).J EMORANDUM REPO)W.1' IRL IL-MR -3709

1938 - Serving the Army for Fifty Years - 1988

GYROSCOPIC TESTING OF ACCELEROMETERSTO DETERMINE CONING ANGLE

NINA MISIIRAJONATHAN A. HARRISON

DAVID J. HIEPNER

NOVEMIBER 19,88

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&NOV 0 219880Cc=

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BALLISTIC RESEARCH LABORATORY

ABERDEEN PROVING GROUND, MARYLAND

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Aberdeen Proving Ground, MD 21005-5066

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PROGRAM PROJECT TASK WORK UNITAberdeen Proving Ground, MD 21005-5066 ELEMENT NO. NO. 1L1 NO. ACCESSION NO._______________________________ 62618A 16261 BAH80 I

11. TITLE (include Security Caification)

( rroscopic Testing of Accelerometers to Determine Coning Angle (U)

12. PERSONAL AUTHOR(S)Mishra, Nina; Harrison, Jonathan A.; and Hepner, David J.

13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Year, Month, Day) 15. PAGE COUNTt-Imorarx Rept FROM _ TO 1988 Au ust 23

16. SUPPLEMENTARY NOTATION

17. COSATI CODES 18. SUBJECT TERMS SContinue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROUP G yroscope; L *i 1 S- 503;

01 01 1 /Yawsonde' ,/ Accelercimters ,,19. ABSTRACT (Continue on revrse ifnecessary and identify by block number)'/

An experiment was performed to determine how accurately accelerometers could measure theconing angle of a spinning and coning laboratory gyroscope. Tests showed that coning anglemeasurements were well within expected results. The accelerometer can be used with or inplace of the yawsonde. for determination of flight stability of spin-stabilized projectiles.

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22a. NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE (include Area Code) 22c. OFFICE SYMBOLDavid J. Hepner (301)-278-4103 SLCBR-LF-A

DD Form 1473, JUN 86 Previouseditionsare obsolete. SECURITY CLASSIFICATION OF THIS PAGE

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V-

Table of ContentsPage

List of Figures .. .. ... ... ... ... ... ... .... ... ... .... v

I.Introduction .. .. .. .. ... ... ... .... ... ... ... ... ..... 1

II. Description of the Experiment .. .. .. .. ... ... .... ... ... .....

1. Physical Setup. .. .. ... ... ... .... ... ... ... ... .... 1

2. Constraints .. .. .. ... ... .... ... ... ... ... .... .... 2

3. Geometrical Interpretation .. .. .. .. ... ... .... ... ... .... 2

III. Output .. .. ... ... ... ... ... .... ... ... ... .... .... 3

IV. Discussion. .. .. .. ... ... ... ... .... ... ... ... ... .... 3

V. Conclusion and Recommendations. .. .. ... ... ... .... ... .... 4

References .. .. .. .. ... .... ... ... ... ... .... ... ..... 15

List of Symbols .. .. .. ... ... ... ... ... ... .... ... ..... 17

Appendix. .. .. ... ... ... ... ... .... ... ... ... ... .. 19

Distribution List...... ..... . . ... . ... .. .. .. .. .. .. .. .. .. .1

Accession For_-

NTIS GRA&IDTIC TABUnannounced [Do'Justiffication.l-_

ByDistribution/____

Availability Codes

Aval'i and/or

D~st Opecial

List of FiguresFigure Page

1 Sigma N versus time for DPG B94 M825 PIP for low QE and transoniclaunch with yaw induction .................................. 6

2 Phi dot versus time for DPG B94 M825 PIP for low QE and transonic launchwith yaw induction ........ ................................ 7

3 Fast mode yaw demodulation of DPG B94 (0.5-7.5 s.) ................. 8

4 Forced precession gyroscope apparatus .......................... 9

5 Location of accelerometer in cylinder ...... ...................... 10

6 Predetermined coning angle plate ...... ........................ 11

7 Block diagram of setup ....... .............................. 12

8 Acceleration components at I it, max .......................... 13

9 Spectral display for a = 1.970, p = 19.86 Hz, € = 8.23 Hz ............. 14

tV

I. Introduction

Accelerometer usage at the Ballistic Research Laboratory ranges from measuring in-bore projectile accelerations' to monitoring relative phase between liquid oscillations andcylinder positions in a three-degree-of-freedom flight simulator.2 An interesting applicationwas made by the Raytheon Company when they mounted an accelerometer off the cen-tral axis of a Carco table (gyroscope) and calculated components of acceleration throughrigorous mathematical techniques. 3

However, in-flight measurements of fast and slow precession for spin-stabilized projec-tiles currently include only yawsonde data to track yaw and spin histories. 4 The yawsondeis basically used to determine if the yaw is growing. Yawsondes employ two optical sensorsto determine the motion of the projectile with respect to the sun. The data are telemeteredto a ground station. The raw yawsonde data are a series of pulses (positive and negative)that measure times at which the optical sensors are aligned with the sun. These datayield a solar aspect angle (Sigma-N) (Figure 1) and the Eulerian roll rate of the projectile(Phi-Dot) (Figure 2).5 The yawsonde is restricted to use during nearly cloudless weatherand also has limitations on the relative position of the sun and on firing azimuth and QE.

