推杆针轮活齿齿形方程的简化建模与传动角分析
Tooth Profile Simplified Modeling and Transmission Angle Analysis of Push-rods Oscillatory Transmission with Needle Gears
作者：费宇(四川大学 制造科学与工程学院, 四川 成都 610065)；谢超(四川大学 制造科学与工程学院, 四川 成都 610065)；李华(四川大学 制造科学与工程学院, 四川 成都 610065)；黄缤鸿(四川大学 制造科学与工程学院, 四川 成都 610065)；姚进(四川大学 制造科学与工程学院, 四川 成都 610065)
Author：FEI Yu(School of Manufacturing Sci. and Eng., Sichuan Univ., Chengdu 610065, China)；XIE Chao(School of Manufacturing Sci. and Eng., Sichuan Univ., Chengdu 610065, China)；LI Hua(School of Manufacturing Sci. and Eng., Sichuan Univ., Chengdu 610065, China)；HUANG Binghong(School of Manufacturing Sci. and Eng., Sichuan Univ., Chengdu 610065, China)；YAO Jin(School of Manufacturing Sci. and Eng., Sichuan Univ., Chengdu 610065, China)
收稿日期：2018-06-08 年卷（期）页码：2019,51(1):241-247
期刊名称：工程科学与技术
Journal Name：Advanced Engineering Sciences
关键字：推杆针轮活齿传动;齿形简化建模;传动角分析;误差分析
Key words：push-rod oscillatory transmission with needle gears;tooth profile simplified modeling;transmission angle analysis;error analysis
基金项目：四川省科技厅重点研发项目资助（2017GZ0058）
中文摘要
推杆针轮活齿传动具有结构形式简单、加工方便且加工精度易于保证的优点，而推杆活齿齿形方程是齿形分析的基础和保证传动准确性和稳定性的关键因素。不同于传统使用包络方式推导方程和使用直线近似方程曲线，作者提出了一种新的方程推导和简化方法。应用活齿传动过程中的接触条件，推导了活齿的齿形方程。为简化在活齿齿形和啮合特性等研究过程中的数学计算，应用泰勒展式简化了活齿的齿形方程，并利用该方程推导了活齿传动不失真的参数判别式，以指导活齿传动结构的快速设计。在此基础上，利用简化方程推导了传动角的计算公式，分析了激波器偏心距、针轮回转半径等主要设计参数对最大传动角的影响，结果表明，最大传动角与激波器偏心距成正相关，与针轮回转半径成负相关。进一步， 对活齿齿形简化方程进行了误差分析，分析显示其横、纵坐标误差最大不超过±0.06 μm，因此简化方程可以替代准确方程进行活齿传动的研究。利用活齿简化方程曲线对活齿减速器进行建模，仿真得到其传动比平均误差约为0.007%，表明该机构可以实现定传动比传动。研究结果验证了活齿简化方程的实用性，以及采用活齿简化曲线构建活齿减速器的可行性，并为该机构的设计和应用提供了理论依据。
英文摘要
The push-rods oscillatory transmission with needle gears has the advantages of simple structure, convenient manufacturing and high machining precision. For this kind of transmission, the profile equation of movable tooth is the basis for tooth analysis and the key issue to guarantee the precision and stability of transmission. Different from the traditional way, where the profile equation is derived by enveloping and the profile curve is approximated by line, a new method for tooth profile equation derivation and simplification was proposed. The profile equation of movable tooth was deduced by the contact condition in the transmission process. Then the equation was simplified by Taylor expansion to facilitate the calculation in the research of tooth profile and meshing characteristics. Sequentially, to guide the rapid design of the transmission structure, an analytical discriminant to guarantee the transmission undistorted was established by the simplified equation. On these bases, the computational formula of transmission angle was derived and the influence of the main design parameters, such as surge wheel's eccentricity and needle gear's rotational radius, on the maximum transmission angle were analyzed. Analysis showed that the maximum transmission angle is positively correlated with surge wheel's eccentricity, yet negatively with needle gear's rotational radius. Furthermore, the error of simplified equation was analyzed and the result showed that the maximum horizontal and vertical coordinate errors are not exceeding ±0.06 μm. Thus, the accurate tooth profile equation could be replaced by the simplified equation. Finally, the three-dimensional model of the reducer with simplified tooth profile curve was designed and based on it, the fixed speed ratio transmission was verified by simulating. Simulation result showed that the error of speed ratio is about 0.007%. Consequently, the practicability of the simplified equation and the feasibility of oscillatory reducer with simplified movable tooth profile was validated by both theoretical analysis and simulation. The research results could be used as a theoretical basis for structural design and application.
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