齿廓修形对渐开线直齿轮设计传递误差的影响

Influence of tooth profile modification on design transmission error of involute spur gear

基于齿廓修形原理,建立了齿廓修形数学模型,以弹性变形理论和渐开线形成原理为基础,将轮齿简化为变截面悬臂梁,并且考虑齿轮传动过程中单双齿交替啮合区间随齿形变化的规律,建立了齿廓修形前后齿轮设计传递误差数学模型.为改善齿轮系统刚度激励,以减小齿轮传递误差波动和峰值为目标,修形量、修形起始点和修形曲线为设计变量,建立了齿廓修形优化模型,并采用多目标遗传算法NSGA-Ⅱ进行优化求解.对采煤机摇臂齿轮进行齿廓修形优化设计,并采用定量分析法从时域角度分析了修形量、修形起始点和修形曲线对齿轮设计传递误差的影响.结果表明：适当的修形量可减小设计传递误差波动幅值,当修形量为9μm时齿轮传递误差波动幅值最小;修形起始点可影响设计传递误差峰值,当修形起始点位于单齿啮合最高点时齿轮传递误差峰值最小;抛物线修形齿轮较直线修形齿轮设计传递误差波动更为平缓.

Tooth profile modification mathematical model was established on the basis of tooth profile principle.Gear design transmission error mathematical model before and after tooth profile modification were established by simplifying gear as variable cross-section cantilever beam on the basis of elastic deformation theory and involute forming principle,considering the variation with tooth profile of the odd and even teeth alternating meshing region in the process of gear transmission.In order to reduce gear system stiffness excitation,the reduction of gear transmission error fluctuation amplitude and peak value were taken as objectives,and profile modification,profile modification length and profile modification curve were taken as design variable.The tooth profile modification optimal model was established,and multi-objective genetic algorithm NSGA-Ⅱ was adopted to solve the model.The optimal profile modification for the gear transmission system of ranging arm of shearer was performed,and the influence of profile modification,profile modification length and profile modification curve on gear design transmission error were analyzed from the time domain using quantitative analysis method.The results show that right profile modification can reduce design transmission error fluctuation amplitude which reaches the minimum when the profile modification is 9 μm.The profile modification length has influence on design transmission error peak which reaches the minimum when profile modification starting point is the highest point of odd tooth meshing,and design transmission error curve fluctuation of parabolic modification is more flat than linear modification.