The yawsonde gives a planar representation of the yawing motion about the trajectory.Although this representation is planar, the projectile is at an angle of attack roughly equalto the sum of the peak magnitudes of the fast and slow motion. By filtering the trajectoryand slow mode, the fast mode planar representation can be obtained (dotted line, Figure3). The demodulation of this motion is representative of the fast mode amplitude (solidline, Figure 3). Other yawsonde data have been reduced by this method and display fastmode damping with yaw induction, negligible fast mode motion, and slow mode damping.

To supplement the yawsonde data, an on-board accelerometer could also provideinsight into projectile flight characteristics. An accelerometer might be used to determinespin rates, yaw rates, and amplitudes of motions. In addition, acceleration data could becollected in any kind of lighting or firing conditions.

II. Description of the Experiment

To show that this method has the potential to supplement the yawsonde, simplemathematical derivations and laboratory experiments were carried out to see if the angleof attack could be correctly verified in a laboratory gyroscope.

1. Physical Setup

The mechanical portion of this project involved the mounting of a sensitive, crystal.AC accelerometer (see Appendix) in the canister of a gyroscope (Figure 4).6 The axis ofthe accelerometer was centered perpendicular to the vertical axis of the canister 14.6 cm(53 in) above the pivot center (Figure 5). A dense sponge material with a small cavity tohold the accelerometer was used to mount the device in the top of the cylinder. The coning

plate, located at the bottom of the apparatus, predetermined the coning angle (Figure 6).In addition, a slip ring at the top of the gyroscope enabled the accelerometer signal to beconnected to a signal analyzer. This signal analyzer provided an ICP current through thesesame two input and output lines to power the accelerometer (Figure 7). The gyroscopewas equipped with two optical sensors. One measured the inertial spin and the other theinertial coning of the gyroscope. Two frequency counters provided a visual output of eachfrequency. The spin was limited to 30 Hz and the coning was limited to 13 Hz to avoidfixture vibrations.

2. Constraints

Figure 8 represents the geometric configuration u. ,he accelerometer in the gyroscope.This representation is only useful for earth-fixed, single-mode, coning motion where theaccelerometer is placed on the spin axis with the sensitive axis oriented perpendicular tothe long axis of the projectile (1). It does not include components for off-axis accelerometerplacement, epicyclic motion, or coriolis forces. In essence, only centripetal acceleration isunder consideration.

3. Geometrical Interpretation

The following three basic equations are used:

I', - 1- r(27r ,) 2 (1)

d t=1 I cosa (2)

a = sin- 1 (3)

where:

I = magnitude of maximum acceleration along sensitive axisof accelerometer

I d I = magnitude of maximum acceleration along rr = radius of circular motion of accelerometera = coning angleSl = length from the accelerometer to the gimbal axis

= earth-fixed inertial coning rate (Hz)

Raw voltage output is converted to I , I by:

2

Im I= (g)( / )(s) (4)cal

where:

cal = calibration of accelerometer (milli-volts/g)

S = accelerometer output (rms milli-volts)g = gravitational conversion factor

Eq. (3) is then solved in terms of the coning rate and measured acceleration:

(k= Li~n (5)2 . ((2)(I)7r 1)2) 5

III. Output

Most spin-stabilized projectiles have the spin and yaw rotations in the same directionalsense (prograde motion). Since the accelerometer is on the spinning frame, responses fromthe accelerometer for circular, single-mode, prograde motion occur at a frequency:

f (6)

where:

p = earth-fixed inertial spin rate (Hz)f = frequency of response with respect to body-fixed frame (Hz)

The typical spectrum output of the accelerometer is shown in Figure 9. The responseoccurs at the expected f = p - €1 = 11.63 Hz. The amplitude of this response representsthe peak acceleration in mVrms resulting from the sensitive axis aligned toward the centerof rotation (along r, Figure 4).

IV. Discussion

Table 1 represents data from six spin and coning sets at a constant coning angle of1.97 ° . The estimated error for this angle is 0.10%. This angle was mechanically measuredusing a cathometer and dial indicators.

3

Table 1. Data with 1.97 ° Coning Plate.

Counter readings Analyzer readings

P ~ i P- f S if.. rc0ie acak.(Hz) (Hz) (Hz) (Hz) (mVrrns) (m/s2) (m) (deg)

29.1 10.0 19.13 19.13 142.1 19.5 0.0050 1.9628.8 8.3 20.50 20.75 98.3 13.5 0.0050 1.9526.04 10.8 15.24 15.13 175.0 24.0 0.0052 2.0519.86 8.2 11.63 11.63 98.7 13.6 0.0051 1.9917.64 12.6 5.05 5.13 240.7 33.1 0.0053 2.0813.55 9.3 4.25 4.25 125.2 17.2 0.0050 1.98

The differences between the coning plate angle and acute give a probable error of 2%.There are three sources of inaccuracy in the mechanical setup of the accelerometer. First.the accelerometer was not rigidly fixed within the cavity. Any unrestrained movement ofthe acclerometer within the cavity causes variations in the output. Second, the verticalheight (1) was measured with a straight edge. And third, the manufacturer's precisionin the calibration was not completely correct. It is expected that a more stable andmeasurable mount would provide more accurate results. Table 2 shows the uncertainty ineach term.

