双圆弧谐波传动刚轮插齿刀设计与齿形误差分析

双圆弧刚轮插齿刀几何参数的计算设计及齿形误差分析是谐波传动制造的难点之一.采用运动学法精确建立双圆弧刚轮插齿刀齿形及齿面数学模型;研究了双圆弧刚轮插齿刀顶刃后角对插齿刀可刃磨长度的影响规律;提出了侧刃后角、侧刃前角等几何参数的计算方法,研究了这些参数的影响因素及从齿顶到齿根的变化规律;分析了顶刃前角、顶刃后角对双圆弧刚轮插齿刀齿形误差的影响规律;通过算例给出了插齿刀前后角的设计方法.结果表明:插齿刀可刃磨长度随顶刃后角增大而减小;侧刃后角的大小与该点半径及压力角大小有关,并随顶刃后角增大而增大;侧刃前角随顶刃前角及顶刃后角增大而增大,其中顶刃前角的影响较大;顶刃前角与顶刃后角均对插齿刀齿形误差有较大影响,设计时应在保证齿形精度的情况下,选择较大的顶刃前角和较小的顶刃后角.

Design and tooth profile error analysis of a rigid gear-shaper cutter with double-circular-arc harmonic drive

The calculation and design of geometric parameters of a double-circular-arc gear-shaper cutter and the analysis of its tooth profile error are one of the challenges in harmonic drive manufacturing. In order to study the calculation method of geometric parameters and the distribution of tooth profile errors, a mathematical model of the tooth profile and tooth surface of the double-circular-arc gear-shaper cutter is established by kinematics method. Based on the model, the influence of the back angle of the top edge of double-circular-arc gear-shaper cutter on the grindable length of the gear-shaper cutter is studied; the calculation methods of the geometric parameters, such as the back angle of the side edge and the front angle of the side edge, are put forward, and the influential factors of these parameters and the change law from the top of the tooth to the root of the tooth are studied; the influence of the front angle and the back angle of the top edge on the tooth profile error of the double-circular-arc gear-shaper cutter is analyzed; and the design method of the rake angle of the gear-shaper cutter is given by an example. The conclusions are drawn as follows. 1) The grindable length of the gear-shaper cutter decreases with the increase of the back angle of the top edge. 2) The back angle of the side edge is related to the radius of the point and the pressure angle and increases with the increase of the back angle of the top edge. 3) The front angle of the side edge increases with the increase of the front angle of the top edge and the back angle of the top edge, and the front angle of the top edge has a greater influence on the front angle of the side edge. 4) Both the front angle and the back angle of the top edge have a great influence on the tooth shape error of the gear shaper. In short, when selecting the parameters, a larger front angle and a smaller back angle should be selected under the condition of ensuring the accuracy of tooth profile.