基于Matlab偏曲轴少齿差行星减速器轮齿啮合刚度计算研究

STUDY ON CALCULATIONS OF MESHING STIFFNESS OF GEAR TEETH OF PLANETARY GEAR REDUCER OF LESS TOOTH DIFFERENCE WITH BIASING CRANKSHAFT BASED ON MATLAB

为了计算偏曲轴少齿差行星减速器内齿轮副不同啮合点刚度问题,建立了该减速器内外轮齿的参数方程、啮合角方程;把轮齿看成变截面悬臂梁,并分别建立了计算不同变形的数学模型,在计算变截面弯曲剪切变形时,采用化微求和的办法,编制了求不同啮合点刚度的Matlab程序,并通过实例及实验进行验证。结果表明,该方法计算准确、快速,为进一步研究该减速器振动及最大承载能力提供重要的理论依据。

To calculate the different meshing points stiffness of the internal gear pairs of planetary gear reducer of less tooth difference with biasing crankshaft, the parameter and engagement angle equation of the internal and external tooth of the reducer is established; the tooth is regarded as a cantilever beam with variable sections, the numerical model used to calculate the different deformation of the tooth is built respectively, and adopts the differential quadrature method when calculating the bending and shear deformations of the variable section beams, the Matlab program to compute the different meshing points stiffness is also compiled, the method is verified with living example and experiment. The results show that this method is accurate and quick, and provide an important theoretical basis for the further study on the vibration and the maximum carrying capacity of the reducer.