Table 2. Uncertainty in Variables.Variable Uncertainty

cal - 1 mV/g

1 + 0.508 cmS 4.1.0 mVrrns_ _ 4. ±0.2 Hz

The uncertainties in the elements listed in Table 2 combine in the propogation of errortechnique to determine an uncertainty in acajc of 6%. Thus the true error in 0 calc isestimated to be between 2 and 6%. The propogation of error also shows that the estimatederror of 6%, in the present experiment, can be significantly reduced by a more accurate

determination of j and 1.

V. Conclusion and Recommendations

The experiment showed that using simple geometrical principles, accelerometers canaccurately measure the coning angle on a gyroscope. In this laboratory experiment, theaccelerometer can measure the coning angle to within 6% of its actual value. The inaccu-racies that were generated in the setup may not occur when the accelerometer is actuallymounted on a more suitable fixture. The Ballistic Flight Simulator can be used to pro-vide complex motions required for more advanced laboratory testing. Experience must begained in determining which method is better for finding fast and slow mode rates found

4

in actual flight cases. Flight testing of the device may be required to determine addi-tional problems with the measurement technique, including launch failure or calibrationvariation, effects of coriolis and dynamic range of instrumentation required to effectivelyyield both fast and slow mode rates and a wide range in yaw amplitudes. This method ofmeasuring yaw rates and amplitudes has the potential to be used in conjunction with orin place of the yawsonde.

5

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8

CYLINDER CONING AXIS- 0 CYLINDER ROTATION AXIS

SLIP RING ASSEMBLY

PIOTCINDNGE

CSNIN

- i1/5 H P

Figue 4.Fored pecesiongyrScPN parts

MOO

COIN ANL

RIGID MATERIAL ACCELEROMETERTOP INSERT(ALUMINUM)

CYLINDER

(LUCITE)

PIVOT AXIS

BOTTOMINSERT(ALUMINUM)

Figure 5. Location of accelerometer in cylinder.

10

EARINGSHAFT FROM GIMBAL CAGE

CYLINDER CONING AXIS - CYLINDER ROTATING AXIS

I iFigure 6. Predetermined coning angle plate.

il

LABORATORY FRAME BODY-FIXED FRAM'E

SPECTRUM RN

ANALYZERACCELEROMETER

COIGNTRO

(CONING)CONING SEOTOR

SPNING CONTROL

COING MOTOR

Figure T. Block diagram of setuip.

12

ym

x

z PIVOT AXIS

Figure 8. Acceleration components at max.

13

0

* .° . .. * *

II

..........

14D

000

L -~

14|

References

1. Evans, J.W.,"In-Bore Measurement of Projectile Acceleration and Base Pressure Us-ing an S-Band Telemetry System," BRL-MR-2562, US Army Ballistic Research Lab-oratory, Aberdeen Proving Ground, Maryland, December 1975. (ADBOO8421L).

2. Hepner, D.J.,"Pressure Measurements in a Liquid-Filled Cylinder Using a Three De-gree of Freedom Flight Simulator," BRL-MR-3560, US Army Ballistic Research Lab-oratory, Aberdeen Proving Ground, Maryland, December 1986. (ADA177872).

3. Raytheon Company, "Coriolis Oscillator Roll Reference for the Spin Stabilized GuidedProjectile," April 1984.

4. Mermagen, W.H.,"Measurements of the Dynamical Behavior of Projectiles Over LongFlight Paths," BRL-MR-2079, US Army Ballistic Research Laboratory, AberdeenProving Ground Maryland, November 1970. (AD717002).

5. Clay, W.H., Mermagen, W.H., "The Portable Yaw Processor," BRL-MR-2785, USArmy Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland, September1977. (ADB0221041).

6. Hepner, D.J., Soencksen K.P., Davis, B.S., Maiorana, N.G., "Internal Pressure Mea-surements for a Liquid Payload at Low Reynolds Numbers," BRL-MR-3674, US ArmyBallistic Research Laboratory, Aberdeen Proving Ground, Maryland, June 1988.

15

List of Symbols

[ f maximum magnitude of acceleration along sensitive axis

of accelerometer

I fir maximum magnitude of acceleration alongr

cal calibration of accelerometer

f frequency of response with respect to body-fixed frame

I length from the accelerometer to the gimbal axis

p earth-fixed inertial spin rate

r radius of circular motion of accelerometer

S accelerometer output

a coning angle

earth-fixed inertial coning rate

17

AppendixCalibration Data for Accelerometer

19

.x'l inI

&~ + 3

LMcc cu-n LM IM.

- '1-

cr ISL. C E I v -

r\ L c c S 'H

cc0 M

Ln L

L, >

WNI

to li

c- LM

~VA - m I HIA w N~

L -L

'I ~ 20

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