考虑时变摩擦的直齿轮副啮合刚度计算及其影响因素分析

针对直齿轮副啮合过程存在时变摩擦问题,建立直齿轮副啮合模型,推导齿轮副在啮合点处的相对滑动速度、卷吸速度、滑滚比、综合曲率半径及轮齿接触压力,研究单双齿交替啮合过程中单齿承载变化下的齿面摩擦因数变化规律。基于势能法推导计及时变摩擦的直齿轮副啮合刚度解析式,分析无摩擦力、定摩擦力和时变摩擦力作用下直齿轮副啮合刚度的变化规律,进而研究时变摩擦作用下齿轮模数、齿宽、压力角、粗糙度、输入转矩等参数对直齿轮副时变啮合刚度的影响规律。研究结果表明,时变摩擦因数在单双齿交替啮合区发生突变,在节点处趋于0;摩擦力作用下单齿刚度在啮入阶段将增大,啮出阶段将减小;定摩擦力作用使啮合刚度在节点处发生突变;时变摩擦力作用使啮合刚度在单双齿交替啮合处发生突变,在节点处与无摩擦时变化规律一致;齿轮副啮合刚度随模数、齿宽增大而增大,随压力角增大而减小;啮合刚度变化量随齿面粗糙度增大而增大,随输入转矩增大而减小。

Stiffness Calculation and Influence Factor Analysis of Spur Gear Pair Considering Time-varying Friction

Aiming at the problem of time-varying friction in the meshing process of spur gear pair,the meshing model of spur gear pair is established,and the relative sliding velocity,rolling speed,sliding-rolling ratio,comprehensive radius of curvature and tooth contact pressure of the gear pair at the meshing point are deduced.The variation of the friction coefficient of the tooth surface under the change of single tooth load during the single-to-double tooth alternating meshing process is studied.Based on the potential energy method,the analytical formulas of meshing stiffness of spur gear pair with time-varying friction are deduced,the variation law of meshing stiffness of spur gear pair under non-friction,constant friction and time-varying friction is analyzed, and then the influence of the parameters such as gear modulus,tooth width,pressure angle,roughness and input torque on the time-varying meshing stiffness of spur gear pairs under time-varying friction is studied.The results show that the time-varying friction coefficient changes suddenly in the single-to-double tooth alternating meshing zone,and tend to zero at the pitch point;the effect of friction makes the stiffness of single teeth increase at the approach process,and decreases during the recess process;the constant friction force makes the meshing stiffness change suddenly at the pitch point;the time-varying friction force makes the meshing stiffness change suddenly at the single-to-double tooth alternating meshing zone,and the change law is consistent with the nonfriction situation at the pitch point;the meshing stiffness of gear pair increases with the increase of modulus and tooth width,and decreases with the increase of pressure angle;the variation of meshing stiffness increases with the increase of tooth surface roughness;and decreases with the increase of input torque.