experimental study on vibration reduction characteristics
TRANSCRIPT
Research ArticleExperimental Study on Vibration Reduction Characteristics ofGear Shafts Based on ISFD Installation Position
Kaihua Lu Lidong He and Yipeng Zhang
Beijing Key Laboratory of Health Monitoring and Self-Recovery for High-End Mechanical EquipmentBeijing University of Chemical Technology Beijing 100029 China
Correspondence should be addressed to Lidong He 1963he163com
Received 25 August 2017 Accepted 28 November 2017 Published 19 December 2017
Academic Editor Marc Thomas
Copyright copy 2017 Kaihua Lu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A novel type of integral squeeze film damper (ISFD) is proposed to reduce and isolate vibration excitations of the gear systemthrough bearing to the foundation Four ISFD designs were tested experimentally with an open first-grade spur gear systemVibration reduction characteristics were experimentally studied at different speeds for cases where ISFD elastic damping supportswere simultaneously installed on the driving and driven shafts installed on the driven shaft or only installed on the drivingshaft Experimental results show that the ISFD elastic damping support can effectively reduce shock vibration of the gearsystem Additionally resonant modulation in gear shafts caused by meshing impact was significantly reduced Different vibrationamplitudes of gear shafts with ISFD installed only on driven or driving shafts were compared Results indicated that vibrationreduction is better when ISFD is only installed on the driven shaft than on the driving shaft
1 Introduction
Gear mechanisms are among the most widely used powerequipment and motion transmission devices in machineswith applications in aerospace shipping machining petro-chemical and energy industries It is important to notethat working condition of a gear system is extremely com-plex Typically the primary motor introduces an externalload however internal incentives introduced by time-varyingmeshing stiffness and gear error become the main source ofvibration in the transmission system This vibration wouldaffect overall performance of the equipment [1] Largervibration noise will be produced when there are preexistingmanufacturing and installation errors or in cases when oper-ating conditions are strict Excessive vibration would resultin fatigue failure of the mechanical structure and in turnaffect production safety Vibration characteristics of the gearsystem are relatively complex and can be categorized mainlyinto two pulsesThese two pulses aremeshing frequency withits high harmonics and rotating frequency with its low-orderharmonics [2]
Vibration control of a gear system can be broadly clas-sified in two methods In the first method exciting force is
reduced to control and effectively reduce the vibration sourceIn general first structural parameters of the gears should beadjusted to improve theirmeshing A dampingmaterial in thetooth or wheel of the gears can aid in avoiding resonance ofthe gear system In the second approach source of vibrationcan be controlled to isolate or reduce transmission of thevibration Therefore some local vibration isolation measurescan be added in appropriate locations in the gear systemwhich would reduce transfer of meshing vibration in thegear system to the whole structure through the bearings [3]Research reported in literature by both domestic and interna-tional research groups has been primarily focused on the firstmethod This method can be divided into active design andpassive vibration suppression [4] Active design takes geardynamics and vibration theory into perspective to reducevibration by optimizing design parameters modifying geartooth and improving manufacturing accuracy [5] Frictiondampers (damping ring and damping plug) and viscoelasticdampers (free damping layer and constrained damping layer)used in passive vibration suppression have some limitationsFor example use of damping ring and damping plug isconfined to lower natural frequency vibration componentsand is not appropriate for broadband vibration suppression
HindawiShock and VibrationVolume 2017 Article ID 7246356 10 pageshttpsdoiorg10115520177246356
2 Shock and Vibration
[6 7] Vibration suppression effect of viscoelastic material isgreatly influenced by thickness of the damping layer
Squeeze film damper (SFD) and bearing are used cooper-atively in turbomachinery such as the compressors turbinesand generators to solve problems associated with vibrationand stability of the rotor SFD allows the support structureto simultaneously have a lower stiffness and higher dampingLow support stiffness reduces dynamic loads transmittedthrough the bearings to nonrotating structures This helps inprolonging bearing life and minimizing structural vibration[8] In a gear compressor SFD has been used to reduce andisolatemeshing incentives of a gear Chen et al [9] establisheda calculation model for the gear system with SFD supportand analyzed bend torsion coupling vibration of the systemunder unbalanced excitation Calculation results show thatSFD can significantly reduce mode dominated by radialvibration Additionally It was observed thatmode dominatedby torsional vibration was sensitive to meshing damping ofthe gear system Chen et al [10] investigated stability andcomplex dynamic characteristics of a nonlinear gear systemunder unbalanced incentive with one SFD support Resultsshowed that unstable periodic response could be simul-taneously accompanied with quasiperiodicity and chaoticmotion within the frequency response range Chang-Jian [11]analyzed dynamic behavior of the gear-bearing system withone porous squeeze film damper (PSFD) support and theresults show that PSFD can improve dynamic stability of thegear-bearing system
Specific structure of an integral squeeze film damper(ISFD) allows many problems in traditional squeeze filmdampers to be resolved Problems such as nonlinear oil filmcomplex structure large occupation space difficult assem-bling high-accumulated error and nonlinear change of thestiffness and damping characteristics can be solved ISFD hasbeen applied in many turbine machines such as compressorsturbines and engines [12 13] However there are only fewresearch reports in literature which have discussed use ofISFD to reduce and isolate gear meshing excitation to sup-press vibration of the gear system
In this paper a novel method to control vibration ofgear system is proposed This is achieved by isolating gearmeshing vibration to reduce vibration transmitted to thefoundation through the bearings A new ISFD was designedand vibration suppression characteristics of gear system werestudied through experiments Four sets of experimental ISFDelastic damping support structures were processed and anopen first-grade spur gear system was built Vibration reduc-tion characteristics of gear shafts were studied with ISFDinstalled on both driving shaft and driven shaft only installedon the driven shaft or only installed on the driving shaft atdifferent speeds
2 Vibration Model and Analysisof Gear System
Here vibrationmodel of a simple transmission gear system isfirst established The intermeshing gear pair is simplified as avibration source with a concentrated mass and the gearboxis simplified as another excited concentrated mass Bearings
K C
K1 K2
Gear pair
Housing
Foundation
Figure 1 Vibration of gear system
F = F0
Foundation
Equipment
ejt
Figure 2 Single-degree-of-freedom vibration isolation system
between the gear and housing are regarded as springs with acertain stiffness and damping Generally front and rear endsof the gearbox are supported by the engine and main shafton the base Concentrated mass of the gearbox is elasticallyconnected with the foundation and vibration model of thewhole gear system can be simplified as shown in Figure 1 [3]
According to vibration isolation theory [14] in order toreduce vibration response of the gear system radial stiffnessof the bearing should be decreased and vibration dampingof the bearing should be increased In other words stiffnesscoefficient119870 is decreased damping coefficient119862 is increasedand natural frequency of the system is decreased As a resultvibration transmission coefficient of the system is decreased
In this experiment vibration of the bearing block isconsidered as the evaluation index Model of a single-degree-of-freedom vibration isolation system for a gear pair bearingis shown in Figure 2 Equation of motion for the system isgiven by
119872 + 119862 + 119870119909 = 1198650119890119895120596119905 (1)
where 119872 119870 119862 denote mass stiffness and damping of thevibration isolation system respectively The vibration dis-placement of the system is given by
