Abstract: Taking the involute spur gear pairs with profile shift as the research object， the mesh stiffness calculation models including nonlinear Hertzian contact stiffness， tooth profile curve， fillet foundation stiffness with structure coupling effect were established based on the potential energy method. Considering the influences of gear profile shifts， the calculation formulas for tooth profile curve， half tooth angle of base circle and half tooth angle of dedendum circle in mesh stiffness calculation were revised. The fillet foundation stiffness models were revised by considering tooth surface frictions. The pressure angle models of gear mesh point were derived by considering geometric eccentricity errors. The effects of profile shifted， tooth surface frictions and geometric eccentricity errors on mesh stiffness were studied. The results show that the center distance， stiffness amplitude and contact ratio of the profile shifted gear pairs have great changes. Owing to the profile shift， the moment when the direction of frictional force changes on a pair of meshing gears no longer occurs within the single tooth meshing interval， thereby affecting the characteristics of the mesh stiffness. Geometric eccentricity increases the peak-to-peak values of the mesh stiffness， and at the same time， sideband frequencies with intervals corresponding to the rotational frequencies appear in the frequency domain of the meshing stiffness. In the presence of eccentricity errors in both the driving and driven gears， a new sideband frequency arises with an interval equal to the difference in rotation frequency. Considering the combined effects of three factors， the mesh stiffness characteristics may be significantly influenced. The research results provide the references for further researches of the dynamics of profile shifted gears. 

Key words:  , profile shifted gear pair, mesh stiffness, tooth surface friction, geometric eccentricity error

摘要： 以含变位的渐开线直齿轮副为研究对象，基于能量法建立了包含非线性赫兹接触刚度、真实的齿廓型线和基体刚度耦合效应的齿轮啮合刚度计算模型。考虑齿轮变位的影响，修正了啮合刚度计算中齿廓型线、基圆半角和齿根圆半角的计算公式；修正了考虑齿面摩擦时的基体耦合刚度模型；推导了考虑几何偏心的齿轮啮合点压力角模型。研究了变位、齿面摩擦和几何偏心对啮合刚度的影响规律。结果表明，变位齿轮副的中心距、啮合刚度幅值、重合度都有着较大变化；由于变位，一对相互啮合的齿轮齿面摩擦力方向改变的时刻不再是发生在单齿啮合区间，进而影响齿轮啮合刚度特征；几何偏心会使啮合刚度峰-峰值增大，同时啮合刚度频域中出现以转频为间隔的边频，当主从动轮都存在偏心时会出现以转频之差为间隔的边频；综合考虑三种因素作用，可显著影响齿轮啮合刚度特性。研究结果为进一步研究变位齿轮动力学提供了参考。

关键词: 变位齿轮副, 啮合刚度, 齿面摩擦, 几何偏心误差