考虑磨损的直齿轮啮合刚度计算与分析

基于能量法和Archard磨损模型,提出了一种考虑磨损的齿轮啮合刚度数值计算方法。根据展成法原理,建立了精确的齿廓曲线方程。利用能量法计算齿轮单齿啮合刚度,并通过分段1阶傅里叶级数拟合获得齿轮总啮合刚度。以Archard磨损模型为基础,计算得到齿面法向磨损量与啮合点处压力角的关系。计算分析了不同磨损量对齿轮啮合刚度的影响。结果表明,磨损量在齿根、齿顶处较大,在节点处的理论磨损量为0 mm,随着压力角的逐渐增加,磨损量先减小后增大;齿面非均匀磨损会降低齿轮啮合刚度,随着磨损量的逐渐增加,啮合刚度逐渐减小。该方法为考虑磨损的齿轮系统动力学建模提供了理论基础。

Calculation and Analysis of Spur Gear Mesh Stiffness with Considering Wear

A numerical method is proposed to calculate the mesh stiffness of spur gear with considering wear based on the potential energy method and Archard wear equation.A precise profile equation is constructed by generating method principle.Mesh stiffness for a pair of spur gears is calculated by energy method,and the piecewise Fourier serious expansion is employed to fit the total mesh stiffness.The relationship between the normal wear volume and the pressure angle at the meshing point is calculated by adopting the Archard wear equation.And the influence of wear volume on meshing stiffness is analyzed.The numerical results revealed that the wear volume at the root and top of tooth is larger than that at other meshing points,and the volume of the wear is zero at the pitch point.With the increase of the pressure angle,the wear volume decreases first and then increases.Uneven wear of the tooth surface reduced the meshing stiffness of the gear,and the meshing stiffness decreases with the increase of the wear volume.This method provides a theoretical basis for the dynamics modeling of gear system with tooth surface wear.