公切线式双圆弧齿廓谐波齿轮传动设计

Design of Double-Circular-Arc and Common Tangent Tooth Profile of Harmonic Drive

谐波传动轮齿齿廓对装置啮合性能具有显著影响.为提高谐波传动的啮合性能,采用公切线式双圆弧齿廓作为柔轮齿廓,基于改进运动学理论计算双圆弧齿廓谐波传动共轭区域、共轭齿廓,并采用最小二乘拟合方法对理论共轭齿廓进行圆弧拟合;利用MATLAB对谐波传动侧隙、重合度、装配变形、运动轨迹等进行仿真分析.研究结果表明:所设计的双圆弧谐波传动轮齿啮合连续、啮合点不断改变,且存在'双共轭'现象,理论啮合弧长为109.3mm,重合度达到69.03,啮合性能显著优于传统渐开线齿廓谐波传动,并且优选径向变形量系数是消除谐波传动啮合干涉的重要方式之一.

The tooth profile has significant effect on the engagement performance of harmonic drive （HD）. In order to improve the engagement quality of HD, double-circular-arc and common tangent tooth profile （DCTP） as the tooth profile of flexspline （FS） were used, the conjugate existent domain （CED） and the conjugate tooth profile were established in Modified Kinematic Method, and the Least-squares fit- ting approach was adopted to fit it. The backlash, contact ratio, assembly state and relative movement trail were calculated to analyze the meshing performance of HD with a double-circular-arc and common tangent tooth profile. The results have shown that the tooth profile of the FS and the circular spline （CS） used with the DCTP remain continuous engagement, and the engagement point is changed continuously. Moreover, the double-engagement phenomenon is found, the theory conjugate arc length is 109.3mm, and the contact ratio reaches 69.03; compared with the harmonic drive with traditional involute tooth profile, the high engagement performance of harmonic drive can be obtained with the double-circular-arc and common tangent tooth profile. What＇s more, preferably selecting the coefficient of radial displacement is an important way to eliminate the interference of HD.