非圆锥齿轮球面齿廓数值计算方法

Numerical calculation algorithm for spherical tooth profile of noncircular bevel gear

非圆锥齿轮传动是宽窄行分插机构实现空间插秧轨迹的重要组成部分,而满足不同机型的宽窄行分插机构需要设计不同参数的非圆锥齿轮。针对目前设计不同非圆锥齿轮需建立不同齿廓计算模型的问题,该文开展了基于样条曲线拟合封闭球面曲线的非圆锥齿轮大端齿廓数值计算方法研究,利用三次Nurbs曲线拟合方法建立了球面节曲线的统一表达式;根据齿形法线法和球面三角形性质建立了大端齿廓和齿根过渡曲线的数值计算模型,编写了基于Matlab的非圆锥齿轮大端齿廓计算程序;以一种步行式宽窄行分插机构的传动齿轮为例,当节点数取720时,齿槽齿厚差值可达到0.0037mm,可以满足加工要求;并在ADAMS软件中采用齿间加载接触力的方式得到了与理论计算结果相吻合的齿轮传动比,验证了该齿廓计算方法的正确性,从而实现了非圆锥齿轮的通用化设计,为行星轮系式的宽窄行分插机构、取苗机构、植苗机构等种植机械关键部件实现期望运动轨迹提供技术支持。

It is an important issue for a wide-narrow distance transplanting mechanism with planetary gear trains to obtain the spatial planting trajectory that meets the wide-narrow distance transplanting. A noncircular bevel gear transmission, one kind of spatial non-uniform velocity transmission mechanism could form such a trajectory. What is more, the pitch curve of the non-circular bevel gear is general, and a transplanting mechanism with this kind of bevel gears can achieve more potential spatial planting trajectories for wide-narrow distance planting than those with specific bevel gears such as an elliptical bevel gear or an eccentric-noncircular bevel gear. In order to meet diverse agronomic requirements, a variety of wide-narrow distance transplanting mechanisms and noncircular bevel gears with different parameters and pitch curves are needed. However, due to the lack of a uniform tooth profile calculation method, the designer has to establish different tooth profile calculation models for different pitch curves. A uniform method which could be applied to calculate the tooth profile of the non-circular bevel gear is put forward in this paper. Because of the spherical tooth profile of the non-circular bevel gear and the standard parameters of the big end, the uniform expression of big end pitch curve and the numerical model of big end tooth profile are essential to designing the noncircular bevel gear. In this paper, a cubic Nurbs curve was used to fit the spherical pitch curve of a bevel gear, which can ensure second order continuity of the points on the pitch curve. A smooth, continuous and closed spherical pitch curve could be obtained from several data points of the spherical surface by the proposed method. According to the included angle of two adjacent tangent vectors of the points on the pitch curve, the concavity and convexity of the pitch curve could be determined, and the radius of the big end pitch circle of a maximum bevel gear for enveloping concave pitch curve gear could be calculated. Then, the allowable maximum gear modulus of the concave pitch curve could be determined by calculating the minimum undercutting number of the circular bevel gear. By using the tooth profile normal line method and spherical triangle property, the numerical calculation model of a spherical tooth profile and dedendum transition curve were established. Furthermore, the undercutting phenomenon could be judged by analyzing the concavity and convexity of the tooth profile curve. Finally, the numerical calculation program for the tooth profile was compiled in Matlab, and several noncircular bevel gears for the transplanting mechanism of a walking-type wide-narrow distance transplanter were designed. The transmission ratio obtained by simulation in ADAMS software was highly identical with the one obtained by theoretical calculation, which verified the feasibility of this method.