1199090 =1003816100381610038161003816100381610038161003816100381610038161198650119870
1(1 minus 1199112 + 1198952120577119911)
100381610038161003816100381610038161003816100381610038161003816 (2)
where 1205960 = radic119870119872 denotes natural frequency of the system119911 = 1205961205960 is frequency ratio and 120577 = 119862(2radic119870119872) denotesdamping coefficient Disturbance force is transmitted to the
Shock and Vibration 3
foundation through the vibration isolation spring 119870 anddisturbance force on the foundation is calculated as
119875 = 119862 + 119870119909 (3)
Its amplitude is shown as
1198750 = 10038161003816100381610038161198951205961198621199090 + 11987011990901003816100381610038161003816 (4)
Vibration transmission coefficient of the system is expressedas
119879119891 =100381610038161003816100381610038161003816100381610038161198750119865010038161003816100381610038161003816100381610038161003816=1003816100381610038161003816100381610038161003816100381610038161119870119895120596119862 + 119870(1 minus 1199112 + 1198952120577119911)
100381610038161003816100381610038161003816100381610038161003816
=radic1 + (2120577119911)2
radic(1 minus 1199112)2 + (2120577119911)2
(5)
As seen from (5) when vibration disturbance frequency120596 is significantly larger than natural frequency of the system1205960 vibration transmission coefficient is less than 1 and systemhas a vibration isolation effect Higher vibration disturbancefrequency compared to natural frequency of the systemresults in a lower vibration transmission coefficient As aresult vibration isolation effect is improved Vibration fre-quency and its higher harmonics of gearmeshing are high fre-quency components these are generally significantly higherthan natural frequency of the gear shafts Therefore thesevibration isolation measures are effective Disturbance fre-quency may not be completely eliminated in a certain fre-quency band especially when the equipment starts or shutsdownThis disturbance has a broad bandwidth So vibrationisolation system must have an appropriate damping to avoidsystem resonance
3 Integral Squeeze Film Damper
31 Structural Features ISFD differs from other dampers inthat it is an integral bearing damper made using wire electricdischarge machine (EDM) technology This allows thebearing support to have a better damping effect for the rotorsystem The integral design provides improvement inmachining thereby allowing precise concentricity stiffnessand rotor position ISFD designed for experiments usedin this work is shown in Figure 3 The structure consistsof an outer rim and inner rim The outer rim and innerrim are connected by a fixed number of S-shaped springstructures S-shaped springs allow pressure to be distributedevenly Radial static stiffness of the bearing support system isdetermined by these S-shaped elastic structures Clearancebetween the S-shaped springs forms squeeze films therebyproviding damping required by the system Displacementcloud of the experimental ISFD under the loading conditionsis shown in Figure 4
Figure 5 shows mechanical models of the traditionalbearing support system and ISFD bearing support systemComparing the twomodels it can be seen that stiffness of theISFD structure is several orders of magnitude lower than thatof the bearing Vibration deformation during transmission is
Outer rim Integral spring
Squeeze film damper land
Inner rim
Figure 3 Experimental S-type elastomer
mainly concentrated on the elastic support which can absorbsome vibration energy In addition the oil film dampingprovided by ISFD can dissipate vibration energy
32 EnergyDissipationMechanism Energy dissipationmech-anism of the conventional squeeze film damper (SFD) isbased on generating fluid pressure Δ119901 by squeezing the oilfilm This promotes movement of lubricating oil along thecircumference Flow friction due to circumferential motionof the fluid produces damping to dissipate energy There isobviously significant nonlinearity as a result of this approachStiffness and damping in the new ISFD structure are relativelyindependent such that stiffness and damping in the supportsystem do not have a direct relationship that is elasticdamping structure decoupling ability As a result ISFD canprovide a relatively low stiffness through the S-type structurewhile providing a greater damping in the squeeze filmdamper effectively increasing damping ratio of the system[15 16]
4 Experimental Setup
41 Support Structure In order to study vibration reductioncharacteristics of ISFD for gear shafts two kinds of supportstructures were designed for use with the laboratory rotorrigid support and ISFD elastic damping support Specificstructure for both these structures is shown in Figure 6 Therigid support is made up of a bearing block a sleeve and arolling bearing whereas the ISFD elastic damping supportconsists of a bearing block an S-type elastomer a rolling bear-ing O-type rubber rings and sealed-end covers Figure 6(c)is a bearing cover with O-type rubber rings on which thereare a grease hole and oil drain hole The bigger sized O-type rubber ring provides a static seal between the bearingcover and bearing block while the smaller size O-typerubber ring guarantees a dynamic seal between the bearingcover and shaft Vibration reduction characteristics of ISFDare studied by comparing vibration amplitude of the twotypes of supported gear systems
4 Shock and Vibration
018168 Max0161220140760120290099832007937005890800384460017984minus0002478 Min
A static structuralDirectional deformationType directional deformation (x-axis)Unit mmCoordinate systemTime 1201745 2038
0000 10000 20000 (mm)
5000 15000
(a) 119883 direction
A Static structuralDirectional deformationType directional deformation (y-axis)Unit mmCoordinate systemTime 1201745 2040
018205 Max016155014105012056010006007956300590650038568001807minus0002427 Min
0000 10000 20000 (mm)
5000 15000
(b) 119884 direction
Figure 4 Displacement cloud of ISFD under a loading of 6000N
Bearing
Foundation
KB CB
KP CP
(a) Traditional bearing sup-port system
ISFD
Foundation
BearingKB CB
KS CS
KP CP
KS ≪ KB
(b) ISFD bearing supportsystem
Figure 5 Mechanical models of traditional bearing support system and ISFD bearing support system
Shock and Vibration 5
Rigid sleeve Rolling bearing
Bearing block
(a) Rigid support
Bearing block
End cover Grease hole
Oil drain hole
(b) ISFD elastic damping support
Big O-type rubber ring
Small O-type rubber ring
(c) Bearing cover with O-type rubberrings
Figure 6 Two kinds of experimental support and bearing cover used in the elastic damping support
(1) (2) (3) (4) (5)
(13) (12) (11) (10) (9) (8) (7) (6)
(1) Motor(2) Photoelectric sensors(3) Acceleration sensor 1(4) Acquisition system LC-8008(5) Driving gear(6) Computer(7) ISFD elastic damping support(8) Motor speed controller(9) Driven gear(10) Acceleration sensor 2(11) Driven shaft(12) Driving shaft(13) Flexible coupling
Figure 7 Test apparatus
42 Experimental Parameters The experimental gear trans-mission system is shown in Figure 7 The gear system iscomposed of involute spur gears on the driving and drivenshafts Parameters of the gear pair are listed in Table 1 Diam-eter of two shafts is 10mm Driving and driven shaft spansare 320mm and 180mm respectively The driving shaft isdriven by a permanent magnet DC servomotor By adjustingthe speed controller output speed can be controlled in the
Table 1 Parameters of the gear pair
Gear parameters ValueNumber of teeth of the driving gear 30Number of teeth of the driven gear 20Gear ratio 23Gear modulus (mm) 3Pressure angle (∘) 20Tooth thickness of the driven gear (mm) 30Tooth thickness of the driving gear (mm) 28Theoretical center distance (mm) 75
range of 0ndash10000 rmin Using the drip method during theexperiments lubricates the gear pair
During the experiment the LC-8008 vibration monitor-ing and diagnosis system was used for vibration test Thissystem included 8 input channels which can collect storeand analyze vibration in time and frequency domains alongwith other real-time data during transmission of gear systemAcceleration sensor adsorbed on the driving and driven bear-ing blocks is used to collect the vibration signal Accelerationsensor 1 measures vibration in the horizontal direction of thedriving bearing block whereas vibration in the horizontaldirection of the driven bearing block is measured by accel-eration sensor 2 Photoelectric sensors collect rotating speed
5 Results and Discussion
51 Simultaneous Vibration Reduction Using ISFD ElasticDamping Supports Installed on Two Shafts Acceleration inboth time and frequency domain for bearing blocks iscollectedwhen gear shafts are installedwith rigid support andISFD elastic damping support Rotating speed of the drivingshaft was measured as 1198991 = 300sim1600 rmin by adjusting thespeed controller Next rotating speed of the driven shaft wasdetermined to be 1198992 = 1198991119894=450sim2400 rmin Frequencywas
