Modeling and Optimization Design of Vehicle Powertrain System Considering Effect of Auxiliary Components

doi:10.12068/j.issn.1005-3026.2025.20230293

Abstract

Abstract:

Based on the neural network parameter indentification method and component mode synthesis （CMS）， a modeling approach for the nonlinear powertrain system is proposed to investigate the coupled vibrations of the engine and auxiliary components， and the multi-objective optimization design using genetic algorithms is applied to optimize the connection stiffness and damping. Firstly， a neural network-based model was employed to fit the dynamic model of the powertrain system. According to the experimental modal parameters， the genetic algorithms were applied to identify the connection stiffness and damping of the powertrain system. The results showed that the maximum discrepancies between simulated and experimental modal frequencies and damping ratios were -5.98% and -15.72%， respectively. Subsequently， the CMS is employed to reduce the degrees of freedom of the powertrain system， and the engine-equipment coupling vibration response is evaluated. Finally， a multi-objective optimization design was performed to achieve the optimal vibration performance of the auxiliary components. The maximum peak values displacement of the intercooler and air filter for the optimized model decreased by 34.6% and 4.61%， respectively， compared to the original ones.

Key words: powertrain modeling, auxiliary components, neural network, parameter identification, substructure, multi-objective optimization

CLC Number:

TH 11.1

Yang-jun WU, Zhen-ping LI, Hong-liang YAO, Sheng-dong HAN. Modeling and Optimization Design of Vehicle Powertrain System Considering Effect of Auxiliary Components[J]. Journal of Northeastern University(Natural Science), 2025, 46(4): 43-51.

Figures/Tables 18

Fig.1 Structure of the powertrain system

Fig.2 Modeling of the powertrain system

Fig.3 Reduction method of the powertrain model

Fig.4 Acceleration frequency response function curve

Fig.5 LSTM network structure

Fig.6 Process of the genetic algorithm

Fig.7 Technical implementation route for powertrain modeling

Fig.8 Position of exciting and measuring points

Table 1 Inertial parameters of the powertrain

惯性参数		空气滤清器	中冷器	发动机
质量/kg	m	0.509	1.816	4.820
重心坐标/m	x_c	0.112	0.821	0.193
	y_c	0.054	0.174	-0.195
	z_c	-0.065	-0.029	-0.079
转动惯量kg·m²	J_xo	0.005	0.047	1.609
	J_yo	0.007	0.028	0.917
	J_zo	0.004	0.073	0.179

Fig.9 Supporting position of the air cleaner

Table 2 Identification results of supporting stiffness and damping parameters for each component

支撑位置	x		y		z
支撑位置	阻尼/（N·s·m^-1)	刚度/(N·m^-1)	阻尼/(N·s·m^-1)	刚度/(N·m^-1)	阻尼/(N·s·m^-1)	刚度/(N·m^-1)
弹簧1	6.125	5.62×10⁴	6.125	5.62×10⁴	0.234	4.31×10⁴
弹簧2	5.412	4.51×10⁴	6.013	4.62×10⁴	4.122	0.12×10⁴
弹簧3	7.621	0.32×10⁴	7.943	0.67×10⁴	8.142	4.23×10⁴
弹簧4	7.213	6.48×10⁴	7.213	6.48×10⁴	6.145	4.01×10⁴
弹簧5	4.706	8.20×10⁷	0.079	0.95×10⁸	0.079	0.95×10⁸
弹簧6	0.606	7.32×10⁷	1.402	1.46×10⁸	1.602	8.12×10⁷
弹簧7	0.588	8.36×10⁷	1.080	8.20×10⁷	0.685	0.42×10⁸

Table 3 Modal parameters of simulation and experiment

模态阶数	模态频率			模态阻尼比
模态阶数	实验/Hz	仿真/Hz	误差/%	实验	仿真	误差/%
1	9.098	8.554	-5.98	0.083	0.074	-10.37
2	15.205	14.537	-4.39	0.050	0.044	-11.89
3	21.995	21.000	-4.52	0.034	0.030	-11.77
4	32.907	31.708	-3.64	0.024	0.020	-15.72
5	50.108	48.451	-3.31	0.015	0.013	-1.81

Table 4 Identification of supporting stiffness and damping parameters for the engine

支撑位置	x
支撑位置	$k 1$ /(N·m^-1)	$k 2$ /(N·m^-1)	阻尼/(N·m^-1)
弹簧8	4.23×10⁵	6.72×10⁵	1.3
弹簧9	8.43×10⁵	9.15×10⁵	44.1
弹簧10	4.63×10⁵	8.43×10⁵	1.6
支撑位置	y
支撑位置	$k 1$ /(N·m^-1)	$k 2$ /(N·m^-1)	阻尼/(N·m^-1)
弹簧8	4.23×10⁵	6.72×10⁵	1.3
弹簧9	4.68×10⁵	5.63×10⁵	15.6
弹簧10	8.12×10⁵	1.53×10⁶	40.1
支撑位置	z
支撑位置	$k 1$ /(N·m^-1)	$k 2$ /(N·m^-1)	阻尼/(N·m^-1)
弹簧8	9.12×10⁵	1.43×10⁶	31.3
弹簧9	4.68×10⁵	5.63×10⁵	15.6
弹簧10	4.63×10⁵	8.43×10⁵	1.6

Table 4 Identification of supporting stiffness and damping parameters for the engine

支撑位置	x
支撑位置	$k 1$ /(N·m^-1)	$k 2$ /(N·m^-1)	阻尼/(N·m^-1)
弹簧8	4.23×10⁵	6.72×10⁵	1.3
弹簧9	8.43×10⁵	9.15×10⁵	44.1
弹簧10	4.63×10⁵	8.43×10⁵	1.6
支撑位置	y
支撑位置	$k 1$ /(N·m^-1)	$k 2$ /(N·m^-1)	阻尼/(N·m^-1)
弹簧8	4.23×10⁵	6.72×10⁵	1.3
弹簧9	4.68×10⁵	5.63×10⁵	15.6
弹簧10	8.12×10⁵	1.53×10⁶	40.1
支撑位置	z
支撑位置	$k 1$ /(N·m^-1)	$k 2$ /(N·m^-1)	阻尼/(N·m^-1)
弹簧8	9.12×10⁵	1.43×10⁶	31.3
弹簧9	4.68×10⁵	5.63×10⁵	15.6
弹簧10	4.63×10⁵	8.43×10⁵	1.6

Fig.10 Position of exciting and measuring points

Fig.11 Vibration response curves of the powertrain system

Fig.12 Genetic convergence curves

Table 5 Optimized support stiffness and damping of the auxiliary components

支撑位置	x		y		z
支撑位置	阻尼/(N·s·m^-1)	刚度/(N·m^-1)	阻尼/(N·s·m^-1)	刚度/(N·m^-1)	阻尼/(N·s·m^-1)	刚度/(N·m^-1)
弹簧1	7.810	4.83×10⁴	7.87	4.16×10⁴	4.120	0.65×10⁴
弹簧4	9.160	6.64×10⁴	9.37	7.98×10⁴	7.970	4.32×10⁴
弹簧5	5.960	1.03×10⁸	0.77	0.43×10⁸	0.300	0.47×10⁸
弹簧6	0.614	5.58×10⁷	1.29	1.35×10⁸	1.920	7.35×10⁷
弹簧7	0.653	1.08×10⁸	1.29	1.01×10⁸	0.843	1.79×10⁷

Fig.13 Frequency response curves of the auxiliarycomponnts

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