Compensation method for tooth surface measurement error of spiral bevel gear of automotive drive axle

doi:10.3969/j.issn.1674-8484.2025.02.002

Abstract

Abstract:

In order to ensure the safety and energy saving performance of the vehicle, it is crucial to improve the machining quality of spiral bevel gear tooth surface. An Iterative Closest Point (ICP) error compensation method optimized by dual quaternion was proposed for the measurement error of the measured and theoretical tooth surface. The error compensation problem was transformed into the matching of two surfaces. Dual quaternions were used to represent the tooth surface matching model, which helped to obtain the error matrix. The error matrix was linearized and a convex relaxation global optimization algorithm was applied to optimize the real part of the matrix. And then the precision matching of the spiral bevel gear tooth surfaces was achieved. The results show that the error compensation for the concave tooth surface reaches up to 77%. Specifically, the maximum error is reduced from 22.11 μm to 5.64 μm and the average error is reduced from 10.34 μm to 2.38 μm. Compared with the traditional Singular Value Decomposition (SVD) method, Quaternion method and Levenberg-Marquardt (L-M) method, the proposed algorithm has higher accuracy and stability, proving that the proposed compensation method is feasible.

Key words: drive axle, spiral bevel gears, dual quaternions, iterative closest point (ICP) algorithm, global optimization

CLC Number:

U463.2

LIU Yongsheng, TAN Jiamin, WANG Ruifu, HU Panru, GAN Xinbin, CHEN Yixin. Compensation method for tooth surface measurement error of spiral bevel gear of automotive drive axle[J]. Journal of Automotive Safety and Energy, 2025, 16(2): 197-206.

Figures/Tables 15

References 15

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算法名称	最大误差/ μm		平均误差/ μm
算法名称	粗配准前	粗配准后	粗配准前	粗配准后
SVD分解法	22.11	5.91	10.34	3.01
四元数法		6.35		3.20
L-M法		8.72		3.54
本文算法		5.87		2.46

算法名称	最大误差/ μm		平均误差/ μm
算法名称	粗配准前	粗配准后	粗配准前	粗配准后
SVD分解法	22.11	5.91	10.34	3.01
四元数法		6.35		3.20
L-M法		8.72		3.54
本文算法		5.87		2.46

算法	权重/ %	误差补偿率 P_g / %	E_max / μm		F_min/ μm		10次独立运算时间均值/ s
算法	权重/ %	误差补偿率 P_g / %	精配准前	精配准后	精配准前	精配准后	10次独立运算时间均值/ s
SVD法	40	65.26	7.97	7.47	4.36	3.59	1.14
	70	73.88	5.90	5.67	3.01	2.71	1.28
	90	73.07	5.97	5.41	3.12	2.78	1.31
四元数法	40	65.26	7.93	7.49	4.41	3.59	1.19
	70	73.87	6.35	5.79	3.20	2.70	1.30
	90	73.05	6.37	5.45	3.15	2.79	1.43
L-M法	40	59.70	16.78	14.75	4.83	4.17	1.04
	70	73.86	8.72	6.38	3.54	2.70	1.23
	90	73.72	6.23	4.92	3.69	2.72	1.34
本文算法	40	66.77	9.18	8.37	3.87	3.43	1.27
	70	76.98	5.87	5.64	2.46	2.38	1.39
	90	76.87	5.56	5.29	2.54	2.39	1.51

算法	权重/ %	误差补偿率 P_g / %	E_max / μm		F_min/ μm		10次独立运算时间均值/ s
算法	权重/ %	误差补偿率 P_g / %	精配准前	精配准后	精配准前	精配准后	10次独立运算时间均值/ s
SVD法	40	65.26	7.97	7.47	4.36	3.59	1.14
	70	73.88	5.90	5.67	3.01	2.71	1.28
	90	73.07	5.97	5.41	3.12	2.78	1.31
四元数法	40	65.26	7.93	7.49	4.41	3.59	1.19
	70	73.87	6.35	5.79	3.20	2.70	1.30
	90	73.05	6.37	5.45	3.15	2.79	1.43
L-M法	40	59.70	16.78	14.75	4.83	4.17	1.04
	70	73.86	8.72	6.38	3.54	2.70	1.23
	90	73.72	6.23	4.92	3.69	2.72	1.34
本文算法	40	66.77	9.18	8.37	3.87	3.43	1.27
	70	76.98	5.87	5.64	2.46	2.38	1.39
	90	76.87	5.56	5.29	2.54	2.39	1.51

算法名称	$ $\bar{E}$ $ / μm	s²_E / 10^-5
SVD法	2.708	0.258
四元数法	2.785	0.262
L-M法	2.702	3.36
本文算法	2.392	0.147