made has some accuracy problems. A secondmodel, which was constructed with a qre-'ter number of elements, is suffi-ciently detailed to allow reasonable predictions of mode shapes and re-sonance frequencies up to frequencies of about 300 Hz. Extension above

-3-

400 Hz using the current nodal arrangement is not recommended. Good pre-dictions of the measured vertical idler inertance function have been madewith the developed model, 7buct t•e measured horizontal intertance functionis underpredicted by about 10 dB.

A preliminary calculation using frequency and space averaging to predictinterior noise levels was encouraging and showed reasonable agreement be-tween measred data and results predicted using finite element analysisfor the noise-to-force transfer function corresponding to one third oc-tave hand vertical excitation of the idler spindle on the M113A1 vehicle.

Frequency and space average calculations using finite element analysisresults indicate that the interior noise levels at frequencies above 31.5Hz are controlled by resonant response of the hull, rather than by stiff-ness controlled response as was considered a possibility at an earlierstage of the work. This suggests that, in theory at least, damping ofthe structure should be an effective means of interior noise control. Inpractice however it is~difficult to effectively damp the important hullmembers due to the long structural wavelengths involved.

Statistical energy analysis provides a useful framework for understandingthe power flow between the hull structure and vehicle interior space,even at low frequencies. This allows frequency averaged interior noiselevels to be accurately calculated from frequency and space averagedstructural response data which may be measured experimentally or calcu-lated using the finite element model.

Frequency and space averaging of the modal output data (using statisticalenerqy analysis) from the finite element model is the most efficient anduseful means of evaluating the effects of hull structure modifications onstructural response and hence interior noise levels. It is anticipatedthat this method will be used in the future to evaluate the effect ofhull structural changes on interior noise levels, as evaluating the datamode by mode is tedious and the results are difficult to interpret.

To date, the entire noise reduction program has identified the idler asthe major noise source, with the sprocket and roadwheels being 3-4 dB(A)less intense. A computer program has been written to predict the changesin sound level resulting from configuration changes in the track and sus-pension system. Idler noise has been reduced by the predicted amount of15 dB(A), and the first generation sprocket design has produced up to a10 dB(A) reduction. It is anticipated that roadwheel isolation will pro-vide a 10-12 dB(A) reduction of roadwheel noise. A complete suspensionsystem incorporating the above quieted wheels should provide an interiornoise level at least 10 dB(A) (65% noise reduction) quieter than a stan-dard M113 vehicle.

The additional 7 dB(A) of desire' noise reduction will be achieved bymodifications to the hull. Preliminary results indicate that simple,conventional noise reduction techniques provide only marginal results and

-4-

may not be practical. Therefore, a more extensive approach is requiredto reduce hull generated noise. It is anticipated that hull noise can bereduced by 5-7 dB(A) which combined with the suspensinn noise reductionwill provide the desired total of 17 dB(A). This reduction will producea vehicle which meets the noise limit of 100 dB(A) prescribed by MIL-STD-1474B.

The fielding of light armored track-laying vehicles meeting this 100dO(A) lifnit will provide a vehicle which is less detectable and operatesmore efficiently, and will permit the crew and cavalry personnel toperform their mission in a more effective manner.

2. OBJECTIVE AND GOALS

The basic objective of this program was to develop feasible noise controlconcepts to aid in construction of a lightweight tracked vehicle thatwill permit crew members to perform their duties without the additionaluse of hearing protectors. They are presently required to use hearingprotectors in addition to the DH132 Combat Vehicle Crewman's Helmet.Reduction of the interior noise level also would improve communicationbetween crew members.

Accordingly, the goal of an interior A-weighted noise level of 100dB hasbeen set, in conformance with the quidelines of MIL-STD-1474B, CategoryB. Achievement of this goal requires a 17 dB(A) noise reduction in theMI,13AI, primarily at low frequencies. In a weight-critical machine de-signed for survivability in an extreme environment, this represents amajor technical challenge.I The U.S. Army Human Engineering Laboratory (HEL) and the U.S. Army Tank-Automotive Command (TACOM) have recognized that practical design modi-fications required to achieve significant interior noise reductions werenot available. It also was realized that the development of these noisecontrols must be based on experimental and analytical evaluations of boththe noise sources and their transmission paths. Studies prior to the HELsponsored work [2, 11, 18 and 19] had identified the major noise sourcesbut had not quantified their contributions. Two preceding studies by FMCCorporation, sponsored by HEL, have been conducted. The first studyidentified the separate contributions to interior noise generated by theidlers, the sprockets, and the roadwheels. This work also identified sev-eral promising concepts for tracked vehicle noise reduction. The secondstudy developed an experimental idler to prove and optimize noise reduc-tion concepts. Concepts for reducing hull-generated noise also wereexplored.

Beginning with the third phase of this progrdm, TACOM, which has recog-nized the operational advantages of reducing both interior and exteriornoise, has provided funding for this joint HEL/TACOM effort. The M113AI

¶ vehicle was chosen as the demonstration vehicle for this study because itwas used in the previous HEL-sponsored studies, because of vehicle

-5-

4• ÷

availability, and because of the relative availability and low cost ofreplacement parts. However, all noise reducing concepts developed Inthis study could be adapted to other tracked vehicles with suitablescaling changes.

Only suspension noise sources were considered in this study. Previousstudies [3, 16] have shown that other noise sources are secondary; suchas the engine, power train, and final drive gearing. Furthermore,suspension noise sources are common to high-speed tracked vehicle noiseproblems and the technology needed to successfully reduce the noise fromthese sources does not exist at present. Developing practical noise con-trols for these suspension noise sources is the fundamental purpose ofthis program.

This present phase of the work follows largely from the results of theprevious two phases [16, 17]. The most important conclusions obtainedfrom that research were:

1. The technology to reduce tracked vehicle noise does not exist andwill require development.

2. Very careful control of testing parameters is necessary to accur-I ately measure the incremental noise reductions obtained whenevaluating potential noise reduction methods.

3. At and below 20 mph, both idler and sprocket noise must bereduced to meet the noise reduction goals.

4. Above 20 mph, roadwheel noise also must he controlled in additionto idler and sprocket noise.

5. Engine and power train noise is not significant compared to sus-pension induced noise.

6. Vehicle interior sound absorptive treatments are not practical.

7. Making the idler and sprocket wheel rims more compliant is an ef-fective noise reduction technique.

8. The best spring material for compliant idlers and sprockets ap-pears to be either natural or synthetic base "natural" rubber.Steel springs would be difficult to engineer into the limitedspace available.

9. A number of highly resilient elastomers were evaluated as springmaterials, but were found to have inferior mechailcal or dampingproperties.

* 10. In a compliant idler wheel, axial as well as radial and tangen-tial compliance need to be investigated.

11. A very compliant experimental idler wheel was designed, fabri-cated, and found to be rugged enough for extensive acousticaltesting. Measurements showed that the compliant wheel is 10-12dB(A) quieter than the standard idler wheel.

12. Local stiffening of the hull at the roadarm and idler loca-tions provided no significant changes to the mechanicalimpedances and, therefore, no noise reduction potential.

13. A damping treatment applied to both sporsons provided appreciablesponson vibration reduction at 500 Hz and higher trequencies.This treatment also gave a modest vibration reduction of otherhull plates, and noise reduction of approximately 0-2 dB(A).

14. To achieve appreciable noise reduction b v means of hull platedamping, a promising technique is constrained layer damping.(This was later found to be much less effective than initiallyexpected.)

15. The computerized simulation of track dynamics, while producingpromising results, would require incremental refinement before it

should be used in desigrin] lower noise suspension components.

The reported program extends the previous work. The purposes are toevaluate and optimize the noise reducti 'on of the previously developed ex-perimental compliant idler, to demonstrate a practical reduced noise

idler, to demonstrate the feasibility of a compliant sprocket, and togain a better understanding of how the suspension vibration is conveyedthroughout the hull and can be reduced by hull changes. This researchwas divided into five independent tasks, each of which could help reducenoise. These tasks were to:

1. Measure noise and durability characteristics of the previously devel-oped experimental idler. Determine the importance of axial, radial,and tangential compliance on idler noise -,eduction.

2. Based upon the results above, desion, fabricate and test a prototypequiet idler with a goal of A-weighted interior noise level of 95dBand a service life of greater than 2000 miles. Exterior noise reduc-tion will also be assessed.

3. Design, fabricate, and test an experimental sprocket carrier basedupon concepts developed for the compliant idler.

4. Determine the source of differences in interior and exterior noiselevels between M113AI and AIFV vehicles. Consideration would be

* given to individual noise sources, the method of attachment of thesuspension components, and the coupling and radiation properties ofthe hulls.

5. Construct and exercise a finite element nodel to predict the vibra-tional mode shapes and dynamic response of the M113A1 vehicle.

4

•, -7-

SThe first tAsk yalidated the concept of a compliant-rimmed idler, anddetermine those eatures which were most important for noise reduction,The second task showed that the concept could be used in a practical,production-feasible idler that has the durability required of trackedvehicle suspension components, and will still lead to reduced interior A.weighted noise level produced by the idler of 95 dB. The third taskshowed that the concept proven on the idler also could be adapted to apractical sprocket design which could transmit torque through the compli-ant elements to the track. The fourth and fifth tasks compared the hullstructures of two vehicles of similar desiqn, one of which is, on theaverage, 5 d3(A) quieter than the other. The fourth task approached thisproblem with an experimental comparison, while the fifth task addressedthe problem from an analytical approach.

In this project, FMC Corporation, the producer of the M113A1 vehicle, wasthe prime contractor responsible for the design, test, fabrication, andoverall management of the program. Mr. Thomas Norris of Consultants inEngineering Acoustics produced the idler concepts and preliminary design,and assisted in the final hardware design and testing. The experimen-tal cohmparison of the hull dynamics of the AIFV and M113A1 vehicles wasconducted hy Dr. David Rennison of Bolt Beranek and Newman Inc. ofCanoga Park, California. The finite element modal analysis work wasconducted by Dr, Rennison, with the computer modeling done by Dr. KennethFoster of Foster Engineering Company.

3. DISCUSSION OF TRACKED VEHICLE INTERIOR NOISE

3.1 General Discussion

Interior noise in tracked vehicles results from track interaction withthe drive sprockets, idler wheels, and roadwheels. The engine andpower train are secondary noise sources in most tracked vehicles. Somevehicles, such as the M60 tank and the Infantry Fighting Vehicle (IFV),have track support rollers which also may produce significant interiornoise. The track-ground interaction was not found to be a significantsource in any of the vehicles tested. Figure 3.1 is a schematic repre-sentation of tracked vehicle noise sources and vibration paths.

Noise in moving tracked vehicles results from vibration of the hull whichis excited by suspension and engine-power train components. The interiornoise levels at the driver and crew locations consist of direct and re-verberant contributions. Due to space and other practical limitations,noise reduction in lightweight tracked vehicles can only be obtained byreducing hull vibration, rather than by installing barriers or absorbers.Consideration of "conventional" acoustic noise control barriers and ab-sorbers showed that, because the entire hull radiates noise, the A-weighted noise goal of 1OOdB could not be met within practical weight,cost, durability, and size limits. Therefore, the noise control conceptsaddressed in this study were: (1) the reduction of vibration at the vari-ous sources, and (2) attentuation of vibration energy paths between sour-ces and the hull.

8S~-8-

Engine and Noise 1 Noise Reverberant Driver andDrive Train Contribution Crew

on Locations

Noise

Vibration ViDration

Vehicle Hull Structure

Vibrdtion Vibration Vibration jVibration

Roadarms

00 0

Sprocket Idler Roadwheels SupportRollers

Figure 3.1 Schematic Diagram of Sourcis and Paths Responsible

for Interior Noise in Tracked Vehicles.

A9'

4

-9-

-_..P- LL!nfI ll JII _lII1lII• _llin!I Al.i 1___ ]

v- , / L...,-PRODUCTION•, ,A MI. 13-A_:I ->- -1'

RIGHT IDLER ONLY . 1S- - SPRCKETQNY

~,j/ - IMIL-STU*1474. . . - . . .. . . .

-~ (CATEGORY 8) 34- 4-

110-: -------- '.; - - -. :i

A 90 A /ý H I,, ON i tLY i O ' P ,i ', •" •

1 , ' . -• - _ -- 4 -• . . , _- .ow 10 -low

31 .5 6.1 12ý 250 5 W 1000 2000l 000 BODO• 16000 -OCTAVE BAND CENTLR FREQUENCY-HERTZ

| ~Figure 3,2 Noise Source Spectra at 15 mph• at Center of Crew Compartment

* L

PR-,-•DUCTION ÷_ _

S[ : • ,• : "°.. : RIGHT iLETSROC ONLY"- _1 0 1 .....

L ON SROKE OL

~~4LY 1760 HPý 1 *.

S•oI " I !p

v , , loci -- *1

--4

Wi1N( .'IN ' ONLY (230 RPMNI1-

31 5 63 15 250 Soo 1000 2000 4000 B000 16000

OCTAVE BAND CENTER FREOUENCY- HERTZ

figure 3.3 Noise Source Spectra at Z5 mph at CenLer of Crew Compartment

410--. "

-. ( 0 Nu~ IMr IL I ~I

12 I~ ---.-.---- ~-~A. _ IGHT SPLROCKET ONL

I .*-. CATEGORY 8

100

0JIN ON Y S"

31.5 63 12-5 -2 50U -50-0 -1000 -2 00 4f00 8000 16000

I .AVE BAND I.ENTER FP.EOIFNOCV HERT7

Figure 3.4 Noise Source Spectra at 32 ir-ph at Center of Crew Com~partmenet

1201

110oj 1

15 MPH 7C MPH.,.

Figure 3.' Tracty System, Source Contr,LJýJons to '., I1>1 Crevw A¾reaJise Iev e at Vý.ariouts Si-cdc.

t . ' ! - -

-- ' -, : , %.*A,•6 fl

"- '.LEVE 4LS --

S- x-, -,,4 - /-s x4•_,. _-• ': -- -,,, -, -.- " , .fr - --- • .. , 20.3. ,

241

i' '~~, f.IILiL f Sf"':E ( MIL.ES Pi:R 1IOU1,

SFigure 3.6 Speed Dependence of Production MEl3A1 Noise at the Crew PositionOperating on Paved Track.

4-12-

Ina ..

7 . .. . . . .. . .. . . . .0 .. .. . . .. . . . . .

The basic phenomena responsible for tracked vehicle hull vibration attypical operating speeds are tension changes due to the geometry of trackengagement with the idler and sprocket wheels, and for.es resulting fromimpacts between track shoes and the idler dnd sprocket wheels. Both ofthese phenomena occur at track-layinq rate. A further discussion ofthese phenomena appears in Reference [16].

3.2 M113AI Interior Noise Levels

When under way, the airborne noise levels in both the crew area anddriver space on the MlI3A1 armored personnel carrier exceed comfort,cn:umtinicat ion, and hea-inq conservation standards.

For example, at 30 miles per hour the A-weiqhted noise level near thedriver's head 1cLt ion is 117 (Wi. At the same speed, the noise levelis P?- dM in the ?L)0 Hz octave hand, These levels are, resnectively, 17and 2I dlR ahove those noise levels specified as acceptable in MIL-STn-117411, Categlory 0, which is the maximum allowable level for systems re-(knirin q e ectr'icallv-aided communication via an attenuatinq helme. orheadset..

The octave hand spectra for 15, ?5 and 3? Ilph in the crew compartmentare presented in Finures 3.2, 3.3, and 3.4. The noise levcls of the pro-(uction MI13AI exceed the soecification goal hy 12 to Iq dO at 250 Hz,,1oeioendinG, on vehicle speed.

The relative noise contributions of the idlers, sprockets, and roadwheels!re presented in Figqure 3.5. The dependence on speed of both the A-weightod noi se 1 ovel an,I o ctave hand! noi se 1 evel s is presented in Fi qure3.6). in.or- coii plete discussion of these noise source levels appears in

4. ,PFRITlNIAI COMPAR I SON OF THE HULL PIYNAMI CS OF THI AIFV AND M113AIVI I C' ý, !

4. 1 ;Conceptual Approach

, ha; b)een observed that the A-weiqhted noise levels inside certain AIFVVvehic:les are on the averaqe 5 dOl lower than inside the similar MI13AI ve-hicles. The pri-nary structural differences between these two vehicles ofalmost ide('tical size are the upper hnll shape and the idler attachmenttiotails, the track and suspension system being essentially the same forthe twn vehicles. An excellent opportunity was therefore available toexplore Ithe potential tnr interior noise reduction as a function of thesehn Ih I des i (in diffferences

e; ir, ff or t to deve 1 of) an elipi ri ca 1 understand i nq of the importance oft wo,' sWnt 1ie st rmmctural dif ferences , two studies were undertaken to exam--if, o nenrqv flow within both vehicles. The first investigated noise and

4&

vinration characteristics hy usinq the concepts of statistical ererqyanalysis and the second contrasted the attachment point transfer func-tions of the vehicles' suspension systems. The results of these analyseswere then used to guide the developrment of an analytical ,.iodel , which is Ato be used to predict the effects of proctical structural hull modifica- -•

tions on the vehicle interior noise leve,3.I

4.2 Vehicle Structural Characteristics I

The A[FV evolved from the baseline MI3 concept insofar as the suspen-sion, track, and lower structure are almost identical for the two clas-ses of vehicles; in fact, many of the structural component'; are inter-changeable. Various differences exist, soI:;e Miaior and others rathersubtle; this discussion will concentrate on these differences. Fijures4.1 to 4.6 present alternative views of the two hulls selected to hiqh-light the major structural ele ",ents expected to ha ve the oreatest influ-ence on the noise differences between the two vehicles. Emphasis hasbeen placed on the vehicles' rear sections and the ,,ier attachmentareas. In each figure the M1i3AI hull is used as the haseline and theAiFV apoears on the overlav.

Fiqure 4.1 shows a section view looking f',or1 t0e vehicles' left. sides.The largest differerces at the vehicle front are the snallower slope ofthe AIFV nose and its relatively thinner hull thickness. The use ofbolt-on arl:,or protection m'ounted over buoyancy foam equalizes the hullsurface dersity, out rec,.;ceS :parIel: hendin.,o roi'ii,1it1 . Th- final drivemountino system, flooring configuration, box bear, lower side plate, andsponsun details appear the same for the two vehicles. Roadarms aremounted in the same positions in the box beamis.

Major ,•'.ferences occur in the vehicle top socrfaces and rear configu'ra-tions. The A!7V has provision for a turret (lrass about 1200 kg) and itsrear half is conposed of more anr s",:a11,er elate eleaments, foroling , sti f-fer hull in the circulnferential direction (see Figure 4.2 for a rearview). Fiqure 4.3 ccntrdsts the vehicle cross sections in the 'turret'plane: the added turret mass ind the more riiid hull cross section mighthe expected to redice the po)wer acceptin'l characteristics of the hull andthereby reduce the itnflw ow or v irit i,) Tld] Pergyv, d'. I tast at low frequen-cy. A commparison of the details o4 tne horizontal section toward therear of the hull and at a olane above the sponsors .s shown, in Figure4.4. The fuel tanks are relocated from, an inboard left position on theMII 3AI to a rear-mounted overhanging position on thc AIFV (see Figure4.1). A considerable difference in hull vertical inert.ance could resultat the idler attachment position. !r! (general, the thi-knesses of the"upper side' plates on the AiFV are some 30', less than on the M1l.3A1, due

to the use of space-laminate bolt-on arrlor. Ramp details for the twovehicIes are similar.

Sdl er plate detai's are cooparJ iro Fi0 q es I.5 an, 4. 6. The former

compares the configuration of left dld riqht idler plate shapes for tbe

4 Ii

7'!

M113AIo FM','C L)WG 109R1/50

.7<

A1FV, Irm'S DWG 41,-5"30

FIqjt;r•., 4.1 Comparison of Hull Vertical Sections, Taken Along Vehicle Length

-15-

I

-�.1I

- -

IIII -�

IiII

I I

------,----.j I

K_______

�" - --------

I 7

I.I,

Z = =

LIV, �C DwG 4I73�2O

*1

.. �. �oc¶4�ar1SOn 0' A.IFVMfl3A� Uull Detai1� - Re� View

4

AlA

IIL_

* ~AIN, FMC DWG 4175730

4Figur-e 4.3 Hull Section 'Views, tooklnll rorward

Uppe, Side 11910 (44. .5m

Sponson -Roo, Plo'. (38.2 n --)

Al r /'~ 4~*~f

I 11gure .4 Cb)rf,ar 1 sOn ifHoryI Zonta I Sect Ion~ of Veh Icles, Above Spons on

Idler Pad Ba

Left Idler Pad (Viewed from Right FMC DWG 4169492)

Right Idler Pod (FMC DWG 4169490)

Figure 4.5 Cornparisofl of Left and Right Idler Pads for A1FV

4 -19i

38. I mmBox Beam f.."Box Beo_

• Rear Wall

I '

I I

t- 0

Idler Pad

Ml13AI, FMC DWG 10932751

I75 mm Idler Axis

I.'

AlFV, FMC DWG 4179145

.. •Figure 4.6 Comparison of Left Idler Pads for AIFV and M113

-20-

S,

AIFV; the differences suggest the likelihood of asymmetries in the noisetransmission characteristics of the idler attachments. Similar differ-ences in longitudinal position of left and right idlers occur on theM113A1 and are to allow for fitting of the torsion bars from left andright sides; the left track has one more shoe than the right track.Figure 4.6 shows the differences in idler attachment pad location, withregard to vertical positioning of the idler spindle relative to the box-beam: the idler spindle on the AIFV is located some 64rmm higher than onthe M113A1 (on each side of the vehicle).

Certain directions for the comparison of the two classes of vehicles be-come clear from this brief comparison. Experimentally,it would be ofinterest to explore, in addition to absolute differences between the twovehicles, the potential asymmetries in hull dynamic response and attach-ment point inertance which may occur between left and right sides of eachvehicle, and whether, for the AIFV, these are influenced by the turretmass. On the other hand, the influences of alternative idler locations,of fuel tank/rear plate configuration, and of the details of changes inhull cross section are more practically studied analytically with thefinite-element model of the hull structure. This work is described laterin the report. The work reported below describes the experiments carriedout and the results of the various comparisons made of the two vehicles.

4.3 Power Flow Analysis

4.3.1 Review of Concepts

Statistical energy analysis (SEA) provides a convenient means of describ-ing the flow of vibrational and acoustic power between connected systems,in terms of gross parameters such as the energy levels, modal densities,and overall physical properties of the connected structures and/or acous-tic spaces involved. A review of the concepts involved can he found inreferences [16] and [17]; a surnary of relevant equations, using metricunits, is presented below.

The vibratory power dissipated in a panel structure Wd (in watts) isgiven by

Wd = Wrl<v 2 >m, (1)

where

W (=2nf) is the circular frequency (radians/s),n~ is the total structural loss factor (that is, the sum of the

acoustic radiation and str4icturai dissipation cqmnponents),<v2 > is the space-average mean-square velocity (m/s), 2<a2 > is the space-average mean-square acceleration (,n/s )2 andm is the panel mass (kg).

Expressed in engineering units and in te-ms of space-average mean-squareaccelerations, this equation becomes

-21-

Lwd (dOB re 10"12 watts) = AL (dB re I g) + 10 log - + 131.8 (2)

where

2I g = 9.8 m/s andAL is the acceleration level, calculated as AL=10 log [<a 2 >/(l g) 2J

The power radiated from a plate Wr (in watts) is calculated from mea-sured plate acceleration levels according to

Wr (3)A

whereS is the panel surface area (m-).

cc is the characteristic impedance of the acoustic medium (for air,pc is about 415 mks rayls, where mks rayls kg/mr/s), and

a is the (nondimensional) radiation efficiency of the plate.

0 is a function of the plate critical frequency fc' the plate area, andthe length of attached stiffeners fc is calculated as 12600/h, where his the plate thickness in mm. In engineering form, equation 13) becomes

Lwr (dB re I pW)= AL (dB re 1 g) + 10 logu + 10 log (S/f 2 ) + 150.0 (4)

The net acoustic power flow into the vehicle interior is balanced bythat absorbed on the vehicle bounding surfaces and by its occu-pants, Wabs (in watts). For a reverberant acoustic space, with airas the acoustic medium this balance is given as

Lwr = Wabs = <Pi> V•.rni/C 2 (5)

where

<pi 2 is thý space-averaged mean-square interior acoustic pressure

(Pa ) , 3V is the interior volume (m ), and

n~i is the interior acoustic loss factor

Equation (5) may be expressed in engineering terms by

Lwa (dB re I pW) = Lp (dB re 20PPa) + 10 log (Vfrll) - 17.5 (6)

where the interior speed of sound is taken as 343 m/s. It is noted thatthe interior acoustic loss factor relates directly to the interior re-verberation timeT as ri =2.2/(Ttof). Equations (2), (4),and (6) describe ?he balance of structural and acoustic energy levelswithin the vehicles: these may be calculated from measurements ofacceleration levels and structural loss factors, measurements of theinterior noise levels and acoustic loss factors, and from the systemgeonmetry.

