Ring gears with thin rims are widely used in lightweight applications, such as aircraft, and space facilities. The axial vibration is usually neglected in the analysis of gear vibration. Besides, in the vibration analysis of cylindrical shells, the shells are usually supported or stiffened in the axial direction. However, the ring gears with thin rims are supported by bolts and mesh stiffnesses in the circumferential direction. This paper studied the vibration of ring gears with thin rims supported by distributed bolts and mesh stiffnesses. The ring gears with thin rims are modeled as thin cylindrical shells, and the governing equations are derived based on Hamilton’s principle and Love’s shell theory. The modal functions of the cylindrical shells are represented by beam functions and trigonometric functions of multiple components to satisfy the complex boundary conditions. The governing equations are solved by Galerkin’s method and validated by experimental results. The natural frequencies are calculated, and the vibration modes are presented. The influences of parameters on the natural frequencies and vibration modes are also investigated.

具有薄轮辋的齿圈广泛用于轻型应用，例如飞机和空间设施。在齿轮振动分析中，轴向振动通常被忽略。此外，在圆柱壳的振动分析中，壳通常在轴向上得到支撑或加劲。然而，具有薄轮辋的齿圈由螺栓和圆周方向的啮合刚度支撑。本文研究了由分布式螺栓和啮合刚度支撑的薄轮圈齿圈的振动。具有薄轮辋的齿圈被建模为薄圆柱壳，并且基于汉密尔顿原理和洛夫壳理论推导出控制方程。圆柱壳的模态函数由多分量的梁函数和三角函数表示，以满足复杂的边界条件。控制方程由伽辽金法求解并得到实验结果的验证。计算了固有频率，并给出了振动模式。还研究了参数对固有频率和振动模式的影响。