PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Factors Analysis of Gear Sound by Using Numerical Simulation
Chengfeng Pu1; Takafumi Takeda2; Toru Hama3; Takeshi Toi4
1 , 2, 3

Graduate School of Science and Engineering, Chuo University, Japan
4

Department of Precision Mechanics, Chuo University, JapanABSTRACT
As an approach to identiﬁcation of a factor that contributes to gear sound, in the quasi - staticloading condition of low speed operation, estimation of gear transmission error of spur gear wasinvestigated from combination of vibration measurement and numerical simulation. Furthermore,build a numerical simulation approach to analyze the prediction and contribution of vibration andsound under high speed operation conditions.
Keywords: Dynamic Mesh Force, Transmission Error, Acoustic Power

1. INTRODUCTION
The dynamic characteristics of gear system have great influence for the vibro-acoustic phenomenaof gear systems. Therefore, capturing all relevant factors influence, such as for transmission error,
gear mesh stiffness, mesh dynamic force, component and system flexibility. It is significant to study
the vibro-acoustic phenomena of gear system.
The gear whine noise is one of main vibro-acoustic phenomena of gear system due to gear meshing,
it is caused by meshing force transmitted to the housing via the bearing supporting the gear shaft andis generated by the vibration of the housing.
In this paper, modeling the gear system into an excitation Source-Transfer-Receiver. First, ameasurement and simulation approach to estimated transmission error and calculate the mesh dynamicforce. The combination of vibration measurement and numerical simulation and estimated the geartransmission error in the quasi-static loading condition of low speed operation. In addition, using thesimulation model calculate each component contribution for mesh dynamic force and acoustic
radiation power.

2. ESTIMATION OF MESH TRANSMISSION ERROR
The transmission error is caused by factors such as micro geometry, assembly error, and bendingor twisting of the shaft due to the torque of the operating load. Separately from the resonance due tothe vibration mode of the gear system, the frequency response function in the low frequency range ismeasured to capture the vibration caused by the mesh transmission error. Finally, estimatetransmission error from correlation analysis of experimental and analytical vibration results.
2.1 Vibration Measurement
The main shaft of the gear system is put into rotation by an electric motor with a speed controller
connected in series through a flexible coupling, the output shaft is braked by a gear head motor with,
fix the shaft by mounting the flange type bearing unit on the shaft fixing bracket. For lubrication,
apply grease to the tooth surface before each test. As a quasi-static low-speed operating condition, a1chengfeng_pu@camal.mech.chuo-u.ac.jp
takafumi_takeda@camal.mech.chuo-u.ac.jp
3
toru_hama@camal.mech.chuo-u.ac.jp
4
toi@mech.chuo-u.ac.jp25196

PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

load condition with a rotational speed of 30 rpm and a torque of 30 Nm is placed on the main shaft.
Three-axis accelerometer used for vibration measurement; it was positioned at the bracket of the gearsystem.
The Figure 1 below illustrates the gear system and position of accelerometer.
Single phase motor

BracketDriven gear

Gear head motor

XY

BrackeCoupling

Driving gear

Three-axis accelerometer

ZFigure 1 – Measurement Gear System and Position of Accelerometer

Acceleration [m/s^2]

8.00E-03
X direction
Y direction
Z direction

6.00E-03

4.00E-03

2.00E-03

0.00E+00
11325
37Frequency [Hz]49

Figure 2 – Translational Acceleration on the Bracket
Figure 2 shows the acceleration data of measurement of a gear system under low-speed operating
condition, approx. 30 rpm with a corresponding gear mesh frequency of 13 Hz. From the significant
peak value of acceleration with a period of 13 Hz, the gear system was excited periodically at 13 Hz
because of transmission errors.
2.2

Build Simulation Model
The full integrated gear system model is generated, search as gear macro geometry, bearing, gear
blanks and bracket in full FE in this simulation model. Table1 and Table2 lists the different parameters
used to generate the gear pair. Then, the gear geometry computation allows to create in accordancewith the ISO 21771 standard. Figure 3 displays the 3D simulation model modeled measurement gearsystem.
Table 1 – Gear Specification
Parameter

Pinion

Wheel

Number of Tooth

2848Module(mm)2.5Pressure Angle (°)

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PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Table 2 – Gear Specification
Parameter