6 Shock and Vibration
7
6
5
4
3
2
1
00 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD(a) Comparison of vibration of the driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800
12
10
8
6
4
2
0
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD
(b) Comparison of vibration of the driven shaft
Figure 8 Curve of acceleration amplitude at measured points versus rotating speed with different supports
12
10
8
6
4
2
0
minus2
minus4
minus6
minus8
minus10
minus12005 010 015 020 030 035025 040
Time (s)
Am
plitu
de (m
s2)
Rigid supportISFD
(a) Comparison of time domain waveform of driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
09
08
07
06
05
04
03
02
01
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD
(b) Comparison of frequency spectrum of driving shaft
Figure 9 Comparison of vibration of driving shaft measuring point
determined as 2 kHz with a total number of 2048 samplingpoints and was analyzed using the data acquisition systemLC-8008 The data is recorded every 100 rmin Figure 8shows acceleration amplitude of gear shafts as a function ofrotating speed during the process of speeding up
As seen from experimental results in Figure 8 vibrationvalue at measured point of a gear shaft at each rotatingspeed is reduced when support is changed from rigid supportto ISFD elastic damping support Within the experimen-tal rotating speed range maximum amplitude of vibrationreduction for the driving and driven shafts in horizontaldirection is 236 and 413 respectively
Due to space limitations time domain and frequencyspectrum for each measurement point vibration accelerationis analyzed when the rotating speed of the driving shaft is1200 rmin Time domain and frequency spectrum at mea-sured points of two shafts in horizontal direction are shownin Figures 9 and 10 respectively for gear shafts with rigidsupport and ISFD elastic damping support
From time domain waveforms shown in Figures 9(a) and10(a) it can be seen that there is a modulation phenomenonseen in the waveforms Besides there is an obvious impactvibration seen in the gear meshing transmission process anda periodic phenomenon is not obvious It is known from
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
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2 Shock and Vibration
[6 7] Vibration suppression effect of viscoelastic material isgreatly influenced by thickness of the damping layer
Squeeze film damper (SFD) and bearing are used cooper-atively in turbomachinery such as the compressors turbinesand generators to solve problems associated with vibrationand stability of the rotor SFD allows the support structureto simultaneously have a lower stiffness and higher dampingLow support stiffness reduces dynamic loads transmittedthrough the bearings to nonrotating structures This helps inprolonging bearing life and minimizing structural vibration[8] In a gear compressor SFD has been used to reduce andisolatemeshing incentives of a gear Chen et al [9] establisheda calculation model for the gear system with SFD supportand analyzed bend torsion coupling vibration of the systemunder unbalanced excitation Calculation results show thatSFD can significantly reduce mode dominated by radialvibration Additionally It was observed thatmode dominatedby torsional vibration was sensitive to meshing damping ofthe gear system Chen et al [10] investigated stability andcomplex dynamic characteristics of a nonlinear gear systemunder unbalanced incentive with one SFD support Resultsshowed that unstable periodic response could be simul-taneously accompanied with quasiperiodicity and chaoticmotion within the frequency response range Chang-Jian [11]analyzed dynamic behavior of the gear-bearing system withone porous squeeze film damper (PSFD) support and theresults show that PSFD can improve dynamic stability of thegear-bearing system
Specific structure of an integral squeeze film damper(ISFD) allows many problems in traditional squeeze filmdampers to be resolved Problems such as nonlinear oil filmcomplex structure large occupation space difficult assem-bling high-accumulated error and nonlinear change of thestiffness and damping characteristics can be solved ISFD hasbeen applied in many turbine machines such as compressorsturbines and engines [12 13] However there are only fewresearch reports in literature which have discussed use ofISFD to reduce and isolate gear meshing excitation to sup-press vibration of the gear system
In this paper a novel method to control vibration ofgear system is proposed This is achieved by isolating gearmeshing vibration to reduce vibration transmitted to thefoundation through the bearings A new ISFD was designedand vibration suppression characteristics of gear system werestudied through experiments Four sets of experimental ISFDelastic damping support structures were processed and anopen first-grade spur gear system was built Vibration reduc-tion characteristics of gear shafts were studied with ISFDinstalled on both driving shaft and driven shaft only installedon the driven shaft or only installed on the driving shaft atdifferent speeds
2 Vibration Model and Analysisof Gear System
Here vibrationmodel of a simple transmission gear system isfirst established The intermeshing gear pair is simplified as avibration source with a concentrated mass and the gearboxis simplified as another excited concentrated mass Bearings
K C
K1 K2
Gear pair
Housing
Foundation
Figure 1 Vibration of gear system
F = F0
Foundation
Equipment
ejt
Figure 2 Single-degree-of-freedom vibration isolation system
between the gear and housing are regarded as springs with acertain stiffness and damping Generally front and rear endsof the gearbox are supported by the engine and main shafton the base Concentrated mass of the gearbox is elasticallyconnected with the foundation and vibration model of thewhole gear system can be simplified as shown in Figure 1 [3]
According to vibration isolation theory [14] in order toreduce vibration response of the gear system radial stiffnessof the bearing should be decreased and vibration dampingof the bearing should be increased In other words stiffnesscoefficient119870 is decreased damping coefficient119862 is increasedand natural frequency of the system is decreased As a resultvibration transmission coefficient of the system is decreased
In this experiment vibration of the bearing block isconsidered as the evaluation index Model of a single-degree-of-freedom vibration isolation system for a gear pair bearingis shown in Figure 2 Equation of motion for the system isgiven by
119872 + 119862 + 119870119909 = 1198650119890119895120596119905 (1)
where 119872 119870 119862 denote mass stiffness and damping of thevibration isolation system respectively The vibration dis-placement of the system is given by
1199090 =1003816100381610038161003816100381610038161003816100381610038161198650119870
1(1 minus 1199112 + 1198952120577119911)
100381610038161003816100381610038161003816100381610038161003816 (2)
where 1205960 = radic119870119872 denotes natural frequency of the system119911 = 1205961205960 is frequency ratio and 120577 = 119862(2radic119870119872) denotesdamping coefficient Disturbance force is transmitted to the
Shock and Vibration 3
foundation through the vibration isolation spring 119870 anddisturbance force on the foundation is calculated as
119875 = 119862 + 119870119909 (3)
Its amplitude is shown as
1198750 = 10038161003816100381610038161198951205961198621199090 + 11987011990901003816100381610038161003816 (4)
Vibration transmission coefficient of the system is expressedas
119879119891 =100381610038161003816100381610038161003816100381610038161198750119865010038161003816100381610038161003816100381610038161003816=1003816100381610038161003816100381610038161003816100381610038161119870119895120596119862 + 119870(1 minus 1199112 + 1198952120577119911)
100381610038161003816100381610038161003816100381610038161003816
=radic1 + (2120577119911)2
radic(1 minus 1199112)2 + (2120577119911)2
(5)
As seen from (5) when vibration disturbance frequency120596 is significantly larger than natural frequency of the system1205960 vibration transmission coefficient is less than 1 and systemhas a vibration isolation effect Higher vibration disturbancefrequency compared to natural frequency of the systemresults in a lower vibration transmission coefficient As aresult vibration isolation effect is improved Vibration fre-quency and its higher harmonics of gearmeshing are high fre-quency components these are generally significantly higherthan natural frequency of the gear shafts Therefore thesevibration isolation measures are effective Disturbance fre-quency may not be completely eliminated in a certain fre-quency band especially when the equipment starts or shutsdownThis disturbance has a broad bandwidth So vibrationisolation system must have an appropriate damping to avoidsystem resonance
