弧齿锥齿轮螺旋变性展成法切齿原理与仿真分析

Cutting principle and simulation analysis of spiral bevel gear by spread-out helix modified roll

传统加工方法加工弧齿锥齿轮副会使其接触区呈现对角线接触的不良现象,针对该现象,提出一种新型螺旋锥齿轮加工方法——螺旋变性展成法。为揭示螺旋变性展成法的切齿原理,根据机床、刀具和工件间的运动位置关系,以微分几何和齿轮啮合原理为基础,运用矢量分析法,以齿面中点为计算点建立切齿数学模型,分析推导机床调整参数计算公式;以一对弧齿锥齿轮为例进行了几何参数、刀具参数及机床调整参数的计算,建立弧齿锥齿轮三维虚拟仿真加工模型并进行齿面接触分析;最后,基于以上参数在数控铣齿机上进行切齿试验,齿面接触分析与滚检试验结果说明了螺旋变性展成法消除对角线接触的有效性。

In order to eliminate the poor performance of the teeth contact zone of spiral bevel gear, a new method called spread-out helix modified roll is proposed. To reveal the cutting principle of spread-out helix modified roll, the cutting mathematical model at the calculation point is established, according to the relative position and motion among the machine tool, cutter, and workpiece, and based on the vector analysis as well as the gear engagement theory and the differential geometry.Then, the machine-tool adjustment parameters are deduced. The geometric parameters, cutting-tool parameters and machinetool adjustment parameters of a pair of spiral bevel gear are calculated, the three-dimensional virtual emulational model of spiral bevel gear is established, and the analysis on teeth contact is made. Finally, based on the above parameters, the cutting experiment is performed on the CNC gear milling machine. The results of TCA and rolling tests show the effectiveness of spread-out helix modified roll which can eliminate the poor performance of teeth contact.