汽车驱动桥螺旋锥齿轮齿面测量误差补偿方法

doi:10.3969/j.issn.1674-8484.2025.02.002

汽车安全与节能学报 ›› 2025, Vol. 16 ›› Issue (2): 197-206.DOI: 10.3969/j.issn.1674-8484.2025.02.002

汽车驱动桥螺旋锥齿轮齿面测量误差补偿方法

刘永生¹^,²(), 谭佳敏¹, 王瑞富¹, 户盼茹², 甘鑫斌¹, 陈一馨¹^,^*()

1.长安大学道路施工技术与装备教育部重点实验室，西安 710064，中国
2.中航光电科技股份有限公司，洛阳 471003，中国

收稿日期:2024-05-28 修回日期:2024-10-28 出版日期:2025-04-30 发布日期:2025-04-22
通讯作者: * 陈一馨，副教授。E-mail：chenyx@chd.edu.cn。
作者简介:刘永生（1985—），男（汉），山东，副教授。E-mail：lysh@chd.edu.cn。
基金资助:
陕西省自然科学基金项目(2022JM-295);陕西省自然科学基金项目(2022JQ-576)

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

LIU Yongsheng¹^,²(), TAN Jiamin¹, WANG Ruifu¹, HU Panru², GAN Xinbin¹, CHEN Yixin¹^,^*()

1. Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an 710064, China
2. AVIC JONHON Optronic Technology Co., LTD., Luoyang 471003, China.

Received:2024-05-28 Revised:2024-10-28 Online:2025-04-30 Published:2025-04-22

摘要/Abstract

摘要：

提升汽车驱动桥螺旋锥齿轮齿面加工质量对整车的安全与节能性能有重要意义，该文针对汽车驱动桥螺旋锥齿轮实测和理论齿面存在的测量误差，提出了一种基于对偶四元数优化的迭代最近点（ICP）齿面测量误差补偿方法。将误差补偿问题转化为两曲面的配准问题，利用对偶四元数对齿面配准模型进行表示并得出误差矩阵，将误差矩阵线性化并使用凸松弛的全局优化算法对其实部进行优化，实现螺旋锥齿轮齿面的精确配准。结果表明：螺旋锥齿轮凹齿面的误差补偿率最高达77%，最大误差由补偿前的22.11 μm降至5.64 μm，平均误差由补偿前的10.34 μm降至2.38 μm，该算法与传统奇异值分解法（SVD）、四元数法和Levenberg-Marquardt法（L-M）相比有更高的求解精度和稳定性，证明所提出的补偿方法具有可行性。

关键词: 驱动桥, 螺旋锥齿轮, 对偶四元数, 迭代最近点算法（ICP）, 全局优化

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

中图分类号:

U463.2

刘永生, 谭佳敏, 王瑞富, 户盼茹, 甘鑫斌, 陈一馨. 汽车驱动桥螺旋锥齿轮齿面测量误差补偿方法[J]. 汽车安全与节能学报, 2025, 16(2): 197-206.

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.