-22-

In the following sections, these quantities ;neasiared on the AIFV vehicleare contrasted. with existing data for the M113AI vehicle presented 41nReference [17]. M113A1 data were recorded or vehicle number SJ136, at32 kiin/hr- (20 miph) during normial underway paved track operation. AIFVnumbers NSJ00OS and tNSJO00fl were used for- tests; underway data at arange of track speeds were recorded and analyzed for both. Emphasi shere is placed on the NSJO005 vehicle, as this vehicle is the quieter ofthe two, although limited NSJO002 data is presented to allow comparisonsbetween these two vehicles to be made. Comparisons between vehicles aremade at 32 kiii/hr (20 miph) .

4.3.2.1 Hull Vibhration Levels

Vibration l evel s were cieasured at about, 40 locat -ions on those interiorradiatinq surfaces of the AIFV expected to deternine the interior acous-tic 1;ower flow. Tab! e 4. 1 [%resents spdCe-3veraned m~nsquare accel era-tion levels for the major radiating interior panels. The analysis wasca.r r ied ouijt in, one-third octave bands, but! data ýis presentled in cctaveb and s, and inr uonero 1 , t hree ieas u rement Iloca t ions were u sed to c al1cu -1,4,-e the aseraqe fý)r each Panel . The standard deviation in accelerationI evel between different locations on the same paniel was, in general,less than 1 (di ait 250 Hz and less than) 0.5 dB at 100.0 Hz.

Thep A IF V vibrat ion llevelý oiui the i eft-hai-K hLA l anl are generallIy 31to ") d P greater than those or-. the corresponding right-hand panels, asshown in Figure 4.7(a) for the sinonsons and uop.,er si:de plates. T'his isi ! cont ra st to r.¶113P.1 data which shows the riqht-hand panel vibrationlevels to be margina lly greater than those or, the left-hand side (Figure4i.7 (b))). Similar but weaker trends were observecý on the NSj0002 vehicleas for the NSJOOO5 vehicle.

I quries 4. ?) an 4. ) b coyi;-are the underway accel eration levels ons i-ili1ar hull 1 surfaces of t he A:FV and l-1113A1 trackedl vehicl es : almiost:m'vuer-Sall1v., the AIFY levels adr-e 7 to 10 dBM lower than those en the

1 i31A1 h[.11 1

P is c 1 car- f rin; t nose d'ate, that the susipension at tachment pIn resp[o nse and the force-to-noise transfer functions should be examined foras~y'dmetries between left anid right sides -)f the vehicle.

4.3.2.? inter-or lioise Levels

The d'ependence on forward speed o)f the A-weicihted interior- sound levelsfor the !'IFV vehicles tested is presented in figure 4.9. The mean soundI e'.P'1s and t he associated lo liimits are shown for The 'ISJO0CS vehicle

ad ), ri~d, to 1 a can t a i'Iaxi'iuil level of 110 dB(") as fnrwardl sp'eed'~creases above 4Pý kn/hr (7niphl . This is in contrast to data -ieasiired.

t* r t'WO ot her vehi cles, NSd0O,"0? aid NSJ143, in which the soundi leveýlincreases wi h increasingq speed above 30 k::i'hr.

-23-

TABLE 4.1

SPACE-AVERAGED MEAN SQUARE ACCELERATION LEVEL, 0B RE I G FOR THEAIFV NSJOO05 AT 32 KM/HR (20 MPH).

THICK- Octave band Center Freauency - HzP L AREA NESS 63 175 250 ';W . k k - k --

Botto.1 PIlate 4.1 2M.1 -1.( -1.4 -2.? -5.0 -5.P -5.3 -7.2 -16.1

Floor Plates 4.1 5.0 -0.8 3.4 0.4 0.2 2.2 -4.3 -5.6 -13.8

Lipper Side Plate;

Left 3.4 28.1 -S.0 -6.? -4.1 -6.9 -F. -7.1 -5.7 -14.2Ri(iht 2.4 -11.7 -13-3 -6.9 -5.6 -6.R -9.4 -8.7 -17.8

Incline' Side elate:Loft 1.4 3,t.I -2.6 -6.5 -s.? -8.2 -7.3 -9.7 - . R -17.1Rioht -9.1 -9.2 -7.4 -10.2 -10.2 -13.7 -14.7 -22.n

Spon son•Left 2.0 12.5 -A.5 -8.3 -6.4 3.8 2.8 . 5.3 -.3.9Rioht 1.3 -7.8 -10.4 -7.4 0.9 -2.6 -1.1 1.0 -9.6

Lower Side Plate:Left 1.1 31.S -2.1 -5.0 -5.4 -r.1 -3.R -6.2 -5.7 -12.2Right o.8 -3.3 -10.R -7.? -8.3 -4.q -4.5 -4.9 -13.6

Engine Access

a.0el 1.0 6.n -1.Q -?.3 -0.6 -2.5 -1.4 -1.2 -4.1 -13.4

Ra•,p 2.3 38.1 -9.9 -8.8 -11.9 -11.5 -12.2 -20.2 -20.6 -30.5

Tn)p Plate 9.6 38.1• -5.5 -2.1 -7.1 -7.9 -7.5 -14.9 -14.3 -23,8

Carmo Hatch I.0 3R. 1 2.3 -5.5 -6.4 -7.7 -8.5 -8.2 -9.1 -11.6

4 - 2

"- . C- __

'r_ joper Side Plate

Left Side

-% -- --- Ight Side

-J - I ' Sponsori Top

to t-- - - & Sid

- ~ ----- Rigt Side

63 125 250 500 Ik 2k 4k ek -I(j) AIFV Frequen~cy kHz)]

V'!~er Side Plate

'Lef t S i e

0 \ \,..~~titSile.2 SCor'sor 7oD

O .10''-e't Side

~ Side

-2063 125 250 500 1k 2k 4k 8k

W )M I 13A I Frequency (Hz)

Figure 4T.7 Comparison of Hull Acceleration Levels on Left and Right Hand Sidesof Tracked Vehicles at 32 km/h (20 mph) (a) AMIF kSJO005,Wb M113Al (on blocks (16)).

44

- ~- Maim

[ (0)

104

'ci

S/" \/ \

- o / /• •

- ' 01

o I/oi .I - - .•

L.. . ."." -

-2o i ' ' I I

03 125 250 500 1k 2k 4k 8akFreQuencv 01z' :

,10 b)

c\

63 125 25 00 l 2k 4k

.n A1VadM13ITake eils newy t3 mh 2 p)

Ja

o

53 125 250 500 1k 2k 4k 8k

"". Frequ~vicv (H z)

Figure 4.8 Comparison of Acceleration Levels on Similar Hull Surfaceson AIFV aind Mll3Al Tracked Vehicles Underway at 32 km/h (20 mph).

i

, I ~-26-

C.

204o- I0.

C*4/NSJ0002

115 - NSJ143

S110 "00, NSJO005

• • 105 -/[0

/oo -

95 -

5 10 15 20 25 30 35 mph90 1I I I 1 1 I -----

t0 20 30 40 50

Forward Speed

Figure 4.9 Dependence of A-Weighted Interior Sound Levelon Vehicle Speed for the Vehicles Tested.

6.

4:

Fiqure 4.10 shows interior sound level spectra for the under way AIFVvehicles tested at a forward speed of 32 km/h (20 mph). Also shown isthe spectrum of the M113A1 sound level, taken from Figure 6 of [16]. Theinterior spectrum levels for the AIFV are generally 5 dB lower thanthose in N1I3AI vehicle, the differences for AIFV NSJO005 being onlymarginally less than the differences in hull panel acceleration levelspresented in Fiqure 4.8. Measured octave band spectra of the AIFV in-terior sound levels, showing the dependence on vehicle forward speed,are given in Figures 4.11 and 4.12 for vehicles NSJO005 and NSJOOO2,respectively; the speed characteristics of the two vehicles are quitedifferent, reTiectinq slight differences in construction detail, toler-ances, or track condition. The differences in interior sound levelsbetween the two AIFV vehicles compare closely witn the differences inhull panel acceleration levels. For example, at those forward speedswhere NSJO002 sound levels exceed the NSJO005 levels, NSJOO02 accel-eration levels exceed the NSJO005 acceleration levels by similaramoun ts.

4.3.2.3 Hull Radiation Efficiencies

While the structural characteristics of the liwer section of the AIFVand M113AI vehicles are essentially the same in terms of their radiaticnproperties, the upper portions of the AIFV are smaller in area and thin-ner than for the M113AI, with resulting differences in radiation effi-ciencies. Figure 4.13 compares the calculated radiation efficiencies forvarious AIFV hull elements with those for the MI13A1 hull taken fromReference [17]. The AIFV appears to have slightly greater radiationefficiencies, but the differences are generally less than 3 dB. This 3dB, when subtracted from the 7 to in d3 difference in accelerationlevels between AIFV and M113AI vehicles, matches closely the differencesin interior sound level shown in Figure 4.10 to exist between the twovehicles.

4.3.2.4 Structural and Acoustic Loss Factor Data

Loss factor information for the hull and interior space is used to de-terinine the energy dissipation occurrinq in the two systems. Structuraldecay measurements were made using an impulse technique, while acousticdecays involved interrupting a steady-state interior acoustic signal andobserving the oecay rate.

Structujral loss factors for AIFV and M113A1 vehicles are presented inFigures 4.14 and 4.15. Data were measured on the larger hull surfaces,

but there appears little significant difference between the differentlocations. Further there are no significant differences between thploss factors of the two vehicles, being typical of welded built-upaluminum or steel structures. The bolt-on armor plating does notappear to provide any sionificant hull damping because the foam coreis not sufficiently stiff to resist deformation. The calculatedradiation loss factor for the AIFV roof is shown in Figure 4.14,T(rad=?•CSO / w): this curve, which is representative of all the

-29-

C, • •

* . . .4•,•. ---•• • m..

L\

u~~~~ Va Vtiotion " ,

""cc

i - e , NSJO002

0 NSJO005

aI

70

0

I

63 125 250 Soo 10300 2000 4000 B000 16, 000Cctove Bond Center Frequencies in Hz

-- NSJ005

• Figure 4.10 Crew Position Interior Sound Level Spectra for• Underway AIFV Vehicles at 32 km/h (20 mph).

4

-29-_ _

I

120

SI ' "

Iaf w o - , - ,

(-4

- I-

* I I i i 1 2 mpn

,.?,-_ _ I _ _ _ _ _ _ _ _ _

so

i~~2 mphmp

63 125 250 500 1000 2000 4"XT--000 16,000

A. Ocltve Bond Center Frequ~nciet ;n Hz

Figure 4.21 Interior Sound Level spectra, AIFV NSFOQO5,Showing the Effect of Forward Speed.

4K-,

120

NN

S 100

0i3

Ia Irmph\ 20 mph

C

0 0163 15 20 50U0 00 00 80 600

oeav Bon CotfFeuI c mH

Figure~~~~ 4.2 Efc fFradSee nItro on ee

Spcr foIIVNJ02

4I

Lef -/

U ,-er side Olate_,a..ft SponsoI. -OD

:..._.Dottorn. Plate

- -nil Access PanelsA

I~Plates

6J 125 25 k- 2k 4k Sk

()AIPV (NS100O5) Frequ*olfc (Hz)

4-

;per Sice Plates

-s tf VD P a tes

I A~ccess P ?, e

-20

63 125250 00 1k 2 k ý4k Bk

Ib MI 3A I (S.1136) Frequeficy (Hz)

Figure 4.13 Calcualted Radiation Efficiencies for Typical

Hull Panels.

-32-M

F I I

L I II ' I

€ 3 Ot .om P! ateIL 3o:o-nef q '-e- c bI-•r de F•.•te - :

II J-• RQ•,t Sio•'eo *.! e" Siie l ateIi I I

I I I

I I I

10- ,

I I7 I , i

I I!

10 --- -"-• 2.{

I I

I I I I I

"RadiaP•lltion 0L i

I I10 63 125 25( 500 I 2 k 8 6

! • Figure 4.14 Structural Loss Factor Data AIRV (NSJO005).

"" -33-

' II

*R a ih't ~ Side 3f 3p

K'Q 'ht ~'ner S'3e Diate

10,

102'

'-rev ous 4k' \I data?26

63 125 250 500 Ik 2k 4k 3k 16k ~Fr owcmy (H4%)

Figure 4.15 Structural Loss Factor Data M113AI (F-136).

-34-

radiating surfaces, lies well below the hull total loss factor curvessuggesting that internal losses dominate the energy dissipation process. -As noted previously [26] there appears considerable scope for increasingthe hull total loss factors, particularly at frequencies above 125 Hz.Whether this is practical Delow 500 Hz in view of the influence of lonqwavelength vibration modes [], remains to be seen.

Acoustic loss factors of the interior soace are presented in Table 4.2, 1together with the averaged hull loss factors. Good similarity betweenprevious acoustic reverberation times and Dresent data was found.

I

4.3.2.5 Power Flow Calculations

Calculations for the underway AIFV (NSJO005) of the power dissipated inthe hull structure and the power dissipated by radiation frcol hull pan-els into the hull interior, and calculations of the interior acousticpower level ebsorbed in the hull, were made following equations (1)thruuqh (6). The interior acoustic dissipated power levels were calcu-lated from the mpasured octave-band noise levels (Fiqure 4.10) and the

TA6LE 4.?

LOSS FACTOR DATA FOR HULL STRUCTURE AND INTERIOR ACUUSTIC VOIUMEFOR THE AIFV VEHICLE

Octave Band Center Hull Loss Factor Interior Volu.meFrequency (Hz) Loss Factor

63 0.30 0.065175 0.055 0.037250 0.015 0.02150 0. 0065 n.01?1k 0.0040 0.00742k 0.0028 0.0037;k 0.0022 0.00259K 0.0016 0.0014

loss factor data in Table 4.2. Hull dissipated and radiated power lev-els for individual panels were calculated from. averaqed panel octave-band acceleration measurements (Table 1.1), hull loss factors (Figure4.14) and calculated radiation efficiencies (Figure 4.13(a)).

The power balance results are presented in Fiqure 4.16 for 32 km/hr (20;qph) forward speed. Also shown are the baseline interior acoustic powerlevels for the M113A1 vehicle [?6]. The acoustic power radiated from

4 toe hull surfaces (Fiqure 4.16, curve 3) closely matches the acousticpower level dissipated (i.e., absorbed) within thp hull interior space(curve 2), as WdS found for the M113AI vehicle [17]. The hull dissipatedpower .:lue to structural clamping nleLhmn i s3,s ,qi re 4P , curve

A -35-

I

130

IN,

90

I80 (1

-I !, N I,SII ',_ __"_ _.

S125 250 50.0 1 3 2 4'0 "\ :

Ccoove 3arvd Ceptcr ;:re~qujenc~ :n 'W

gHull Dissipated (L), Hull Radiated (L

dnd Acoustic Dissipated (L ) Power Levels; A 'FV ( )SJOCoS)Via

"at 32 k"/hr (20 mph). Test Trdck Data.

tO n l • ;..

S' 5 125 250 00 I?,O OOO •-"30 •00-,,h-

4¢oe•r•Cm~ rqec• ••

C'!

exceeds by up to 10 113 the power dissipated by radiation from the hullsurfaces, even allowing for radiation froin the vehicle exterior, Theacoustic disipated pawer levels for the M1I3AI (Figure 4.16, curve 4)taken froain 17], are up to 103 dB greater than those presently measured onthe AIFV NSJLJ005 under similar test conditions (curve 2), consistent withthe differences in interior noise level spectra.

Figure 4.1/ snows the calculated major contributors to the hull radiatedpower levels for the AIFV at 32 kmn/hr (20 mph). The bottom plate isclearly the dominant source at frequencies less than 5(00 liz, and the pan-el elemnents on the left side of che vehicle contribute significantlygreater power than those on Ohe rignt side. Figure 4.17b shows the cdl-cuiated major contributors to the hull radiated power levels tor theM113AI at 32 km/hr (20 mph) tor comparison with the A[FV. The contribu-tioris frori the top panel, upper side panels and lower Side panels (bothleft and right combined) are siiu lar and to avoid confusion are repre-sented by a single curve. The data used for the curves are from refer-ence [17], where data for the left arid right sides have been combined andonly the totals presented. Thus, no distinction is wade ds to which sideradiates more power. For the M113AI vehicle, Figure 4.17b shows that thesides and top are the iiiost important contributors. The A!FV top plate isa relatively weak contributor, in contrast to the situation for theMII3AI. The smaller-element, stiffer cross-section of the AIFV hull ap-pears to blocK the flow of vibrational energy froai attachment point tothe vehicle top surface.

As for toe '1113A1, however, barriers would not oe a p.'actical form ofnoise control due to the relatively large radiating areas.

4.3.3 ULIscussion

The major observations to be made troi.i these measurements and calcula-tions are:

1. The AIFV hull vibrdtion levels, particularly in the top plate, aresignit1cantly lower than in the M11,3I1 vehicle during underway trackoperation. These oitterences are si-niliar to the differences i-, in-teriur sound levels.

2. The adjor radiating null elements are the bottom plate and the upperside plates at low frequencies, with the sponsons becoming dominantat trequencies above their fundamental spanwise resonance. This isin contrast with the .1I3AI where the top plate controlled the inter-ior sound levels.

3. statistical Lnergy Analysis provides a useful trainework for under-stanL, mig the power flow between structure arid interior space evenat frequencies as low ds 250 HZ.

-37- i

120I

90

0 '~ ~ re 4cc.ess -'ne'.S

T_ IS

63 125 250 5013 1000 10-30 4X0 A00 rh ,300Cctove Bond ':em~er Fre'quenciei nmH

Maor Confributocs Within IU dB of ThtoI Radiated Po'wer

Figure 4.17a Mlicjr Contributors to t-he Hull Radiated Power Levels,AIFV (NSJOOO5) at 32 kp,/H (20 mph) Test Track Data.

'49

120

j0 Plate

6 Averoge, lop, Lippe' Side -

,g 80 --4___ _

63 125 250 S00 1000 2000 4000 80000'Octave Bond C.~.fter Frequencies in Hz

Figjure 4.17: 5~ ,i'or COntrib)utor's to the Hull Radiateo Power Levels, M113AI Vehicleat R~ kriv') h(2," nqp',j) Suprorrtpd on jackstands

4~- 30-

Previous experiments showed that surface damping treatments are unlikelyto significantly reduce interior sound levels, even though the responseof the hull is primarily resonant. This is mainly due to the difficultyin damping modes with a long structural wavelength, which are importantcontributors to the overall structural response and acoustic radiation.

Composite structures of the same mass and bending stiffness (for strengthpurposes), and consequently having the same resonance frequency distribu-tion, will be no more amenable to damping than the existing plate confi-guration: this is because the wavelength of the structural modes will beunchanged as a function of frequency. Composite structures of the samemass but lower stiffness (ignoring strength considerations) will have ahigher modal density, but will be more amenable to structural dampingtechniques. It is believed that these two factors will offset eachother, since the vehicle's resonant response is proportional to the modaldensity (which will increase) and inversely proportional to the structur-al loss factor (which will in~rease). In fact, preliminary analysis in-dicates that the vehicle response will increase, rather than decrease asrequired. While composite structures involving laminated damping layersma provide an advantage, an analysis of the potential benefits as a

nction of structural stiffness, mass, and loss factor (which itselfdepends on these two parameters) should be developed to guide any empir-ical study. It is recommended that such studies be undertaken before anyexperimental work is considered.

4.4 Hull Attachment Point Transfer Function Analysis

4.4.1 General

Attachment point noise-to-force transfer functions (TF.'s) and inert-ances were measured on AIFV and MI13A1 vehicles for various configura-tions in an attempt to determine the influence of the differences in hullconstruction on the power accepting capability of the two hulls. Themeasured data are presented and discussed below. The instrumentationsystem used is shown in Figure 4.18. Inertance is defined as the trans-fer function between acceleration output and force input, where the ac-celeration is measured at the point of application of the force,

H(jw) = a(jw) - a_ýJ: a. ej(c-B)F (jw) IFIeJB JFJ

so that IH(jw)l ='j is the inertance magnitude and

O(jw) = (o-t) is the inertance phase angle.

4.4.2 Noise-to-Force Transfer Functions

Differences between left- and right-side noise-to-force T.F.'s at theidler spindle in both vertical and horizontal directions were measuredon the AIFV NSJO(05 and M1I3AI SJ136 vehicles: the reduced data are

-40-

CDi

T u

o ~CN

4-J

jLL

4-JI LM

CL 0000w

r4U

d< ý MC

13

shown in Figures 4.19 to 4.21. Figure 4.10 (a) shows left- and riqht-side noise-to-force T.F.'s for horizontal excitation of the idler spin-dle. The right-side T.F. is marqinally higher than the left-side in themid-frequency range, in comparison to the situation for the MI13AI hull(Figure 4.19 (h)), where d'.fferences of up to 6 d1 in T.F. occur between400 Hz and 1 k0z. Comparison of the average of left- and right-sidehorizontal data for the two hulls, as in Figure 4.21, shows that thenoise-to-force T.F. for M113AI hull exceeds that for the AIFV by 3 dRover most of the frequency ran(e from 100 Hz to I kHz. (These trendsare also reflected in the left/right AIFV/MII13AI horizontal iriertancemeasurements as seen in Fiqures 4.2? and 4.23 in Section 4.4.3).

Data for vertical excitation of the idler spindles are presented in Fig-ures 4.2(1 and 4.21. The riqht-side T.F. for the A]FV exceeds that for .the left side by a ýalue of about 3 d5 over the whole frequency ranqe I(Figure 4.2n(a)) in contrast to the case for the MI13AI hull (Fiqure4.20(b)) where the left and right T.F.'s are similar. These are incontrast to the acceleration level differences hetween left and riqhtsides of the AIFV vehicle shown in Figure 4.7(a). Left/right averaqeddata for the two hulls are compared in Figure 4.21(a), where the ahso- -

lute differences in T.F. magnitude are seen to he about 10 d13 at aboit12S liz decreasino to I to 2 dl0i at I k0z. (Aqain, these differences arein general aqreement with those foind in inertance measurement to hepresented in Section 4.4.3).

We note that the present T.F. 's for the .1-13Ai hul 1 are in rgooal agree-nent with those previously presented in [16]. Fiqure 39, which involveda similar measurement configuration.

4.4.3 Hull Inertance Transfer Functions

4.4.3.1 Left/Riqht Asymmetries - AIFV

Left- and riqht-side idler inertance, umeclsures'ents, both ma(InitudeH and phase , for horizontal and vertical excitation of the

AIFV hull, with turret mounted on vehicle, ire orpsented in Figures 4.22and *1.?3. 'n both directions, considerable asymn,ýtrv between left andright sides nt the AIV L;l I iiPler i ner t • (i vx • 1 st, al thou(ih fbi s isstronqPSt in the vertical direction and in the rý,,ion of I kHz. At lowfrequencies, the horizontal hull i nertances -icreaso sronnthl v at alout12 dlM per doublinq of frequency, and the phase anqle between accelera-tion and force is 1,0c, characteristic of a stiffness-cnntrolled svster.As freouency increases, hull resonances produce fluctuations in inert-ance magnitude and decreases in phase anqle. In the vertical ýirection,the inertance nau!nitude fluctuates strono1 y at low frequencv about thegmnonth horizorntal inertance function; correspnndin ol y strono variationsin phase angle occur. Hull resonances are appdrently more easily driven

by .vertical idler force than by o.,e in the hori ortal direction. This 4is mlore cledrly seen in !iqgre 4. ?4 where horizonta3 and v*'rt i al inert-ances are c1l)Idred over the fre,,uency rarn e mii, t. 2•;. Hz.

-4?-.I

404. (a) r --...

S,4,/'

Rim Had id

fIz/

.f 3 • • Le ft H a nd Sid e

00o2

" ' • ~ R i g ih t H a n d • S id e

16 31.5 63 125 250 500 1000 20AO

Cctave Bond Center Frequencies ;m Hz

, Figure 4.19 Noise-to-Force Transfer Functions for Horizontal• Excitation of Idler Spindle (a) AIFV (b) M II3AI.

-43-

70

60-

50 -z _

-0-

60-/50

0 -Rigt Hand Sde

- RgLeft Hand Side

40-

4 , -o

3 0

16 31.5 ý,3 125 2 550 500 1000 2000Octavo Bond Center Frequencies in PHz

SFigure 4.20 Noise-to-Force Transfer Function for Vertical;jExcitation of Idler '-nindle (a) AIFV (b) MII3AI.

Lea-44-

404

70 1(a) Vertical

• 0 /

60/

/Z 501

I IIo -AI

L ~ 40-

U 0/

C /

40--

%%•/" " " -,-----AIF

V

3053

20'

310 63 I2 5 0 00 W 4

Cctove Bond Center Frequencies in Hz

SFigure 4.21 Noise-to-Force Transfer Functions for (a) Vertical and (b) Horizontal,•Excitation of Idler Spindles. (Avera e of Left and Right IdlersSPresented: 50N Pink Noise Force Inp u )

I Ii

-45-

- AIFA

000 0

'0o 0

00LI

C)V

4 )

Ci

9p U)HU-~ialIM

0

I '-

4/ S-

'Ir

S-U

SP (J H 4.3H

-47-0

*ýO Puo u09DJ&I&3'3V u~a'40qa l~ 010%4d'0

0 ii0 cc

e

~A

0

- -0 ---- 0 1

(CL

i-i-

04~~~~, 1CoJ)H.,O a:U42u nz0

4 N-;j

TAT

Similar results are observed at the final drive attachment points. Fi-gures 4.25 and 4.26 show the horizontal and vertical inertances respec-tively. Only small inertance differences between left and right sidesexist in the horizontal direction, but in the vertical direction strong-er asymmetries (up to 8 dB) occur. Of greater importance is the 5 to 8dB difference between vertical and horizontal inertance over the lowfrequency range up to 250 Hz. As for the idler spindle, stronger cou-pling occurs betweEi the hull and final drive attachment point for ver-tical excitation than for the horizontal direction. We also note that - -

the magnitudes of the idler inertances are greater than those for thefinal drive, in both excitation directions.