3 Integral Squeeze Film Damper
31 Structural Features ISFD differs from other dampers inthat it is an integral bearing damper made using wire electricdischarge machine (EDM) technology This allows thebearing support to have a better damping effect for the rotorsystem The integral design provides improvement inmachining thereby allowing precise concentricity stiffnessand rotor position ISFD designed for experiments usedin this work is shown in Figure 3 The structure consistsof an outer rim and inner rim The outer rim and innerrim are connected by a fixed number of S-shaped springstructures S-shaped springs allow pressure to be distributedevenly Radial static stiffness of the bearing support system isdetermined by these S-shaped elastic structures Clearancebetween the S-shaped springs forms squeeze films therebyproviding damping required by the system Displacementcloud of the experimental ISFD under the loading conditionsis shown in Figure 4
Figure 5 shows mechanical models of the traditionalbearing support system and ISFD bearing support systemComparing the twomodels it can be seen that stiffness of theISFD structure is several orders of magnitude lower than thatof the bearing Vibration deformation during transmission is
Outer rim Integral spring
Squeeze film damper land
Inner rim
Figure 3 Experimental S-type elastomer
mainly concentrated on the elastic support which can absorbsome vibration energy In addition the oil film dampingprovided by ISFD can dissipate vibration energy
32 EnergyDissipationMechanism Energy dissipationmech-anism of the conventional squeeze film damper (SFD) isbased on generating fluid pressure Δ119901 by squeezing the oilfilm This promotes movement of lubricating oil along thecircumference Flow friction due to circumferential motionof the fluid produces damping to dissipate energy There isobviously significant nonlinearity as a result of this approachStiffness and damping in the new ISFD structure are relativelyindependent such that stiffness and damping in the supportsystem do not have a direct relationship that is elasticdamping structure decoupling ability As a result ISFD canprovide a relatively low stiffness through the S-type structurewhile providing a greater damping in the squeeze filmdamper effectively increasing damping ratio of the system[15 16]
4 Experimental Setup
41 Support Structure In order to study vibration reductioncharacteristics of ISFD for gear shafts two kinds of supportstructures were designed for use with the laboratory rotorrigid support and ISFD elastic damping support Specificstructure for both these structures is shown in Figure 6 Therigid support is made up of a bearing block a sleeve and arolling bearing whereas the ISFD elastic damping supportconsists of a bearing block an S-type elastomer a rolling bear-ing O-type rubber rings and sealed-end covers Figure 6(c)is a bearing cover with O-type rubber rings on which thereare a grease hole and oil drain hole The bigger sized O-type rubber ring provides a static seal between the bearingcover and bearing block while the smaller size O-typerubber ring guarantees a dynamic seal between the bearingcover and shaft Vibration reduction characteristics of ISFDare studied by comparing vibration amplitude of the twotypes of supported gear systems
4 Shock and Vibration
018168 Max0161220140760120290099832007937005890800384460017984minus0002478 Min
A static structuralDirectional deformationType directional deformation (x-axis)Unit mmCoordinate systemTime 1201745 2038
0000 10000 20000 (mm)
5000 15000
(a) 119883 direction
A Static structuralDirectional deformationType directional deformation (y-axis)Unit mmCoordinate systemTime 1201745 2040
018205 Max016155014105012056010006007956300590650038568001807minus0002427 Min
0000 10000 20000 (mm)
5000 15000
(b) 119884 direction
Figure 4 Displacement cloud of ISFD under a loading of 6000N
Bearing
Foundation
KB CB
KP CP
(a) Traditional bearing sup-port system
ISFD
Foundation
BearingKB CB
KS CS
KP CP
KS ≪ KB
(b) ISFD bearing supportsystem
Figure 5 Mechanical models of traditional bearing support system and ISFD bearing support system
Shock and Vibration 5
Rigid sleeve Rolling bearing
Bearing block
(a) Rigid support
Bearing block
End cover Grease hole
Oil drain hole
(b) ISFD elastic damping support
Big O-type rubber ring
Small O-type rubber ring
(c) Bearing cover with O-type rubberrings
Figure 6 Two kinds of experimental support and bearing cover used in the elastic damping support
(1) (2) (3) (4) (5)
(13) (12) (11) (10) (9) (8) (7) (6)
(1) Motor(2) Photoelectric sensors(3) Acceleration sensor 1(4) Acquisition system LC-8008(5) Driving gear(6) Computer(7) ISFD elastic damping support(8) Motor speed controller(9) Driven gear(10) Acceleration sensor 2(11) Driven shaft(12) Driving shaft(13) Flexible coupling
Figure 7 Test apparatus
42 Experimental Parameters The experimental gear trans-mission system is shown in Figure 7 The gear system iscomposed of involute spur gears on the driving and drivenshafts Parameters of the gear pair are listed in Table 1 Diam-eter of two shafts is 10mm Driving and driven shaft spansare 320mm and 180mm respectively The driving shaft isdriven by a permanent magnet DC servomotor By adjustingthe speed controller output speed can be controlled in the
Table 1 Parameters of the gear pair
Gear parameters ValueNumber of teeth of the driving gear 30Number of teeth of the driven gear 20Gear ratio 23Gear modulus (mm) 3Pressure angle (∘) 20Tooth thickness of the driven gear (mm) 30Tooth thickness of the driving gear (mm) 28Theoretical center distance (mm) 75
range of 0ndash10000 rmin Using the drip method during theexperiments lubricates the gear pair
During the experiment the LC-8008 vibration monitor-ing and diagnosis system was used for vibration test Thissystem included 8 input channels which can collect storeand analyze vibration in time and frequency domains alongwith other real-time data during transmission of gear systemAcceleration sensor adsorbed on the driving and driven bear-ing blocks is used to collect the vibration signal Accelerationsensor 1 measures vibration in the horizontal direction of thedriving bearing block whereas vibration in the horizontaldirection of the driven bearing block is measured by accel-eration sensor 2 Photoelectric sensors collect rotating speed
5 Results and Discussion
51 Simultaneous Vibration Reduction Using ISFD ElasticDamping Supports Installed on Two Shafts Acceleration inboth time and frequency domain for bearing blocks iscollectedwhen gear shafts are installedwith rigid support andISFD elastic damping support Rotating speed of the drivingshaft was measured as 1198991 = 300sim1600 rmin by adjusting thespeed controller Next rotating speed of the driven shaft wasdetermined to be 1198992 = 1198991119894=450sim2400 rmin Frequencywas
6 Shock and Vibration
7
6
5
4
3
2
1
00 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD(a) Comparison of vibration of the driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800
12
10
8
6
4
2
0
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD
(b) Comparison of vibration of the driven shaft
Figure 8 Curve of acceleration amplitude at measured points versus rotating speed with different supports
12
10
8
6
4
2
0
minus2
minus4
minus6
minus8
minus10
minus12005 010 015 020 030 035025 040
Time (s)
Am
plitu
de (m
s2)
Rigid supportISFD
(a) Comparison of time domain waveform of driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
09
08
07
06
05
04
03
02
01
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD
(b) Comparison of frequency spectrum of driving shaft
Figure 9 Comparison of vibration of driving shaft measuring point
determined as 2 kHz with a total number of 2048 samplingpoints and was analyzed using the data acquisition systemLC-8008 The data is recorded every 100 rmin Figure 8shows acceleration amplitude of gear shafts as a function ofrotating speed during the process of speeding up
As seen from experimental results in Figure 8 vibrationvalue at measured point of a gear shaft at each rotatingspeed is reduced when support is changed from rigid supportto ISFD elastic damping support Within the experimen-tal rotating speed range maximum amplitude of vibrationreduction for the driving and driven shafts in horizontaldirection is 236 and 413 respectively
