Journal of Jilin University(Engineering and Technology Edition) ›› 2025, Vol. 55 ›› Issue (2): 444-455.doi: 10.13229/j.cnki.jdxbgxb.20230347

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Parameter design method of multiple dynamic vibration absorbers for suppressing multi-frequency resonance of automotive powertrain

Jun-long QU(),Wen-ku SHI,Sheng-yi XUAN(),Zhi-yong CHEN   

  1. State Key Laboratory of Automotive Simulation and Control，Jilin University，Changchun 130022，China
  • Received:2023-04-12 Online:2025-02-01 Published:2025-04-16
  • Contact: Sheng-yi XUAN E-mail:qujl21@mails.jlu.edu.cn;xuanshengyi@jlu.edu.cn

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Abstract:

A parameter design method of multiple parallel dynamic vibration absorbers is proposed in order to suppress the powertrain system torsional resonance that exists in various gears of automotive. First， a four degrees of freedom powertrain model is presented， and the expression of the frequency response functions of the vibration system are derived based on the equivalent system with n parallel dynamic vibration absorbers attached. Then， the Nondominated Sorting Genetic Algorithm II is adopted to optimize the frequency ratios and damping ratios of the four parallel dynamic vibration absorbers in order to minimize the angular displacement and acceleration of the vibration system under three different gear ratio conditions. The Technique for Order Preference by Similarity to an Ideal Solution combined with the Entropy Weight Method is utilized to sort the Pareto solutions. Finally， the proposed optimization method is validated effective by comparing with three other traditional methods， and the time and frequency domain simulations are also implemented for the validation. The proposed method can provide references for the optimal parameter design of the dynamic vibration absorber when the eigenvalue of the target system is variable.

Key words: vehicle engineering, automotive powertrain system, torsional vibration, dynamic vibration absorber, multi-objective optimization, multi-frequency vibration damping

CLC Number: 

  • U461.1

Fig.1

Test data of torsional vibration"

Fig.2

Tested resonant modal shape of drivetrain"

Fig.3

4-DOF drivetrain model"

Table 1

Powertrain parameters of each gear"

参数挡位
4挡5挡6挡
J1/（kg·m2）0.7330.7330.733
J2/（kg·m2）0.0400.0630.094
J3/（kg·m2）0.3490.6281.006
J4/（kg·m2）13.96225.10840.231
k1/（Nm·rad）3.44×1033.44×1033.44×103
k2/（Nm·rad）1.07×1031.92×1033.08×103
k3/（Nm·rad）5.56×1031.0×1041.60×104
c1/［Nm·（s·rad-1）］0.90.90.9
c2/［Nm·（s·rad-1）］0.5010.91.442
c3/［Nm·（s·rad-1）］0.0060.010.016

Table 2

Fourth order natural frequency of drivetrain"

项目挡位
4挡5挡6挡
试验测试/Hz54.3351.9344.20
仿真计算/Hz54.4147.6243.20
误差/%+0.15-8.29-2.26

Fig.4

Modal shape of drivetrain at 6th gear"

Fig.5

Equivalent modal system equipped with multiple dynamic vibration absorbers"

Fig.6

Flowchart of multi-object optimization"

Fig.7

Calculation method of EWM-TOPSIS"

Table 3

Parameters of equivalent system"

挡位

等效惯量

/（kg·m2）

等效刚度

/（Nm·rad-1）

等效阻尼

/［Nm·（s·rad-1）］

6挡0.100 457 401.22.634 7
5挡0.066 325 936.91.982 2
4挡0.041 674 871.61.509 1

Fig.8

Parallel coordinate graph for Pareto solution"

Table 4

Decision schemes based on EWM-TOPSIS"

参数

方案1

（Ci =0.720 7）

方案2

（Ci =0.718 6）

方案3

（Ci =0.712 1）

定调比α1

0.710 0

0.816 6

0.950 5

1.264 3

0.691 9

0.819 0

0.944 9

1.260 5

0.679 1

0.935 8

0.824 3

1.264 3

α2
α3
α4
阻尼比ζ1

0.150 3

0.152 8

0.196 8

0.280 9

0.150 6

0.152 8

0.196 5

0.280 4

0.148 6

0.194 9

0.153 0

0.287 1

ζ2
ζ3
ζ4

max［He6（λ）］/10-4

rad·（Nm）-1

3.679 23.696 33.723 4

max［He5（λ）］/10-4

rad·（Nm）-1

3.811 73.849 43.913 7

max［He4（λ）］/10-4

rad·（Nm）-1

4.087 93.935 73.866 9

max［Ha6（λ）］/

rad·s-2·（Nm）-1

28.191 128.433 628.907 1

max［Ha5（λ）］/

rad·s-2·（Nm）-1

36.411 536.646 937.351 4

max［Ha4（λ）］/

rad·s-2·（Nm）-1

54.221 354.503 754.382 9

Fig.9

Comparison of different design methods"

Fig.10

Model for validation"

Fig.11

Transient torque of engine"

Fig.12

Relative speed fluctuation between the clutch"

Fig.13

Displacement-frequency response and Acceleration-frequency response"

Fig.14

Time domain response of drivetrain"

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