减小螺旋锥齿轮齿面加工误差的参数修正方法

宋碧芸; 唐进元; 容铠彬; 丁撼

doi:10.7652/xjtuxb202202011

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减小螺旋锥齿轮齿面加工误差的参数修正方法

更新时间：2025-05-08

- 减小螺旋锥齿轮齿面加工误差的参数修正方法
- A Machine-Settings Compensation Method for Reducing Machining Error of Spiral Bevel Gear Tooth Flank
- 西安交通大学学报 2022年56卷第2期页码：101-109
- 作者机构：
  
  中南大学高性能复杂制造国家重点实验室,长沙,410083
- 作者简介：
- 基金信息：
  
  : 2021-06-21。作者简介: 宋碧芸(1997—),女,硕士生;丁撼(通信作者),男,副教授。基金项目: 湖南省自然科学基金资助项目(2020JJ4115)
- DOI：10.7652/xjtuxb202202011
  中图分类号： TH161;TH132.416
- 网络首发：2022-02-10，
  
  纸质出版：2022
- 稿件说明：
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宋碧芸, 唐进元, 容铠彬, 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.

A Machine-Settings Compensation Method for Reducing Machining Error of Spiral Bevel Gear Tooth Flank[J]. 2022, 56(2): 101-109.
宋碧芸, 唐进元, 容铠彬, 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. DOI： 10.7652/xjtuxb202202011.

A Machine-Settings Compensation Method for Reducing Machining Error of Spiral Bevel Gear Tooth Flank[J]. 2022, 56(2): 101-109. DOI： 10.7652/xjtuxb202202011.

摘要

针对螺旋锥齿轮加工过程中因无法避免误差而导致齿面加工精度难以保证的问题

提出螺旋锥齿轮加工误差控制模型及加工参数修正方法。首先

基于实际加工中的刀具与工件相对位置与相对运动关系

依据坐标齐次变换与啮合原理

确定加工参数与加工曲面之间的函数关系

建立螺旋锥齿轮精确齿面模型; 然后

计算实际加工齿面与理论齿面的法向距离

从而建立由加工参数驱动的齿面几何误差控制模型; 接着

对加工参数进行敏感性分析

选取敏感性较高的加工参数作为误差补偿模型优化变量

以提高优化效率; 最后

将齿面误差最小化问题转化为最小二乘法问题

基于改进的L-M算法进行求解

得到加工参数补偿量

以此对加工参数进行修正达到减小齿面加工误差的目的。采用一对由双重螺旋法磨削加工得到的螺旋锥齿轮副作为应用实例

对该方法进行实际加工验证

结果表明:加工参数调整后

螺旋锥齿轮齿面加工误差降低了65%以上

实际测量的齿面绝对误差均不超过0.005 mm

能够满足工程实际需求

证明该方法能够有效提升齿面加工精度。该方法可为螺旋锥齿轮乃至其他复杂曲面零件加工提供一种加工误差补偿思路。

Abstract

A machining error control model and a machine-settings compensation method of spiral bevel gears are proposed to solve the problem that it is difficult to ensure the machining accuracy of tooth flank due to unavoidable errors in the process of spiral bevel gears. Firstly

based on the relative position and motion relationship between tool and workpiece in actual machining

the functional relationship between the machine-settings and tooth flank is determined according to the coordinate homogeneous transformation and meshing principle and an accurate tooth flank model of spiral bevel gear is established. Then

the normal distance between the actual tooth flank and theoretical tooth flank is calculated to establish a geometric error control model driven by the machine-settings. Next

the sensitivity of the machine-settings is analyzed

so that the machine-settings with high sensitivity are selected as optimization variables of the error compensation model to improve the optimization efficiency. Finally

the tooth flank error minimization problem is transformed into a least square problem

which is solved based on the improved L-M algorithm to revise the machine-settings and to reduce the machining error of tooth flank. A pair of spiral bevel gears ground by duplex helical method is used as an example to verify this method. The results show that after the compensation of the machine-settings

the machining error of spiral bevel gear tooth flank is reduced by more than 65%. The measurement error of tooth flank is no more than 0.005 mm

which can meet the actual needs of engineering. It is proved that this method can effectively improve the machining accuracy of tooth flank. And it can provide an idea of machining error compensation for spiral bevel gears and other complex curved surface parts.

关键词

Keywords

references

曾韬. 螺旋锥齿轮设计与加工 [M]. 哈尔滨: 哈尔滨工业大学出版社, 1989: 47-52.

栗世豪, 张俊, 唐宇阳, 等. 零件加工误差与机床几何误差映射关系建模 [J]. 西安交通大学学报, 2021, 55(10): 50-59.

LI Shihao, ZHANG Jun, TANG Yuyang, et al. Modeling of mapping relationship between machining error and geometric error of machine tool [J]. Journal of Xi'an Jiaotong University, 2021, 55(10): 50-59.

余文利, 邓小雷, 王胜, 等. 基于指数积螺旋理论和雅可比矩阵的五轴机床几何误差补偿 [J/OL].(2021-08-09)[2021-08-10]. http: ∥kns. cnki.net/kcms/detail/11.5946.TP.20210809.1134.00 6.html.

LITVIN F L, FUENTES A. Gear geometry and applied theory [M]. 2nd ed. New York, USA: Cambridge University Press, 2004: 627-699.

SHIH Y P, FONG Z H, LIN G C Y. Mathematical model for a universal face hobbing hypoid gear generator [J]. Journal of Mechanical Design, 2007, 129(1): 38-47.