Due to space limitations time domain and frequencyspectrum for each measurement point vibration accelerationis analyzed when the rotating speed of the driving shaft is1200 rmin Time domain and frequency spectrum at mea-sured points of two shafts in horizontal direction are shownin Figures 9 and 10 respectively for gear shafts with rigidsupport and ISFD elastic damping support
From time domain waveforms shown in Figures 9(a) and10(a) it can be seen that there is a modulation phenomenonseen in the waveforms Besides there is an obvious impactvibration seen in the gear meshing transmission process anda periodic phenomenon is not obvious It is known from
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
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Shock and Vibration 3
foundation through the vibration isolation spring 119870 anddisturbance force on the foundation is calculated as
119875 = 119862 + 119870119909 (3)
Its amplitude is shown as
1198750 = 10038161003816100381610038161198951205961198621199090 + 11987011990901003816100381610038161003816 (4)
Vibration transmission coefficient of the system is expressedas
119879119891 =100381610038161003816100381610038161003816100381610038161198750119865010038161003816100381610038161003816100381610038161003816=1003816100381610038161003816100381610038161003816100381610038161119870119895120596119862 + 119870(1 minus 1199112 + 1198952120577119911)
100381610038161003816100381610038161003816100381610038161003816
=radic1 + (2120577119911)2
radic(1 minus 1199112)2 + (2120577119911)2
(5)
As seen from (5) when vibration disturbance frequency120596 is significantly larger than natural frequency of the system1205960 vibration transmission coefficient is less than 1 and systemhas a vibration isolation effect Higher vibration disturbancefrequency compared to natural frequency of the systemresults in a lower vibration transmission coefficient As aresult vibration isolation effect is improved Vibration fre-quency and its higher harmonics of gearmeshing are high fre-quency components these are generally significantly higherthan natural frequency of the gear shafts Therefore thesevibration isolation measures are effective Disturbance fre-quency may not be completely eliminated in a certain fre-quency band especially when the equipment starts or shutsdownThis disturbance has a broad bandwidth So vibrationisolation system must have an appropriate damping to avoidsystem resonance
3 Integral Squeeze Film Damper
31 Structural Features ISFD differs from other dampers inthat it is an integral bearing damper made using wire electricdischarge machine (EDM) technology This allows thebearing support to have a better damping effect for the rotorsystem The integral design provides improvement inmachining thereby allowing precise concentricity stiffnessand rotor position ISFD designed for experiments usedin this work is shown in Figure 3 The structure consistsof an outer rim and inner rim The outer rim and innerrim are connected by a fixed number of S-shaped springstructures S-shaped springs allow pressure to be distributedevenly Radial static stiffness of the bearing support system isdetermined by these S-shaped elastic structures Clearancebetween the S-shaped springs forms squeeze films therebyproviding damping required by the system Displacementcloud of the experimental ISFD under the loading conditionsis shown in Figure 4
Figure 5 shows mechanical models of the traditionalbearing support system and ISFD bearing support systemComparing the twomodels it can be seen that stiffness of theISFD structure is several orders of magnitude lower than thatof the bearing Vibration deformation during transmission is
Outer rim Integral spring
Squeeze film damper land
Inner rim
Figure 3 Experimental S-type elastomer
mainly concentrated on the elastic support which can absorbsome vibration energy In addition the oil film dampingprovided by ISFD can dissipate vibration energy
32 EnergyDissipationMechanism Energy dissipationmech-anism of the conventional squeeze film damper (SFD) isbased on generating fluid pressure Δ119901 by squeezing the oilfilm This promotes movement of lubricating oil along thecircumference Flow friction due to circumferential motionof the fluid produces damping to dissipate energy There isobviously significant nonlinearity as a result of this approachStiffness and damping in the new ISFD structure are relativelyindependent such that stiffness and damping in the supportsystem do not have a direct relationship that is elasticdamping structure decoupling ability As a result ISFD canprovide a relatively low stiffness through the S-type structurewhile providing a greater damping in the squeeze filmdamper effectively increasing damping ratio of the system[15 16]
4 Experimental Setup
41 Support Structure In order to study vibration reductioncharacteristics of ISFD for gear shafts two kinds of supportstructures were designed for use with the laboratory rotorrigid support and ISFD elastic damping support Specificstructure for both these structures is shown in Figure 6 Therigid support is made up of a bearing block a sleeve and arolling bearing whereas the ISFD elastic damping supportconsists of a bearing block an S-type elastomer a rolling bear-ing O-type rubber rings and sealed-end covers Figure 6(c)is a bearing cover with O-type rubber rings on which thereare a grease hole and oil drain hole The bigger sized O-type rubber ring provides a static seal between the bearingcover and bearing block while the smaller size O-typerubber ring guarantees a dynamic seal between the bearingcover and shaft Vibration reduction characteristics of ISFDare studied by comparing vibration amplitude of the twotypes of supported gear systems
4 Shock and Vibration
018168 Max0161220140760120290099832007937005890800384460017984minus0002478 Min
A static structuralDirectional deformationType directional deformation (x-axis)Unit mmCoordinate systemTime 1201745 2038
0000 10000 20000 (mm)
5000 15000
(a) 119883 direction
A Static structuralDirectional deformationType directional deformation (y-axis)Unit mmCoordinate systemTime 1201745 2040
018205 Max016155014105012056010006007956300590650038568001807minus0002427 Min
0000 10000 20000 (mm)
5000 15000
(b) 119884 direction
Figure 4 Displacement cloud of ISFD under a loading of 6000N
Bearing
Foundation
KB CB
KP CP
(a) Traditional bearing sup-port system
ISFD
Foundation
BearingKB CB
KS CS
KP CP
KS ≪ KB
(b) ISFD bearing supportsystem
Figure 5 Mechanical models of traditional bearing support system and ISFD bearing support system
Shock and Vibration 5
Rigid sleeve Rolling bearing
Bearing block
(a) Rigid support
Bearing block
End cover Grease hole
Oil drain hole
(b) ISFD elastic damping support
Big O-type rubber ring
Small O-type rubber ring
(c) Bearing cover with O-type rubberrings
Figure 6 Two kinds of experimental support and bearing cover used in the elastic damping support
(1) (2) (3) (4) (5)
(13) (12) (11) (10) (9) (8) (7) (6)
(1) Motor(2) Photoelectric sensors(3) Acceleration sensor 1(4) Acquisition system LC-8008(5) Driving gear(6) Computer(7) ISFD elastic damping support(8) Motor speed controller(9) Driven gear(10) Acceleration sensor 2(11) Driven shaft(12) Driving shaft(13) Flexible coupling
Figure 7 Test apparatus
42 Experimental Parameters The experimental gear trans-mission system is shown in Figure 7 The gear system iscomposed of involute spur gears on the driving and drivenshafts Parameters of the gear pair are listed in Table 1 Diam-eter of two shafts is 10mm Driving and driven shaft spansare 320mm and 180mm respectively The driving shaft isdriven by a permanent magnet DC servomotor By adjustingthe speed controller output speed can be controlled in the
Table 1 Parameters of the gear pair
Gear parameters ValueNumber of teeth of the driving gear 30Number of teeth of the driven gear 20Gear ratio 23Gear modulus (mm) 3Pressure angle (∘) 20Tooth thickness of the driven gear (mm) 30Tooth thickness of the driving gear (mm) 28Theoretical center distance (mm) 75
range of 0ndash10000 rmin Using the drip method during theexperiments lubricates the gear pair
During the experiment the LC-8008 vibration monitor-ing and diagnosis system was used for vibration test Thissystem included 8 input channels which can collect storeand analyze vibration in time and frequency domains alongwith other real-time data during transmission of gear systemAcceleration sensor adsorbed on the driving and driven bear-ing blocks is used to collect the vibration signal Accelerationsensor 1 measures vibration in the horizontal direction of thedriving bearing block whereas vibration in the horizontaldirection of the driven bearing block is measured by accel-eration sensor 2 Photoelectric sensors collect rotating speed
5 Results and Discussion
