直纹面面齿轮共轭小齿轮的滚齿加工研究

Hobbing of Pinions Conjugate with Ruled Surface Face Gears

针对直纹面面齿轮与圆柱齿轮不满足共轭关系而限制其在小传动比应用场合的情况,提出与直纹面面齿轮共轭的小齿轮及其滚齿加工方法。首先建立了直纹面面齿轮及其共轭小齿轮的齿面方程,获得共轭小齿轮相比圆柱齿轮的齿面偏差形貌;随后推导了阿基米德齿轮滚刀的齿面方程,并根据滚齿加工运动坐标系和啮合原理建立了圆柱齿轮的数学模型;在滚齿加工圆柱齿轮的运动基础上,通过增加滚刀的径向移动和工件的附加转动使滚刀切削刃逼近共轭齿面,附加运动由泰勒多项式表示,通过建立敏感矩阵方程并采用奇异值分解法迭代求解方程获得附加数控运动多项式系数,最后获得数控加工齿面;为评价直纹面面齿轮副的传动性能,进行了齿面承载接触分析,并与传统面齿轮-圆柱齿轮副进行了对比。研究结果表明:相同参数下,直纹面面齿轮副与传统面齿轮副的承载性能基本相同,完全能够代替传统面齿轮副传动;数值算例和仿真加工对该方法的验证表明,其数值算例误差不超过1μm,仿真结果误差不超过6μm,证明了该方法的可行性和准确性。

To address ruled surface face gears’limited application in small transmission ratios resulting from the lack of conjugacy with cylindrical gears,pinions conjugate with ruled surface face gears and outlines a corresponding hobbing method is proposed.Firstly,the equations of ruled surface face gears and the conjugate pinion are established,and the deviation morphology between a conjugate pinion and a cylindrical gear is obtained.Subsequently,the equation of Archimedes worm hob is derived,and a mathematical model of the cylindrical gear is developed according to the motion coordinate systems used in hobbing and meshing principles.Based on the motions of cylindrical gear hobbing,the hob’s cutting edge approximates the conjugate surface through radial movement of the hob and additional rotation of the workpiece,expressed using Taylor polynomials.A sensitivity matrix equation is established,the singular value decomposition method is used to iteratively solve the equation to obtain the polynomial coefficients,and finally,the machining tooth surface is obtained.To evaluate the transmission performance of ruled surface face gear pairs,load tooth contact analysis is conducted,with a comparison made with conventional face gear pairs and cylindrical gear pairs.The research results reveal that with the same parameters,the load performance of the ruled surface face gear pairs aligns closely with that of the conventional face gear pairs,which indicates the potential for the former to fully replace the latter.Finally,the method is validated through numerical examples and simulation processing,with a numerical example error of less than 1μm,and a simulation result error of less than 6μm.This underscores the feasibility and accuracy of this method.