Background

This paper proposes an analytical method to study the nonlinear phenomena of a simple dual-rotor system in the case of primary resonances.

Purpose

According to the assumed mode method (AMM), the dynamic equations of the system with four degrees of freedom (4DOF) are established by considering the nonlinearities of the inter-shaft bearing as a nonlinear spring. The 4DOF dynamic equations in real coordinate are transferred into 2DOF dynamic equations in complex coordinate because of the symmetry of the system in two directions.

Methods

Then the amplitude-frequency response equations for both primary resonances are obtained by the multiple scales method and the numerical verification shows that the simplified method of the dynamic equation is correct. Moreover, the primary resonances affected by the typical parameters such as the linear stiffness and the nonlinear stiffness of the inter-shaft bearing, and the rotation speed ratio are discussed in detail afterwards.

Conclusions

The results show that the system will show the jump phenomenon and resonance hysteresis phenomenon when the linear stiffness is rather small and the nonlinear stiffness is rather large. The linear stiffness will suppress these nonlinear phenomena while the nonlinear stiffness will promote them. The results obtained in this paper will contribute to the mechanism analysis of the nonlinear phenomena in a dual-rotor system, which is beyond the reach of the numerical method.

中文翻译：

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一次共振时双转子系统非线性现象的解析分析

背景

本文提出了一种分析方法，用于研究在一次共振情况下简单双转子系统的非线性现象。

目的

根据假定模式法（AMM），通过将轴间轴承的非线性视为非线性弹簧，建立了具有四个自由度（4DOF）的系统动力学方程。由于系统在两个方向上的对称性，实坐标中的4DOF动力学方程被转换为复坐标中的2DOF动力学方程。

方法

然后通过多尺度方法获得了两个主共振的幅频响应方程，数值验证表明简化的动力学方程是正确的。此外，随后将详细讨论受轴间轴承的线性刚度和非线性刚度以及转速比等典型参数影响的一次共振。

结论

结果表明，当线性刚度较小而非线性刚度较大时，系统将表现出跳跃现象和共振滞后现象。线性刚度将抑制这些非线性现象，而非线性刚度将促进它们。本文的结果将有助于双转子系统中非线性现象的机理分析，这是数值方法无法实现的。