GABICCINI M, BRACCI A, GUIGGIANI M. Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments [J]. Journal of Mechanical Design, 2010, 132(4): 041010.

蒋进科, 方宗德, 刘钊. Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法 [J]. 西安交通大学学报, 2019, 53(6): 44-53.

JIANG Jinke, FANG Zongde, LIU Zhao. Design of multi-objective tooth optimization for hypoid gear with ease-off topological modification [J]. Journal of Xi'an Jiaotong University, 2019, 53(6): 44-53.

李丽霞, 李培军, 刘新状. 机床调整误差对弧齿锥齿轮大轮齿面形状影响规律的研究 [J]. 机械传动, 2006, 30(4): 13-15.

LI Lixia, LI Peijun, LIU Xinzhuang. Research on the influence of the gear tooth surface shape of spiral bevel gear by adjustment error of machine tool [J]. Journal of Mechanical Transmission, 2006, 30(4): 13-15.

王小椿, 王军, 姜虹, 等. 螺旋锥齿轮的齿面测量及机床加工参数修正 [J]. 机械工程学报, 2003, 39(8): 125-128.

WANG Xiaochun, WANG Jun, JIANG Hong, et al. Tooth surface measurement and machine-settings correction of spiral bevel gear [J]. Journal of Mechanical Engineering, 2003, 39(8): 125-128.

唐进元, 邢彬. 基于三坐标测量机的螺旋锥齿轮加工参数反调修正 [J]. 北京工业大学学报, 2010, 36(11): 1451-1456.

TANG Jinyuan, XING Bin. Machine-settings correction of spiral bevel gear based on coordinate measuring machine [J]. Journal of Beijing University of Technology, 2010, 36(11): 1451-1456.

唐进元, 李友元, 周超, 等. 螺旋锥齿轮数控磨齿机机床空间误差与机床调整参数的关系 [J]. 机械工程学报, 2009, 45(4): 148-154.

TANG Jinyuan, LI Youyuan, ZHOU Chao, et al. Relation between CNC bevel gear generator spatial errors and machine setting errors [J]. Journal of Mechanical Engineering, 2009, 45(4): 148-154.

DING Han, TANG Jinyuan, ZHONG Jue, et al. A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears [J]. Journal of Manufacturing Systems, 2016, 41: 228-238.

ARTONI A, GABICCINI M, GUIGGIANI M. Nonlinear identification of machine settings for flank form modifications in hypoid gears [J]. Journal of Mechanical Design, 2008, 130(11): 112602.

彭山东, 丁撼, 唐进元. 改进的6σ设计的螺旋锥齿轮加工参数反调修正方法 [J]. 西安交通大学学报, 2019, 53(6): 35-43.

PENG Shandong, DING Han, TANG Jinyuan. Corrected calculation of machine settings for spiral bevel and gears using an improved 6σ method [J]. Journal of Xi'an Jiaotong University, 2019, 53(6): 35-43.

DING Han, TANG Jinyuan, ZHONG Jue. Accurate nonlinear modeling and computing of grinding machine settings modification considering spatial geometric errors for hypoid gears [J]. Mechanism and Machine Theory, 2016, 99: 155-175.

DING Han, WAN Guoxin, ZHOU Yuansheng, et al. Nonlinearity analysis based algorithm for indentifying machine settings in the tooth flank topography correction for hypoid gears [J]. Mechanism and Machine Theory, 2017, 113: 1-21.

DING Han, TANG Jinyuan, SHAO Wen, et al. Opti-mal modification of tooth flank form error considering measurement and compensation of cutter geometric errors for spiral bevel and hypoid gears [J]. Mechanism and Machine Theory, 2017, 118: 14-31.

SHAO Wen, DING Han, TANG Jinyuan. Data-driven operation and compensation approaches to tooth flank form error measurement for spiral bevel and hypoid gears [J]. Measurement, 2018, 122: 347-357.

李杰, 谢福贵, 刘辛军, 等. 五轴数控机床空间定位精度改善方法研究现状 [J]. 机械工程学报, 2017, 53(7): 113-128.

LI Jie, XIE Fugui, LIU Xinjun, et al. Analysis on the research status of volumetric positioning accuracy improvement methods for five-axis NC machine tools [J]. Journal of Mechanical Engineering, 2017, 53(7): 113-128.

WU Shunxing, YAN Hongzhi, WANG Zhiyong, et al. Tooth surface error correction of hypoid gears machined by duplex helical method [J]. Journal of Central South University, 2021, 28(5): 1402-1411.

唐进元, 聂金安, 王智泉. 螺旋锥齿轮HFT法加工的反调修正方法 [J]. 中南大学学报(自然科学版), 2012, 43(6): 2142-2149.

TANG Jinyuan, NIE Jinan, WANG Zhiquan. Reverse correction of spiral bevel gear HFT method [J]. Journal of Central South University(Science and Technology), 2012, 43(6): 2142-2149.

RONG Kaibin, DING Han, KONG Xiannian, et al. Digital twin modeling for loaded contact pattern-based grinding of spiral bevel gears [J]. Advanced Engineering Informatics, 2021, 49: 101305.

范金燕, 袁亚湘. 非线性方程组数值方法 [M]. 北京: 科学出版社, 2018: 21-51, 81-96.

YAMASHITA N, FUKUSHIMA M. On the rate of convergence of the levenberg-marquardt method [J]. Computing Supplementum, 2001, 15: 239-249.

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