• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2019, Vol. 55 ›› Issue (7): 234-242.doi: 10.3901/JME.2019.07.234

• 制造工艺与装备 • 上一篇    下一篇

基于摆线刀齿轨迹的未变形铣屑厚度分析

窦炜1, 崔岗卫2, 袁胜万2, 何晓聪1   

  1. 1. 昆明理工大学机电工程学院 昆明 650500;
    2. 沈机集团昆明机床股份有限公司 昆明 650203
  • 收稿日期:2018-04-11 修回日期:2018-09-26 出版日期:2019-04-05 发布日期:2019-04-05
  • 通讯作者: 何晓聪(通信作者),男,1955年出生,博士,教授,博士研究生导师。主要研究方向为薄板材料连接、机械动力学和系统可靠性理论。E-mail:xiaocong_he@126.com
  • 作者简介:窦炜,男,1980年出生,博士研究生。主要研究方向为机床动力学和机械可靠性。E-mail:Mech_2010_dou@163.com
  • 基金资助:
    国家科技重大专项资助项目(2016ZX04004002)。

Analysis of Uncut Milling Chip Thickness Based on Trochoidal Tooth Path

DOU Wei1, CUI Gangwei2, YUAN Shengwan2, HE Xiaocong1   

  1. 1. Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500;
    2. Shenji Group Kunming Machine Tool Company Limited, Kunming 650203
  • Received:2018-04-11 Revised:2018-09-26 Online:2019-04-05 Published:2019-04-05

摘要: 利用动态变化的未变形铣屑厚度与铣削力之间的相互作用关系,研究铣削过程的动态特性是铣削过程建模的基本思路。未变形铣屑厚度的值取决于相继切入工件的刀刃在工件上留下的切削痕迹之间的相对位置关系。处于切削状态的刀刃与前一齿尖所经过的摆线运动轨迹相交,以其方位角与前一刀齿过同一交点时的方位角之差为辅助变量,建立满足铣屑形成条件的运动学超越方程。若该辅助变量已知,则可进一步求出铣削迟滞参数及未变形铣屑厚度。基于这一思路,给出两种新的求取铣屑厚度的方法:一种是将原方程转化为解描述辅助变量动态变化的微分方程,采用数值方法求得其数值解;另一种是以辅助变量的线性函数近似原方程中的三角函数,采用近似解析法解出其显式表达式。仿真结果表明:对于当前制造业普遍采用的铣削参数,所提近似解析法可以满足实际应用的精度要求,并且与现有摆线铣屑厚度模型相比数学表达式更为简洁;所提数值法不需要循环迭代求解超越方程,非常适合嵌入到对分析精度和运算效率有较高要求的铣削过程仿真或稳定性预测算法。

关键词: 摆线刀齿轨迹, 近似解析解, 时变迟滞, 数值方法, 未变形切屑厚度, 铣削过程

Abstract: One of the key issues in the modeling of milling processes is to determine the response of the cutting forces to the dynamic variations of the uncut chip thickness. The uncut chip thickness depends on the relative position between the milled surfaces left by the successive cutting teeth of the tool. A cutting tooth intersects the path of its previous tooth, and forms an angle with the previous tooth passing through the same point of intersection. Given the intersection angle, both the variable time delay and the instantaneous uncut chip thickness can be calculated directly. Through the analysis of trochoidal tooth paths and using the intersection angle as an auxiliary variable, a transcendental equation is developed to model of the geometry of chip formation. Then two new approaches are proposed to determine the intersection angle. The first approach converts the transcendental equation into an ordinary differential equation of the intersection angle, then solving it numerically without recursive root-finding algorithms; assuming the intersection angle is infinitesimal, another approach approximates the transcendental equation by replacing the sine function with a liner function, and then solve it analytically. Case studies with different process parameters show that the analytical approach can provide a high accuracy in practical milling operations, with a simpler expression compared with other models. The proposed numerical method is suitable for embedding into the milling process simulation or stability prediction algorithms which are sensitive to accuracy and efficiency.

Key words: approximate analytic solution, milling processes, numeric method, trochoidal tooth path, uncut chip thickness, variable delay

中图分类号: