基于数字法的成形砂轮廓形计算及包络面仿真

doi:10.3901/JME.2018.01.205

机械工程学报 ›› 2018, Vol. 54 ›› Issue (1): 205-213.doi: 10.3901/JME.2018.01.205

基于数字法的成形砂轮廓形计算及包络面仿真

何坤¹, 李国龙¹, 蒋林^1,2, 董鑫¹, 刘鹏祥¹

1. 重庆大学机械传动国家重点实验室重庆 400030;
2. 重庆机床(集团)有限责任公司重庆 400055

收稿日期:2017-01-30 修回日期:2017-04-10 出版日期:2018-01-05 发布日期:2018-01-05
通讯作者: 李国龙(通信作者),男,1968年出生,博士,教授,博士研究生导师。主要研究方向为智能数控技术与系统、精密加工技术与装备、复杂曲面磨削技术。E-mail:glli@cqu.edu.cn
作者简介:何坤,男,1990年出生,博士研究生。主要研究方向为精密磨削技术。E-mail:hekun_cqu@163.com;蒋林,男,1971年出生,博士研究生。主要研究方向为智能机床、磨齿机设计与开发。E-mail:jianglin@chmti.com;董鑫,男,1991年出生,硕士研究生。主要研究方向为数控磨齿机界面设计与开发。E-mail:13896630732@163.com;刘鹏祥,男,1990年出生,硕士研究生。主要研究方向为精密磨削技术。E-mail:jixielpx@163.com
基金资助:
国家科技支撑计划（2014BAF08B02）和国家自然科学基金（51375512）资助项目。

Calculation of Form Grinding Wheel Profile and Simulation of Envelope Surface Based on Digital Method

HE Kun¹, LI Guolong¹, JIANG Lin^1,2, DONG Xin¹, LIU Pengxiang¹

1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030;
2. Chongqing Machine Tool(Group) Co., Ltd., Chongqing 400055

Received:2017-01-30 Revised:2017-04-10 Online:2018-01-05 Published:2018-01-05

摘要/Abstract

摘要： 成形磨齿过程中，砂轮的廓形精度直接影响到最终齿轮的加工精度。针对成形磨削时砂轮廓形精确计算的需求，提出了一种基于点矢量包络的数字法，用于砂轮廓形计算及包络面仿真。将齿轮的端截面廓形离散为一系列点矢量，利用点矢量完整地描述廓形离散点处的几何特征，将曲面的包络转换为点矢量沿齿面螺旋线的运动包络；通过坐标变换及旋转投影，将点矢量包络运动形成的空间点矢量族投影到选取的计算平面上形成点矢量族；建立点矢量逼近算法，求取计算平面上各点矢量族的包络点，所有的包络点通过拟合的方式构成砂轮廓形。利用点矢量在包络过程中的空间映射关系，确定砂轮廓形点对应的空间接触点，所有的接触点构成砂轮与齿轮的接触线；在确定的砂轮廓形及磨削路径前提下，采用点矢量包络法计算不同磨削位置处的接触线，利用所有的接触线完成对砂轮包络面的仿真，并提取包络面的端截面廓形进行误差显化和预测。最后以一种齿轮为例，完成了对成形砂轮廓形的计算和包络面的仿真，并通过标准齿轮磨削试验验证了点矢量包络方法的计算精度，通过齿向修形齿轮磨削实验验证了包络面仿真结果的准确性。

关键词: 包络面, 成形磨, 成形砂轮, 仿真, 廓形计算

Abstract: In the process of forming grinding, the profile accuracy of the grinding wheel directly affects the machining precision of the gear. Aiming at meeting the requirement of accurate calculation of the grinding wheel profile, this paper propose a digital method based on the point-vector envelope to calculate the profile of the wheel and simulate the envelope surface. Firstly, the transverse profile of the gear is divided into a series of point-vectors and the geometrical features of the discrete points are completely described by the point-vector. The envelope of the surface is converted into the motion envelope of the point-vector along the helix. Secondly, the point-vector group formed by the envelope motion of the point-vector is projected onto the selected plane by coordinate transformation and rotation projection. A point-vector approximation algorithm is established to calculate the envelope point of the point-vector group on the calculation plane and the profile of the grinding wheel is formed by fitting all the envelope points. Thirdly, by using the space mapping of the point-vector in the enveloping process, the spatial contact line between the grinding wheel and the gear is determined. The contact lines at different grinding positions are calculated by the point-vector envelope method and the envelope surface of grinding wheel is simulated by all the contact lines, and the transverse profile of the envelope surface is extracted for error manifestation and prediction. Lastly, a kind of gear is taken as an example to complete the calculation of the grinding wheel profile and the simulation of the envelope surface. The accuracy of the point-vector envelope method is verified by the grinding experiment of standard gear, and the accuracy of the simulation results of the envelope surface is verified by the grinding experiment of lead modification gear.