4.4.3.2 Left/Right Asymmetries - M1I3AI

Left- and right-side inertance asymmetries in the horizontal and verti-cal directions on the M1I3AI idler spindles are shown in Figures 4.27and 4.28. The right side idler attachment is 3 to 5 dB stiffer in thehorizontal direction over much of the frequency range to 2 kHz. Thereis close correspondence in vertical inertance over most of the frequencyrange except oelow 200 Hz, where ýtronger coupling to resonant modes oc-curs for the right idler. These asymmetries are reflected in the noise-to-force transfer functions presented in Section 4.4.1.

The vertical ard horizontal idler inertance functions for the MII3AI arecompared at low frequencies in Figure 4.29. A 10 dB difference in in-ertance function riagnitude reflects the great differences in hull stiff-ness in the horizontal and vertical directions. Further, the mean phaseanqle difference (about 900) between veitical and horizontal directionsreflects the oifferences in the nature of the hull dynamic response andpower acceptance characteristics: the hull response is influenced atsome frequencies by structural resonances for vertical excitation, butdoinated by ullI stiffness (mainly in the horizontal direction) forhorizontal excitation. These trends were also evident in the AIFVresults, in particular Figure 4.24.

4.4.2.3 Effect of tht AIFV Turret

inertances at idler and final drive attachment points were measured withthe turret mass both mounted on and removed from the AIFV hull. Sincethe turret mass represents only 10% of the total vehicle mass, the tur-ret was not expected to have a significant effect on the attachmentpoint inertances at high frequency where the turret effect will belocalized to the turret area. In contrast, at low frequencies wherestructural wavelengths are of the order of the vehicle length,differences were expected since the turret effect is no longerl oca! i Zed.

Figure 4.30 shows the left-side, horizontal idler inertance functionswith and without the turret mass in position: no significant differencesin inartance .ani.tu.e or phace exist. Similar results are found forthe vertical inertance function, although at frequencies below 200 Hz,somle m in or changes in magnitude and frequency response occurred, as

-,9

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00

CD

% I-

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CCC

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-4'

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S- c0U

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shown in Figure 4.31. Results for the right side of the AIFV were gen-erally the same as for the vehicle left side. Likewise, the turret massh~d no significant effect on final drive inertance functions. An exam-ple is shovn in Figure 4.32.

4.4.3.4 AIFV/M113A1 Comparisons

Figure 4.33 presents direct comparison of the left-side, idler spindleinertance functions measured for vertical excitation. While there aregeneral similarities in the results, certain differences are clear. Atfrequencies below 250 Hz both vehicles exhibit a resonant response.This is characterized by phase variations from 0*° and strong fluctua-tions in inertance magnitude with frequency. The frequency range overwhich this occurs is wider for the M1I3A1 than for the AIFV. At thesame time the inertance magnitqde of the M113A1 is up to 10 d3 greaterthan that for the AIFV. It appears that the MI13A1 structure willmore easily accept low frequency power for vertical idler forces thanwill the AIFV structure. The same trend exists for measurements on theright side of the vehicles. At higher frequencies, the M113AI inertanceexceeds that of the AIFV by about 3 dB, while the phase variations areessentially the same. The power accepting character of the right idlerat high frequencies is similar.

The horizontal inertance functions of the idlers of the two vehicles aresimilar as shown in Figure 4.34.

Figure 4.35 compares final-drive vertical and horizontal inertancefunctions for AIFV and MI13AI: the instrurtentation system involved wassimilar to that in Figure 4.18 and is described in [17]. The MI113A!vertical inertance is much the same as that of the AIFV, but the mid-frequency horizontal inertance of the :'413AI final-drive is about 2 dBgreater than that of the AIFV.

Figure 4.36 showis the inertance measured at the bottom of the roadarmattachment (on the bearing housing) for the AIFV and M113AI vehicles:the transfer functions are similar, and both indicated a primarilystiffness-controlled response at the roada•r/hull attachment points.

It appears that the major differences between the two vehicles lie inthe power accepting characteristics of the idler in the vertical and, toa minor extent, horizontal directions at low frequencies.

4.4.4 Discussion

The following major observations can be made fron these measurements:

1. At frequencies below 250 Hz, the vertical inertance of each hull isgreater than that in the horizontal direction.

2. The vertical idler inertance of the M113AI hull is greater than thatof the AIFV hull, particularly between 100 and 300 Hz.

-56-

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(N ~ ~ ~ ~ ~ ~ ~ I tCa.9 zIHCI i4ul'Ol:4

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c

o -50

Z

0 50 100 200 500 1000 2000 50 0Frequency (Hz) , ,

(b) Horiot, a !

---- M I3AI

Fia rv ....aAcF'

- 1-20

-,r

-' -400

,i,,

S-6 I IIh f I I 1 ill J 1.

0% 50 10O0 200 500 1000 2000 5000

* Frequency' (Hz)

t'( (b) Horizonta'

I•';Figure 4.35 Comparison of AIFV and MII3AI Inertance Functions:

Final Drive Attach.

IL-61 -

.I-1

0 -.

- ii

E

-M 113A I

-20 -A I FV

0•

IN"- ---- M 3AI0p-.

.2 -40

-60 -- i20 50 100 200 500 1000 2000 5000

Frequency (Hz)

Figure 4.36 Roadwheel Attach Inertance,Neasured at Bottom of Attach.

-,64 -6?

3. Assuming equal force input to the attachment points in both hor.izon-tal and vertical directions, the vertical idler forces will controlthe interior noise levels in each hull. However, from [16] it canbe deduced that the horizontal idler forces can exceed by up to 10dE those developed in the vertical direction.

4. The turret mass does not significantly impact the vehicle inertancefunctions.

5. Strong asymmetries between left- ard right-side inertances andnoise-to-force T.F.'s exist for the AIFV, but these are less evidentin the M.113A1 data. These may result from longitudinal idler mount-ing differences.

In Section 4.4.2, the noise/force T.F.'s for the MII3AI were found to bebetween 3 and 10 dB greater than the corresponding T.F.'s for the AIFVvehicle and these differences are similar to the inertance differencesreported in Section 4.4.3. This is not necessarily expected since theinertance function is an integrated measurement of the power acceptingand structural dissipation characteristics of the hull structure, whilethe noise/force T.F. also incorporates the hull radiation characteris-tics. A more direct relation between response/force and noise/forceT.F.'s would be found if response measuremcnts were made on the majorradiating areas such as the top and bottom plates. However, in generalit is believed that reductions in the attachment point inertances willlead to similar reductions in the hull vibration response and in turn inthe interior noise levels.

Appropriate structural modifications are not imnmediately obvious from thereported measurements and so an analytical model was to be developed toprovide guidance in the hull redesign process which aims to produce a5 to 10 dBA noise reduction through practical hull modifications. Theanalytical modeling study cn the baseline •1113AI vehicle is presented inthe next section.

5. FINITE ELEMENT MODAL ANALYSIS OF AN M113A1 VEHICLE

5.1 General

The vibratory power acceptance characteristics of the M113A1 hull overthe critical frequency range up to 500 Hz is influenced strongly by wholevehicle vibration modes, that is by modes whose wavelengths are compar-able to typical hull dimensions. Finite-element (F-E) analysis was pro-posed as a feasible, economic modeling technique which would allow accur-ate calculation of hull resonance frequencies and mode shapes and, inturn, hull inertance and force-to-acceleration transfer functions andfacilitate an understanding of the hull power flow for noise control pur-poses. This chapter reports the-tresults of the F-E modeling study con-ducted: included are discussions of the basic modeling concepts andassumptions, a theoretical discussion for the prediction of vibration andnoise levels, study results for initial and final F-E hull models, andstudy conclusions and recommendations for model use.

-63-

5.2 SuP,'inary of Equations for Generalized Structural Vibration Response andTnterior Acoustic Power Radiation

The vibrational response of a bounding structure and the associated in-terior acoustic radiation into the bounded cavity can be derived fromclassical theory. A brief derivation of these results is presented inAppendix A and the major results are suninarized below.

The vibrational response of the structure w(R,w) due to a point harmonicforce of amplitude F(w) located at xF at circular frequency w is givenby

w(x,.: = F,rrr

Here, the structure is represented by its set of normal modes, where•r' Mr' and Yr are the node shape, generalized mass, and modal re-ceptance of the rth normal node. in particular,

21

where wr and nr are the resonance frequency and loss factor of therth mode, and

>ci

where 11(i) is the surface mass density of the structure at x.

When several modes are resonant in a narrow frequency band of widthAwand the a-nTilitude of the excitation force F(w) at iF is constant over theanalysis band, the vibrational response of the structure will bedetermined by the resonant peaks of those nodes resonant in the analysisband (r$,). In assessing the effects of structural modifications,esti:mates of snace-averaged, mean-square displacements averaged overthe narrow band of frequencies _ý are more useful than point-to-pointtransfer functions, due to the s;patial variation in surface displacement.An expression for these displacements is derived in Appendix A asequation (A.12). The band-averaged displacement spectrum is

N. T i: 2. r ý

(

4 -64-

IC

where FA 2 AW . is the band-limited force spectrum level.A 2

Here W-2AA is the space-averaged mean-square displacement, averagedover A ', developed on the structural element A in response to the band-limited force F A acting at 7F. Such an element could be the roof orfloor or sidewall, and each contribution to the total energy of vibrationis indicated by the expression

The term in square brackets describes the restraint provided by thestructure on the region A of interest.

The quantities M , 'Pr(i), and 'P(XF) are calculated in the F-E computingprocedure so thaf equation (A.12ý can be evaluated by manipulation of theoutput file data.

The band-limited acoustic power VA Amin watts radiated to the cavity in-terior from the structural element A'is derived as (Equation (A.19))

L,A W RradA (13)

T- 2 A

A6' 7T fA R__ _A, W •-m Rrad,A•nr

where •rad A is the band-averaged radiation resistance for the structuralelement r,'calculated from Statistical Energy Analysis. Such an approachwill be valid within reasonable limits for frequencies of about 200 Hzand above. For example, using Equation (9.5.16) from [15] for the modaldensity of a rectangular parallelopiped, the M113AI of interest will have5 acoustic modes in the 200 Hz one-third octave band. Alternativeapproaches, while theoretically practical, will be excessively expensive,yet cannot be guaranteed to be more accurate due to imprecision in inputdata.

[quation (13) shows that the results for structural response of the vari-ous hull elements can be used to directly calculate the interior radia-tion. Likewise,noise reductions associated with different hull configur-ations can be assessed by changes in w A,A and Rrad,A"

5.3 Model ing Procedure

The basic concept of the finite element method is that every structuremay be considered to be an assemblage of individual structural components

-65-

or elements. The structure must consist of a finite number of such ele-ments, interconnected at a finite number of joints or nodal points. Thisfinite character of the structural representation makes possible theanalysis by means of matrix equations, as distinct from the continuummechanics approach which becomes impractical for complex structures.Thus, and on account of the general simplicity of the M113 hull, F-Eanalysis was selected as the modeling procedure.

To make the validation of the finite-element model more direct, the barehull was modeled in the configuration corresponding to the inertance andnoise/force transfer function measurements described earlier. Extensionof results to underway operation will require some additional modeling ofthe idler linkages. The hull model presently includes the idler spindleonly. The bilateral symmetry of the hull suggested that only half of thestructure needed to be modeled, and this was done with a combination ofplate and beam elements using qnly about 150 nodes. In the modal extrac-tion process symmetric and antisymmetric modes were generated in twocomputer runs where the hull centerline boundary conditions are main-.'tained to have, respectively, zero vertical displacement but may rotate,or zero rotation but may deflect vertically: computer costs are thussignificantly reduced. Very stiff members, such as the longitudinal boxbeams, the bottom plate stiffeners, the narrow sill plates bounding theramp door and the cupola support frames, were modeled with equivalentbeam elements. Massive elements such as the batteries, fuel tanks,hatches, and the ramp door were represented as lumped mass.es located atboundary nodes. The vehicle engine, roadwheels, track, and suspensionelements were considered isolated from the hull and therefore omitted, aswere the forward engine hatch cover plates.

Large plate elements such as the top plate, bottom plate, and upper sideplates were represented by plate elements connecting a grid of nodepoints distributed approximately uniformly over the hull surfaces. Thelocal stiffness characteristics of the idler spindle and mounting padwere represented by a beam of equivalent stiffness, determined from astatic analysis of the idler pad area using a finite element modelingtechnique, EASE2, which is supported by Engineering Analysis Corporation,Los Angeles. The local stiffness characteristics were added into thehull model.

Mode shapes, resonance frequencies, and modal masses were computed usingthe STAR program of the MRI/STARDYNE Static and Dynamic Structural Anal-ysis System, developed by Mechanics Research Inc., Los Angeles.

Transfer functions, both drive point inertance and hull acceleration-to-idler force T.F.'s, were calculated usingq nYNRE2 proqram of theMRI/STARDYNE System. In this,4oss factor data from previous measure-ments were used. T.F.'s were computed for hoth symmetric and antisym-metric modes and combined as vectors.

Validation was to be carried out hy comparison of rmeasured and computedidler inertance and hull acceleration-to-force T.F.'s. Limited noise-to-force T.F. 's were to be computed for cormparisonr 'ith measurement.

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5.4 Results

5.4.1 Initial Model Configuration

The initial modeling array of nodes and plate elements is shown in Fi-gures 5.1 (a), (b) and (c) in isometric view, and Figure 5.1 (d) in asingle projection where all the elements and nodes are connected asmodel ed.

The top plate consisted of a rectangular array, 9 elements along the topplate length and 4 elements across half the top plate width. Rectangularcutouts represent the cargo hatch and the commander's cupola. The in-clined front was represented as 9 rectangular plate elements, the asym-metry of the engine access opening being ignored due to its remotenessfrom the drive point. The hatch plates were omitted for simplicity.

The upper side plate was represented by rectangular and triamla plateelements, with two interior nodes from the sponsu.1 to the top plate, andabout 10 interior nodes longitudinblly. The sponson was represented by asingle longitudinal line of plates, i.e. no interior nodes were usedacross the sponson width following the argument that the lowest sponsonmode was measured to be above 500 Hz. Likewise the lower side plate con-tained no interior nodes across its vertical dimension, being representedby a line of rectangular plates.

The bottom plate was represented by a set of rectangular and triangularplates with a series of beams located approximately where the floorplate supports exist in the actual vehicle. To include the effects ofthe engine bulkhead, bottom and top plates are tied together with plateelements at node locations 400, 412, and 310. Only one interior node wasused between the center of the bottom plate and the lower side plate.

The box beam was represented by a line of beam elements located at thejunction of the lower side plate and the bottom plate, with appropriatetorsional and bending stiffnesses. The rear hull above the sponson wasrepresented by a set of three plate elements bounded on the ramp side bya stiffening beam element. The sill which extends around the ramp wasrepresented by beam elements, although the sill at the bottom plate linewas omitted. The mass of the ramp was represented by a series of pointmasses located at the base of the ramp-nodes 1200 and 1201, the ramp be-ing considered to provide no significant stiffening to the bounding sillof the hull rear panel.

The eqiivalent beam representing the local stiffness characteristics ofthe idler pad was attached to the hull at node 1202 and extending essen-tially as on the real vehicle: thus a node at 1250 occurs 125 mm (5 in)from 1202, which is the corner of the vehicle. Two additional nodes,1251 and 1252, oriented verticaliy and horizontally, are located veryclose to node 1250, and this allows the response to be calculated at thepoint of application of the force (1250).

Pm isometric view of the nodal arrangement is shown in Figure 5.2. TheSIippr)rt system for all nodes corresponds to the hull supported to allow

-67-

(b) Bottom Plate

figurr, 5.1(a) to (c). Isometric View of Node Locati4ons -Initial Hull Model.

-68-

- I

- E ,J !

- -4- - -• - -• -•• 4-

-- .

* ? - I - ? I ,

"ff /" ' --• . ,-

r N N r r- N " 'J .3

- - - - 9-

Top Plate

Nose

Bottom Plate

Figure 5.2. Isometric View of Hu~ll Elements-- Initial Hull Model

-70-

unrestrained vibration.. Thus,the actual grounding occurring during mea-

surements (i.e., wooden cribbing arbitrarily placed in from each cornerof the hull under the rear sill) was not modeled directly -- rather thefree-force supports were thought most representative of the actual sup-port conditions, although at high frequencies the supports should notafeect the results to any great degree.

The degree of detail employed in the hull model adequately represents theelastic behavior of the vehicle in all but one respect; the local deflec-tions near the point of application of force. Providing sufficient de-tail in the vicinity of the idler attach pad in the hull model would beprohibitively expensive and ould decrease overall accuracy. Instead thelocal flexibility is simulated in another finite element model, a detail-ed representation of the rear lower corner region using the local geome-try model shown in Figure 5.3 (a), which shows the nodal arrangement ofthe left-hand idler pad viewed from the centerline of the vehicle. Inthis analysis the idler was considered as a rigid body attached to thehull at the eight bolt locations. Loads developed in the idler in re-sponse to a horizontal or vertical force at the idler free-end weretransmitted to the idler pad and surrounding structure through the boltlocations common to both idler and pad. The results constitute thestiffness matrix of only those local elastic details which are not repre-sented in the hull elements. This local stiffness matrix is incorporatedinto the hull model as an equivalent beam. (The equivalent beam methodis used because it is more convenient than applying an actual stiffnessmatrix; the solution is exact.)

Figures 5.3 (b) and (c) show the idler pad distortions produced by ver-tical and horizontal idler forces. Considerable out-of-plane deflectionsare produced by an in-plane force, as indicated in the idler pad flexi-bility matrices presented in Table 5.1. In this the deflections of theidler free-end to vertical and horizontal forces are presented in Table

TABLE 5.1 IDLER ATTACH PAD FLEXIBILITY

M113AI Left Side Pad M113A1 - Right Side Pad

6 d6x •zF .2633 .0440Fx x . 0-G in - .5983 .1227 -6 inx 0.- 10IO

Cx <•x Ib . 1 2 2 7 .4 2 0 1~-F~ .0440 .2959

Z Z(x - direction is horizontal (longitudinal) and z - direction is vertical)

Equivalent Beam: Length 5 in.z

Ix, = 22.52 in 4 z I', = 20.58 in4

Iz, = 31.60 in" =. 0 / z, 11.12 in"•- x

O 34.814" 1 x 0 = 27.01'

-71-

(a) Idler pad flex bilitymodel-left side

(b) Idler pad 1.i(c) Idler paddeflectionis far deflections forhorizontal Force vertical force ~4~~

Figure 5.3. Idler Pad Static Flexibilities.

-72-

5.1. In this table, the deflections of the idler free-end to verticaland horizontal forces are presented for both left and right sides of theMI13AI idler attach. The left side horizontal and vertical flexibilitiesare approximately equal, but are less than the corresponding right sideflexibilities by about a factor of 2: the mounting location of the leftidler spindle is more forward of the plane of hull rear plate than thatof the right side idler, and this forward location appears somewhat stif-fer to idler forces. Table 5.1 also includes the characteristics of theequivalent beams used to represent the local deflection characteristicsof the idler attach area. The equivalent beam has different vertical andhorizontal stiffnesses and is inclined at angle 0 (the angle of the prin-cipal axes of displacement relative to vertical) to produce the cross-coupling shown in Figures 5.3 (b) and (c). These characteristics areadded to the F-E model in the modal extraction process in the programSTAR.

The STARDYNE procedure consists of stiffness matrix formulation,eigenvalue/eigenvector determination, and dynamic response analysis, thefirst two steps being carried out in the program, STAR and the latter inDYNRE2. In formulation of the stiffness matrix [K], the stiffness ma-trices for the individual finite elements are first computed and trans-formed, as required, in a form relating to a global coordinate system.Finally, the individual element stiffnesses contributing to each nodalpoint are superimposed to obtain the total assemblage stiffness matrix[K]. The eigenvalues (natural frequencies) w2 and eigenvectors (normalmodes) q of the structural system are found by solving the equation

W2 [m] (q} - [K] tq} = 0

where [m] is the (diagonal) mass matrix: the LANCZOS Modal ExtractionMethod was used. DYNRE2 uses these results to calculate the dynamic re-sponse (T.F.) of the structure for a set of unit sinusoid excitationsapplied to a specific node (idler) on the structure. References [5] and[6] contain theoretical and user information.

Appendix B contains sample input and output data for the initial hull F-Emodel for both the STAR and DYNRE2 programs. Sections B and C ofReference [6] will demonstrate the formats used for the various input andoutput data. In summary, Tables B.1 and B.2 contain, respectively, inputand output data for program STAR and Tables B.3 and B.4 contain, respec-tively, input and output data for program DYNRE2: information in thesetables should be self-explanatory. More general results for the initialmodel are described in the following paragraphs.

Table 5.2 presents abbreviated modal extraction data for both antisym-metric and symmetric centerline boundary conditions with comments con-cerning the nature of the resonant modes. Mode numbers I to 3 are trans-lational modes of the undistorted vehicle, while higher modes involvedistortion of the vehicle shape in bending and twisting. Figures 5.4 (a)to (o) show isometric views of typical vehicle mode shapes: both synme-tric a(nd antisymmetric examples are included. The annotation in TableC,.? under the ** columns seeks to suggest the regions of the hull struc-tur, 1r)sosr, sin(I the maximum kinetic energy. At low frequencies the

-73-

LL. U--L

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vibration modes involve twisting, dilatation, and bending of the wholevehicle; as frequency increases, the structural wavelength decreases andthe modal kinetic energy becomes confined to elements of the structure,in particular the bottom and top plates. This behavior is reflected inthe generalized weight parameter Mr which decreases as mode order in-creases. The density of hull vibration modes generally tends to increasewith increasing frequency, approaching at 250 Hz the modal density of aflat plate of area and mass equal to the total area and mass of the barehull, viz., about (1.35 modes/Hz, as shown in Figure 5.5. The modal over-lap, i.e., the ratio of modal bandwidth (=frnr) to separation betweenres-onant modes, is greater than unity so that a relatively smooth resonantidler inertance would be expected.

Examination of these mode shapes suggests certain potential modeling de-ficiencies. For example, in Figures 5.4 (c) and 5.4 (d) the deflectionof the lower rear plate sill is large and out of, character with the near-by deflection pattern suggesting incorrect stiffness representation inthe sill. In Figure 5.4 (q) substantial bottom plate, lower side plate,and sponson bending and twisting occurs, and one expects that inaccur-acies in deflection adjacent to the idler may be generated due to therebeing no interior nodes in the sponson and lower sideplate. In Figure5.4 (J) locally high deflections of the cupola boundary suggest alack of boundary stiffness. In Figures 5.4 (1) and 5.4 (o) thenode spacing is barely one-half the structural wavelength: moreinterior nodes are probably required for good representation of thebottom plate and top plate dynamics above 160Hz.

Root-mean-square inertance functions for the vehicle left-side idler forhorizontal and vertical excitations are shown in Figures 5.6 (a) and (b),where the acceleration is measured in the direction of the applied force.In this calculation, modes of order greater that 13 were given a lossfactor of 0.040, while lower order modes had a loss factor of 0.1. Asboth symmetric and antisymmetric modes have the same phase angle spec-trum, the sum is found by arithmetic addition. In general, the antisym-metric modes are computed to make a stronger contribution than the sym-metri c.

We note that the vertical idler response to horizontal excitation (Figure5.6 (c)) is much stronger at low frequencies than the horizontal due tocross coupling induced by the inclined rear plate of the hull. The ver-tical response to vertical excitation (Figure 5.6 (b)) is much strongerthan for horizontal, reflecting the more direct coupling of verticalidler forces to resonant and nonresonant hull modes.

Cori mp arisons between measured data and computed inertances are shown inFiqupre 5.7. In general, the measured and computed data have quitesimilar characteristics for both vertical and horizontal excitations.For the horizontal direction, fair agreement occurs at low (less than 40I'/) ind high (qrfater than 14(0 Hz) frequencies, but the computed curve isdbn it f d10 , less than the measured results at about 80 Hz: it appearsthut sifrnificant errors in the horizontal hull stiffness have been made.In ,ho. ve rtical direction, however, the computed inertance generally

oI'; fh iow;iirnd Hata, but has thle same fluctu atinq (modal)

-7,-

0.5 Fict Plate VA 2PEstirinte A-

S 04 /MCL

0.2 hi--0. 1

o

'44

5 0 100 150 200 250 300 350

Frequency (Hz)

IFicoure i'1M d l'e -it%

kA

oI ~,p..••"-•4

SMC.-

•" 0. -- Estmnte = •

• I. •I-\L r

\,A

10-- 3

0/

3 /1 ,'L, ,''/

Co .I 10 ~ ~ 7'Total

C K

- ." !V~i- /

AAntisymretric Modes

10-- , Symmetric Modes

-6.-- ~ ~~10- i " - !

20 50 100 150 200Frequency (Hz)

Finure %5.6(a'. Horizontal Idler Response to Horizontal Idler Excitation.u Tc

IIIQ

-. Anitisyrrmo~ric Modes-4- S\vrtlrrptric Modes

20o 5010 5 200FreaoenC', (H:)

.a re 56k b- !Verti cali Idler .?esý;fls:-, tk) 'erti a1 LIdler [x\ci tation.

