螺旋锥齿轮机床五轴联动数学模型创成算法  

Mathematical model of kinematics transformation for five-axis linkage CNC hypoid generator

作　　者：唐进元[1] 聂金安[1] 王智泉[1] 

机构地区：[1]中南大学机电工程学院,现代复杂装备设计与极端制造教育部重点实验室,湖南长沙410083

出　　处：《中南大学学报（自然科学版）》2011年第10期3033-3039,共7页Journal of Central South University:Science and Technology

基　　金：国家重点基础研究发展规划(“973”计划)项目(2005CB724100);国家自然科学基金资助项目(50875263)

摘　　要：研究螺旋锥齿轮机床五轴联动数学模型创成新算法;通过空间运动等效转换,得到准双曲面齿轮加工由机械型机床向五轴联动机床转换的解析解公式;用麦克劳林级数拟合机床各轴的非线性运动方程,推导出螺旋锥齿轮制造最复杂的工艺方法即HFT(Hypoid format tilt)加工方法下螺旋锥齿轮机床五轴联动数学模型。由五轴联动运动方程在机床坐标系下虚拟制造准双曲面齿轮齿面与GLEASON公司的理论齿面进行比较,通过对比验证五轴联动数学模型的准确性与精度。研究结果表明:本文提出的螺旋锥齿轮机床五轴联动数学模型创成新算法原理正确,转换精度高。Based on the spiral bevel gear spatial kinematics equivalent transform theory,in order to redisplay the traditional machine manufacturing process in free-form machine,a new algorithm resolving the analytical solution formulas of five-axle linkage transformation equations was developed.Nonlinear items of five-axle linkage equations were approximately represented with Maclaurin series.A virtual gear,which is made by the simulation software with the conducted five-axle linkag equations,was compared to the theoretical discrete points computed by GLEASON corporation,with a set of HFT parameters to verify the transformation precision.The results show that the proposed new method for developing spiral bevel gear machine tool five-axis equations is correct,simple in calculation,and has high precision.

关 键 词：螺旋锥齿轮 五轴联动数控机床 运动学等效转换原理 麦克劳林级数 

分 类 号：TH132[机械工程—机械制造及自动化]