51 Simultaneous Vibration Reduction Using ISFD ElasticDamping Supports Installed on Two Shafts Acceleration inboth time and frequency domain for bearing blocks iscollectedwhen gear shafts are installedwith rigid support andISFD elastic damping support Rotating speed of the drivingshaft was measured as 1198991 = 300sim1600 rmin by adjusting thespeed controller Next rotating speed of the driven shaft wasdetermined to be 1198992 = 1198991119894=450sim2400 rmin Frequencywas
6 Shock and Vibration
7
6
5
4
3
2
1
00 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD(a) Comparison of vibration of the driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800
12
10
8
6
4
2
0
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD
(b) Comparison of vibration of the driven shaft
Figure 8 Curve of acceleration amplitude at measured points versus rotating speed with different supports
12
10
8
6
4
2
0
minus2
minus4
minus6
minus8
minus10
minus12005 010 015 020 030 035025 040
Time (s)
Am
plitu
de (m
s2)
Rigid supportISFD
(a) Comparison of time domain waveform of driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
09
08
07
06
05
04
03
02
01
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD
(b) Comparison of frequency spectrum of driving shaft
Figure 9 Comparison of vibration of driving shaft measuring point
determined as 2 kHz with a total number of 2048 samplingpoints and was analyzed using the data acquisition systemLC-8008 The data is recorded every 100 rmin Figure 8shows acceleration amplitude of gear shafts as a function ofrotating speed during the process of speeding up
As seen from experimental results in Figure 8 vibrationvalue at measured point of a gear shaft at each rotatingspeed is reduced when support is changed from rigid supportto ISFD elastic damping support Within the experimen-tal rotating speed range maximum amplitude of vibrationreduction for the driving and driven shafts in horizontaldirection is 236 and 413 respectively
Due to space limitations time domain and frequencyspectrum for each measurement point vibration accelerationis analyzed when the rotating speed of the driving shaft is1200 rmin Time domain and frequency spectrum at mea-sured points of two shafts in horizontal direction are shownin Figures 9 and 10 respectively for gear shafts with rigidsupport and ISFD elastic damping support
From time domain waveforms shown in Figures 9(a) and10(a) it can be seen that there is a modulation phenomenonseen in the waveforms Besides there is an obvious impactvibration seen in the gear meshing transmission process anda periodic phenomenon is not obvious It is known from
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
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Shock and Vibration
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Navigation and Observation
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DistributedSensor Networks
International Journal of
4 Shock and Vibration
018168 Max0161220140760120290099832007937005890800384460017984minus0002478 Min
A static structuralDirectional deformationType directional deformation (x-axis)Unit mmCoordinate systemTime 1201745 2038
0000 10000 20000 (mm)
5000 15000
(a) 119883 direction
A Static structuralDirectional deformationType directional deformation (y-axis)Unit mmCoordinate systemTime 1201745 2040
018205 Max016155014105012056010006007956300590650038568001807minus0002427 Min
0000 10000 20000 (mm)
5000 15000
(b) 119884 direction
Figure 4 Displacement cloud of ISFD under a loading of 6000N
Bearing
Foundation
KB CB
KP CP
(a) Traditional bearing sup-port system
ISFD
Foundation
BearingKB CB
KS CS
KP CP
KS ≪ KB
(b) ISFD bearing supportsystem
Figure 5 Mechanical models of traditional bearing support system and ISFD bearing support system
Shock and Vibration 5
Rigid sleeve Rolling bearing
Bearing block
(a) Rigid support
Bearing block
End cover Grease hole
Oil drain hole
(b) ISFD elastic damping support
Big O-type rubber ring
Small O-type rubber ring
(c) Bearing cover with O-type rubberrings
Figure 6 Two kinds of experimental support and bearing cover used in the elastic damping support
(1) (2) (3) (4) (5)
(13) (12) (11) (10) (9) (8) (7) (6)
(1) Motor(2) Photoelectric sensors(3) Acceleration sensor 1(4) Acquisition system LC-8008(5) Driving gear(6) Computer(7) ISFD elastic damping support(8) Motor speed controller(9) Driven gear(10) Acceleration sensor 2(11) Driven shaft(12) Driving shaft(13) Flexible coupling
Figure 7 Test apparatus
42 Experimental Parameters The experimental gear trans-mission system is shown in Figure 7 The gear system iscomposed of involute spur gears on the driving and drivenshafts Parameters of the gear pair are listed in Table 1 Diam-eter of two shafts is 10mm Driving and driven shaft spansare 320mm and 180mm respectively The driving shaft isdriven by a permanent magnet DC servomotor By adjustingthe speed controller output speed can be controlled in the
Table 1 Parameters of the gear pair
Gear parameters ValueNumber of teeth of the driving gear 30Number of teeth of the driven gear 20Gear ratio 23Gear modulus (mm) 3Pressure angle (∘) 20Tooth thickness of the driven gear (mm) 30Tooth thickness of the driving gear (mm) 28Theoretical center distance (mm) 75
range of 0ndash10000 rmin Using the drip method during theexperiments lubricates the gear pair
During the experiment the LC-8008 vibration monitor-ing and diagnosis system was used for vibration test Thissystem included 8 input channels which can collect storeand analyze vibration in time and frequency domains alongwith other real-time data during transmission of gear systemAcceleration sensor adsorbed on the driving and driven bear-ing blocks is used to collect the vibration signal Accelerationsensor 1 measures vibration in the horizontal direction of thedriving bearing block whereas vibration in the horizontaldirection of the driven bearing block is measured by accel-eration sensor 2 Photoelectric sensors collect rotating speed
5 Results and Discussion
51 Simultaneous Vibration Reduction Using ISFD ElasticDamping Supports Installed on Two Shafts Acceleration inboth time and frequency domain for bearing blocks iscollectedwhen gear shafts are installedwith rigid support andISFD elastic damping support Rotating speed of the drivingshaft was measured as 1198991 = 300sim1600 rmin by adjusting thespeed controller Next rotating speed of the driven shaft wasdetermined to be 1198992 = 1198991119894=450sim2400 rmin Frequencywas
6 Shock and Vibration
7
6
5
4
3
2
1
00 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD(a) Comparison of vibration of the driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800
12
10
8
6
4
2
0
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD
(b) Comparison of vibration of the driven shaft
Figure 8 Curve of acceleration amplitude at measured points versus rotating speed with different supports
12
10
8
6
4
2
0
minus2
minus4
minus6
minus8
minus10
minus12005 010 015 020 030 035025 040
Time (s)
Am
plitu
de (m
s2)
Rigid supportISFD
(a) Comparison of time domain waveform of driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
09
08
07
06
05
04
03
02
01
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD
(b) Comparison of frequency spectrum of driving shaft
Figure 9 Comparison of vibration of driving shaft measuring point
determined as 2 kHz with a total number of 2048 samplingpoints and was analyzed using the data acquisition systemLC-8008 The data is recorded every 100 rmin Figure 8shows acceleration amplitude of gear shafts as a function ofrotating speed during the process of speeding up
As seen from experimental results in Figure 8 vibrationvalue at measured point of a gear shaft at each rotatingspeed is reduced when support is changed from rigid supportto ISFD elastic damping support Within the experimen-tal rotating speed range maximum amplitude of vibrationreduction for the driving and driven shafts in horizontaldirection is 236 and 413 respectively
Due to space limitations time domain and frequencyspectrum for each measurement point vibration accelerationis analyzed when the rotating speed of the driving shaft is1200 rmin Time domain and frequency spectrum at mea-sured points of two shafts in horizontal direction are shownin Figures 9 and 10 respectively for gear shafts with rigidsupport and ISFD elastic damping support
From time domain waveforms shown in Figures 9(a) and10(a) it can be seen that there is a modulation phenomenonseen in the waveforms Besides there is an obvious impactvibration seen in the gear meshing transmission process anda periodic phenomenon is not obvious It is known from
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 5
Rigid sleeve Rolling bearing
Bearing block
(a) Rigid support
Bearing block
End cover Grease hole