SII

icr

0N

_ 4 / \, =

.-. I0 • - I - - ,--..o/ / ' 'i

/ /-

CI

o i\.-,. / / l ! \ /

.£ f\, / i\."

"2) / \ f

IA !Total

Ant isymmetric Modes

10- -5-- Symmetric Modes

1 -6,I0

20 50 100 150 200Frequency (Hz)

Fioure 5.6(cY. Vertical Idler Resoonse to Horizontal !dler Excitation.

-83-4'"

C (U

a S- c

oo 0-

L A

-4-)

14~

1E,1

H 6-1 1

-84--

Upqrading the loss factor to conform with measurements will improve theagreement only slightly for vertical excitaticn, but not effect the hor-izontal results.

Fiaures 5.8 (a) and (b) present measured and computed acceleration-to-force transfer functions for a single point on, respectively, the hulltop and bottom plates for both vertical and horizontal excitations at theidler. For horizontal excitation, the computed top plate response liesahout 10 dB above the measured data over most of the frequency range, buttends to agree reasonably with the measur,-uments above 160 Hz. Similarly,for vertical excitation the computed top plate response matches the i';ea-surements fairly well above 100 Hz. In Figure 5.8 (b), fair agreementexists between measured and computed bottom plate response over most ofthe frequency range, except for horizontal excitation at frequenciesabove 100 Hz, where the Computed resoonse lies 10 to 15 (I1 above the mea-sured data. While single point comparisons tend to be poor due to thespatial variability normally encountered, it appears that the bottomplate and, to a lesser extent, the top plate, are perhaps insufficientlystiff so that larger deflections are being produced than occur in prac-tice. The simple model for the structural loss factor used in these ini-tialcalclations was a stepped function of frequency, i.e.,:- : n.1ln formodes of order less than and equal to 12, and ri= 0.n4 for hinoher ordermodes.

To refine the dampinu representation, the solid loss factor curve froi.Figure 4.15, representing the mean of the MI13A1 experimental data, wasthen input to DY0RE2 and the various transfer functions recalculated. 'nthis way, for frequencies below about 100 Hz and above 160 Hz, the lossfactors were increase_ , hilt ntherwise were inareinallv decreased, Figure5.9 provides a comparison of the calculated inertances for, the initialstepped and the measured loss factor formulations. At most frequenciesthe stronq oscillating behavior of the inertance curves has been si'iootnedso that the qeneral similarity between measured and comiputec results forboth directions has been improved. The effect is weaker for horizontalexcitation than for vertical excitation. However, the qeneral In dcldifferences between measured and computed inertances remain.

Figqure 5.10 com1pares the b~ottom plate transfer functions for the initialstepped and measured loss factor data with the measured data: a aeneralimprove,9ent in the aqreement between measured and calculated results hasbeen achieved, a!thouqh the strong calculated response peaks at 100 Hzand 160 Hz are unaffected. The hottom plate appears to he i•.•utfmcientlysti ff. The transfer functions for the top plate at two different nodes(70 and 1008), using the measured loss factor data, are c.,pared with

the top plate transfer function for node 1009 in Figure 5.11, where theeffect of loss factor changes on the T.F. result for node 1i071C was ex-pected to he small. Of interest here are (i) the closer aureerient whichf exists at :iost frequencies below 200 Hz, hetween measured ani comnputedresults, and (ii) the considerable variation between the calculated dataat different nodes in the top plate. Node 1009 is located at the free"edge of the carno hatch, where the predicted mode shapes have somewhatSunrealistic deflections, whereas the nodes 70F4 ano 100M are located awayfrom model and hatch boundaries where relative node displacements areminrc , cmrdte. S1ace-ave.•raulnn e results, r, b ~tlecSUm ed on.i ,.' . ,e,is necessary for reliahle evaluation of data!

e4 -- 5

C>

Cc

0L

7 tz

ý -DoCC14 N kn 1

Ia

(N/ S,"WI a.,gp WHI 601 t : 14.nd '~su JI l(N

78~

o~~C 0

cc

CC

CD C)

C14~~~ $nL 0 o

(N z I/ j a. W I51C ulDn 9sDI HnH

4 -26-

Mii

CD 0 :C14 LO 0

(N, / j jq_IJH 0 1 :O4u d lju i i)

z

C.

0C

C;

zL

Lr)nI~ U

U ;- Coc

-37--

'LI : s-.. oo. --01

roo r_

Q 3 0

-n m

0* 'C3 -

~~0o

A. 4-31~.*' I !J

0 . I1. 1) III qp L.)I 0 0 SuojuO

30Y

-- -Calcula Stoppd s

S. ... M easur ed D ata -

~-60Js-IB

'--70 --- - j0 200 400

Frequenc:y (Ha)

SFigure 5.10. Effect of Loss Factor Changes on Calculated Bottom PlateTransfer Function (Node 1001) for Vertical Idler Force.

tU

2 AO - Os

uI t Node 1009: Stopped

"" .o,- Node 7M. Meurer

SJ Measured Data

g.60

-70 1 ,

0 200 400Frequency (Hz)

Figure 5.11. Top Plate Transfer Functions for Vertical Idler Force.

_89-

Modal extractions and transfer functions for the riqht-side idler werecomputed using the beam equivalent to the right-si de idler deflectioncharacteristics from Table 5.1. Results, identical to those already com-puted for the left-side idler (five significant figures), were calcula-ted. In evaluation of the data it became apparent that the structuralmembers controlling the overall stiffness characteristics of the idlerinertance were located adjacent to the idler attach area, rather than theidler and the local structure themselves. For example, the flexibilityof the box beam is much greater than that of both the idler beam itselfand the combined idler and local attachment area, so that, to first ap-proximation, the idler and attachment area rotate and deflect as a solidbody against the restraint provided by the attached hull members, com-prised of torsion box beam, bottom, side, and rear plates. Examinationof the mode shapes reveals that little relative distortion of the boxbeam is predicted to occur between nodes 1002 and 1202, as shown in Fig-ures 5.12(a) and (b) for two antisymmetric modes (85 Hz and 199 Hz). For

example, the slope of the vertical displacement curve (X3) and the rota-tion of the box beam about its axis (0) adjacent to the idler location(node 1202) are essentially constant between nodes 100? and 1202. Sincethe idler and attachment area are more stiff than the connected structureby a factor of at least Io, chanqes in local stiffness by factors oftwo, as occur between left and right idler, will produce no significantchanges in overall stiffness, mode shapes, or hull transfer functions, inaccordance with the calculated results. Using tnis initial model, itappears that the hull stiffness, rather than the stiffness of the idlerattach area, controls the hull power flow so that even large stiffnesschanges local to the (already very stiff) idler will have little impacton the hull vibration response.

Comparison of resonance frequency predictions with the limited experimen-tal data available suggested that the geometry of hull had been represen-ted sufficiently well. Errors in inertance magnitude were therefore pro-posed to result from inadequacies in modeling the stiffness characteris-tics of hull, including the area local to the idler attach. These tend tocontrol the local mode shapes, i.(., the parameter p r('F). Therefore,detailed revision of the modeling processes was conducted for thestiffness contributions of the idler spindleý and pad, box beam, and rearplate ramp sill. A minor error in the torsion constant of the box beamand the omission of the horizontal beam representing the lower rear platewere discovered. It was also considered that the support on woodencribbing during inertance experiments may have strongly influenced thelocal mode shapes, but futher computations (modal extraction and transferfunction for antisymmetric modes) showed that the hull support conditionwas of second order importance, resultinq in only minor changes in low-frequency resonance frequencies, mode shapes ý r(;F), and transferfunctions.

5.4.2 Revised Hul Dynamic Model

While the initial finite-element model of the M113 hull produced valuesOT natura; frequency which were in good agreement with experimentalvalues, the vibration response levels were noticeably different. Re-sponse to vertical excitation was in excess of measured values, both at

-90C-

I

lg'0 as s Torsion Beam

A

1 12

X 0 X- I 11 2 1

X 3

-08

(a) Antisymmetric Mode Shope at 85.9 Hz

('X2

%7 a 9 0O 11.i 12 -0Ow -

Shpe oTorso o em

-9.)

-O

Jhg dcijinq p~iq Ind ithe migr panels Respoyse at the drivinq Dointth idner qpOlne to norztnhaj xcitation wa ess than hat measured. _

Investigation of the problem included revision of the values of loss fac-tor used and modification of the method of support. The results havesuggested that second-order details in structural modeling were the mostlikely cause.

The model has therefore been made somewhat more aetailed to representthose structural effects which provide local stiffness, introduce -

boundary effects, or provide interpanel couplinq. As an example, thegeometry of the driver's hatch and cupola was refined, and the flexuralstiffness of the hatch rims were added. Also, the element detail wasrefined in the region of the idler to better accomodate the load pathsresulting from idler excitation. An additional measure of the effects ofchanging idler location can be performed with this model, and betterpanel-averaged deflections can be computed. The effect of the lower sideplate is now better represented, and possibly significant geometricdetails in the location of floor supports and in rear panel size havebeen re'ised. The model revision has required additional nodes, whichwith extension of the frequency range of interest, has caused thesolution cost to roughly double.

The revised modeling array of nodes and plate elements is shown in Figure5.13(a), in isometric view, and in Fiqure 5.13(b) in a singleprojection where all the elements and nodes are connected as modeled.As already noted, more detailed representations for the top and bottomplates have been made, including adding in the driver's hatch, refiningthe cupola, and upgrading the interpanel coupling characteristics ofthe stiffening members at the top of the rear plate and at the rampsill. Plate elements have been used more extensively in the rear panel.Idler "equivalent beams" have been located at four positions (nodes 103and 203, and 104 and 204) representing the oeometric location of theleft and right idlers on the M1I3AI and AIFV vehicles, respectively. fhestiffness of the floor plate Supports has been increased from the initialincorrect and low values, and the longitudinal centerline floor platesupport has now been included. The geometric location of these supportsis now more accurate. More definition in the lower side plite has beenincluded.

The local flexibility characteristics of the idler attach area was thesame as used in the initial model, but the different idler characteris-tics are now located at different nodes to correspond to different idlerconfigurations.

Modal extractions and dynamic response (T.F.) calculations for the re-vised hull model were performed as before, except for two loading condi-tions corresponding to sets of unit sinusoidal excitations applied atnodes 1 and 4 (the most extreme idler positions). Appendix C containesample input and output data for this revised model for both the STAR andDYNRE2 programs. In summary, Tables C.1 and C.2 contain, respectively,input and data for prigrams SIAR, and labies C.3 and C.4 contdin, fespec-tively, input and output data for program DYNRE2. General results aredescribed below.

-92-

S . . . . . . . . . . . . . .. . .. . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . .. . . . . . . .. . . . ..

Top Plate

Nose

Bottom Plate

Figure 5.13(a). Isometric View of Hull Elements -Revised Hull Model.

0 U.

'4-)

0

_____ ____I>

Ella

A -94-

Table 5.3 presents abbreviated modal extraction data for both antisym-metric and symmetric centerline boundary conditions. Comparison of datain Table 5.3 with data from the initial hull model (Table 5.2) revealsthat the distribution of resonance frequencies has remained much the sameas for the initial model. However, the frequencies of the lowest ordersymmetric and antisymmetric modes have been increased by 50% and 100%,respectively, by correcting the bottom plate stiffness modeling; themodes associated with flexure of the rear sill have been eliminated byupgrading the representation for the rear hull plate. About 70 hullmodes exist below 300 Hz.

Figures 5.14 (a) to (k) show isometric views of typical vehicle modeshapes, with symmetric and antisymmetric examples included. These shapesare, in general, very similar to those computed with the initial model,but are more precise and realistic due to the greater density of nodes inbottom, top, and lower side plates, and to the refined representation byplate elements of the rear hull plate. For example, Fiq•,• 5.14 (h) and(i) demonstrate the stronq deformations occuring in tte hull rear plate,which influence the power flow from idler to top plate. Figure 5.14 (k)shows how, even at frequencies as low as 300 Hz, the floor motion is re-strained by the spanwise stiffeners, and suhpanels tend to vibrate asindividual elements.

Comparison of measured and computed inertances for the idler attach loca-tion on the left-side of the M113A1 is presented in Figure 5.15. Themeasured loss factor data from Figure 4.15 is used in the calculations.The agreement for vertical idler force is close, particularly at frequen-cies above 100 Hz, and much improved in comparison with the calculatedresults from the initial hull model. In general, the calculatedinertance exceeds the measured data by about 3 dB. The calculatedhorizontal inertance is about 10 dB below the measured data over thewhole frequency range. The horizontal stiffness of the hull has beenoverestimated even in the revised hull model with its improved hulldefinition in the idler attach area. However, since the verticalinertance is higher than the horizontal, and is closely predicted,further refinement of the representation for the idler attach area is notwarranted at this stage. Further comparisons will be limited to verticalidler forces.

The calculated responses of the hull top plate at nodes 313 and 813 forvertical force input at the left-side idler is presented in Figure 5.16together with the measured response near node 312. Considerable varia-bility in response is predicted over the surface of the top plate; thecomputed variation between the two nodes at a particular frequency isgenerally about 7*dB. The measured data is quite similar to the calcu-lated response of node 813. It is clear that space- and frequency-a'veraging of both measured and calculated. transfer functions would makecomparisons more valid. Similar comparisons with measured data for otherhull surfaces have not been carried out on this basis but are left untilsuitable space-averaging software is available to automate the reductionof modal extraction data following the methods suggested in Section 5.?.

-95-

0i iaYk-)C) 4) . x !: w U~ - (A xU

ne = I I I I I I I I I I I I I I I I I I I I

0' ) C\ )C -.- --- -- C', 'N-%J(J(J : j _

LLL-

L!) I-) e-J .- In -=r I: Dý TO ý - l oý l la

*D *- 00*. a .r- - C\J *L ~ ~ ~-U.J -3: - CD *o C7 *C' f)'~ 0 * O C -r OWC ,j C)- --

2-1 M- "L'J C\ - . r, (n M C~Z LA A( LAC\aAJ 0n ; 3

0-.

"C cc 'r- cu

I--

00

CY E)

LL.O

4' Cl I n -lI n CiI)t)(iý n( n C ~ - l.- I ii

(U 1.-. " (U ~~

Ai 96

11

'IZ

it-i

0:0.1 __ a)

-97-I

V 4

-'=

'""I ,,C.)''•

-, -,

--

*-,• -. '-

* _A-9• - i )

C.•

C.)!

-i-

E -V

NC

;', • , t - - !Ci"< '-

IL.,

' ..N

, °E-

S• • (

C,.........• , ! • ,,)

!\ \.• , o .d

-'

S-99-1

-30

7r J

-50 /

0- M/M aue

C- Calculated

M

C

50 10~0 150 200 25030rreqvencý (Hz)

F~~rc5.15Con-pari son of Measuired and Calculated Horizontal and verticalInertances for IMll3Al Left Idler Spirdle: Revised Hull Model.

-4C

Measured: Node 312b.~ Calculated: Node 313

E -- Calcvlated: Node 813

50 l0 150 200 250 300Freavencý (Hz)

Fi-lure 5.16 Accelceration-to-Force Transfer Function for Hull Top Plate:Comparison of Calculations and M~easured Data.

-100-

The effect of different idlers and their location on idl-r inertances are-shown in Figures 5.17(a) and (b) for horizontal and vertical force in-puts, respectively. In these, different idler representations corre-sponding to left- and right-side idlers on both M113 and AIFV vehicles,as summarized in Table 5.4, have been incorporated into the hull model. 4Forces were applied to each idler in turn.

Table 5.4 EQUIVALENT BEAM PROPERTIES (5-inch idler spindle)

Idler Ix Iz Equivalent Beam 1inj' (in" (degrees) Node Location

M113Ai-Left

Side 22.52 31.6 34.R4 103

M113AI-Right

Side 20.58 11.12 27.01 203

AIFV-Left Side 21.11 35.77 27.46 104

AIFV-Riqht Side 23.42 13.14 32.04 2n4

The drive positions corresponding to the M113AI idlers are 10 and 20 forleft and right-sides respectively, while, for AIFV idlers, they are 30and 40, respectively. R.M.S. inertance magnitudes (in g's/lb) are shownin Figures 5.17(a) and (b). In Figure 5.17(a) the horizontal ltcationof the idler makes little difference to the horizontal inertance magni-tude, hut the upper location is calculated to have lower horizontalinertance; the difference being about 5 dB over the frequency range 125to 250 Hz. These differences result from the locations of the idlerequivalent beams at their 'correct' hull positions rather than fromdifferences in idler properties (Table 5.4). In contrast to the hori-zontal inertance data, little significant difference in vertical inert-ances exists between the different idler locations, as seen in Figure5.17(b). Fiqure 5.13 shows the calculated effect of idler characteris-tics, stiffness, and location on the toP plate transfer function at node313 for a vertical force input. No significant changes in transferfunction are produced by varying the idler characteristics.

5.4.3 Frequency and Space-Averaqed Calculations

The approach outlined in Section 5.2 may he used to calculate frequency-and space-averaged hull response-to-force and interior noise-to-forcetransfer functions. Several examples are now presented to demonstratethe nature of the predicted results.

Consider first the idler inertance. On frequency-averaqinq the inertancefunctions, (equation A.lla in Appendix A) and neglecting the cross-terms(i.e. r # s) in the equation following (A.lla), we find approximations to

'.1

4 i l

t

10-4./C

.- I I J -10 (Lef t Side)

-- ~ Id le r L o c a t io n s'- -_ 2 -, (R i oh t S id e )

, -I M.P3^ (Left Side)/. Idier Lrcctiof,sn _ ._40 (Riog t Side)

S 50 130 150 200 250 300Frequenc. (Hz)

Figure 5.17(a) The Effect of Different Idlers and Their Locations onHorizontal Idler Inertance Functions.

& 1! 13 I 10 (Leit Side)Ifer Locotionsl-- _20 (Right Side)

AIFV - . 3D (Left Side)Idler Locations' ..... 40 (Right Side)

I-3

53 10 0 150 200 250 3-0

FreQluenc) (H:')

Figure 5.17(b) The Effect of Different Idlers and Their Locations on-Vertical Idler Inertance Functions.

-102-

-30 ______________________________________________

z

* -40 -

VI

c ~Idler Location

LL -6 10--- ~-20

2 ......... 30I- -. * - 40

Froquency (Hz)

Figure 5.1S3 Effect of Idler Location on Top Plate Response-: Vertical Excitation.j

4

4

the idler inertance in terms of the vibration mode shapes at the idler,-the modal masses and loss factors. The contributions due to nonresonant

modes (i.e., -.odes with resonance frequencies outside the analyses har,i-width ,', both stiffness-controlled (w u>'L) arid mass-controllOed (,r'.') )can he distinguished from that duerto resonant modes (whose resonacefrequencies lie in the analysis hand (w'rcA,.)).

rA typical set of results is shown in Figure 5.1Q, -.here the contributions.of the nonresonant and resonant modes to the vertical idler inertancefor idler i0 (left side 11I3Al) are compared with the total idler inert-anCe, conputed on a frequency-averaqed basis. It is clear that, in oen-

eral, resonant modes control the vertical idler inertance; only at "f) i! 7and 160 Hz, and below 31.5 Hz, do nonresonant nodes influence the idler A]I-inertance siqnificantly. Comparison with the narrow-band vertical inert- Iance function as in ciqure 5.15, shows that close aqreenient exists he-tween the two analytical results: the band-averaged data is ;,iore usetul'•because the role of resonant mnodes is clearly identified.

The space- and frequency-averaqed response transfer functions for thehull top plate, derived fror, equation (A.12) for resonant contrihutions,and trom si -ilar expressions for nonresonant modes, are prespnt;d! iiFiqure 5.20. Aqain the vibration response in resonant Nodes controls thetvithration level of the tot) plate. Comparison with the narrow-band calc-qlated result from DYNRE 2 shown in Fiqure 5.16 shows aQrvement to h.close.

Values of the parameter describing the contributiun of panel elements tc ,the hull vibrational enerqy (equation A.14) total nodal masses Mr, apresented in Table 5.4 for several modes. As the normalized riass para.;-:eter approaches unity for any element, the energy of vibration hecories zconcentrated in that element. For example, for the antisymmetric -modIoresonant at 66.9 Hz, (see Fiqure 5.14(d)) the top plate contributes d, .of the modal generalized mass, while for the symmetric modes at 55Q0 Hz(Figure 5.14(c)) and at 296.0 Hz (Figure 5.14(k)), the major contriho-tions to the modal qeneralized mass are provided by the vehicle sides andsporson (82?,,) and the bottom (at least 771ý), respectively. we note how-ever, that for frequencies well above 10n Hz the norialized qenerilize,'masses of the top, bottom, and upper side plates tend to he about thesame, suqqestinq the vibrational energy will be uniformly distributo-over these similar structural surfaces.

The interior noise-to-idler force transfer function for each strLucturalelement can be derived as

.<p?> A c3 <a. A >

U Vni

where, in frequency band .<p2 > is the space-averaqe mean square inter-I ior acoustic pressure, F2 is the mean-square idler force and <a•,A) is

t::e s qa-3guare accelerat 'iu uf elemental area A. v,oc and rli are the

4 -104- -

-30 ____

CI1,m -60

C4 N

V60

-80 1____16 31.5 63 125 250 500 1000

Octave Bond Center Frequency in Hz

Fuqure 5.19 Vertical Idler I1nertance (10) of Mi113 Vehicle.

vol kdpe, characteristic. impedance and acoustic loss factor of the hullinterior spacc, and u is the radiation ratio of area A. The transferf.Anction hoeteen surtace response and idler force <.. ,A/F is cal cu-lated with equation (A.12), for example, as shown in ilure 5.20. From r

l., v.l u< (- o A and d the noi se-t'-force transfer functionsfor eaach of the major radiating elements can be caiculatedl, and thensu',."d to qi ve the overall measured noise-to-fo,'ce tr nsfe' finct ion. Aty pi c,i exa:uple i:; presented in FiQure 5.21 where predicted and measuredon s-to-force transfer functions for vertical excitation of idler 10(left-side M,13) are compared. The agreerient is quite satisfictoryaltimngh a 3 dR overprediction has resulted,

TA•LE. 5.53

.,UW'•AL'Z1D GENERALIZED M.IIASS OF STIUCTURAL ELEM•[TS

Pe ;w•,•aine Structural ElemientI-e ,r,,ry '.pper Lower Rear *

(Lh1) TnD Side Side Sponson Bottom Plate Total

..0, .,1.1 .i14 .024 .213 . 1).

..!l .2o5 .252 .2. .. 569,

(h1.t .n' 1 .,36 .022 .035 *2?3 .Q09

J 3..) .q5E2 .069 .026 .401 019 .2412

134.Q 4;2 .[3 .00 .005 .003 W003 1.nno

176.1 .233 .10i .1014 .009 .?63 .011 .634

2 . ."53 .062 ?o)4 . 1. I

25..o .0 0 044 o73 .031 .143 .983

0. •)40 .0 ;- .015 .91 0 .765 . (' .

* ]n ovi ijat inq the vehicIe (ieneral ized . nasses the mnc1i ned sections -

the vehiclo nose have been omitted from present calculations for si -p1 icity. W1,en the 'total' normalized qeneralized mass is less thanS.0, si in(fI car't vibrational energy occurs in this area of the vehicle.z, Sichk hJl 1 vitbrations are scrt'ened by the engine cover aLJ ,] not rai-ate if,.to) the inpterior space.

ikhile I t, s presentation ot !and-averaqed results is onl v prel iliinar , it(ai )ears that the approach is valid. The procedure qives results oirectlv

- .. 1Sefu' in teip nredi :ti or of ror:hicml ly measured qant i ties ot oan.d- and"s pace-a veraued trans fem funrction. The savi nqs iin data aral ys s marinpower1! A 1 cpltoittinq (imsts usinqg this approach are at least in order of maqni-

-- ,'4 -1-i6

I AI I I il.l l-i . . . . . . .. . . --. .- =

-~ -30

Cl)

4A,

-70 -I -

.s16 31.5 63 125 250 500 1000

Octave Band Center Frequency in Hz

P~gue 520 Con~tributionl of Resonant and Nonresoflaft Modes to

fiur 5,: Top Plate Response for Vertical Excitationl of Idler(1)

A

70

50

L=--

Co

0

o: 50 ..

'-,

-o .svW

I 0 -- Right Hand Side

o - Left Hand Sidez

- Predicted

30 - I i I I16 31.5 63 125 250 500 1000 2000

Octave Bond Center Frequency in Hz

i

Figure 5.21 Comparison of Measured and Predicted Noise-to-Force TransferFunction for Vertical Excitation of Idler Spindle on M1t13Al.

108 -

Ii

5.5 Discussion and Recommendations

The main results of this development phase of the hull modeling study aresummarized below.

1. An analytical model for the M113A1 armered personnel carrier has beenconstructed using the finite-element method. This model has beensufficiently detailed to allow reasonable predictions of mode shapesand resonance frequencies up to frequencies of about 300 Hz. Exten-sion above 400 Hz using the current nodal arrangement is not recom-mended.

2. The idler has been represented by a beam of stiffness equivalent tothe local hull stiffness at the idler attach position as determinedfrom a separaLe static analysis. This approach seems to give con-sistent results and alternative modeling procedures would be extreme-ly expensive.