PinionWheel

Face Width(mm)25Center Distance(mm)97.5

Tip Diameter(mm)

75

125

Root Diameter(mm)63.75

113.75Figure 3 – Simulation Gear System

2.3 Correlation between Simulation and Experiment
Figure 4 shows the comparison acceleration data of bracket with measurement and simulation of agear system under low-speed operating condition. As a result, the vibration values from the 1 to 4
order of meshing due to the transmission error of the simulation is in almost agreement with themeasurement value. Therefore, it is assumed that the simulation model can represent the dynamic
characteristics of gear system.
1.E-02

Acceleration [m/s^2]

Measurement
Simulation
8.E-03

4.E-030.E+00
12

Order

34

Figure 4 – Translational Acceleration of Measurement and Simulation

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PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

3. CONTRIBUTION ANALYSIS BY SIMULATION
The gear whine noise is affected by mesh dynamic force and structure of gear system etc. To reducenoise level is to lower level of mesh force and system vibration. Therefore, require contribution
analysis of mesh dynamic force and acoustic power that capturing which structure modes efficient toit. Two methods are used to calculate contribution. The one is modal superposition structural repose
analysis calculate component compliance and find which structure mode contribute mesh dynamicforce. The other is use the ISO/TS 7849 calculate acoustic power and acoustic power contribution.
3.1 Contribution Analysis for Mesh Dynamic Force
The aim is to solve the equations of motion of the gear systemM𝑢̈ +Ku=f(1)

f is the dynamic mesh force, in the line of action; u is an n-dimensional, time dependent vector,
representing the displacements of the system; M is the n×n mass matrix for the full system is the n×n;
K stiffness matrix for the full system.
Dynamic mesh force
f= D× δ(2)D is the dynamic mesh stiffness, in the line of action; δ is the static transmission error.
Dynamic mesh stiffness
D=1/(Cp+Cw)(3)

Cp,Cw is the compliance of pinion and wheel sides respectively.
When torque and rotation excite input shaft through bearing, bracket and gear, the mesh dynamic force
at the line of action was same as Figure 5. There were 2 peaks in Fig 5. Those peaks had higher
probability occurring pinion and wheel side compliance.

Dynamic Mesh Force [KN/μm]

1.E+00530Hz

1.E-01

1.E-02

1.E-03

1.E-041200 1,607
1600 2000
2400 2,799
2800 3,202
3200 3,6043600 4000
11 400398 800
799 1,203
2,001 2,401
Frequency [Hz]Figure 5 – Dynamic Mesh force of Gear system
Figure 6 shows the compliance amplitude and phase, acceleration data of measurement of a gear system, thevalue of pinion side compliance is close to value of pinion side compliance at 530 Hz and 1100 Hz,

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PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

furthermore, it could be confirmed that dynamic mesh force became a peak at 530 Hz and 1100 Hz due tothe phase difference.

0Pinion side compliance
Wheel side compliance

1.E+00Phase [°]

Compliance [μm/N]

Figure6 – Gear mesh force and compliance
1.E+01
1.E-01
1.E-02530Hz

1.E-03
1.E-04
1.E-05

11-100-150-200

400
2000
4000
399 799 1,2021,6042,0012,4042,8033,2023,602

Pinion side compliance
Wheel side compliance

-50

1400

Frequency [Hz]

2000

4000

Frequency [Hz]Figure 6 – Gear Mesh Compliance
Figure 7 showed Modal Compliance Factor for dynamic mesh force, modes were separated pinion side modes
and wheel side modes. The results showed that 6th wheel side mode and 9th pinion side mode was more

Modal Compliance Factor [μm/N]

effective to mesh dynamic force at 530 Hz.
6.E-04

4.E+00

6th Wheel side modes
351Hz
9th Pinion side modes
961Hz

2.E+000.E+0001530

Modes number

Figure 7 – Modal Compliance Factor
Figure 8 showed the torsional mode of 6th wheel side modes and 9th pinion side mode effect to dynamic meshforce.

6th Wheel side modes
351 HzFigure 8 – Component Mode Shape5200

9th Wheel side modes
961 HzPROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

3.2 Contribution Analysis for Acoustic PowerThe acoustic power contribution analysis is focused on the effect frequency finding. This method
is to find which structure modes is correlated with acoustic power level. Therefore, it is useful to findspecific structure modes.
Figure 9 showed the total acoustic power and each component acoustic power; the results showed the acoustic
power at 530 Hz is due to the vibration by dynamic mesh force. The acoustic power of input shaft affected
the total acoustic power at 270 Hz, and the acoustic power of output bracket affected the total acoustic power
at 1620 Hz.