Oil drain hole
(b) ISFD elastic damping support
Big O-type rubber ring
Small O-type rubber ring
(c) Bearing cover with O-type rubberrings
Figure 6 Two kinds of experimental support and bearing cover used in the elastic damping support
(1) (2) (3) (4) (5)
(13) (12) (11) (10) (9) (8) (7) (6)
(1) Motor(2) Photoelectric sensors(3) Acceleration sensor 1(4) Acquisition system LC-8008(5) Driving gear(6) Computer(7) ISFD elastic damping support(8) Motor speed controller(9) Driven gear(10) Acceleration sensor 2(11) Driven shaft(12) Driving shaft(13) Flexible coupling
Figure 7 Test apparatus
42 Experimental Parameters The experimental gear trans-mission system is shown in Figure 7 The gear system iscomposed of involute spur gears on the driving and drivenshafts Parameters of the gear pair are listed in Table 1 Diam-eter of two shafts is 10mm Driving and driven shaft spansare 320mm and 180mm respectively The driving shaft isdriven by a permanent magnet DC servomotor By adjustingthe speed controller output speed can be controlled in the
Table 1 Parameters of the gear pair
Gear parameters ValueNumber of teeth of the driving gear 30Number of teeth of the driven gear 20Gear ratio 23Gear modulus (mm) 3Pressure angle (∘) 20Tooth thickness of the driven gear (mm) 30Tooth thickness of the driving gear (mm) 28Theoretical center distance (mm) 75
range of 0ndash10000 rmin Using the drip method during theexperiments lubricates the gear pair
During the experiment the LC-8008 vibration monitor-ing and diagnosis system was used for vibration test Thissystem included 8 input channels which can collect storeand analyze vibration in time and frequency domains alongwith other real-time data during transmission of gear systemAcceleration sensor adsorbed on the driving and driven bear-ing blocks is used to collect the vibration signal Accelerationsensor 1 measures vibration in the horizontal direction of thedriving bearing block whereas vibration in the horizontaldirection of the driven bearing block is measured by accel-eration sensor 2 Photoelectric sensors collect rotating speed
5 Results and Discussion
51 Simultaneous Vibration Reduction Using ISFD ElasticDamping Supports Installed on Two Shafts Acceleration inboth time and frequency domain for bearing blocks iscollectedwhen gear shafts are installedwith rigid support andISFD elastic damping support Rotating speed of the drivingshaft was measured as 1198991 = 300sim1600 rmin by adjusting thespeed controller Next rotating speed of the driven shaft wasdetermined to be 1198992 = 1198991119894=450sim2400 rmin Frequencywas
6 Shock and Vibration
7
6
5
4
3
2
1
00 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD(a) Comparison of vibration of the driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800
12
10
8
6
4
2
0
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD
(b) Comparison of vibration of the driven shaft
Figure 8 Curve of acceleration amplitude at measured points versus rotating speed with different supports
12
10
8
6
4
2
0
minus2
minus4
minus6
minus8
minus10
minus12005 010 015 020 030 035025 040
Time (s)
Am
plitu
de (m
s2)
Rigid supportISFD
(a) Comparison of time domain waveform of driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
09
08
07
06
05
04
03
02
01
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD
(b) Comparison of frequency spectrum of driving shaft
Figure 9 Comparison of vibration of driving shaft measuring point
determined as 2 kHz with a total number of 2048 samplingpoints and was analyzed using the data acquisition systemLC-8008 The data is recorded every 100 rmin Figure 8shows acceleration amplitude of gear shafts as a function ofrotating speed during the process of speeding up
As seen from experimental results in Figure 8 vibrationvalue at measured point of a gear shaft at each rotatingspeed is reduced when support is changed from rigid supportto ISFD elastic damping support Within the experimen-tal rotating speed range maximum amplitude of vibrationreduction for the driving and driven shafts in horizontaldirection is 236 and 413 respectively
Due to space limitations time domain and frequencyspectrum for each measurement point vibration accelerationis analyzed when the rotating speed of the driving shaft is1200 rmin Time domain and frequency spectrum at mea-sured points of two shafts in horizontal direction are shownin Figures 9 and 10 respectively for gear shafts with rigidsupport and ISFD elastic damping support
From time domain waveforms shown in Figures 9(a) and10(a) it can be seen that there is a modulation phenomenonseen in the waveforms Besides there is an obvious impactvibration seen in the gear meshing transmission process anda periodic phenomenon is not obvious It is known from
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Shock and Vibration
7
6
5
4
3
2
1
00 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD(a) Comparison of vibration of the driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800
12
10
8
6
4
2
0
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD
(b) Comparison of vibration of the driven shaft
Figure 8 Curve of acceleration amplitude at measured points versus rotating speed with different supports
12
10
8
6
4
2
0
minus2
minus4
minus6
minus8
minus10
minus12005 010 015 020 030 035025 040
Time (s)
Am
plitu
de (m
s2)
Rigid supportISFD
(a) Comparison of time domain waveform of driving shaft
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10
09
08
07
06
05
04
03
02
01
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD
(b) Comparison of frequency spectrum of driving shaft
Figure 9 Comparison of vibration of driving shaft measuring point
determined as 2 kHz with a total number of 2048 samplingpoints and was analyzed using the data acquisition systemLC-8008 The data is recorded every 100 rmin Figure 8shows acceleration amplitude of gear shafts as a function ofrotating speed during the process of speeding up
As seen from experimental results in Figure 8 vibrationvalue at measured point of a gear shaft at each rotatingspeed is reduced when support is changed from rigid supportto ISFD elastic damping support Within the experimen-tal rotating speed range maximum amplitude of vibrationreduction for the driving and driven shafts in horizontaldirection is 236 and 413 respectively
Due to space limitations time domain and frequencyspectrum for each measurement point vibration accelerationis analyzed when the rotating speed of the driving shaft is1200 rmin Time domain and frequency spectrum at mea-sured points of two shafts in horizontal direction are shownin Figures 9 and 10 respectively for gear shafts with rigidsupport and ISFD elastic damping support
From time domain waveforms shown in Figures 9(a) and10(a) it can be seen that there is a modulation phenomenonseen in the waveforms Besides there is an obvious impactvibration seen in the gear meshing transmission process anda periodic phenomenon is not obvious It is known from
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 7
Rigid supportISFD
025005 010 015 020 030 035 040
20
16
12
8
4
0
minus4
minus8
minus12
minus16
minus20
minus24
Time (s)
Am
plitu
de (m
s2)
(a) Comparison of time domain waveform of driven shaft
Rigid supportISFD
0 200 400 600 800 1000 1200 1400 1600 1800 2000
30
25
20
15
10
05
Am
plitu
de (m
s2)
Frequency (Hz)
(b) Comparison of frequency spectrum of driven shaft
Figure 10 Comparison of vibration of driven shaft measuring point
12
10
08
06
04
02
110 120 130 140 150 160 170 180 190
10103
0165
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
30
25
20
15
10
05
110 120 130 140 150 160 170 180 190
25767
05678
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 11 Comparison of data in the range of 110sim190Hz
the transmission parameters that meshing frequency of thegear pair is 119891 = 11989111198851 = 11989121198852 = 600Hz As seen fromthe frequency spectrum in Figures 9(b) and 10(b) multiplefrequency components exist in the spectrums Vibrationvalue near meshing frequency is relatively large and a widesideband is observed Otherwise vibration values observedin the vicinity of 140Hz and 1100Hz are also relatively largeAccording to theory of vibration [17] this result indicatesresonance of the gearbox and gear shafts
As seen from the time domain waveforms in Figures9(a) and 10(a) modulation phenomenon in time domainwaveform has been improved and shock vibration has beenreduced in ISFD elastic damping support compared to rigid
support Peak value of acceleration for driving shaft isreduced from 351ms2 to 276ms2 a decrease of 214Acceleration peak for driven shaft is reduced from 634ms2to 456ms2 a decrease of 281