3. Good predictions of the measured vertical idler inertance functionhave been made with the developed model, but the measured horizontalinertance function is underpredicted by about 10 dR. The reasons forthis latter difference are unresolved, but it is felt that the dif-ferences do not result from the representations of the floor, boxbeam or idler. While some effort could be expended to resolve this,it is felt that the model should be used in its present form, sincethe required output fron further stages of the model study will bechanges in transfer function rather than the absolute value and it isfelt that these changes will be accurately calculated.

4. The predicted effects of changes in the local stiffness of the idler,corresponding to left and right idlers on the M113 and AIFV vehicles,on the idler inertance suggest that changes in idler stiffness up toa factor of 10 will produce no significant changes in hull power flowor interior noise levels.

5. The frequency and space-averaging approach in interpreting the modaloutput from the finite element analysis is consistent with the con-ventional approach of using narrow band transfer function data. How-ever, the averaging procedures developed are much more efficient andprovide results directly useful and more related to the physics ofthe problem. While narrow-band information is useful, particularlymeasured modal data, in the present example only the frequency- andspace-averaged results can be handled practically in the predictionprocess.

6. Using these averaging procedures, close prediction has been made ofthe measured noise-to-force transfer function for vertical excitationof the left-side idler of the M113 vehicle. The najor contributorsto the interior noise levels are predicted to re the top, upper sideand hottom hull plates.

-109-

The following recommendations are made:

1. Further effort should be directed to finish the analysis of thenoise-to-force transfer functions using the space- and frequency-averaging procedures developed. This should include completeautomation of the space- and frequency-averaging procedures, forcalculation of both hull response-to-force and noise-to-forcetransfer functions.

2. A model of the AIFV hull should be developed using similar principlesto those followed for the M113AI. Calculations should then be madeof the noise-to-force transfer function. Computed differences be-tween AIFV and M113 results should be compared with measured differ-ences as the final test of the modeling philosophies.

3. A limited experimental modal analysis of the M113 hull should beconducted as modeled to provide additional measured data with whichto compare baseline predicted results.

6. PROTOTYPE CnMPLIANT IDLER WHEEL DEVELOPMENT

6.1 Background

Earlier work has shown that an idler wheel would qenerate less interiornoise if the wheel rim compliance were increased, that is, if the wheelhad a "sprinq-like" rim, such as could he f:lade with rubber or steelsprings [2,18]. In a 1977 report of that work, an estimation was madeof the noise reduction potential of compliant idler rims and hubs [16].In subsequent work, an experimental idler wheel was designed and fabri-cated to validate the compliance concept and to optimize parameters. Thedescription of this development is contained in Reference [17]; theacoustic testing was conducted in the current phase of work and isreported in Section 6.2.2 of this report.

Guided by the results of the experimental idler discussed above, a proto-type idler was designed, fabricated, and tested. Compared to the experi-mental idler, the prototype was intpnded to be more practical and closerto a production design. The prototype demonstrated that the conceptspreviously developed could be utilized in a practical piece of hardwaresuitable for tracked vehicles. This prototype idler wheel is describedin Section 6.3.

6.2 Experimental Idler Wheel

6.2.1 Conceptual Approach

The experimental idler served as a design tool to address specific areasof concern in the use of compliance for idler applications. These areasincluded the following considerations:

1. Magnitude of compliance needed for noise reduction (verification ofestimates)

-110-

2. importance of compliance in the tanqential and axial directions, as

compared with the radial direction

3. Selection of compliant material

4. Investiqation of heat buildup problems due to hysteresis in the com-pliant material

5. Importance of the registration of track blocks with compliant ele-

'nents

6• Assessment of the effect on exterior noise

7. Importance of "guide scrub" on interior noise

,. Estiiate of durahility

Itelnms 3 an.l 4 are addressed extensively in Reference [17] anti will nothe disussed here.

A 'iia(irai of tne experimental idler wheel appears in Figure 6.1, andphotoqraphs of the wheel mounted to the idler test Stafid are shown inFigures 6.? and 6.3. This idler half consists of eleven sorinq-mounted"paddles" that support the track. During experimentation, the varioussprinq rates and the shapes of the surfaces that hear aqainst the trackwere varied. Nooise, vibration, and temperature were then monitored.

This expfrilnental idler is necessarily complex in design to permitchanges tc he 'nade easily for experimental evaluation. This desirablefeature necessitated the holted-toqether design.

The ex neri iental idler was designed to have a radial spring rate vari-, 1 ole fror, approxiqately ,n0OO to ?O,000 lh/in (per paddle) through achoice of c-n:mpliant element dimensions and materials. Initially, theradi,fl sprinn rate was set at a calculated value of 4,000 lb/in for eachpaddle. The noise reduction was documented at this compliance, usingthe flat paddl ends rather than the traisPd paddle caps visible inFi ,ure 6.3. 1A riore comnletp description of the experimental idler design rationale -

is contained in Reference [17].

6.?.? Test Results

6.2.2.1 Compliance

Load-deflection tests were conducted to determine the actual values ofradial and axial compliance in the experimental idler paddles. Values-per piaddle rf 4,040 lb/in for radial spring rate and 6,568 lb/in for ax-ial sprinq rate were ohtained [4]. These are in close agreement withoesim prill f0.1cti ors.

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6.2.2.2 Interior Noise Reduction of the Experimental Idler Wheel

Figure 6.4 shows the crew area A-weighted noise levels of the standardand experimental compliant idlers as a function of speed. A-weightednoise reductions of between 7 and 12 dB were achieved. The tests wereconducted on the FMC test stand so there was no noise input from the-sprocket or roadwheels. This stand is described in Reference [17].

Octave hand spectra of crew area noise are compared in Fiqure 6.5. Inthis figure, the upper curve is the standard idler tested at a tracktension of 2,500 lh, which is typical of vehicles in operation. Com-pared to the standard idler, the octave hand noise reductions are asmuch as 13 dB.

For the entire vehicle to comply with MIL-STD-1474 Category B, alsoshown in Fiqure 6.5, tie expeerimental idler would require siqnificantadditional noise reduction. This assumes that the combined noise of thetwo sprockets, two idlers, and ten roauwheels has the same spectrumshape as the experimental idler wheel, but at a level 7dR higher. Whilethis qualification probably will not be exactly met, it is a necessaryassumption due to the unknown spectra of other prototype quietedsuspension components that are not yet built. These additional reduc-tions are as follows: For the crew area, 3 dR at 125 Hz: P dB at 250Hz; and I d3 at S00 Hz. For the driver's position, rouqhly 5 dB ofadditional noise reduction would be required, based on comparisons ofidler noise spectra in the cre, and driver locations [16].

In Reference [16], a simple estimation procedure, based on theory only,suqqests "that interior noise will he reduced by about 4 dB(AV per halv-ing of [idler wheel] rim stiffness." For the experimental idler, thestiffness has been halved almost four times, for a prediction of ahout

15 dB of A-weiqhted noise reduction. The observed noise reduction was 9to 1? dB, with the most reduction conino at the hiqhest soeed tested (30moh). Therefore, the reduction achieved is about 2.5 to 3 dB per halv-ing of rim stiffness.

This estimaate does not predict enouqh noise reduction to meet the qoalfor any teasonable rim stiffness. Therefore, to meet the Categorynoise level in the crew area, the prototype idler must depend on a com-pliant huh, which is a more powerful noise reduction technique for agiven total compliance.

6.2.2.3 Exterior Noise Reduction of the Experimental Idler Wheel

The exterior signature of the idler consists of two components: noiseemitted due to hull vihration, and noise emitted directly from the idlerand track. Noise due to hull vibration has a spectrum shape similar tointerior noise, while the suspension-radiated idler noise may includesqueaks, a clattering sound, or a rubbinq sound caused by metal-to-metalcontact.

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icre6.S Interior Noise Spectra a 0mhDetRight Idler wheel Only.

Exterior noise measuiremients were made on the standard (baseline) idlerand on the experimental idler wheel. Because of test stand noise, theexperimental idler data are inconclusive and are not presented here.Listening tests made while taking baseline data at 10, 20 and 30 mphrevealed that the hull-radiated signature is most intense at and below125 Hz and that sprocket clatter is audible at and above 1000 Hz. How-ever, test stand suspension noise may be significant below 125 Hz andnear 8 KHz. The data in Figure 6.6 show that the baseline idler signa-ture level becomes roughly 5 dB more intense when the track speed isincreased from 10 to 20 mph, and increases another 4 dB for a furth:rspeed increase to 30 mph.

Also plotted in Figure 6.6 are standard and specially quieted M113AI ex-haust noise spectra. Comparison of these spectra shows that, with theaccelerator pedal fully depressed, the standard vehicle exhaust noisewould probably be detected more easily than idler noise at 10 and 20mph, but exhaust noise and track noise could be roughly equally detect-able at 30 mph, depending on whether background noise and other condi-tions allowed the 125 Hz idler noise to be more audible than the higherfrequency exhaust noise. For TARADCO's low-signature 4113A0 with aspecially quieted exhaust, the standard idler noise would be more read-ily detectable at 20 and 30 mph even with the accelerator fully de-pressed. Thus, reducing idler noise would result in a reduction in thevehicle's distance to detection at the higher speeds, provided theexhaust noise is also reduced.

6.2.2.4 Durability of the Experimental Idler Wheel

Durability of the compliant elements, including heat buildup and fa-tigue testing, is discussed in References [9] and [16]. Durability onthe test stand was very good, based upon approximately 220 miles of sim-ulated operation and over ,two years of existence, most of that timemounted under tension to the test stand.

After about one year, the compliant elements were cut down in size anddrilled to provide more axial and tangential compliance. During thisoperation, it was discovered that several of the bonds had begun to sep-arate, with one separation occurring through about 25% of the bondedsurface. The separations were a result of rubber extending beyond theedge of the mating steel surface to which it was bonded. This caused alarge stress concentration. Most of the failures were entirely withinthe rubber material itself, although one failure involved actual separ-ation of the adhesive from the steel surface. Failures were found onlyat points of major stress concentration.

For ease of manufacture, the main body of the idler was constructed ofaluminum. Because the track strand on the test stand did not run "true"over the experimental idler, considerable wear occurred on the paddlesurfaces, and where track guides contacted the inner idler disc. Partof the misalignment problem was due to the fact that a single wheel con-figuration was tested in a dual wheel application. Steel materialwould he used on production components and would greatly reduce thesewear pronlems.

-l13-

IDLER INDUCED NOISE

A 10 mph, 96 dB (C), 78 dB (A)

B 20 mph, 99 dB (C), 83 dB (A)

C- 30 mph, 105 dB (C), 88 dB (A)

ENGINE EXHAUST NOISE

D Maximum noise levels in 2 - 3 gear, 600 to 2000 RPM,accelerator fully depressed, brakes "on",

standard M1 13A 1 production vehicle.

E....... Same, but for TARADCOM low signature demonstrationM113A1 vehicle fData taken at 50 feet, 6dB then added

for distance compensation)

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-119-

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6.2.3 Further investigations with the Experimental Idler Wheel

6.2.3.1 Sources of Rapid Noise Level Variations

A test series was run on the experimental compliant idler wheel to de-termine any potential noise control benefits of indexing the track tothe idler or sprocket, that is, by controlling the position of contactbetween the track shoe arid a properly shaped noncircular wheel. Thesetests were inspired by the observatior that track interior noise variesseveral decibels but with no obvious periodicity.

The purpose of the test was only to identify sources of noise levelvariations, but not to quantify each of them. A quantified analysiswould have required the added expense of designing and constructingspecial electronic circuitry.

The data recordinq and analysis were done as follows. First, interiorand exterior noise were simultaneously recorded. Then, two types ofdata analysis were conducted. In the first, the synchronized exteriorand interior noise data were plotted, using a Bruel & Kjaer 2305 graphiclevel recorder (set to a paper speed of 10 mm/s and a writing speed of100 ram/s). To synchronize the interior and exterior channels, hammerblows and a qain change were recorded simultaneously on both channels.The exterior noise channel recorded the relative positions of the trackan(d idler paddles by a definite metal -on-metal clatter which occuredonly when the idler paddles contacted the bushing bosses of the tracks.The relative interior noise level changes were then identified by coni-paring the appropriate interior and exterior time histories. This com-parison revealed the relative track-idler phasing which caused minimumand maximum interior noise levels.

The second type of analysis was to plot narrow band spectra of theD.C. level of octave-band-filtered interior noise, to reveal any cy-clical nature in the normal fluctuations of interior noise. This wasaccomplished by setting a GenRad Model 1933 sound level meter to theappropriate octave band, and then taking the spectrum of the dc outputusing a Hewlett-Packard Model 5420 digital signal analyzer andplotter system. Because this dc signal is logarithmic, and the meterrisetime may differ from the decay rate, the results are nonlinearand are not easily interpreted quantitatively.

All data discussed below were taken with the rounded idler capsshimmed to slightly increase their diameter. This caused the indexingbetween the track and idler to shift about every 1.5 seconds at 30mph.

Lookinq at the sound level time histories, such as the samples shownin Figure 6.7 and 6.2, the following observations and conclusions werereachedI

-120-

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6.2.3.1.1 2000 Hz Octave Band Exterior Noise

The 2000 1Iz octave-band exterior sound level time history plot Figure6.7, shows a peak that corresponds to each ,hift of the track withrespect to the idler wheel. These peaks are caused by periods ofmetal-on-metal impacts when the aluminum idler paddles strike thesteel bushing bosses of the track shoes. During the moments of lower2000 11z noise, the idler paddle contact is against the rubber innertrack pad.

The following paragraphs discuss the interior noise level variations

in the most important octave hands:

6.2.3.1.2 1000 Hz Octave Band Interior Noise

At lower speeds, 10-20 mph. the exterior metal-on-metal impacts co-incide with the interior noise peaks. However at 30 mph, the patternis barely evident. Therefore, to minimize noise in this octave band,cushioning rather than indexing will be more reliable in reducinginterior noise.

6.2.3.1.3 500 H1z Octave Band Interiom Noise

At very low speeds, the sharp metal -on-metal impacts correspond toslight interior noise level peaks. No clear pattern is evident athigher speeds, and no definite conclusions are justified regarding theeffectiveness of indexing for reducing interior noise.

. 2.3.1.4 250 Hz Octave Band Interior Noise

The sharp metallic impacts predominately correspond to interior noisepeaks. However, a signi ficant number of impacts correspond to minimdof interior noise, especially at 30 mph, as shown on Figure 6.P. At30 mph, the interior peaks occurred slilhtly more often than the ex-terior peaks. "(qain. no definite conclusions ir(e .lustified.

6.2.3.1.5 63 Hz and 125 Hz Octave Interior Noise

At low speed, no clear pattern is evident, although a number of inter-ior noise peaks correspond to the metallic impacts. At 30 mph, twointerior noise peaks occur per 2000 01iz exterior peak, and every otherone of these peaks corresponds to the metallic impacts. This obser-vation suggests that the greatest amount of impact energy is convertedto hLIll vibration when the track is contacted at the center of theshoes or at the pins. It follows that the least low frequency noisewould be expected for contact at roughly the 1/4 and 3/4 locationsbetween the pins. Clearly, indexing is a potentially useful means ofreducing noise in these octave bands.

-123-

6.2.3.1.6 Summary of Interior Noise Level Variation

- -- In the noise level time histories discussed, the A-weighted and octaveband interior noise levels varied by the amounts tabulated below:

TABLE 6.1 VARIATIONS OF INTERIOR SOUND LEVELSA-

Frequency 63 125 250 500 1000 2000 WeightedBand (Hz)

Sound Level +5.5 +4 +4 +1.5 +4 +2 +2.5 SVariations (dB)

Other than at 500 and 200t) Hz, indexinq appears to hdve a marked ef-

-fect on interior noise levels.

To summarize these observations:

1. At the higher frequencies, the interior noise peaks occur when the[ metallic noise peaks occur. This suqqects that the high frequency

vibration is simply transmitted into the hull.

2. At the lowest frequencies, there is no simple correlation between

noise maxima and the amount of cushioninq between the track andthe idler paddles. Instead, the least noise occurs when thetrack impacts the idler at the 1/4 and 3/4 location on each shoe,which is an area of intermediate cushioning. Therefore, in-dexinq is ootentially more effective than cushioninQ for reducinqlow frequency noise.

3. At intermediate frequencies (250 and 500 Hz), both indexinq andcushioning are probably moderately effective.

4. In the sprocket desiqn,adjustinq the position of the cushionrelative to the sprocket teeth is a potentially useful tech-nique for -achieving up to 4 dR of A-weiqhted noise reduction. Anestimate of 2 dB is more realistic.

6.2.3.1.7 Sources of Interior Noise Level Variations

Even casual observation reveals that the idler exterior and interiornoise levels vary as the idler wheel goes in and out of phase with thetrack shoes. In addition to the indexing between the idler paddlesand the track, there are apparently other sources of modulation.Because of the irreqular pattern of indexing and interior noise, noone periodic phenomenon can account for all the previously discussednoise level variations. One night intuitively expect, therefore, thatinterior noise is also modulated by the revolution of the entiretrack, idler wheel rotation, and the low frequency oscillationsbouncing) of the upper track strand, and possibly other drive

*1 motor-related cycles.

-124-

Because the intericr noise is amplitude modulated, AM signal theoryMight apply, and the detected interior noise would therefore containthe mentioned fundamental rotational frequencies and their harmonics,as well as assorted sum and difference frequencies of each fundamentaland its harmonics. This is indeed the case, as is discussed next.

The various frequencies of spectral peaks of the sound level meter dc.output include those listed below, at 30 mph. An example of a corre-sponding spectrum appears in Figure 6.9.

TABLE 6.2 CALCULATED INTERIOR NOISE MODULATION FREQUENCIES

Modulation Source Fundamental 1st Harmonic 2nd Harmonic

Track Rotatior (T) 1.371 Hz* 2.742 Hz* 4.1136 Hz

Idler Whee& Rotation (I) 8.107 * 16.214 ** 24.32 **

Unproven (Ui) 0.99 1.98 * 2.96

T + U 2.36 * 4.72 7.08

S- UJ 7.12 * 14.2 ** 21.4 **

I T 6.74 * 13.48 ** 20.2 **

- 2T 5.37 * 10.7 16.1 **

I - 3T 4.00 * 8.00 12.00

I - 4T 2.63 * 5.26 7.89

I - 5T 1.26 * 2.52 3.78

Codes: * Spectral peak observed•* Not analyzed

No Mark N;ot clearly observed

On most plots, the track dnd idler rotation (designated T and I, re-spectively, in Table 6.2) are evident. A peak at 0.99 Hz, possiblycorresponding to a track strand resonance, is also apparent. A seriesof hiqher frequency period peaks begins at the idler rotation frequen-cy and at each track multiple below this peak. Because of the approx-iinately one percent uncertainty in spectral peak location, identifica-tion of the lower difference frequencies is uncertain in this briefanalysis. Numerous iminor peaks are also apparent; these may corre-spond to other sum, difference and multiple frequencies.

The qualitative data analysis suqqests that nonuniformities in thetrack and idler wheel are the primary sources of altering the rate of

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indexing, which in turn affects interior noise level. It also demon-strates that the variation is not random, but instead is stronglylinked to many regular periodic events - perhaps even the impact ofparticular track shoes against particular idler paddles.

It was observed that the track wandered from side to side. At times,this motion appeared to correlate with the idler-track indexingchanges, but no definite conclusions could he reached regarding thisobservation.

6.2.3.2 Shape of Experimental Idler Paddle Contact Surfaces

The experimental idler wheel was tested with both rounded and flatpaddle surfaces contacting the track. The rounded paddle caps, simi-lar to those visible in Figure 6.3, tended. to contact the track at thepins. With the rounded caps removed, the exposed flat surfaces tendedto contact the inner track pad rubber on the track shoes.

Figure 6. 10 shows the increased noise level due to fir,-i metallic im-pacts between the idler rounded paddles and track shoe steel forgings.While the metallic impacts caused no differences in the 250 Hz octaveband, all higher octaves show a noise level increase, with the largestat 6 dB in the 8 kliz octave band. The A-weighted sound level was alsoslightly increased. For exterior noise, the ,:ietal-on-'uetal impactsare very objectionable and should he ivoided in the prototype idlerdesign.

6.2.2.3 Fffects of Combined Axial and Radial Compliance Changes

As discussed in Section 6.2.2.4, the experimental idler was nodifiudto increase axial and tangential compliance. Radial compliance re-duced correspondingly. It was oostulated that the axial idler vibra-tion might be a major contributor to experimental idler interiornoise. Consequently, tests were designed and executed with the re-duced stiffness. The reduction w'as accomplished by drilling holesinto and cutting away dortions of the rubber springs. Radial and tan-qential compliance wore calculated as being reduced by about 30 per-cent. The resulting axial stiffness was very low; axial hand pressureon the paddles caused an obvious deflection.

Vibration o measurelients taken near the edge of the disc on the experi-mental idler at 30 mph showed modest level s of radial vibration and:.much higher levels of axial and tangential vibration (Figure 6.11).The vibration spectra for the modified experimental idler are shown inFigure 6.12. The increased axial compliance resulted in raising andequalizing the vihration levels for the three directions. Greatervibration levols were due partially to the fact that the idler paddlesoccasional 1)' "bottomed-out" on the disc suiport..

The resulting A-weigjh.'d interior noise level was 101 dB which is 2 dP"higher than the original expCrimeental idler. The i.nterior octave hand

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Ociave Band Center Frequency Hertz

Figure 6.10 Effect of Metallic Track - Idler Impacts.Compliant Idler, Rounded Paddle Tops versus Flat Tops.

-128-

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spectra are shown in Fi gure 6.13. Noise levels in the 63 and 125 Hzoctave bands are the lowest ever measured for the experimental idlerwheel . however, an apparent resonance appeared at 250 liz, which nul-lified any potential acoustic advantage gained by the axial compli-ance. The noise levels of the 500 to 2000 Hz octave bands were essen-tially unchanged. The 4000 and 8000 Hz octave hand sound levels arethe lowest yet measured for an idler wheel. This high frequency re-duction was not unexpected, based on experience with other rubbervibration-isolated systems. Unfortunately, it is of little valuehere, as the noise reduction is required at lower fre(luencies.

The apparent 250 Hz resonance is of concern because of its objection-able 110.8 dB level. It may be due to the soft axial compliance de-coupling the idler wheel disk from the track. This decoupling wouldallow increased idler disk axial motion and also reduce any damping ofidler resonances by the track. However, this seemingly plausibleresonance is not supported by the acceleration spectra made on theidler wheel.

With regard to all future idler and sprocket designs, these experimen-tal results strongly suggest that a low axial stiffness is not ofgreat benefit and may allow resonances of the whee.l to occur becauseof reduced damping.

6.2.3.4 Track Guide Scrub Noise'

During some testing of the experimental compliant idler wheel, thetrack guides rubbed and scraped against the idler wheel. This scrub-bing caused rapid wear of the aluminum idler disk and generated anaudible scraping sound. This noise was barely audible inside thevehicle, and was more easily heard outside. To determine the signifi-cance of the scrubbing noise, the idler was tested with and withouttrack-guide-to-wheel contact. The scrubbing was eliminated by cantingthe idler mount slightly so that the track shifted sideways and thequides did not touch the wheel.

1igure 6.14 shows the effect on interior noise of metal-on-metal rub-bing between the track guides arid the compliant idler wheel. Thescrubbing produced a 2 dOl increase in the 500, 1000 and 2000 Hz octavebands, and an overall A-weighted increase from 93 to 99 dB. These in-cr'eIses are consistent with earlier but inconclusive data. These(Iata suggest that "hard" track guide scrub creates a 94 dB(A) noiselevel. Clearly, this number is approximate. Even so, the data suggestthat scrub noise must be reduced in the prototype idler design.

6.2.3.5 Increased Diameter Idler

Since the experimental idler was larger in diameter than the standardM1I3A1 idler, a portion of the noise reduction was suspected to be duesimply to the large size. The standard idler is 17.25 inches in dia-me ter whereas the experimental idler diameter is 19.06 inches, a dif-ference of 1.-1 inches.

- 131 -

130

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EXEIMNA IDEIHE+ 4

-132-

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I31 5 63 126 280 Soo 100)O 2000 4000 8000 165000Octave Band Center Frequency -Hertz

Figure 6.14 Tlhe effect of Track Guide Scrubbing on Interior Noise.

-133-

To investigate this concept, an increased diameter idler wheel, modi-

fied from a standard idler wheel, was tested. The increased diameterwheel measured 21 inches. Using the 2.75-inch larger wheels, it was

found that at test stand speeds of 30 mph, A-weighted interior crew

noise levels were reduced hy 4 dB to a level of 106 dB. Consequently,up to 2 dB of the A-weighted noise reduction realized with the exper-imental idler may be due to the increased size. A comparison of stan-dard and increased diameter idler noise is shown in Figure 6.15.

6.3 Prototype Idler Wheel

A prototype idler wheel was designed, fabricated, and tested. Figure6.16 is a photograph of the prototype idler wheel mounted on an M113AIvehicle. This prototype, compared to the previously described experi-mental idler wheel, is a simpler and more practical design which ismore suitable for production. The A-weighted noise level goal for oneidler wheel is 92 dB inside the crew area. Attaining 92 dB(A) foreach idler, each sprocket, and for the roadwheels on each side wouldresult in 100 dB(A) for the total vehicle noise level.