Acoustic Power [dB]

1.E+028.E+01

1620Hz

530Hz
270Hz

6.E+01

Total acoustic power
Acoustic power: Input shaft
Acoustic power: Output shaft
Acoustic power: Pinion gear blank
Acoustic power: Wheel gear blank
Acoustic power: Bracket on input shaft right side
Acoustic power: Bracket on input shaft left side
Acoustic power: Bracket on output shaft right side
Acoustic power: Bracket on output shaft left side

4.E+01

2.E+01
1.E+011005001500

2900

Frequency [Hz]Figure 9 – Acoustic Power
Figure 10 showed the system coupled modal participation factor analysis results, 3 rd modes andModal Participation Factor

19th modes are influence the peak of acoustic power at 270 Hz and 1620 Hz.
8.E-0419th modes 1618Hz

3rd modes 260Hz

0.E+00-1.E-0301530

Modes number

Figure 10 – Modal Pacification Factor
Figure 11 showed the 3rd modes is bending mode of input shaft and 19th modes is bending modes of wheel
side.

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PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

19th modes 1618Hz

3rd modes 260Hz

Figure 11 – Coupling Mode Shape

4. Estimation of Noise Reduction Potential

Dynamic Mesh Force [KN/μm]

Two methods can use to reduce the gear whine noise. The one is using the micro geometry
optimization and reduce the amplitude value of transmission error. Other is optimized the structure
based on the results of the contribution analysis in the previous section that is tuning the structuremodes and reduce the mesh dynamic force and modes contribution for acoustic power.
In this section, examine the possibility of tuning the structure modes and reduce the mesh dynamicforce, finally evaluate the total acoustic power and effectiveness of simulation approach.
Necessary to provide a tuning approach for increase the compliance of meshing point of either
pinion or wheel side for mesh dynamic force reduction. Based on compliance value of simulation,build simulation model that increase the wheel side stiffness and reduce the pinion side stiffness.
1.E+00530Hz

1.E-011130Hz

Before modification
After modification

1.E-02
1.E-03
1.E-04

1
1400
546

1200
2000
970
1313
1715
Frequency [Hz]

2800
2430

Figure 12 – Comparison of Dynamic Mesh Force Before and After Modification
Figure 12 showed the comparison of values of dynamic mesh force before and after modification,
as a result, able to reduce the targeted 530 Hz peak. However, the peak value of mesh dynamic force
is shift to lower frequency with increase in low frequency domain and 1130 Hz due to by changing
the stiffness of the pinion and wheel side models, the natural frequency of system model is changed.
Acoustic Power [dB]

1.E+02530Hz

8.E+011130Hz

Before modification
After modification

6.E+01
4.E+01
2.E+0111273400545

1200
20002,1772400
817 1,089
1,361 1,633 1,905
2,449
Frequency [Hz]Figure 13 – Comparison of Total Acoustic Power Before and After Modification

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PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Figure 13 showed the comparison of values of total acoustic power before and after modification,
as a result, able to reduce the acoustic power at 530 Hz peak.

5. CONCLUTION
The combination measurement and numerical simulation in of external component vibration ofgear system seems to be a promising approach to significantly identify transmission error in gearsystem. Further, to identify affective mode for reduce gear whine noise was used modal participation
factor analysis and acoustic power contribution analysis. In numerical simulation approach, able tomodify stiffness of the component of gear system and tuning modes to reduces the gear whine noiseof the specific frequency domain. accommodate numerical simulation approach to the actual gearsystem is in progress.

REFERENCES
1. Owen J. Harris, Paul P. Langlois and G.A. Cooper. Noise Reduction in an EV Hub Drive Using a Full
Test and Simulation Methodology. UK: Gear Technology May 2016. p. 44-53.
2. Houser, D.R. et al. Determining the Source of Gear Whine Noise. Gear Solutions, February 2004.
3. Toshiya Nagumo, Shigeki Matsumura and Haruo Houjoh. Estimation of loaded static transmission errorof helical gears by vibration measurement under operating load conditions. JSME Japan 201682,(844)，
16-000429.

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