From the frequency spectrum in Figures 9(b) and 10(b)it can be concluded that frequency components with rela-tively large vibration amplitude are significantly attenuatedwhen support is changed from rigid support to ISFD elasticdamping support In order to carry out an unambiguouscomparison here frequency spectrum ranges between 110sim190Hz 560sim640Hz and 1060sim1140Hz are shown Figures11ndash13 show correlation data corresponding to these threefrequency ranges
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Shock and Vibration
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
04676
00784
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
07
06
05
04
03
02
01
560 570 580 590 600 610 620 630 640
05818
01496
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 12 Comparison of data in the range of 560sim640Hz06
05
04
03
02
01
1060 1070 1080 1090 1100 1110 1120 1130 1140
05236
01254
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(a) Frequency spectrum of driving shaft
1060 1070 1080 1090 1100 1110 1120 1130 1140
14
12
10
08
06
04
02
11959
00629
Am
plitu
de (m
s2)
Frequency (Hz)
Rigid supportISFD(b) Frequency spectrum of driven shaft
Figure 13 Comparison of data in the range of 1060sim1140Hz
Tables 2-3 show vibration reduction for the measuredpoints of the driving and driven shafts in the vicinity of140Hz 600Hz and 1100Hz It can be seen that the vibrationreduction for all these three frequency points is above 50and resonance modulation of the gear shaft is obviouslyimproved
52 Vibration Reduction for ISFD Elastic Damping SupportsInstalled on a Single Shaft In order to study control of gearshaft vibration when only ISFD is installed on a single shaftvibration of gear shafts is measured under two conditionsFirst when ISFD is installed on driven shaft rigid support isinstalled on driving shaft and second when ISFD is installed
Table 2 Vibration reduction with different supports (driving shaft)
Frequency(Hz)
Acceleration amplitude of driving shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 10103 0165 8376075 04676 00784 8321115 05236 01254 761
on driving shaft rigid support is installed on driven shaftRotating speed of driving shaft is set as 1198991 = 300sim1600 rminVibration measurement results under these two conditionsare shown in Figure 14
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 9
7
6
5
4
3
2
1
0 200 400 600 800 1000 1200 1400 1600 1800
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft(a) Comparison of vibration of driving shaft
12
10
8
6
4
2
Am
plitu
de (m
s2)
Rotating speed (rmin)
Rigid supportISFD installed on driving shaftISFD installed on driven shaft
0 200 400 600 800 1000 1200 1400 1600 1800
(b) Comparison of vibration of driven shaft
Figure 14 Comparison of vibration under two conditions
Table 3 Vibration reduction with different supports (driven shaft)
Frequency(Hz)
Acceleration amplitude of driven shaftmeasuring point (ms2)
Rigid support ISFD support Decreasing ()140 25767 05678 780605 05818 01496 7431115 11959 00629 947
Table 4 Average amplitude of vibration reduction under twoconditions
Decreasing () ISFD installed ondriving shaft
ISFD installed ondriven shaft
Driving shaft 107 117Driven shaft 169 251
From themeasured results in Figure 14 it can be observedthat vibration of gear shafts is reduced in all cases that isvibration is reduced irrespective of ISFD support locationon either the driving or driven shafts Table 4 lists averageamplitude of vibration reduction under two conditions
As seen fromTable 4 for the driving shaft average ampli-tude of vibration reduction between the two conditions hasno significant difference For driven shaft amplitude of vibra-tion reduction is largerwhen ISFD is installed on driven shaftIn addition it can be concluded that the vibration reductioneffect is better for cases when ISFD is only installed on thedriven shaft compared to installation on driving shaft Fromthe vibration measuring results it can be seen that vibrationof driven shaft is larger compared to driving shaft Thereforeif ISFD can be installed only on a single shaft with the aimof maximum vibration reduction then installation should becarried out on the shaft with the larger vibration
6 Conclusion
ISFD elastic damping support can effectively reduce trans-mission of gear meshing excitation effectively No additionalchanges need to be made to the equipment and foundationto achieve good vibration control From the experimentalresults the following conclusions can be reached
(1) ISFD support can reduce shock vibration of the gearsystem with excellent damping vibration attenuationcharacteristics
(2) The ISFD support structure effectively reduced vibra-tion in gear shafts and maximum amplitude of vibra-tion reduction reached 413
(3) The proposed ISFD support structure reduced reso-nance modulation caused by meshing shock in gearshafts
(4) Comparison of vibration reduction characteristics atdifferent rotating speeds revealed that vibration for allgear shafts is reduced by the ISFD support
(5) No significant difference was seen for vibrationreduction of the driving shaft in cases when ISFDis installed on either the driving or driven shaftsHowever for the driven shaft vibration reductionwas observed to be significantly better when ISFD isinstalled on the driven shaft
Conflicts of Interest
There are no conflicts of interest regarding the publication ofthis paper
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 Shock and Vibration
Acknowledgments
The work described in this paper was supported financiallyby 2015 Beijing Scientific Research and Graduate Train-ing Project (0318-21510028008) This support is gratefullyacknowledged
References
[1] J Zhou W Sun and G Liu ldquoReview of vibration and noise ingear reducerrdquo Journal of Mechanical Transmission vol 38 no 6pp 163ndash170 2014 (Chinese)
[2] K Ding X Zhu and Y Chen ldquoThe vibration characteristicsof typical gearbox faults and its diagnosis planrdquo Journal ofVibration and Shock vol 20 no 3 pp 7ndash12 2001
[3] G Wang P Sun and K Fang ldquoA research on the reduction ofvibration and noise of the gearbox by using damping alloysrdquoJournal of Jiangsu University of Science and Technology (NaturalScience Edition) vol 8 no 3 pp 14ndash20 1994
[4] C Gu and X Wu ldquoPassive vibration damping technology ofgearrdquoMachinery Design amp Manufacture vol 9 pp 74ndash76 2010
[5] Z Youchen Research on Vibration Reliability And VibrationDamping Strategy with Modification of Gears NortheasternUniversity Shenyang China 2010
[6] B Mao L Lin and T Cao ldquoStudy on reducing vibration andnoise of the gear transmissions by using damped ringrdquoMachineDesign and Research vol 21 no 1 pp 47ndash49 2005
[7] Q-Y Wang D-Q Cao and J-B Yang ldquoAxial vibration reduc-tion characteristics of a gear system with a damping ringrdquoJournal of Vibration and Shock vol 32 no 6 pp 190ndash194 2013
[8] J Vance F Zeidan and B Murphy Machinery Vibration andRotordynamics John Wiley amp Sons Inc 2010
[9] C-S Chen S Natsiavas and H D Nelson ldquoCoupled lateral-torsional vibration of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 120 no 4pp 860ndash867 1998
[10] C Chen S Natsiavas and H D Nelson ldquoStability analysis andcomplex dynamics of a gear-pair system supported by a squeezefilm damperrdquo Journal of Vibration and Acoustics vol 119 no 1pp 85ndash88 1997
[11] C-W Chang-Jian ldquoBifurcation and chaos analysis of the poroussqueeze film dampermounted gear-bearing systemrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 798ndash8122012
[12] B Ertas V Cerny J Kim andV Polreich ldquoStabilizing A 46MWmulti-stage utility steam turbine using integral squeeze filmbearing support dampersrdquo in Proceedings of the ASME TurboExpo 2014 Turbine Technical Conference and Exposition (GTrsquo14) Dusseldorf Germany June 2014
[13] O De Santiago and L S Andres ldquoDynamic response of arotor-integral squeeze film damper to couple imbalancesrdquo inProceedings of the ASME Turbo Expo 2000 Power for Land Seaand Air (GT rsquo00) Munich Germany May 2000
[14] S Zhu J Lou Q He and X Weng Vibration Theory andVibration Isolation National Defense Industry Press 2006
[15] O C De Santiago and L A San Andres ldquoImbalance responseand damping force coefficients of a rotor supported on endsealed integral squeeze film dampersrdquo in Proceedings of theASME 1999 International Gas Turbine and Aeroengine Congressand Exhibition (GT rsquo99) Indianapolis IN USA June 1999
[16] O De Santiago L San Andres and J Oliveras ldquoImbalanceresponse of a rotor supported on open-ends integral squeezefilm dampersrdquo Journal of Engineering for Gas Turbines andPower vol 121 no 4 pp 718ndash724 1999
[17] K Ding W Li and X Zhu Gears and Gearbox Fault DiagnosisPractical Technology China Machine Press 2005
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of