对角修形斜齿轮径向剃齿设计

Grinding plunge shaving cutter for diagonal modified helical gears

摘要:

为减小齿轮振动与噪音,设计对角修形斜齿轮齿面,根据啮合原理推导其径向剃齿刀齿面;根据齿条展成渐开线齿面原理,结合Y7432平面砂轮磨齿机,建立有齿向平移运动的平面砂轮磨齿CNC模型;建立基于CNC机床各轴及砂轮轴向廓形敏感性分析的齿面修正模型,各轴运动用6阶多项式表示,分析0阶及1阶系数变化对齿面误差的影响;通过判断砂轮与剃齿刀齿面的接触状态,确定磨削齿面的误差,以误差平方和最小为目标函数,采用粒子群优化算法,得到机床各轴运动及砂轮轴向廓形参数．结果表明:该算法计算结果稳定,降低了磨削误差;对角修形斜齿轮的径向剃齿刀拓扑修形曲面基本为齿向反鼓形与对角修形曲面叠加;沿齿向方向的压力角、展成运动角、螺旋角参数微调可分别实现一定的对角修形加工;砂轮增加齿向运动构成3轴联动,减小了砂轮半径,可用于磨削大螺旋角、大齿宽对角修形斜齿轮．

Abstract:

An approach based on CNC grinding machine of plunge shaving cutter for diagonal modified helical gear was proposed to reduce grinding errors and improve meshing performance. Firstly, the corresponding plunge shaving cutter surfaces for the diagonal modified helical pinion was established based on gear theory. Secondly, a free-form flank topographic correction method based on Y7432 grinding machine, with flat wheel translated along normal sections of invented rack-cutter, was established according to principle of rack-cutter generating involute pinion. Thirdly, an error correction model based on a sensitivity analysis was determined, each axis of the machine was formulated as a six-degree polynomial and a disturbed polynomial coefficient on the topographic flank errors was developed by estimating whether the wheel contacted with the pinion. Finally, using minimum squared error as the objective function to get the smallest grind errors, the PSO optimization algorithm was introduced to solve equations of the corrections, and the polynomial coefficients were ascertained. The result shows that the methods can effectively reduce the grinding error, and the topologically modified tooth for plunge cutter can be represented by sum of longitudinal and diagonal deviations surface. The slight variations in pressure angle and generating angle and helix angle can attain some specific diagonal modified tooth respectively, besides, the diagonal modified helical gear with big size and helix angle can then be efficiently ground by slightly adjusting three-axis movement with a smaller translating flat wheel.