Key words: envelope surface, form grinding, grinding wheel, profile calculation, simulation

中图分类号:

TH161

何坤, 李国龙, 蒋林, 董鑫, 刘鹏祥. 基于数字法的成形砂轮廓形计算及包络面仿真[J]. 机械工程学报, 2018, 54(1): 205-213.

HE Kun, LI Guolong, JIANG Lin, DONG Xin, LIU Pengxiang. Calculation of Form Grinding Wheel Profile and Simulation of Envelope Surface Based on Digital Method[J]. Journal of Mechanical Engineering, 2018, 54(1): 205-213.

参考文献

[1] LITVIN F L,FUENTUS A. Gear geometry and applied theory[M]. 2nd ed. Cambridge University Press,2004.
[2] LITVIN F L. Development of gear technology and theory of gearing[R]. Washington,D.C.:NASA Reference Publication 1406,1997.
[3] FAYDOR L,LITVIN F L,IGNACIO G P,et al. Design, simulation of meshing,and contact stresses for an improved worm gear drive[J]. Mechanism and Machine Theory,2007,42:940-959.
[4] SU X,HOUSER D R. Alternative equation of meshing for worm-gear drives and its application to determining undercutting and reverse engineering[J]. ASME Journal of Mechanical Design,2000,122:207-212.
[5] YOU H Y,YE P J,WANG J S,et al. Design and application of CBN shape grinding wheel for gears[J]. International Journal of Machine Tools and Manufacture,2003,43:1269-1277.
[6] CHIANG C J,FONG Z H. Undercutting and interference for thread form grinding with a tilt angle[J]. Mechanism and Machine Theory,2009,44:2066-2078.
[7] CHIANG C J,FONG Z H. Design of form milling cutters with multiple inserts for screw rotors[J]. Mechanism and Machine Theory,2010,45:1613-1627.
[8] RADZEVICH S P. Design of shaving cutter for plunge shaving a topologically modified involute pinion[J]. Journal of Mechanical Design,2003,125(3):632-639.
[9] RADZEVICH S P. Computation of parameters of a form grinding wheel for grinding of shaving cutter for plunge shaving of topologically modified involute pinion[J]. Journal of Manufacturing Science and Engineering,2005, 127(4):819-828.
[10] RADZEVICH S P. On the accuracy of precision involute hobs:An analytical approach[J]. Journal of Manufacturing Processes,2007,9(2):121-136.
[11] ISHIBASHI A,YOSHINO H. Design and manufacture of gear cutting tools and gears with an arbitrary profile[J]. The Japan Society of Mechanical Engineers,1987,30:1159-1166.
[12] 周玉山,邵明. 粉末冶金齿轮模具成形磨齿砂轮的廓形计算方法[J]. 机械工程学报,2005,41(1):162-165. ZHOU Yushan, SHAO Ming. Form grinding technology for the mold of powder metallurgy gears[J]. ChineseJournal of Mechanical Engineering,2005,41(1):162-165.
[13] WU Y R,FONG Z H,ZHANG Z X. Simulation of a cylindrical form grinding process by the radial-ray shooting (RRS) method[J]. Mechanism and Machine Theory,2010,45(2):261-272.
[14] 李国龙,李先广,刘飞,等. 拓扑修形齿轮附加径向运动成形磨削中的砂轮廓形优化方法[J]. 机械工程学报,2011,47(11):155-162. LI Guolong,LI Xianguang,LIU Fei,et al. Method of profile optimization of a form grinding wheel for grinding with additional radial motion of topologically modified gear[J]. Journal of Mechanical Engineering,2011,47(11):155-162.

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基于数字法的成形砂轮廓形计算及包络面仿真

Calculation of Form Grinding Wheel Profile and Simulation of Envelope Surface Based on Digital Method

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