非圆齿轮齿条机构及其数学模型  

A New Type of Non-circular Gear Rack Mechanism and its Mathematical Model

作　　者：黄宗星 张志瀚[1] 郑方焱[1] 刘有源[1] 陈定方[1] 

机构地区：[1]武汉理工大学智能制造与控制研究所,湖北武汉430063

出　　处：《机械传动》2014年第10期138-142,共5页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51175395);教育部博士点基金(20090143110005)

摘　　要：在非圆齿轮传动中,按照齿轮齿条传动的原理,可得到一种非圆齿轮齿条机构,此时,齿条的节曲线不再是直线,而是平面曲线,利用该机构仅需一级传动即可在改变速度的同时改变运动形式,以满足特殊的运动要求或提高装置的动力学性能。从基本的运动关系出发,推导了机构中齿轮以及齿条的节曲线方程,并根据啮合原理和坐标变换关系,得到了齿廓的包络方程。最后以实例的方式,完成了该机构的几何设计和ADAMS虚拟接触仿真,通过与理论曲线的对比,证明这种机构设计的合理性以及其数学模型的正确性。A new non- circular gear rack mechanism is designed according to the principle of gear rack transmission in non- circular gear transmission. The pitch curve of the rack is no longer a straight line,but a plane curve. With the new gear,only a level- 1 transmission can change the speed of the gear to satisfy special motional requirements,as well as the pattern of motion to enhance the dynamics performance of the device. Based on the basic motion relationship and the pitch curve equation of both the gear and rack of the mechanism are deduced. The envelope equations of tooth profile are also acquired based on the meshing principle and the coordinate transformation relationship. Finally,by an example,the geometric design and the ADAMS of contact simulation of the mechanism are accomplished. Through the comparison between the model and the theoretical curve,the feasibility of the device on design and the correctness of the mathematical model is verified.

关 键 词：非圆齿轮 节曲线 齿廓 数学模型 

分 类 号：TH132.41[机械工程—机械制造及自动化]