球轴承-转子系统的接触共振特性及其突跳行为的分岔机理研究

The jump vibrations of ball bearing-rotor systems are typical phenomena of nonlinear vibrations induced by the nonlinearities, and a certain type of military aircraft of our country had been repaired many times due to the bi-stability jump faults coming from its aeroengine bearings. The jump vibrations have effects on the stability of rotor systems, and the corresponding impact action is an important factor of cleavage derivative of the bearings，for which case that the behaviors of jump vibrations are given continued attentions at home and abroad. However, the ball bearing, as a nature nonlinear mechanical piece, contains many nonlinearities such as the Hertzian contact between the rolling elements and raceways, the bearing clearance and time-varying compliances (VC), which leads great difficulties encountered to analyze the dynamical mechanism of the behaviors of jumps accurately. Recently, research indicates that the Hertzian contact had complex behaviors of hysteretic jumps in its contact resonances. This project will investigate the characteristics of the Hertzian contact resonances and their behaviors of hysteretic jumps in a ball bearing-rotor system with forcing and parametric excitations from unbalance and VC respectively. With the aid of the harmonic balance and alternating frequency/time domain (HB-AFT) method and Floquet theory, the branches of periodic solutions of the system and its bifurcation behaviors will be traced, and by theoretical-experimental method the bifurcating mechanism and influencing factors of jump vibrations for contact resonances will be studied, including an analysis of the evolution mechanism of intermittence to chaos, all which will provide theoretical basis on suppressing the jump failures of the system.

球轴承-转子系统的突跳振动是轴承非线性诱发的典型非线性振动行为，我国某型军机就曾因航空发动机轴承带来的双稳态突跳故障多次返厂。突跳振动影响转子系统运行稳定性，且其冲击作用也是轴承裂纹衍生的重要因素，因此球轴承突跳振动问题在国内外得到持续关注。然而，由于球轴承作为本质非线性机械件包含滚珠与滚道的赫兹接触、轴承游隙及时变刚度（VC）等多种非线性，使系统突跳行为动力学机理的精确解析极为困难。近年来，研究显示赫兹接触在接触共振区间具有复杂的滞后突跳响应行为。由此，本项目将对不平衡强迫激励与VC参激联合作用下的球轴承-转子系统的接触共振特性及其突跳行为展开分析。利用谐波平衡-频域/时域转换（HB-AFT）法和Floquet稳定性理论追踪系统的周期解分枝及其分岔行为，理论与实验相结合研究接触共振区间突跳振动的分岔机制及其影响因素，并分析系统的阵发性混沌演化机理，进而为抑制系统突跳故障提供基础理论支撑。

滚动轴承由于其低阻尼、大过载和小体积等特点是航空发动机、铁路货车、舰船发动机等旋转机械的主要支承件。变柔度（Varying Compliance, VC）振动是由滚动体公转引起的一种不可避免的时变刚度参激振动。赫兹接触支承刚度给球轴承及其支承转子系统带来的滞后VC共振现象在相关研究中被大量发现，我国某型军机就曾因航空发动机轴承带来的双稳态突跳故障多次返厂。滞后突跳振动不但影响到转子系统的运行稳定性与安全性，而且其冲击作用也是轴承等系统元件裂纹及疲劳破坏的重要诱导因素。因此，球轴承突跳振动问题在国内外得到持续关注。然而，由于球轴承作为本质非线性机械件包含滚珠与滚道的赫兹接触、轴承游隙及VC参激等多种非线性，使系统突跳行为动力学机理的精确解析极为困难。近年来，研究显示赫兹接触在接触共振区间具有复杂的滞后突跳响应行为。由此，本项目对球轴承-转子系统的VC接触共振特性及其突跳行为展开分析。利用谐波平衡-频域/时域转换（HB-AFT）法和Floquet稳定性理论追踪系统的周期解分枝及其分岔行为，理论与实验相结合研究接触共振区间突跳振动的分岔机制及其影响因素，并分析系统的阵发性混沌演化机理。重要研究结果包括：（1）对球轴承的动态刚度、等效刚度的表征进行了深入分析，阐明了系统动态刚度特性与系统复杂共振行为的内在联系，进一步厘清了系统1：2参激内共振的触发条件，给出一套以添加附加刚度抑制系统周期倍化行为的有效方案。（2）从非线性动力学角度出发，采用嵌入弧长延拓的HB-AFT方法结合Floquet理论，提供了一套阵发性混沌演化的研究方法，并分析了球轴承系统阵发I型、III型混沌振动的内在物理机制。本课题对于滚动轴承转子系统的交变载荷激振特性、故障溯源及减振设计具有重要的基础理论意义和工程价值。