渐开线锥形非圆齿轮的啮合原理与仿真模型

根据渐开线锥形齿轮传动理论结合非圆齿轮齿廓包络原理,以齿条作为齿廓形成的媒介,提出一种基于齿条加工渐开线锥形非圆齿轮的方法,并建立了相应的加工数学模型. 基于该模型,证明了齿条与非圆齿轮纯滚动的运动关系,推导出啮合方程和瞬时接触线方程,以及经过坐标变换后得到渐开线锥形非圆齿轮的参数方程,对比了各种形式的渐开线齿轮齿廓形成特点. 借助数值计算软件对上述方程进行了验证,通过三维造型工具给出了渐开线锥形非圆齿轮的直观图形,从而验证了该方法的正确性和有效性. 

Gearing Principle of Conical Involute Non-Circular Gear and Simulation Model

A concept of conical involute non-circular gear transmission and its processing method is proposed. On the theory of conical involute gear transmission and the enveloping principle of non-circular gear teeth profile, a method for processing conical involute non-circular gear was put forward, in which the rack was used as the medium of tooth profile. The corresponding mathematical processing model was built. Based on this model, the motion relationship between rack and non-circular gear pure rolling was revealed and the meshing equation and instantaneous contact line equation are deduced. Meanwhile, the parametric equation of conical involute non-circular gear, which was obtained after a coordinate transformation, could be deduced. And then, the forming characteristics of various forms of involute gear tooth profile were compared. Above equations are verified with the aid of numerical calculation software, and the intuitive graphics of conical involute non-circular gear were drawn using three-dimensional modeling tool. Thus the above results have verified that the proposed method is correct and effective, which provides a theoretical basis for the conical involute non-circular gear trasmission.