图/表 15

参考文献 15

[1]	常镭民, 姚俊. 面向螺旋锥齿轮铣削的齿面几何精度协同优化[J]. 组合机床与自动化加工技术, 2023(6): 158-164.
	CHANG Leimin, YAO Jun. Collaborative optimization of tooth surface geometric accuracy for spiral bevel gear milling[J]. Mod Mach Tool Autom Manuf Tech, 2023(6): 158-164. (in Chinese)
[2]	刘金, 李伟, 刘春立, 等. 基于载荷谱的主减速器耐久性分析与预测[J]. 汽车技术, 2019(10): 19-22. doi: 10.19620/j.cnki.1000-3703.20190883
	LIU Jin, LI Wei, LIU Chunli, et al. Durability analysis and fatigue life prediction of final drive based on load spectrum[J]. Autom Tech, 2019(10): 19-22. (in Chinese)
[3]	黄志超, 赵乙光, 胡义华, 等. 某驱动桥主减速器的振动特性分析[J]. 汽车安全与节能学报, 2021, 12(3): 298-304.
	HUANG Zhichao, ZHAO Yiguang, HU Yihua, et al. Vibration characteristics analysis on driving-axle main-reducer[J]. J Autom Safe Energ, 2021, 12(3): 298-304. (in Chinese)
[4]	ZHOU Lihua, FANG Suping, LIU Yongsheng, et al. A method for determining the actual coordinate system of spiral bevel gears by the measured positions of eight tooth surfaces[J]. Meas Sci Tech, 2024, 35: No 095005.
[5]	韩连福. 齿轮测量中心若干关键技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2015.
	HAN Lianfu. Research on several key technologies of gear measurement center[D]. Harbin: Harbin Institute of Technology, 2015. (in Chinese)
[6]	邢元, 张建勋, 张连洪, 等. 螺旋锥齿轮精密数控加工误差补偿策略[J]. 中国机械工程, 2014, 25(18): 2427-2431, 438.
	XING Yuan, ZHANG Jianxun, ZHANG Lianhong, et al. Error compensation strategy for precision CNC machining of spiral bevel gears[J]. China Mech Engi, 2014, 25(18): 2427-2431, 2438. (in Chinese)
[7]	宋碧芸, 唐进元, 等. 减小螺旋锥齿轮齿面加工误差的参数修正方法[J]. 西安交通大学学报, 2022, 56(2): 101-109.
	SONG Biyun, TANG Jinyuan, et al. A parameter correction method for reducing tooth surface machining errors of spiral bevel gears[J]. J. Xi'an Jiaotong Univ, 2022, 56(2): 101-109. (in Chinese)
[8]	刘翔宇, 王健, 王效盖, 等. 基于3DSIFT特征点的改进ICP点云配准算法[J]. 应用激光, 2023, 43(11): 153-160.
	LIU Xiangyu, WANG Jian, WANG Xiaogai, et al. An improved ICP point cloud registration algorithm based on 3DSIFT feature points[J]. Laser Tech, 2023, 43(11): 153-160. (in Chinese)
[9]	LIU Yongsheng, CHEN Yixin, FANG Suping. A compen- sation method for the eccentricity and inclination errors of spiral bevel gear based on improved ICP algorithm[J]. Advan Mech Engi, 2021, 13(3): 569-694.
[10]	ZHOU Lihua, FANG Suping, LIU Yongsheng, et al. An alignment angle error compensation method of spiral bevel gear tooth surface measurement based on tooth surface matching[J]. Meas Sci Tech, 2021, 32(10): No 105020.
[11]	XIE He, WANG Yaonan, ZHANG Hui, et al. Iterative fine point-set matching of a free-form surface based on the point-to-sphere distance[J]. IEEE-Asme T Mech, 2022, 27(6): 5668-5678.
[12]	孟德安, 舒强, 王建平, 等. 基于SVD-UKF的车用锂离子动力电池传感器故障诊断研究[J]. 汽车工程学报, 2022, 12(4): 528-537.
	MENG De'an, SHU Qiang, WANG Jianping, et al. Research on fault diagnosis of lithium-ion power battery sensors for vehicles based on SVD-UKF[J]. J Autom Engi, 2022, 12(4): 528-537. (in Chinese)
[13]	刘军, 聂斐, 蔡骏宇, 等. 基于安卓的汽车状态测量及预测系统的研究[J]. 汽车技术, 2015(2): 29-33, 38.
	LIU Jun, NIE Fei, CAI Junyu, et al. Research on measurement & prediction system for vehicle motion state based on Android[J]. Autom Tech, 2015(2): 29-33, 38. (in Chinese)
[14]	王龙, 闵华松. 基于LMI优化的对偶四元数手眼标定算法[J]. 机床与液压, 2021, 49(21): 8-14 doi: 10.3969/j.issn.1001-3881.2021.21.002
	WANG Long, MIN Huasong. Dual quaternion hand-eye calibration algorithm based on LMI optimization[J]. Mach Tool Hydra, 2021, 49(21): 8-14. (in Chinese)
[15]	Henrion D, Lasserre J-B, GloptiPoly J. 3 moments optimization and semidefinite programming[J]. Lofberg Optim Methods Softw, 2009, 24(4-5): 761-779.

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

汽车驱动桥螺旋锥齿轮齿面测量误差补偿方法

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

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 15

参考文献 15

相关文章 3

编辑推荐

Metrics

本文评价

期刊信息

在线期刊

作者中心

审稿中心

联系我们

[1]	黄志超, 赵乙光, 胡义华, 柳明. 某驱动桥主减速器的振动特性分析[J]. 汽车安全与节能学报, 2021, 12(3): 298-304.
[2]	宋正超，章斯亮. 基于改进EGO 算法的汽车40% 偏置碰撞优化设计[J]. JASE, 2017, 08(03): 246-251.
[3]	叶海燕, 周驰, 范子杰. 轴向预紧力对深沟球轴承刚度影响的有限元方法[J]. 汽车安全与节能学报, 2016, 07(02): 188-195.