6.3.1 Design Goals

Considerations of production practicality and cost limitation requiredthat the wheel be much simpler than the experimental wheel. A designconsisting of three metal and two rubber pieces was selected, as shownin Figure 6.17. The goals in the design of the prototype ccmpliantidler were as follows:

1. Noise level of 95 dD(A) or lower2. Production feasibility3. Service life of 2,000 miles or more4. Simplicity5. Relatively low cost6. Fail-safe features to permit continued operation (at increased

noise level) in the event of failure of the compliant members

6.3.2 Design Criteria

To achieve the above goals, the following criteria were used to guidedesigjn decisions:

1. Space limits: The idler shall be designed so that no changes tothe hull are required on the M113A1 test vehicle.

2. Fxisting hardware: The idler must fit on to the existing M113A1idler support assembly.

D. Diameter limits: The diameter of the idler shall not he too largeto prevent the track from being accidentally "thrown" or toprevent common passage of dehris drawn up by the track. Ifsufficient clearance is not allowed between the sponson and thewheel rim, the track or debris could become jamuned between theidl er and! sponson. This could cause the idler, idler mount, orhull to fail.

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4. Ribber stresses: To ensure long life of the rubber compliances,shear stresses in the material shall not exceed recomnnended limitsfor rotative dynamic loading. For exaiiple, a limit of 75 psi isrecoimnended for 30-durocieter rubber when shear strain is 225 per-cent [8]. Much higher stress limits can be allowed for infrequentover1 earls.

5. Static load: The load that will be constantly imposed on theidler due to track tension nay be as high as 10,000 lh undernormal conditions. If ar, 1`113 is parked on a 60% slope, however, icontinuous track tension loads may reach 22,100 lb,

n,. ',!y-a ;ic loads: The fluctuating loads imposed on the idler during --

severe vehicle iianeuvers may he as high as 15,000 lb. This loadcould occur if the vehicle bottomed-out' on the idler wheel witha glancing blow.

c7. )vrload li,41it.: An overload device shall be included to react toexcessive loads and prevent excessive stress in the compliantele Ients. This device shall also act as a fail-safe feature.

(3.3.3 iPesign Concepts

oe'. -erl cnncepts were considered for the prototype compliant idle-r. -

The predoeir..ant reasons for acceptino the rubber-in-shear design or,cnnversely, rejecting the other designs included: (1) the attain-ability of the desired radial c3oMl fiance, (?) the degree of ,.wplicityi t the design and (3) the level of difficjlty in inanifacturing. The -degree of simIl icity greatly influenced the expectations of durabilityand 'Fractical ity. The various concepts that were evaluated are,isci cssed below.

,3. 3. i Sectional idler Pi: i;

..• concept. S imllr to the experim:ental compl iant idler, incorporating arii,,ber of radially synv:ietrical , independent comnpliant elements and asccLional idler rim was considered. The concept was rejected becauseof its coml;Ilexity, difficult machining operations, and expensive as-so'IvI pr, m r e ures.

3.3. . Thin I lexiblu e [ii'Rubher in Compression

Th is concept, shown in Figure 6.12, incorporates a flexihl e steel hoop"loated" on rubber in compression around a steel huh. lhe rubbercor,'l ianice will be locally defor med at the poi nt of track/rim contact, -hot will have less detormation on the side of the idler that is not inconitact wit.h the track.

lh i' m or t.w drawbacks are the risk of fati ,ue failure in the flex-1 I r im 1 nd t he I ow c oripl i anrce i n t he rubber- i n-c ompress i on el ement

Als5), excessi-ve point. stresses in the rim could occur durin op trackVwal k-ofef. Because the tio,'omain drawbacks apcar& insurmount-ahlethis concept was rejected.

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FLEXIBLE STEEL HOOP

RUBBER SPRINGS

RIGID CENTER

Figure 6.18 Idler Cuncept: Thin Flexible Rim; Rubber in Compression.

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6.3.3.3 Thick Rigid Rim/Rubber in Compression

Figure 6.19 shows that this concept is similar to the above concept,except the floating rim is rigid. The isolators are fixed at theirinner diameter to the wheel but not to the outer rim. Thus, the com-pliance is never placed in tension. Compressive loads are always dis-tributed uniformly to the isolators because of the rigidity of therim. However, the desired compliance was unattainable in this com-pression node so the concept was rejected.

6.3.3.4 Rim of Rollers

Figure 6.20 shows a proposed idler wheel with compliant rollers actingas the wheel rim:i. The major advantage of this concept is that fric-tion heating due to track shoe sliding is reduced. The disadvantagesare nliited compliance and complexity. Also, the roller concept mightnot he reliable in the required operating environments. Consequently,this design was not utilized.

6.3.3.5 Rigid Rim/Rubber-in-Shear

This concept was judged to he the most acceptable because it met orexceeded all of the design goals and criteria discussed in Sections6.3.1 and 6.3.2. It was, therefore, chosen to be fully developed forprototype hardware. The assembly drawing of the design appearedearlier in Figure 6.17. Features of this design include:

1. Three steel parts and two rubber compliant rinqs. This relativelyfew nomrber of parts will contribute to a low cost productionunit.

2. Adaptability to production techniques. The steel parts are read-ily adaptable to casting or forging processes. The rubber will befastened in place with a cyanoacrylate adhesive or vulcanizationprocess.

3. Fail safe. The idler rimn is held captive by the two wheels in theevent of compl iance f ailure. This would permit continuedoneration at increased noise levels.

4. Twenty-one inch diameter. This is 3.75 inches larger than thestandard MID3AI idler, but will still permit the passage of debrisor track throwing without Jamming. Additional clearance is pro-vided by the radial deflection allowed by the compliance.

5. Low rubber stresses. The maxirrium stress in the rubber compliancesis 1 iited to 45 psi. This is well within the recorvended limitof 95 psi for 40 duroieter rubber undergoing continuous rotativeshear loading. Levels higher than 45 psi are not possible due tobottoming of the rim. The low levels of stress in the prototypedesign will contribute to long service life. (In the experimlentalidler, this type of rubber material was routinely stressed to 210psi during an approximate test time of 220 miles).

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RIGID STE EL HOOP

RUBBER SPRINGS

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RIGID CENTER

Figure 6.19 Idler Concept: Thick Rigid Rini; Rubber iti C~ompression.

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TRACK WRAPS AROUND IDLER iAND ONLY CONTACTS THE IROLLERS

ROLLERS ARE FREE TOROTATE AND HAVE

RUBBER DOUGHNUT-SHAPEDUCENTERS FORCOMPLIANCE AND

I NOISE REDUCTION

\ --- / RIGID CENTER AND DISK -

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Figure 6.20 Idler Concept: Rirm Composed of Rollers.

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6. A very simple working action. The rubber experiences rotativeshear at limited levels of stress and strain. This type oflimited movement is conducive to long service life.

-7. Overload capability. The idler was designed to withstand dynamicloads of over 15,000 lbs.

8. A maximum deflection of .75 inch. This will allow for noise re-duction at all but the most severe of vehicle maneuvers. Shockinput to the vehicle from the idler bottoming during rough terrainoperation will also be greatly reduced.

9. Internal cut-outs to allow passage of debris drawn into the wheelby the track guides. To avoid trapping objects between opposinqspokes, the standard M113A1 idler wheels are mounted with spokesstaggered. Larger cut-outs would be required if this staggeredarrangement was desired on the prototype idler. In either case,the base of the spokes in the rim are the means of limiting thedeflection during overload conditions.

10. Inclined rims. The rims are inclined inward to utilize the com-pliance of the inner track shoe pads. The outer edges are highestand contact the inner track pads first. The *nner pad is deflect-ed most at this point. As the pad deflects, more and more of therim contacts the rubber oad. The effect is that of an increasingspring rate shock absorber.

Another concept for the rim contour was to providc two circum-ferential bumps of different heights [10]. This would have pro-duced a dual rate spring effect when contacting the inner trackpad. However, the valley between the bumps could prevent a mis-aligned track guide from recovering. Therefore, the ramp conceptwas adapted.

11. Chamferred inner edges of each rim. It is known that the track ismost frequently thrown inward toward the hull. The chamferrededges help the track guides to realign into the center of theidler. The exaggerated chamfer on the inboard half significantlyreduces the occurrence of the track throwing problem [13].

46.3.4 Results

The actual prototype idler that was used for testinq was fabricatedfrom high strength steel plate and molded natural rubber. The wheel Ihalves were machined individually but the rim was welded together fromrough-machined halves, then final machined. The basic designs arecompatible with forging or castinq processes for high production Arates. The rubber annuli were molded from a high grade, low loss,natural base rubber compound. They were attached at assembly with a A

cyanoacrylate adhesive. The rubber hardness that was achieved wassomewhat softer than the nominal design specifications: 35A insteadof 40A durometer. Noise reductions for the test prototype may con-sequently be slightly better than expected. Bottominq-out load.-apabui1i ties will, also be reduced.

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6.3.4.1 Compliance

The calculated desiqn spring rate for the prototype idler is 8247lb/in. This value is for a rubber hardness of 40A durometer as re-quired by the design. For a hardness of 35A durometer, as wasachieved, the spring rate is 6927 lb/in. These values consider thatthe dynamic shear modulus exceens the static modulus by 20 percent[8]. No tests were made to determine the actual level of compliance.

6.3.4.2 Interior Noise Reduction of the Prototype Idler

The noise of the prototype compliant idler was measured on the idlertest stand and compared to tests of the standard idler on the samestand. Track tension was 2,500 lbs in both cases.

Figure 6.21 shows A-weighted crew area noise levels of the standardand prototype idler wheels as a function of speed. Noise reductionsof from 10 to 15 dB(A) were achieved. At 30 mph, the noise level was95 dB(A); therefore an additional 3 dR(A) of noise reduction would berequired to meet the idler wheel qoai of 92 dB(A).

Figure 6.22 shows crew area noise spectra of the standard and proto-type idler wheels. The prototype idler octave hand noise levels werereduced by 6 to 20 dB in the frequency range of 63 to 8000 Hz.

For the entire vehicle at 30 mph to comply with MIL-STD-1474, CategoryB, the prototype idler would require an additional noise reduction of5 dR in the 250 Hz octave hand. No further noise reduction would herequired in any other octave band. This statement assumes that thecomhined noise of the two quieted sprockets, two quieted idlers, andten quieted roadwheels has the same spectrum shape as the noise due tothe prototype idler wheel. This assumption, thouqh not exact, ispresently necessary because the other low-noise components have notyet been developed.

6.3.4.3 Exterior Noise Reduction of Prototype Idler Wheel

Figure 6.23 shows the acoustic signatures in octave hands for 30 mphoperation of the standard and prototype idler wheels, as measured onthe FMC test stand.

A reduction of 3 to 6 dR was measured at frequencies hetween 250 and2000 Hz. The actual signature reduction was probably greater and can-not be measured accurately on the present test stand. This is sus-pected because the measured interior noise reduction in these octavehands is 11 to 16 dB, which is far greater than the 3 to 6 dB exteriorreduction. As the interior and exterior noise reduction of hull-radiated noise must be identical, the measured exterior prototypeidler noise must contain noises from other sources; the likely candi-dates are the test stand assembly aid direct radiated noise from thetrack, sprocket and idler. A listening test suggests that the teststand and its drive sprocket are the sources.

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Figure 6.22 Interior Noise Spectra Comparison for the Standardand Prototype Idler Wheels.

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IDLER INDUCED NOISE

A .-. Standard idler,30 mph, 105 dB(C), 28 dB(A)

B Prototype idler, 4

30 mph, 97 dB(Flat), 85 dB(A)

ENGINE EXHAUST NOISE

C - --- - Maximur, noise levels in 2-3 qear, 600 to 2000 RPM,accelerator full) depressed, brakes "on",standard M1lll3A1 production vehicle.

0-- -Same, but for TAADCO•I Iclw-signature demonstration1,ll3AI vehicle. (Lata taken at 50 feet, 6 dB thenadded for distance compensation)

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Fiqure 6.23 Exterior Noise Spectra of M.lII3Al Standard Idler

Pair, Prototype idler anid .113^1 •L ,,•hi t 0 t25 Feet to the Left of the Hull.

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Although the exact acoustic sig3nature of the prototype idler is appar-ently too low to be ineasured on the test stand, it can still be con-cluded that the exterior idler signature has been reduced to wellbelow t h c. maxiimum exhaust noise of a standard M113AI, and thus wouldnot lead to detection. The p)resent data are not, adequate to determine_-if the actual acoustic signature of the prototype idler wheel couldlead to vehicle detection riore readily than exhaust noise froal-TARADCOM's low-signature M113A1.

0.3.4.4 Duaility~fthe-P-ro~totye ldler

A 1 iviaited amount of test mileage was accumuau ted on the prototypeidler during noise m~easureiient tests. It is estimated that a total of4about 31 rail es were conMr eted with the idler ope-a tedý on the '.eStstandi at various trdck tensions up to 2,500 lb. Of the four hood Sur-faces that exist, three were i 'n excellent conoition but one was peel-ing away at the inner dianeiter and peeling slightly at the outer did-mieter. Apparently, poor asse'uhl v efforts were at fauilt because allbonds have endured tL'hec same opor ati1.ng, condi tions and en'.'i runmient.Pub~ber overlap at steel edges was not a factor in th is f ailr.appreciable wear was observed on any of the steel compo1j)nen~ts 1nad'lybecause Of good track align:-ent and no occurrence of idler "botltomi uig-

Ba seo upon earl icer f at i ue ..est in '4 a-0 upon examv at ion of the ex-per iinentalI idler paddle bonds, this ,prototype idler could, easily pro-Ivide over ?,000 miles of service life, excludfiig the possibility ofaforejuin object causing a cata,"tro,-hic failuree of ? ribbepr element.The annuli are, of course, the weakest links 'in the arse-nbly. T1he:iain hazard involving the rubber is the 2.1ossibili')y of a hard or sharrob;OCt becom1i ng jadITned b-etween the rubber and a solid moving steel

com;ponent.- Cut-outs near the inner diameter and the sriall clearancesa t the rvu:- wi 11 ci i~iinii 2e the threat of debr is dai-mage. Further'more,Iconsiderable wear of the r;;<.'er mnaterial could be sustained beforef a i1lure occurs . Ac tual vehicle (lUrab il11ty tests would be the only:mea-is of deterimining accurate fielt service life expectations.

The second weakest link in the assemtbly is the rubber- to- steel hond.

The experimental and prototype idl1er wheel s emupi oyetd a cyanoa7-ryl at~ea dhe s, ve. This ad,-hos, ye proved to ho, thc' i:;(ost desirable in laboratory

I ts shear strenc;th when expcseci, to water, the bond shear strength ex-jceeds that of the rubbher by a factor of up to sixty. A' vulcanizedbend ha s been proposed as an equiallI'Y reliable iieans -f attachirgl therubber. Hlowever, the Lonfiguratior. of the vretotype idler might provet o h n too restrictive for the riolds reoctir'ed ')\ the vujlcanizing pro-

Durability o f t he stevel wheel halves and ri:ii is expected to exceedthat of the standard 111113 idler wheel. This is becaujse (,f the reduced.

4,14

impacts that will be experienced. Excessive wear, of course, couldresult if catastrophic rubber failure occurs. Nevertheless, theseparts could probably be reused several times with new rubber annuli.Rebuild cycles could be predicted with field testing.

6.3.4.5 Conclusions and Recommendations

The prototype compliant idler wheel demonstrated a substantial reduc-tion in idler generated interior noise. Although the design goal of92 dB(A) was not met (95 dB(A) was achieved), development of the pro-totype idler wheel was a very successful step in reducing the M113A1vehicle interior noise. If the sprocket and roadwheel induced noisecan be reduced by as much as was done with the prototype idler, subse-quent hull modifications and/or improvements in the compliant suspen-sion members should enable the interior noise goal of 100 dB(A) to bemet. Although field testing of the prototype idler wheel has not beenconducted, because of the rugged idler wheel construction and conser-vative rubber stress levels, ser-i-e life is estimated to be at least2000 miles.

Future compliant idler work should include the following areas:

1. Investigate design modifications necessary to make the compliantidler wheel completely compatible with standard manufacturingtechniques to reduce unit manufacturing costs. This might includereplacement of the glued rubber to steel bonds used in the proto-type idler with vulcanized-in-place rubber parts.

2. Investigate design modifications to facilitate field replacementof failed compliant elements.

3. Conduct a field test program to determine the durability and ser-vice life of the compliant idler wheel.

7. EXPERIMENTAL SPROCKET CARRIER DEVELOPMENT

7.1 Conceptual Approach

Based upon the successful demonstration of noise reduction on the com-pliant idler, similar concepts were extended to the sprocket. Thesprocket presents a greater challenge for noise reduction than theidler because of the necessity to transmit high torque loads throughthe compliances.

As with the experimental idler, the experimental sprocket is a toolwhich will aid in the design of the prototype sprocket. The designand testing of the experimental sprocket was intended to address thefollowing areas:

1. Exploration of the constraints and limitations involved in com-pliant sprocket design.

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..• . .-----

2. Assessuent of thie practical amomnt of torsional deflection thatshould be allowed before lockout

3. Deterriination of the effects of both torsional and radial loading"on the compliant elements, including heat buildup

4. •eter:,iination of the effects of axial deflections and axial tilt-ng, especially with regard to the overload inechamism

5. Selection of the halance between torsional stiffness and radial -compliance for required torque transmission and optimal noise re-

. . . . d 'ction

6. Selection of a co:;iJli.nt Elaterial

7. ilagnitude of expectcd interior noise reduction 11. ,-ssess~int. of the effect. on exterior noise

9. Esti:;iate of durrability

7.2 ')esign G.oal s

The goal s ii the desiqn of the expcrimental conpl iant sprocket were:

1. A\-wei hted noise level of 95 dR or less

2. A.bili ty t.r: he tested nn hine test stf.cnd or on an iperating vehicle

3. Service life of 100 :;iles or rore

.il- featJuros to :iaintain an operational sprocket and t)reve.a thrown track, ýn the event of co:npliance failure

5. Ahi 1 i ty to transmi tuie torques encountered in typical vehiclea ane. vers

A i,1cc . ut t e co*; 1 ance during thc transi missi on of veryhi .h torque loadinq

7.3 P,1esi In Criteria

To achieve the urove qjoal s, the following criteria were ui.l to guidedesign decisions:

1. Space li,i ts: The sprocket shall e (e!signed so tint no changesto the hull aro required on the oI.3A1 test. vehicle.

2. [.xistinq hardwa;'e: The sprockef ius t fit on to the existingMI13;I final drive assembily.

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3. Pitch: The nitch of the sprocket shall not he changed from thaton the M113AI vehicle. This dictates a 10 tooth sprocket of thesame diameter as the M1I3AI sprocket.

4. Rubber Stress: To ensure adequate life of the rubber compliances, -

stresses in the material shall not exceed recommended limits forrotative dynamic loading, e.g., 75 psi for 30 durometer rubberwhen shear strain is 225% [8].

5. Static load that will be constantly imposed on the sprocket due toconvion track tension nay be as high as 9,000 lb. radially. If anM113A1 is parked on a 60 slope, track tension may impart loads upto 11,200 lb radially and 9,156 ft-lb. torsionally.

6. Dynamic loads: The fluctuating loads imposed on the sprocket dur-ing severe steering maneuvers iiay be as high as 5,600 lb. radiallyand 2,570 ft-lb torsionally [1?]. This occurs during hilly cross-country maneuvers.

7. Torque: The maximum torque that the sprocket must transmit is11,300 ft-lh at an acceleration of up to 1 g. This occurs dur-ing panic skid stops [14].

7.4 Design Concepts

Development of the experimental sprocket initially focused on the corn-pliant mechanism. A complex rubber-in-shear system was finally chosenafter other concepts proved impractical. Design of the overloadtorque device was then pursued. A ten-degree torsional deflection wasused for a torque wind-up limit. This ten-degree anqular deflectionwas considered appropriate for both long-life stress levels in theruher compliances and workable clearances to allow isolation of thesprockat during usual operations. The extremely restrictive size en-velope was the major obstacle throughout the whole design effort.

In the following subsections, the various compliance concepts thatwere evaluated are discussed. A description of the final design,including the overload torque :iec haninsm, is presented in Section;.4.4.2.

7.4.1 Rubber in Radial Coorlression and Torsional Shear

The phrase "rubber in compression" has been used in this report when-ever a design concept employed rubber in radial compression. Almostall of the concepts provided torque transmission via the shear mode.Various concepts using rubber in compression were compared by evaluat-irig predicted performance characteristics for similarily sized struc-tures. Trends in performance changes were observed with certain modi-fications and their particular advantages were investigated. No ef-fort was mdde to systematically identify or categorize these trends.

-0

I-I

Procedures for predicting performances of the rubber-in-compressionconcepts were basically the same, so only the description of the firstconcept will go into any detail.

7.4.1.1 Solid Pair of Rubber Rings

The basic concept for rubber in compression involved a pair of solidrubber rings. The individual ring size was chosen to he compatible >1with standard M113A1 sprocket dimensions: 15.125" O.D. x 12.375" I.D. 1x 3.625" wide. The rings would be press-fit between the inner andoute; hoops for a ten percent preset compression. Each ring wasto be bonded to an inner hoop but not to an outer hoop. This avoided " iplacing any rubber in tension. Torque would be transmitted at theouter mating-part line by friction. This concept is illustrated in _

Figure 7.1.

To evaluate this desinn, it was assumed that the compression loadswere reacted by an equivalent flat block of rubber. This equivalentblock was of the same thickness as the rino but with flat dimensionsequal to the projected area of the ring inner diameter. The shapefactor, rubber hardness and simulated dimensions were then used toapproximate the total sprocket radial compliance. The torque capabil-ity was predicted from the ring dimensions.

This solid rubber ring concept proved unacceptable because excessivelyhigh radial compliances were predicted whenever 3cceptahle torque cap-abilities were found. Conversely, acceptable radial compliancesoccured only with excessively low torque capability. This negativerelationship between the two desired performance characteristics couldnot he reversed by any charge in basic rubber material

Other practical difficulties were anticipated with this concept.First, the task of press fitting these large flat rings between thetwo hoops would be difficult. Second, the probability was low thatthe total outer surface of the rubber would provide enough friction toactually transmit the predicted torque output.

7.4.1.2 Directionally Modified Compliance

The addition of circumferential holes or radial holes were two modifi-catýcns intended to improve the performance of the rubber in compres-

osin concept. The objectives of these two approaches was to decreaseradial compliance while maintaining a high torsional shear strength.Each modification employed a pair of rubber rings that were assembledfrom rectangular blocks with holes through them.

The individual blocks were as thick as the solid ring and as long asthe width of the ring. Orientation of the holes determined whetherthey were circumferential or radial. The blocks were to be press-fitside-by-side between the inner and outer hoops.

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,

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TWO SEPARATE ISOLATEDSPROCKET WHEEL HALVES

Figure 7.1 Sprocket Concept: So1~d Rubber Ring in Compression.

-153

As with the solid rings, the radial compliance was assumed to be pro-vided by an equivalent block of rubber, as thick as the ring and ofan area equal to the projected inner diameter. All blocks contributedto torque. Figure 7.2 shows an assembled modified rubber ring withcircumferential holes. The radial hole modification would have lookedsimilar.

Various sizes and patterns of holes in both directions were investi-gated. However, no modification of either type resulted in suffi-ciently low radial compliance while maintaining a high torsionalstiffness. Only round holes were considered but other shapes did notseem promising. Consequently, rubber in compression was consideredimpractical.

7.4.1.3 Three Concentric Ring Pairs

One of the original design concepts proposed for the experimentalsprocket involved three pairs of rubber rings in compression. Thisdesign is illustrated in Figure 7.3. The large pair of rings providemost of the compliance and torque capability. The other two ringpairs provide additional compliance.

The fact that this concept could not achieve the desired spring ratesproved to be the major drawback. Other difficulties included complex-ity and instability. The concept also depended upon an eleven tooth !sprocket, larger than the MII3A1 sprocket. This was considered unde-sirable since performance and load characteristics of the completevehicle power train would be altered.

7.4.1.4 Rubber <n Radial Compression and Radial Shear A

Another original concept combined the ideas of using rubber in coln-pression and rubber in shear. The proposed design was to have fourpairs of rubber rings; a large and a small set in shear and a set ofsoft and hard pairs in compression. This configuration is shown in -AFigure 7.4. To accomodate the complex structure a larger than stan- -i

dard sprocket was again proposed. 1]

The major drawbacks to this concept were the complexity, the larqesize and the inability to obtain both the desired compliance and tor-sional stiffness.

7.4.2 Compliant Fabric Isolator

An unconventional fabric isolator system was another proposed possi- 2bility. The fabric weave pattern was to have strong "threads" ofvarious co'npliances, woven in three different directions. As assem- 1bled, one set of threads would extend in a radial direction, frorlthe inner hoop to the outer hoop. The other two sets of threads wouldform opposing spiral arcs, stretching frmn the inner hoop, around andoutward to the outer hoop. 4l1 of the threads would he secuired atboth ends.

-154

CIRCUMFERENTIAL HOLESCOULD ONLY BE INSTALLEDVIA SEGMENTS - -4

t-L-

Figure 7.2 Sprocket Concept: Segmented Rubber Ring in Compressionwith Circumferential Holes.

