齿轮成形磨削砂轮廓形优化研究

摘要

砂轮廓形优化对齿轮成形磨削精度和效率的影响至关重要。从齿轮端面建立了完整齿廓数学模型，其中非渐开线过渡部分采用圆弧曲线，利用无瞬心包络法求解了磨削一个齿槽的完整砂轮廓形，推导了左右固定弦齿间点解析式。调整了砂轮安装角以改变砂轮与工件的左右齿面的接触线形状和位置，使左右更对称；调整了固定弦齿间点在齿面上的位置，使之靠近分度圆，接触线分布集中，发散小。基于线性加权和法建立了多目标优化模型，以磨削效率高、左右接触线对称、单齿接触线长度最短为优化目标，利用 MATLAB 开发优化程序对砂轮廓形进行了优化。通过实例计算验证了调整砂轮安装角和固定点位置对砂轮廓形优化的有效性。%It is crucial that optimization of grinding wheel profile for the accuracy and efficiency of gear form grinding.A integrated mathematical model of tooth profile was established,which adopted circular curve as transition part of non-involute form of gear end-face,meanwhile,grinding wheel pro-file of a cogging was solved by non-instantaneous sectional envelope machining principle and analytic expression of constant intersectional point on chord tooth was derived.Adjusting grinding wheel set-ting angle to alter shape and position of contact line between grinding wheel and gear to make it more symmetrical;changing the position of fixed intersectional point on tooth surface to make sure it was close to pitch circle,thus the contact line was more centralized and low divergence.On the basis of u-sing linear weighted sum method to establish muti-goal optimization module,taking highly grinding efficiency,symmetrical contact line,shortest contact line length of single tooth surface as optimization goal,the grinding wheel profile was optimized depend on programme developed on MATLAB.Finally, the effectiveness of adjusting grinding wheel setting angle and fixed point position was manifested through example's analyses.