一种变比齿条齿廓设计优化方法

An Optimal Method for Designing the Tooth Profile of Variable Ratio Rack

提出一种变比齿条数字设计方法。该方法克服了布尔减运算法不能精确建模的弊端;将变比齿轮齿条副中的渐开线齿轮离散成端截面方向上无限薄的齿轮元的集合,建立了变比齿条齿廓点高度值计算的数学模型;通过布尔减运算建模法确定变比齿条齿廓包络区间及变比齿条各个齿廓点对应的渐开线齿轮转角范围和变比齿条位移范围;采用数值计算方法求解变比齿条齿廓点高度值计算的数学模型,得到变比齿条齿廓点云模型。试制了样件,测试了变比齿轮齿条副的实际传动比,通过理论传动比曲线与实际传动比曲线的对比验证了该方法的有效性。

A digital design method for variable ratio rack was put forward in this paper. This method overcomes the problem of Boolean subtraction operation method that it can＇t model accurately. The mathematical model far calculating the tooth profile point height values of the variable ratio rack was established by considering the involute gear of the variable ratio gear pair as a set of some infinitely thin gear elements. The variable ratio rack envelopment intervals were determined based on Boolean subtraction operation, and the corresponding involute gear angle range and variable ratio rack displacement range of every single tooth profile point were solved out. The established mathematical model was solved by numerical calculation method and the variable ratio rack point cloud model was obtained, Besides, the variable ratio gear pair sample was trial-produced, and the effectiveness of this method was verified through comparation of the theoretical transmission ratio curve and the actual transmission ratio curve.