1. .i -155-

STEEL COMPONENT

HARD RUBBER FOR DURABILITY

SOFT RUBBERFOR COMPLIANCE

Fiyur'e 7.3) Sprocketk Concept: Three Rub.'bcr R~ing Pairs in C-ompression.I2

4A

HARD RUBBER

SOFT RUBBER

RUBBER RINGS

IN SHEAR

-N\\i' 0, A

S' } RUBBER RINGS

I.,.,IN COMPRESSION

• •oncev• Rubber in Both Radial Compression -Figure 7.4 Sprocket Wn-e: ;

and Radial Shear. I

-157

A -157-.

The sum of the tensile compliances for the radial threads, beig..stretched in one direction, would have provided the total sprocketradial compliance and strength. The spiral arc threads would havecombined to provide torsional stiffness in either direction.

The configuration is shown in Figure 7.5. The cross section showseach type of thread as a different layer when, in fact, they would beinterwoven.

This concept was not pursued becuase it would have required excessive -

research and experimentation, and therefore, was unpredictable at thisstage. "

7.4.3 Overload Gear with Rubber Separators in Compression

One sprocket concept proposed the use of rubber segments that wereencased by steel on two sides to provide resistance to radial and A

torsional forces. The configuration is shown in Figure 7.6.

This concept was not seriously investigated because the operating de-flections for desired compliances would have been excessive whenrelated to the small size of the individual rubber elements. Designcomplexity, fatigue, instability, and wear were also considered to bemajor drawbacks.

7.4.4 Rubber in Shear

The rubber in shear concept involved pairs of flat rubber rings sim-ilar to those used in the prototype idler. In the sprocket applica-tion, they not only provided radial compliance but torsional stiffnessas well. The contradictory relationship between minimizing radial

compliance while maximizing torsional stiffness was again encountered.A smaller ring had the beneficial effect of reducing radial complianceto desired levels but it also had the negative effect of reducing themoment ann and, thereby, the torsional strength. Similar contradic-tory relationships were found when modifications were made in theareas of size, hardness, stress and strain.

7.4.4.1 Single and Double Pairs of Annuli

In the study of single and double pairs of rubber annuli, acceptablelevels of performance and durability could only be obtained with over-sized designs. At the larger sizes, desired workable deflections pro-duced excessive stresses and strains. Considerable effort was expend-ed to avoid more complex configurations. However, no variation ofrubber strength, size, or shape was found to be practical. Low radialcompliances could easily be designed but compatible torque capabilityonly increased with size or number of annuli. The only recourse wasto increase the number of compliant elements.

4

'4 -1 58-

4I'

ONLY THOSE THREADS IN TENSION ARE ACTIVE

CLOCKWISE SPIRAL~THREADS!

RADIAL THREADS

"COUNTERCLOCKWISESPIRAL THREADS

Figure 7.5 Sprocket Concept: Fabric Isolator.

-159- V

RUBBER SEPARATORSREACT TO RADIAL AND

TORSIONAL LOADS

Nft

Figure 7.6 Sprocket Concept: Overload Gear with RubberSeparators in Compression.

[ -160-

7.4.•4. Triple Annuli Pairs

--A set of three pairs of rubber annuli was found to provide the best 1performance characteristics within the size and stress constraints.The final design is shown in Figure 7.7. The other assembly compon- Ients and the torque overload devicE are also shown. A photoqraph ofthe experimental sprocket mounted on the test stand is shown in Figure7.8. Each rubber annuli is attached, at one surface, to the inner IA'

steel hoop and, at the other surface, to the outer steel hoop. The _attachment is made via the inner and outer steel supports which arewelded to their respective hoops. A preset compression of ten percentis put into the inner and outer pairs of annuli. A preset compressinnof twenty percent is out into the middle pairs. The preset compres-sion improves fatigue life. The orininal means of fastening thesupports was by blind rivets, but since availability was a problem,welds were used.

The outer hoop supports i modified M113AI sprocket wheel and an inter-nal disk with large spline teeth for overload. The main support isholted to the hub which provides mating spline teeth for the sprocketcomponent. Each Sprocket wheel is floating on the compliant structureduring normal operation. There is no metal contact in the internalspline during normal conditions because the design provides enouqhbacklash for up to ten deqrees of angular deflection in either direc-tion. Maximum radial deflections of one-half inch are also limited bytne riechanical stops incorporated into the overload device.

The stanrard M113AI sprocket cuishions were mounted on the outer hoopbefore the halves were assembleo to the hub. No fastening feature wasincluded for the cushions. A proposed large hose clamp could haveheen installed adjacent to the cushions if necessary to stop lateralor rotational movement.

7.5 RESULTS

1.5.1 Compliance

The calc-,lated radial spring rate tor the experimental compliantsprocket is 17,538 lb/in. This value was calculated for a rubberhardness of 40A durometer with a dynamic shear modulus 20% qreaterthan the static shear modulus. No tests were made to measure theactual compliance achieved in the experimental sprocket.

7.5.2 Interior Noise Reduction of the Experimental Sprocket

The experimental sprocket noise was measured on the FMC test stand aswas done for the idler wheels, however, additional measurements weretaken at the driver's position. The sprocket was driven by the trackand was freewheelinq [16]. No torque loading was involved.

-161-

a.

LO ~ N ,%U

a 0 N nN CLM C

M cwU cc z .c c = 0

LUC ~ 5 c3 Ui

z no LI Cn 4-0 z < :) (w

N 4E

000

0d 0

C0)

CS-.- 0)

0~U0)w

-162-

LL

1-i

C-C

Figure 7.9 shows the crew area A-weighted noise levels as a functionof speed. This curve presents the best noise reduction obtained. Tnenoise levels were not steady, but cyclic with track strand revolution.This unsteady noise level at constant speeo was due to an unexpectedmetal-on-metal clatter which is discussed in Section 7.5.4. A-weighted noise reductions are 4 to 11 dU. For a sprocket to meet agoal of 92 dB(A) ir the crew area, at least 11 dB(A) of additionalnoise reduction will be required. This is also true of the driver'sarea, Figure 7.10; at 30 mph the driver's compartment noise level isthe same as in the crew space: 103 dB(A).

Figures 7.11 and 7.12 show octave band spectra of the standard andexperimental sprockets. Noise levels are reduced by 1 to 11 dB be-tween 63 and 8000 Hertz, and an average of 10 dB in the important 125,250 and 500 Hertz octave bands. Considerable additional noise reduc-tion will be required for the sprocket to be 7 dD below IIIL-STD-1474Category B. Achieving that degree of noise reduction is necessary forthe entire vehicle to be below the Category B noise limits.

7.5.3 Exterior Noise Signature of the Experimental Sprocket

Exterior noise levels for the experimental and standard sprockets areshown in Figures 7.13 and 7.14. Because of the unexpected metal-on-metal clatter that was discovered, the exterior noise signature ac-tually increased. The clatter was cyclic and closely associated withtrack strand revolution. When the track was run in reverse, however,this clatter was greatly reduced. The reduction in clatter may havebeen due to improved alignment of sprocket teeth caused by the orien-tation of the decagon sprocket cushion, or may have been due to achanue in the complex dynamic interaction of the track with thesprocket. The cushion fit snugly to the outer hoop and maintained itsoriginal assembly position for forward speed operation. A 1.4 degreerotation was observed after reverse operation.

A detailed investigation of the clatter problem follows.

7.5.4. Experimental Sprocket Clatter

The unexpected metal-on-metal clatter that occurred with the experimen-tal sprocket prevented achievement of the significant steady noise re-ductions which were predicted. Investigation of the problem includedoperational observations, dimensional and alignmlent comparisons, anddetailed analysis of recorded noise data.

Initial test observations with a Strobotac and sound level meter pro-vide(: no significant explanations. Interior noise level variationsdid not precisely follow the cyclic clatter throughout the octavebands. The track appeared to always align toward the outboard side ofthe sprocket. Correspondingly, eacho track shoe showed fresh wearmarks in an ii1ho)ard corner of the sprocket tooth cut-outs. This

-1-61

w I-

.U 0.

LIU 41a

*~QI-SI 4j

. . . . . . . . . . . . . ..

0 CL-tCNj ChCI

I LLJ~ ~d)

0

-,S-~

oý 0C) 0' O.

I .) ý.") alo

....... .. ..

I -LI

0 c

0~0IU U,

. . ._ _ _

~wL

UJJ

zLIJ >

*1i.....

SI C) ~C-

N0 Z U

1;lA~1 Af)l 'JISllljd F' 1"'~1 S P' IfiIIAA V

120 MI L-STD- 1474, CATEGORY B- __

4. 4.

-STANDARD SPROCKET,

I,? LEFT SIDE ONLY

_____ ~EXPERIMENTAL SPROCKET,___909

80

31 b 6ý, 15 250 boo 1000 2000 400 s o 6 0

Ocav 4and 4e e rqec e

Figure7.11 Cew f~ra !,'i seSe tao tnadadEprmnaSpo kt!.'eesa 0m h

MI-SD144 CAEGR B~ -

120- ... -.......

_____STANDARD SPROCKET,

90EF SIDTEIDONLY

110 /___ +__

IINyur. 7.Zir e oprmn os pcr fSadr nIic

Lxeirra EXPERIMENTA WheSPRaKTmh

C90

.1j

l d I 1, 1 1I I

.... . .. . . ... .. . . .

*i 0

..................... ............. ...:...... ...'I......,...... =

.... .. . . . . .. .. . . .

*. .. . . i , . , - .

S .... i ... .... 0

. .0 . . .W•t . . * ' . .. .. .- a r . .. "d ' . . -i - 4 "1 " O. . 4-

S I-'.:'-:T -. I .'- - -

• ' • " I: :. : C..I.. . .•' + • -[ ' . 4 .'

S.. . .. .

LL1J

000

So..- C,)

-q , . j . 3 . .) .,

7 . .... K, .

rw. "-

LLU/ Nn ,OZ aJ (V) 0 1la,"a-l 011)5a~d PunIos Pa1116atA - V A-

- 1 ,'. - ' .1

• Ii

100 + +

EXPERIMENTAL COMPLIANT SPROCKET

- WITH METAL -ON -METAL CLATTEP

90

T + -A

___________ _________ _________ ____________N

3;T ---------100-00 40 SOC 1~

tcaeBn etrFpurc etV igre71;[xeio ~1ScSietr a 3 h uet te ot prcesokyI'3UC Sfe oth zto h ul

14 +

indicates that both the side and driven edge of the sprocket teethwere in contact with the shoes. Wear on the inboard sides of bothsprockets was evident. Some outboard sides were scraped whereasothers were untouched. Finally, no significant torsional vibrationwas observed.

Dimensional measurements taken while the experimental sprocket wasstill mounted showed that assembled dimensions agreed closely with thestandard sprocket. Also, misalignment with the track strand was onlyslight: 1/4 inch difference in offset from the hull between the teststand drive sprocket and the compliant sprocket under test. System-atic rotation of the experimental sprocket revealed that the teethvaried only .048 inch at the most in sideways offset. Nosignificantly odd-shaped shoe or set of shoes was readily apparent onthe track strand itself. Finally, disassembly of the experimentalsprocket showed that no metal-to-metal contact was made at any pointin the overload gear mechanism.

Analysis of the recorded data was conducted to evaluate the possibil-ity of any consistent relationship between the clatter and a particu-lar section of the track. Steady-state interior crew noise at 30-mphwas plotted on time charts for both the experimental and standardsprockets. At 30-mph and with 57 track shoes per track strand, thefollowing cycles are present:

0.114 seconds per sprocket revolution0.65 seconds per track strand revolution6.48 seconds per one sprocket tooth - one

track shoe interaction

The noise-time charts showed a somewhat random cyclic noise level var-iation for the experimental sprocket. As previously discovered, thisvariation was not consistent throughout the noise spectrum. In someoctave bands, cyclic sound pressure level variations corresponded tothe one tooth - one shoe frequency (57 sprocket revolutions per tentrack strand revolutions). This noise variation, however, accountedfor only about thirty percent of the total variations apparent in aparticular octave band time history. The association between thenoise variation and track strand revolution was only observed duringexterior listening tests.

In contrast to the experimental sprocket, high frequency time historyplots for the standard sprocket revealed a definite cyclic variationof noise levels with edch track strand revolution. Total variation ofLhe magnitude of interior noise levels was about the same for the twotypes of sprocket wheels.

-IP1-

Since the analysis of recorded data was inconclusive, the experimentalsprocket was reassembled and mounted on the test stand for more opera-tional observation. Attention was focused on both the sprocket itselfand the test stand system as a whole. A consistent sideways rollingmotion of the test stand hull was discovered, which corresponded totwice the frequency of the track strand rotation. Both vertical andtransverse nonsinusoidal wave motions of the track were observed tocorrespond to the track strand rotational frequency. The wave motionsproduce considerable axial and radial forces on the sprocket. Eachtrack strand revolution included three waves, one of which produced asignificantly stronger downward impulse. Thus, it appears that thetest stand itself is producing strong impulses on the sprocket thatare associated with the frequency of track strand revolution. Rockingof the test stand hull intensifies the axial forces on the sprocketteeth. Of course, the experimental sprocket is compliant in radialdirections but relatively stiff in the axial direction, so side im-pacts are efficiently transmitted into the hull as interior noise.

Reasons for greater exterior clatter noise with the experimentalsprocket, as opposed to the standard sprocket, are not fully under-stood. The increased compliance of the new sprocket may amplify thewave dynamics of the track strand and thereby cause qreater clatter.The problem may also be due to the relatively low inertial mass of theexperimental sprocket which might allow the sprocket to resonate.

Further testing will be performed on the experimental sprocket, in-cluding operation on paved track. The fact that two catenary trackstrands (upper and lower) are free to interact with no influence ofthe ground is not representative of actual vehicle operation. Thisand other test stand influences (vehicle rocking, etc.) must be elim-inated for a meaningful evaluation of the experimental sprocket.

7.5.5 Durability

It was estimated that about 80 miles of free spinning test stand oper-ation has been completed with the experimental sprocket. Most of thistest service was at a track tension of 2500 lb, at 30 mph, and withsome peculiar track dynamics occuring, as discussed in Section 7.5.4.No torque loads were included during these tests. No significant wearor damage was noted during this short service life except for thatassociated with the clatter problem. The sprocket tooth and trackshoe wear patterns which occurred during the clatter may not continueafter the peculiar track dynamics of the test stand are eliminated.Consequently, durability predictions for the compliant experimentalsprocket are drawn from knowledge of the standard M113A1 sprocket per-formance record and from knowledge gained during the idler developmentprogram.

-17?-

As with the prototype idler, the weakest part of the experimentalsprocket is considered to be the rubber annuli. Results of the idlertesting program can be extrapolated to predict that rubber annuli inthis application will provide over 2,000 miles of service life if they

are not subjected to severe damage caused by foreign objects. In thepresent design, hazard of damage froml foreign objects is of concern atonly two areas: (1) the exposed outer diameter of the exterior pairof annuli and (2) the partially exposed inner diameter of the innerpair of annuli, near the overload spline gear mechanism (Figure 7.7).All other surfaces of the rubber annuli are enclosed. The exposedouter diameters are expected to be self-purging. The second area,near the spline gear, will be exposed to small sized debris which maynot be so readily purged. Future design studies should investigatethis potential problem.

The next weakest link in the design is the rubber-to-steel bond. Theexperimental sprocket employed a cyanoacrylate adhesive, as did boththe experimental and prototype idlers. No failures have occured withthis sprocket and no points of possible failure initiation have beenobserved. However, vulcanizing is a preferable bonding method forproduction. Future design studies should investigate if the supportsand rubber annuli could be vulcanized together in a separate subassem-bly. This would permit removal of the molds after vulcanization iscomplete, which is not possible with the present design.

The steel components of the experimental sprocket are expected to havea service life of well over 2000 miles of operation with the capabil-ity to withstand frequent over 7 oading. Catastrophic failure of therubber elements and continued failure mode operation could cause se-vere damage to the overload system. During normal compliant opera-tion, only the sprocket teeth will be exposed to any significant wear.This component is made from the standard M113AI sprocket which is aproven durable item. During overload operation, only limited wearwill be experienced by the spline year, even considering the slidingtooth action which results. This is because overload operation onlytransmits that component of an excessive torque or radial load to thespline gears which is not first taken up in the compliant elements.The long durability expectations for this sprocket under these condi-tions is further substantiated by the fact that the compliant sprocketwheel subassemblies are symmetrical and may be reversed to wear bothfaces of the sprocket and gear teeth equally. During failure modeoperation, when the rubber rings fail completely, severely violentaction will occur. A sliding, impacting load action will be experi-enced by not only the overload spline teeth but also by the sprocketteeth themselves. Single tooth loading will place high loads on thespline teeth which are designed with a factor of safety of only abouttwo in this experimental configuration. Damage to the overload iiech.anism way render this system irrepairable, depending upon the durationand severity of failure mode operation.

-173-

Our-ability of the central area which provides clearance for the trackguides is expected to be very good. Because the sprocket teeth main-tain a lateral alignment of the track shoes, no contact between thetrack guide and sprocket will occur at this point. Foreign objectshave less of a tendency to be drawn up into the sprocket than into theidler. Ingestion of foreign objects into the sprocket could normallyonly occur during reverse operation which is infrequent and slow, alsothe track guides would dislodge an object when forward operation isresumed. No cutouts are provided for debris in this area, becausethere are no structures in which foreign matter may become entangled.

7.6 Recommendat ions

The experimental sprocket design is considered capable of fulfillingall performance criteria, however, it is complex and does not fullymeet the noise rediction goals. The complexity seems unavoidable withthe present severely-restrictive size envelope. The limited noisereduction nay be i problem of test conditions, and not necessarily thedesign itself. Consequently, recommendations for improvement includesome additional testing with improved equipment.

There are two recommendations for improving the basic design of theexperimental sprocket: (1) simplify and (2) toughen. A simpler de-sign is needed to reduce initial cost, as well as improve reliability.The experimental design employs mild steel material designed, in someareas, with factors of safety of two. Future hardware may requireharder or stronger designs. The overload spline gear mechanism, forexample, is designed of mild steel using a factor of safety of abouttwo. This is acceptable for experimentation but not for reliablefailure mode operation. Other areas were similarily designed forexpedient completion and with the knowledge that experimental opera-tions would not be as severe as actual field use.

Before further testing is conducted, consideration should be given tothe test stand. The significance of track strand misalignment, testhull instability, and track strand dynamics must be !. dersLood beforemore measurements are made.

Further, the experimental sprocket must be tested underway to deter-mine the effects of the compliance on various vehicle manuevers, in-cluding high speed turns, pivot steering, hill climbing, etc. Sprock-et tooth disengagement and/or track throwing are potential problems.Also, the dynammic effects on the upper track strand resulting fromboth a compliant idler and sprocket need to be investigated.

-174-

REFERENCES

1. Anatrol Corporation: "Interior Noise Control of the M113A1 Armored Person-nel Carrier by Hull Damping." Anatrol Project No. 78067, Cincinnati, OH.Prepared for FMC Corporation, San Jose, CA., November 1979.

2. Bates, C.L., & Sparks, C.R.: "Development of Measurement Techniques for theAnalysis of Tracked Vehicle Vibration and Noise." SWRI Project No. 04-1421, Contract DA 23-072-AMC-144(I), Southwest Research Institute, October1964.

3. Beranek, L.L. (Ed): Noise and Vibration Control. Chapter 11, New York:McGraw-Hill Book Co., 1971.

4. Brown, R.: "Load-Deflection Tests of the Idler Paddles for the Experimen-tal Compliant Idler Wheel." Test Report Lab No. 792282, FMC CorporationCentral Engineering Laboratories, Santa Clara, CA, 09 April 1979.

5. Cybernet Services: "MRI/STARDYNE - Theoretical Manual", 1973, 1974.

6. Cybernet Services: "STARDYNE - Finite Element Demonstration Problems",1973.

7. Department of Defense: "Military Standard Noise Limits for Army Materiel."MIL-STD-1474B(MI), Washington, DC 20301. (Obtain from the Naval Publica-tions and Forms Center, 5801 Tabor Avenue, Philadelphia, PA 19120.)

8. Goodyear Tire & Rubber Company: Handbook of Molded and Extruded Rubber.(3rd ed.). Akron, Ohio 44316.

9. Hammond, S.: "M113A1 Idler Heat Rejection." Technical Report 3171, FMCCorporation, San Jose, CA, July 1977.

10. Hammond, S.: "Suspension Component Development for Reduced Noise," IR&DData Sheet for Fiscal Year 1979, FMC Corporation, San Jose, CA.

11. Holland, H.H., Jr.: "Noise Levels in the Passenger Areas of a Standard anda Product Improved M113A1 Armored Personnel Carrier." Letter Report No.124, U.S. Army Human Engineering Laboratory, Aberdeen Proving Ground, MD,October 1970.

12. Kasprik, J.E.: "AIFV Final Drive U-Joint Torque Test." Test Report 3579,FMC Corporation, San Jose, CA, 13 May 1980.

13. Kasprik, -J.E.: "AIFV Initiation of Track Disengagement with Standard andModified Idler Wheels." Technical Report 2982, FMC Corporation, San Jose,CA, 13 May 1980.

14. Kasprik, J.E.: "9600 Kilometer (6000 Mile) Durability and Performance ofHydrostatic Steer Differential System for M113 Family of Vehicles." TestReport 3465, FMC Corporation, San Jose, CA, March 1980.

-175-

15. Morse, R.M. and Ingard, V. Theoretical Acoustics, McGraw Hill Book Comipany(1967).

16. Norris, T.R., Hare, R.B., Galaitsis, A.G., & Garinther, G.R.: "Developmentof Advanced Concepts for Noise Reduction in Tracked Vehicles." TechnicalMemorandum 25-77, US Army Human Engineering Laboratory, Aberdeen ProvingGround, MD, August 1977.

17. Norris, T.R., Rentz, P.E., Galaitsis, A.G., Hare, R.B., Hamnmond, S.A.,Garinther, G.R.: "Experimental Idler Design and Development of Hull Con-cepts for Noise Reduction in Tracked Vehicles." Technical Memorandum 3-79,U.S. Army Human Engineering Laboratory, Aberdeen Proving Ground, MD, June1979.

18. Van Wyk, T.B.: Study of Track-Idler Engagement and Its Effect on InteriorNoise. Technical Report 2976, FMC Corporation, San Jose, CA, April 1976.

19. Young, W.J.: "Rubber Tired Sprocket Hub (International Harvester CompanyDesign) Effect on T141 Vehicle Vibration". Report 1201, Test and Develop-ment Department TE-20, Cadillac Motor Car Division, General Motors Corpor-ation, Cleveland Tank Plant, March 11, 1954.

-176-

APPENDIX A

THEORY FOR HULL VIBRATIONAL RESPONSE AND INTERIOR SOUND LEVELS

The generalized theory for the prediction of the vibrational

response of an arbitrarily-shaped structure bounding an enclosed

cavity, and for the development of an acoustic field within the

cavity, has been developed in various forms [Al,A2]. One such

approach, termed the "power flow approach", has been developed by

BBN [A3] and is summarized below in a form suitable to the

present problem.

Figure A.l shows the general situation of a distribution of excita-tion forces and radiated pressure fields which act on the structure

as it vibrates. The structure is represented by its set of'independent normal modes (uncoupled and orthogonal), so that the

total displacement of the structure w(x,W) at a point _ = (x,y)

on it is given by

W(KW Trýr~x)(A.1)r

where T = (w) is the displacement of the rth normal mode. The•r r

wall response to the forces and pressure fields acting is found as

[A31

w G(7/x';w) [pO(X,) - Pi(x,)] dx'

(A.2)

where the integration is over the structural surface area and the

st~ructurels Greens function is given by

C ~';)= MY5 )

SSA-1

A-I1

Rad.ated Field

Pp2

R Diplacement W(sz,w)

External Field, p0

Cai~ Region, V

Internafl F ir d, p.(V

Figure A.1 Cavity 4omenclature.

Here q) ¶S M, and Y are the mode shape o eneraerir-ed m,,iass and

adral ttanc0 Function For the sth strt ct urn.1 mode.

0 /= K; L --~ / ). -- •,;

The interior acoustic Pressu:o field n. (x due to structural

vi b"ation is riven by

f -

" ( k o. 3 )

.. , - -, ;o " .. :. iT

~j~e'e Q i t le t~15 it'' .I c '.h C .d ( ',~

Is th e ( L vit'v I' c'on• . ,; !",Inct , i •l,

while k- s *,-he ncoust lc ;vmrbr 'tK:'ro.edriu

tior, consists or a ront ,cC : ' 1i;! V,(w: =t "cuO- c

leca d x x_ n ,ind tLhe e' II :) 7 an:'d', ,•sa , ei•ier iv' ,e.

1 I I ° ,

'-- : (A.L')

From o (A. I), the modal res r n3- s ns

Best Available CopyA-3

Multiplying through by m(x)'r (7) and integrating over the

structural area, leaves

M r Cr = fin(R) ýr(x) f G(7, _Xw) [ F(w) 6(_X I'XF) + 02 ( ) pi (_I)]I d~x'dx (A.5)

Multiplying Eqs. (A.3) and (A.4) by r( ?) and integrating with respect

to x' leads tt an expression for the generalized force r' on the

rth mode due to, respectively, the interior acoustic field F r

the point force F F, and the radiated pressure field rr 2;

f'or example, FP

Fpi =fPi(7') ýr(7' d3.'

