斜齿轮啮合刚度改进算法及其影响因素分析

Study on an Improved Algorithm for Helical Gear Meshing Stiffness and Its Influencing Factors

在势能法的基础上,提出了一种斜齿轮啮合刚度修正算法。该方法考虑了齿轮真实加工时产生的齿根过渡曲线,齿根过渡曲线是刀具展成运动时齿顶尖角所形成的轨迹线,且齿根过渡曲线与渐开线的交点为渐开线的起始点。在刚度计算时,齿根到渐开线起始点用齿根过渡曲线方程来计算,渐开线起始点到齿顶用渐开线方程来计算,运用该方法计算的啮合刚度与实际更加接近。通过与有限元法的对比,验证了该修正算法的准确性,提升了斜齿轮啮合刚度的计算精度。基于该方法,分析了渐开线形状、啮合位置以及重合度对斜齿轮啮合刚度以及传递误差的影响。结果表明,当压力角增大时,渐开线曲率半径会变大,从而提高了齿轮的端面刚度;同时,端面重合度会先增大后减小,在端面刚度与端面重合度的综合影响下,平均啮合刚度与端面重合度变化趋势相同;当啮合位置更靠近节点时,啮合刚度会提高;增加重合度会使平均刚度增加,并使传递误差峰峰值趋势整体下降;但当重合度接近0.5的奇数倍时,传递误差峰峰值会出现极大值。

Based on the potential energy method,an algorithm for modifying the meshing stiffness of helical gears is proposed.This method considers the real machining of the tooth root transition curve,which is a trajectory line formed by the tip angle of the tooth when the tool rolls into motion,and the starting point of the involute is the intersection of the tooth root transition curve and the involute.When calculating the stiffness,the tooth root transition curve equation from the root of the tooth to the starting point of the involute is used for the calculation,and the involute equation from the starting point of the involute to the top of the tooth is used in the calculation.The meshing stiffness calculated by this method is closer to the reality.Compared with the finite element method,the accuracy of the modified algorithm is verified and the calculation accuracy of the helical gear meshing stiffness is improved.Based on this method,the influence of involute shape,meshing position and contact ratio on the meshing stiffness and transmission error of helical gears is analyzed.The research results show that when the pressure angle increases,the radius of curvature of involute will increase.Thus the transverse stiffness of gears is improved.At the same time,the transverse contact ratio will firstly increase and then decrease.Under the influence of transverse stiffness and transverse contact ratio,the variation trend of average meshing stiffness is the same as that of transverse contact ratio;when the meshing position is closer to the node,the meshing stiffness will increase;an increased total contact ratio will make the average stiffness increase,and the transmission error(TE)decrease as a whole.However,when the contact ratio is close to the odd multiple of 0.5,the TE peak-to-peak value will reach a maximum value.