基于Mindlin理论的齿轮横向振动模型

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针对圆柱齿轮中心带孔，厚径比已经不在经典的薄板理论范围之内的结构特点，将其分别简化为直径等于分度圆、齿顶圆和齿根圆的中厚圆环板。基于Mindlin理论，推导在自由边界条件下中厚圆环板横向振动频率方程，利用MATLAB软件对频率方程进行求解，并与有限元方法计算结果和实验测试结果对比分析。结果表明：只有将齿轮简化为直径等于分度圆的中厚圆环板时，三者结果才基本相符，从而验证了简化模型的可行性。该结论对超声珩齿振动系统设计具有一定的理论指导意义。 A gear was simplified into three moderately thick annular plates with the outer diameters of reference circle, addendum circle and dedendum circle, respectively, according to the structural characteristics of a cylindrical gear with a hole in its center and its ratio of thickness to radius beyond the scope of the classical thin plate theory. The frequency equations for transverse vibration of a moderately thick annular plate were derived with free boundary conditions based on Mindlin＇s theory and solved computationally with MATLAB. The solutions were in good agreement with those using the finite element method and also with the test results only when the diameter of the gear equal to its reference circle. The conclusion had certain theoretical significance to guide designing a vibration system of ultrasonic gear honing.