It is traditionally considered that, due to the Hertzian contact force-deformation relationship, the stiffness of rolling bearings has stiffening characteristics, and gradually researchers find that the supporting characteristics of the system may stiffen, soften, and even coexist from them. The resonant hysteresis affects the stability and safety of the system, and its jumping effect can make an impact on the system. However, the ball bearing contains many nonlinearities such as the Hertzian contact between the rolling elements and raceways, bearing clearance, and time-varying compliances (VC), leading great difficulties to clarify the dynamical mechanism of resonant hysteresis of the system. With the aid of the harmonic balance and alternating frequency/time domain (HB-AFT) method and Floquet theory, this paper will investigate the hysteretic characteristics of the Hertzian contact resonances of a ball bearing system under VC excitations. Moreover, the linearized dynamic bearing stiffness of the system will be presented for assessing the locations of VC resonances, and the nonlinear characteristics of bearing stiffness will also be discussed in depth. Our analysis indicates that the system possesses many types of VC resonances such as the primary, internal, superharmonic, and even combination resonances, and the evolutions of these resonances are presented. Finally, the suppression of resonances and hysteresis of the system will be proposed by adjusting the bearing clearance.

中文翻译：

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球轴承柔度振动变化中的复杂滞回共振的抑制

传统上认为，由于赫兹接触力-变形关系，滚动轴承的刚度具有刚度特性，并且逐渐地研究人员发现系统的支撑特性可能会使其变硬，软化甚至共存。共振磁滞影响系统的稳定性和安全性，其跳跃效应会影响系统。但是，滚珠轴承包含许多非线性，例如滚动体与滚道之间的赫兹接触，轴承游隙和随时间变化的柔度（VC），这给澄清系统共振滞后的动力学机理带来了很大的困难。借助谐波平衡和交变频/时域（HB-AFT）方法以及Floquet理论，本文将研究在VC激励下球轴承系统的赫兹接触共振的滞后特性。此外，将介绍系统的线性动态轴承刚度，以评估VC共振的位置，并且还将深入讨论轴承刚度的非线性特性。我们的分析表明，该系统具有多种类型的VC谐振，例如初级，内部，超谐波甚至组合谐振，并介绍了这些谐振的演化过程。最后，将通过调节轴承游隙来抑制系统的共振和滞后。将介绍系统的线性动态轴承刚度，以评估VC共振的位置，并且还将深入讨论轴承刚度的非线性特性。我们的分析表明，该系统具有多种类型的VC谐振，例如初级，内部，超谐波甚至组合谐振，并介绍了这些谐振的演化过程。最后，将通过调节轴承游隙来抑制系统的共振和滞后。将介绍系统的线性动态轴承刚度，以评估VC共振的位置，还将深入讨论轴承刚度的非线性特性。我们的分析表明，该系统具有许多类型的VC谐振，例如主谐振，内部谐振，超谐波甚至组合谐振，并介绍了这些谐振的演化过程。最后，将通过调节轴承游隙来抑制系统的共振和滞后。并介绍了这些共振的演变。最后，将通过调节轴承游隙来抑制系统的共振和滞后。并介绍了这些共振的演变。最后，将通过调节轴承游隙来抑制系统的共振和滞后。