_() 2f r p'fG(X/xI;)' (R)d,•d.•] Ts(A. Ca)

S

o r F i • • - W 2 I r S s

S

where ITs =:. Gp( ';W)P r(_')t$s (•')dx-d•' (A.6b)

is interior structural-acoustic coupling parameter

Similarly, 7r = F(W)lr(x7) (A.7)

and Fr = pW2 i j

p 2 rs

S

where J = fOf (X/x';W) @r(X')t (X) dxdx'

rs BeP r s

A- 4 Best Available COPY'

and GO(7/7';w) is the Green's function for the radiated pressureP r

field. r will be neglected from further analysis since itsP

contributi n is negligible in the present point force situation.

Then, with Fr= r r + r . and, on substitution of Eqs. (A.6) and (A.7)

into Eq. (A.5), the modal response equation becomes

Y rPr + pW21rrlr + >,2 rs s F _r

s~r

or in matrix form,

[arsi •s} (-rr}

The solution is L= rs] -l-s= [art] (A.8)

where I a{ Y + J jrs r + (A.9)

sThen, the totail structural displacement W(•;w) is found from

Eq. (A.1) as w(t;•) =-Z r •rtrtW(,xw) art r(W)

r,t

(A.1O)r

_ _.•h Ctrr (w)Fr ()

r

on neglecting intermodal coupling terms which are generally small.

Further, the acoustic effects will be negligible for the present

structure in the sense that the acoustic reactance is much smaller

than the structural reactance. Hence

C rr(W) -Yr~r ,-

A-5

and n r is the sum of the structural and external radiation loss

factors, and the structural response becomes

w(7,W) - F(W) Z@ rF) ('A.lla)Mrrr

= H(Jw) Ie-Ij (A.llb)

which is a complex function.

The time average, mean square displacement at frequency w

w'. X %4)= :Re [wL w*]

r s r s r s

rys

Thus the structural respoise depends on the spectrum of the

excitation force, the mode shapes at both the point of application

of the force and the observation point, and on the modal masses

and admittance function. The output from the finite element

procgram STARDYNE used in this study is in the form of Eq. (A.11b)

i.e. providing results in terms of magnitude and phase. Point-

to-point comparison of measured results with prediction tend to

be inaccurate; bettr agreement is found by making space-averaged

comparisons, where the average is performed over at least five

representative positions on the structural element of interest.

As .•2rquency increase,, above the fundamental structural (whole-

bn y) moens, the number of modes accumulates rapidly with frequency.

Cer'tiin str'uctural elements may tend to respond more strongly

A-6

(independently) than connected elements, and may tend to contri-bute most to the structural modal mass and hence kinetic energy

at that resonance frequency. For example, as shown in other

sections of' this report, the M113 hull roof vibrates independently

at about 65 Hz, contributing about 75% of the total modal mass for

this mode. Further, in the one-tbird octave band centered on

160 Hz, F-E modelinr predicts that the roof and floor respond more

stronrly than other hull elements, there being about 7 modes in

this f'requency band. An estimate for the space-averaged, mean-

square displacement to a band-limited force excitation of mean-

square F'opce in Aw oV F2 for each of the major structural elementsAis C cosnsi.lerabie'.interest and use in the evaluation of the

effects of structural modifications on hull vibration response

and the associated interior acoustic radiation.

The spnce-av-rra.e, menn-square disnlacement, f'or an element A of

the structure, averared over a narrow frequency band containing

several resonant modes (rcAw),w',A' is found as

'\,A~ KMA~ N2 - JvJd

f , f(A.12)

r= r * 'A A

r r

lier'O tho •lodal cross-coupling terms (r # s) c0 not contribute to

the response and the response is dominated by the resonant modal

conihution:, Further W2 and F 2 have units of (displacement) 21,A 6

and (force)? respectively.

A-7

",TARYNE calculates values of Q r(7) at model nodes, so that on

manipulation of the output files, the quantity in square braces

[1, which represents the degree of restraint provided by the

remainder of the structure, can be calculated for each major

structural e..ment e.g. Cloor, roof, upper side plate, sponson.

In detail, the calculation is found from

0(02r (T)A~ Ar~ij A(j)

Ai jcA

2 , A(j)

,thwhere A(j) is the area associated with the j mode and

where I and j represent the nodal coordinate directions and node

number respectively, but only the coordinate nor'mal to the surface

(.0) Is:1 Importa:nt.

The contribution of structural elements to the total modal mass

can be calculated as

"A jcA(A. 1 )

r(,j 2 (3,j)

jA

where normal displacements are most important. Here M(i, j) is the modal

mass of the jth mode referred to the ith coordinate direction.

At hl.her' Frquencies the element mode shapes will be essentially

::Inwscldayl, and Eq. (A.101) reduc•-s, usinv band-overaed .oncents,

w• = . '', a ,( i.•1',,r --. * • 'A A v

A-2

where V.' is the time-average, mean-square force input at x iJnband Aw. nr,A(w) is the modal density of' the structural element

of" area A and surface density mA, and where 7(7 ) and are

average values of, 4(x F) and p (assuming. equal loss factors forr r

each element). The relative energy levels between different

structural elements is determined at high frequency by the element

modal density, mass and area, while the coupling of the force to

the structure is described by $(;F).

A redtiction in response level will be oroduced as the force input,

the modal density, and the modal displacement at the point of

api.- , icat; on of' the Corce , are r•educed.

Acoustic Power Radiated to Interior Acoustic Field

Tower beirng, radlated du( to the 11oti.cr.

ort' the l'th sti'uetuval mode is 'iven in terms of the modal radiation

, tnce by I A, I

d( t = Rr (W v2rad( r) >( .. 6'rad ra~r/.r

where <22> = W2 -<w >, is the space-time average, mean-square

velocity ot' the rth mode. If there are N modes in a frequency

ba!nd of' width Aw, the total time average power radiated is found

by 11 ummingl each modal contribution (assuming modes independent)

- r 0.V2

Wdr (A.17)

As;t.min" that equipartition of energy between the r modes applies,

tiLs r'educos to

A-9

N1, = i. S? K r (w)

"A v radrcAw a(A.18)

V2VA * Rrad

where v 2 is the space-average, mean-square velocity of the

radiating surface and Krad is the band-averaged radiation resis-

tance. Vq. (A..2' may be used to calculate v' 2 and rad can be cal-

culated us.in the methods of' statistical energy analysis [A41.

Then, for nn element A of structure, the band-limited radiated

acoustic power (in watts) is found as

A AA (\ A

As before, usinF" modal density relations and band-averaged

express ions,

'A M M ( ") .A,A -ri 2A 2 - rad, A ( ?0)

it in cLear that the rower in'low depends on the magnitude of the'orce inpuu , the radiation efficiency (o = R ad/Aoc), modal

density, loss factor and mass of the driven structure, as well as

on the mode shapes at the ooint of application of the force

.010e t'educt ions will correspond to reductions in WA, and can be

I'eiat•d to ,rhanes in those quantities shown in Ecs. (A.19) and

'I )ao which javrund. 70'-example, if ,2( X,) can be reduced

A-10

by a factor of 10, a lOdB noise reduction will be proouced, all

other parameters remaining fixed.

At those frequencies where several acoustic modes occur in the

analysis band, the band-averaged radiation res~istance will provide

a Food estimatc for the structural-acoustic couplinn.

Eqs. (A.15) for the band-avernoed mean-square displacement w2 (w)

and (A.20) for the band-averaged acoustic rower flow WAW(W) incor-

porate statistical descrintors for the structure, as em:loye oe :'

Statistical Energy Analysis, bnc. also lncludes a prrameter X2(•

which des;cribes the couplIng between the point. Nano' anl(1 t(,,

st rpuctural modal response. Values for M-.(-V) ape cIIlCuIatcd TI"or

the [ri, e element model urp the hlU l tpuct'tir2v Ain the( ,r' t'rt

problem, (but may be compared to the coulin Irlo: s Qcu.. or1 used,

in Statistical Enerrgy Ana lysiis). Thus the detailed oruu•l t•i'

the hull modal analysis can be matched directly with abatntlIsc:tl

descriptors for the structure in calculation of the potential

for vibration and noise reduction associated wtit various,

structural modifications.

A-11

REFERENCES

Al. Richards, E.J. and Mead, D.J. (Editors): "Noise and AcousticFatigue in Aeronautics" John Wiley & Son, Ltd. (London) 1968.

A2. Cremer, L., Heckl, M. and Ungar, E.E.: "Structure-borne

Sound" Springer-Verlap (New York) 1973.

A3. Pope, L.D. and Wilby, J.F.: "Band-Limited Power Flow inEnclosures" J. Acoustical Soc. Am., Vol. 67, March 1980,pp. 823-826.

A4. Lyon, R.H.: "Statistical Energy Analysis of VibratingSystems." The MIT Press (Cambridge, Massachusetts) 1975.

A-12

-_ ]

APPENDIX B

STARDYNE Input and Output Data

Table B.1 STAR Input Data

Table B.2 STAR Output Data

Table B.3 DYNRE2 Input Data

Table B.4 DYNRE2 Output Data

B -1A

Table B.1 STAR Input Data

ssssssssss ssss"SSSSS SS5SESSFE' S!FS~s~sss s ss ccS

S s SS- It 1 Fe v S' F sS sssssssss $5 IS~ sSSS5 V q

s S s SS $5 1!5 s s sssssssssss SS st Ss S! ss

* *9STAO IV$ 9

* LIAUS1 tUSfc 04WA~L~ !! 1ý7q

* LN C~ATE '4CMV~A JUK. lot tiff

"*t" F. oov jFe rr ISFO4 UP. TTIP, 11.17.14.*

* rvY~cKET %CC 1 ''

9 (Uiq?I !T qrvkE-? -ýSyEI Pv wroor rESriPC~H TM'* JS171. CT~rr~kr:3 !'Yr1EF Fy ýtrI'aIk7 FkSEICU vf, .

S* jq 5 ~Tqtr . 5"f* K- SS 9v Sv!-Fl- trýVCLtcrNr, frrcv

* A STArol%:r 1IhFOOO'ATIC~k VLALrrIW I AVAILAcLr* h9TCN CES~r-Trc T,.rCcIA9T Cr-Akr.rr rrkrfxch wxG

QRELEAI;F LEVEL orV Tme rRqrtCPp.9 IN4 Vq~ TV' ACrESS* 1I!S RLLLF71h - E~t-c TO- FCLLf'hT~cCKr C c1 Ct irs. .

AT scccE i.4. AT Ncr I

A91rL!C(!TArrUL1 A;API7 9tUzI~~~

* vWIXPfSTAcrutLj FrwT~ri.frccLL1* CCr1RI!7AcrUL.11 (~rvcrfc1.Acre1.,(t

B-2

Table B.1 (cont.)

.......... . . . . . . .. . . . . . . C t 1 0, t9

7 FLI'YS 7 CUTS11~~ 7" II '1A1 I 6LLL ýNKAI1 'IrnEL - 0r. f.CrATP?' 9101i

PAh I AIUvTPUI' I i2 f c F .2 ! .I 0 f 1 2.' F- cVIIt 2 W I % I ? 2w.1r S 1,1 u FOP *1 A a 19 1 .2 f-U

~cr fr. 1ca 13? 1 t c'? q ..c 197.US 23.2 0 .0 1 1Frdk tCrr 107 171.' 6 .0 21 kCtf

I.. ý Kotrr. I Co. 10 F. 1 1 71. 33.2 2L. 17t.~ m t2 2 1. 'kc~riI t cr Fr. ZL 2le I I(q.' 419.0 !2.t I a. I 17F !'2 .c Wco~rr

I I krrcr, ! .? 2rc 1 177. 3 'q.9.o !. C 117. 3 17. 5 *. 0 0.cnrr14 '. fE~r-o 1 . v0 i 161 IZ C 0. . s¶ .ý 17. 1 0 .0 r . %CnG1'r NO'jtrror ?0,, !C2 t 1!i.cr' !3.? 0.0 131.i 21.2 a0.0crI~ kcctr.cri 3 c3 11Pc 123 Ia. I. c . 9. 704 0.C 0.0 %CF

a Cr'. 1'12 0.0 a0. c I.0 0. 0 ?'3. 2 3.1 EKof rr 20' p'' 1 1 1..' 1'. c 4 . !5 40.O c I F Nctr r.

'C '.o.Ct L(3 .' 1 1'?.' 21 2 ?C.r IY7. 3 40. .C 2 1,rr21 KG corr f;co I 'I 11.11caI!' .2 100 1'.. .32 r q.7% 33. 7 rfr?'2 krrr.cri 2C 411 C . 1 1 '7. 1. 0.0 2 C #-? 49. 0 z - .7.1 cr Fr.r 12 r1123)'. , -. 31 !'3.2 2 -1.1 %qdr 21. r9W

4 '.c rr,~ 310 (4121 CP- 1-7. 3 1.. 214 ;. 121. I 1 '.'S 3.0. KCOV

11 rKtrr( 12121 141 ,'~ 3'..' 220 -'2 3 7 P. (.3 W.rr

2 ,Cr Fr,1 ? cc ?r 1. 7 .. 0 ?.c IIF. CF'F KC~rr1?r I 3rjIIcIt. I 4n.027. 1 .0449c 20 rr

r. 4 1C%2 4,.r 1c 6 C 4o locooli %Crsrr

I.'j ' . r- r ~ ' 1. '2 i. F t. f r . 0h 74 ttIe.7 ckCr r

rA 'r,, r 71J 210 t2 1 NA 12.5 11.c ,.0k2Fý rEr 4 1 211P 10 ?'! I?. I2 I A 2. 3C r.IN n

I ,' r,'I 12.12 22.' 22. L-1 32.0 - rt k.r.

'4 ýcf f1 111 0 C~ik8-3

Ncrrl ci 1.0 c .C W E

Table B.1 (cont.)

Ia " 2 1 A 12 No'. 4'. 1- 552 5~ 0 E. 68 72 7( '

CAC'n KO .U*U .. .... **SUUUSU.....U.S..UU.UUSUSS...* rior IVPVic, ~eC 76 2 ~ 11d 1c C 1., CLAtrq

110CU ur r; 3? 4. F, 3 1~ 0 ?3 138 20' iC 100 1 C0 rtAr.Ii rLAC'! 47 13'. 306' 145 1.?' I.h~12 f.4;Arrl '8 '10' 4.0' 4.0 t ~ r.A

l! Cuern 49 C; d6 4 C4 13 r0 100 SE I1? 10 !.~ 1c0r'0ArIt d rt; PrR n ?A 104 1 l~3 54 3 5 It C0 A 1.' 0

I120 r u tr 79 6 .v Q T 20 1k 38 10 It F7 (1 CLA r,

171 rt;Crn f? Ad. It C I 3P6~ 1 3!7 1 35ý I vrI1'! rufr0 a~ C;0k6 3K7 2 1.07 ? &isa 2 3!A ? CL*1Dq121 CLPCAn A, 10 do. 7 1 R;7 I to& 1 6 A I cL~rs124. rt; ar~ -, S .1 "CU 1 61]? 1 80! 1 51] 4 1 CLIOII17'CI e ;r~ n ~ 54 AC A( 76 ?7 1 709 1 Al I trtex Cu0 rr c? 1 4 10 7 7 1 A3 I eim I 'pp IfLA00127 Itcr'n 1 C i t' P37? 91 Ia So I elf cLArR12A V.ut' e 1r! i C. 4 q7 I11ea? Mae0 I SC! I LIq12S r. r rc iC' r, ic 1C01C lIto? 1 1131 116 l~e Ir t1S1 r.LArn 1 7 11?l ? 11207 1 12U 1Iflip I CAII1,1 rtuArn I1 I 1I01c 121%. I~cq 1212AC137 0rt;A a I I'. 12? 1299 1200 1213 CtAr"

174. r*.p.r*i 116, '.00 112 4.11 1611 7 r.LAri1 19 r L; A( r i M1 t ' .12 #4 10 1 PL0 CAi !A rLhrr II 10 1ý1 102 loll Los 1.9rLr

I ? A i rn-1olt 'IS LAt~r7(,,S 'wCCAt EXTVACTICIK ANI'3SVPMEyor VMS~ L AIC14J~ r v KAm ? f' 0z 36 110 1 -. 1 7N!

B-4

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3* CL)

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Gn w4 14 Is IV J 3 43 3 3.c. 30 433 3.UK3j .

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w Qh IPW IWO. 433.31 L 3-33 15010 .53= 3~ . w o .Is-

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* u * 11L - & 3a 335.3.33* ~ ~ ~ ~ ~ ~ ~ A a. sp 0' 3- 0 3 . 33 -W N.11 5 -*

U or a0* 5 C3 3 t 3 N '*3.~ ~ ~~~~u .5 53 . 33 3.6.

334s usl U 61 ,~~

33 I~s 10-3 6.. 3

4. u- w0 o 41† ††I,†v† † † ††1.

on %c Is" v - -w ... 3 ft * '. - - 1-1*3. .. 3- - .410 3* x4 04 Is go b3 jl D P-.4.~3 V ~ 1 -ý we)3 3.41

3mb 1. 1-U Lý -C ;. u,3 ! . .

.3m W, W)0. 103 3.' w3 wJ p 0 1* lb n -

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U.. I'll 3 3 .b3.3

33ca= ~ . 3 3U1 3. . 4 ~ h ~ . J.4 6 33~ - 4 .

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33~ ~~~~ * -4 - -3 3J... 33 . . .

3 ~ ~ c A 0. 3. * o* 3. 9 As5 0 3-3 3Is 4 3 333~~~ ~~ A.32. . -. 1 . .

33k h *&U 34 4 3 Li.33 B-5 3 .. .3 3 30 -. 1

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B- 7

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APPENDIX C

STARDYNE Input and Output Data

Revised Hull Model

Table C.1 STAR Input Data

Table C.2 STAR Output Data

Table C.3 DYNRE2 Input Data

Table C.4 DYNRE2 Output Data

IC-11

44

APENI C-

Table C.1 STAR Input Data

I

H UA~t

A.l I L -, 1 . , L1Ab

*~ LVei PMu* La ft* . . . S. . . . . . . . . . . , I . S. . L" IN

'...... ...... . I . ..... . .

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* - L I A.t Lt VC JL I' F. 0" A

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* • WitS•; rus..II' oil t T () A- )NIL. ., I NT,. t

* WL hI SIAI t t.t. *t NI,'jIP :A$ •N "b~I 4SARj Kt P LUVn: *vtt4

* L APY UTP(A. LU ITI ..tPY n Of. - U, I 'L II

'C.

ii

Table C.1 (cont.)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - -

U e I to % U 'J 4C ') t, bU tft ba I.: It, 0 U

LAKO .40 00.000.9 00 0. 0 . . . . . . . . . . . . . . . to . . . . . C&.0 Slott

P L 0 1 LISL%20 F L 0 1"MtLJAI MVL L; T #4 1 C MPtL)L t L 14 U;

"I" , 6 :Uvb 1 1. c t

*3 t L Lk 1 0

A " z "I I "oil k ot. I Wj k I i I ( -wo "hILU

6 L No I it.

I out 01. 3 .0 31 Z 3.0 hJultUUL ozj ;b U.0 kUUfAID , Diu 0 0 0 . 13 3 j MUM

10 N 0 it 0 4 Q 6.913 fCjUt11 " L, ý) - k. I ov IQ j, 1 0. c 0.0 Q. 0 ',.a 31:1 V:U Pli ULU1z "Out 6k U 1 .1 ou .10) 1 -,.o 0. U U.0 *A 0 ji d %) U Uultf,1) 4 jil ukcd .00 A01 IOC Id : 0 O.j Q . U ,1 0 J3.1 U.U MuOt U14 0400 t (.01 U I %ou 44 () i I 1., 0 U. ( to . 0 .1 d 0 1 j . I V U riuu L Uis PIOU, bud bu 1 100 4141: ht, I O:U 0: U be jj.i fj 0 MUOE .

6 , 1 1:661

16 P400 L 11 1j 0 " I b 0 0.0 0. tj 1b U jj:t V.u h. Ut 6I I MODE (A C. I Iov 101 1 1 1. 13 3 0 0 Q to ?,. Ili ji e 0 11 ý U it 4

10 m UO t 4, . 0 z 4 V U 0 j 100 101.0 0.0 0 . 0 101.U I i . Q ut19 Mout Gito I vo-j v i I I file . 0 U.0 0 . V tod.0 ji.i U v hU(g 0 ft oat ow 1: d i 1 001 tul 100 1)4.0 O.U Q. V Ij%.0 I J. ý V.0 %uLt 4411 Gt;, tR 01 0% L 6 1) 0 )J: e W4, Ul

I . OUL U 4 W, 00 1 J. 1 0 1 j e U j i z eu 5 UQL13 Hio t t. .1 1 44, : 40(l 1 zz:0 3 J. b.8jj Z4.0 3J.1 IV s %jutd 4 P, UU14. v ()1 00 bob I D 0 1i " 0 Ij. b. a j s pq. 0 3 J. le du.'j 4"E625 #6 U U- 11 0 1 10ý1 lvý i IQ. IQ- ju.0 1J.1 v h.0c.IC6 P4 jot 46 a oi 1 1014 L I ob 100 1314.0 ji. I I U. d " 114.0 j J. i U. poýl)t 1.I I moot to , I at, 1 -1. IDS 3J.i b.0ji -1.611P 3J.1 Iv. hjUEis Haut I L I I I I* I -L:105 I I I b:5 I j j OE649 MODE(. D1 10? 1 U 1 -3 611P 49:1) U v 70 4v 0 L, JUEWJo moot Gitol 1407 410 100 12,0 410.0 10.$ iz.o 49.0 1:05.0 "Outt.

oor f.:Dii*o I LLv JE Id 0 A,# 0 NVUkk,"I to I IU:5 LIZ : 00 14 10 0 55 Uoto, 0 101 110 0 34 0 49: 0 1 u Uut4l

of 0 D I I, a 0 1 110 11(. 1 -4.70 A-4.0 t-,; . 0 -v. to U.0 v pq U at 0.

;41 Pluot f.:Plt 410 1. tb 100 14:00 44:0 jj:v 1": 0 v:Q tO 0 hOD1610 , UO((, UL IkIO ft I , I 1,( 44 0 55 Q 14f 0 v 0 1. 5 Uut.

36 MOiA(,9OdIIIUkLI6 100 1114.0 49.U SJ.u %1%.0 V.0 AUDCU,3? moot (1 110 111 1 -5.6141 34.1 31.1 -5.64e 1? .11 Ie . 0 KýUfi.36 Mook (I M 111 1 -7.6ro )*.& '4 J. 11 -7.670 d 1. 41 14 j . 5 k0L)t619 "Got f. Itb sib too 61.0 *.U Si,.D 9J.0 0.0 %S.6 04 . 0 it 440 kOOt(6 ?is a a 1i too 70.11 ii.9vu % io . 0 sb.j I It . 9V 0 St.v mijuit,14 1 04oDt 4. 91%&115 too I od II:0bI %'P:O 1,16 0 11:061 js:v ftJUI,.14 hoo 40 1063 0 106:093, 11 13 1 SIA a I ": (10, 1 dA t)j %5 0 P, JUI 41 06 out r. 101161111 too 118.0 33.1 SS.0 13,4.0 3A.1 ill .0

*ýh 04 0:,; & i o I't to 14. 1 110. 1111 IV. 1#58 Sj.U 41Y.115 L4.308 5".04.) kUAG Vk4oI11j 199 101.0 1 -A.() 'JA.0 ij,..o dc. 1 J3 1) 5 . Q146 p1jut GO U I L i ov I le 0 1 1 15 7. j O.U U.v 157.,l Ji. I V . 4) h-f

-61 MODE 60 011 ZOoj I i i 1 4 168.5 0.0 10.11 160.5 31.4 IV.$ 1,10"t

44 NUOL 16 111., 1 'd 10 4 166.5 qO 10.5 kqj. s 49.0 q J. " 11"Ut41 MODE&POiMilli? 4 11) Y.0 0.0 11.9 141.5 0.0 4.0. 5 MUU(50 4OD1f6A02IIV)LZ1v 1 111.0 11. 1 Id-9 Lq 5. j I J. I It I. "Juiip I k No52 :t s fr. 1001jou 1001011010

1S 11. 6 , 0 10 0 1 IV114. kloollioto i to to tV

C-3

Table CA1 (cont.)

- -i -Z. -

I 16 i 20 1: 2 3Ic 3 N 41,~ 41 111 5b toj bt to4 ? alb8v

;1: %;: IQI~gIGO 61.H b i.I

:0 :UM1 00,F 6 1:. 13 54. 1?

hI I'm4 21 41. 111. 0hi GHI 10, 6L. 1:1 '1 5.11

61 :GMT? J04; hi. hi. =1 tf

hA w GMT .0. 41. hi. 61. v..IIT

40s~i Aib 22. 2" :. GM~Thess! 7% 47 4. 44. 194

1 0 B~IG" Sb I. ed .4 21.J dO,,!

1?59? 411 21 Ž0. le Žo.h W CHI 141, 10..4 e .'. is .I U5

14 GMT? 41) 10:3 It,.I 10.1:J4?5 uGMT l5 i o.3 10.1 10 j

?6 G I T,940 his 10. 19. to. I941 6 194 14 20, 0. 10 .. ,

79 s WGMT bib 10.0 10.to3 toc : 6 4.T60 "ON? LOLto 2 .4 d'J4 ."4:1 G9tiT51 s*il 101Ž 194: & 5. L%.. 6i~

Iv GCMT LOIS dA 156 I..

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