基于包络法的实时无隙钢球精密传动齿廓顶切研究

Research of Tooth Profile Topcut of Real-time Zero-clearance Steel Ball Precision Transmission based on Envelope Method

实时无隙钢球精密传动实际齿廓是否顶切直接影响其传动性能。基于包络法,对实时无隙钢球精密传动齿廓顶切问题展开研究工作。在基本设计参数给定条件下,分析出外摆线槽和内摆线槽实际齿廓非顶切条件,获取加工外摆线槽和内摆线槽时齿面均不出现顶切的刀具最大进给量(即最大槽深),并通过计算机图形仿真进行验证。根据以上分析结果,推导出钢球和齿面正确啮合时的钢球半径应满足的不等式方程,分析了钢球半径与影响参数之间的关系,结果表明钢球半径随发生圆半径的增大、短幅系数的减小而变大,且发生圆半径愈大、短幅系数愈小,钢球尺寸的选择范围愈广。研究结果可为实时无隙钢球精密传动的设计制造提供一定的理论依据。

Whether practical tooth profile of real - time zero - clearance steel ball precision transmission is topcut directly affects its transmission performance. Based on the envelope method, the tooth profile topcut issue of real - time zero - clearance steel ball precision transmission is indepth study. The non - topcut conditions of the practical tooth profile on epicycloid groove and hypocycloid groove are obtained by analysis under the condi- tionsthat the basic design parameters are given, cutting tool maximum feeding （i. e. maximum groove depth） that all .tooth surfaces do not appear .topcut when machining ~epicyc!oid groove and ~hypocycloid groove .~s obtained. Then, the conclusion is verified by the computer graphic simulation. According to the above analysis results, for ensuring the steel ball and the tooth surface can be properly mesh, the inequality equation that the steel ball radius should be satisfied is derived, the relationship between steel ball radius and parameters is ana- lyzed, the results show that steel ball radius increases with the increase of occurrence circle radius, with decrease of the short amplitude coefficient, and occurrence circle is larger, short amplitude coefficient is smal- ler, the steel ball size range is more widely. The results of research offer a theoretical gist for designing and manufacturing of real - time zero - clearance steel ball precision transmission.