Responses of the bearing system are usually predicted or tested, to analyze its nonlinear dynamic characteristics. However, responses predicted from the bearing model constructed by Hertz contact theory usually show differences with their tested counterparts, denoting the improper setting of the nonlinear contact parameters. It is compulsory to reduce such differences and obtain a precise bearing model using nonlinear model updating techniques. In this paper, a novel nonlinear model updating framework is proposed following the Multi-Harmonic Balance Method (MHBM) and the analytical sensitivity analysis, for updating of the rotor-bearing system using the nonlinear responses in the frequency domain. With the derivation of bearing response sensitivities to the nonlinear contact parameters, increments of the nonlinear parameters can be ascertained by the sensitivity inverse and updating of the nonlinear bearing model can be implemented in an iterative way, until a precise bearing model with the response differences reduced to minima is obtained. Firstly, a novel MHBM model is derived for the bearing system, which is fully described by matrix operations and used to further deduce the analytical sensitivity formulations of the bearing responses to the design parameters. Afterwards, the bearing responses and sensitivities in the frequency domain are predicted by the continuation strategy. Finally, model updating is conducted for the bearing system using the traditional inverse-sensitivity framework. Two cases are used to demonstrate the feasibility of the method. The first case is to update bearing parameters of contact stiffness, clearance and eccentricity of a 2-DOF bearing system in order to match the predicted bearing responses with the measured ones in strong nonlinearity with the multivalued phenomenon. The next is to update the Hertz contact parameters of the left and right bearings, together with the disc eccentricity, of a Finite Element (FE) rotor-bearing system. These results show the validity and superiority of the proposed method.

中文翻译：

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通过多谐波平衡法和解析灵敏度推导对转子轴承系统进行非线性模型更新

通常对轴承系统的响应进行预测或测试，以分析其非线性动态特性。然而，根据赫兹接触理论构建的轴承模型预测的响应通常与测试的对应模型存在差异，这表明非线性接触参数设置不当。必须使用非线性模型更新技术来减少这种差异并获得精确的轴承模型。在本文中，根据多谐波平衡法（MHBM）和分析灵敏度分析，提出了一种新颖的非线性模型更新框架，用于使用频域中的非线性响应来更新转子轴承系统。通过推导轴承对非线性接触参数的响应灵敏度，通过灵敏度倒数可以确定非线性参数的增量，并以迭代的方式更新非线性轴承模型，直到得到响应差异减小的精确轴承模型。获得最小值。首先，为轴承系统推导了一个新颖的 MHBM 模型，该模型通过矩阵运算进行了充分描述，并用于进一步推导轴承对设计参数响应的解析灵敏度公式。然后，通过连续策略预测频域中的轴承响应和灵敏度。最后，利用传统的逆敏感性框架对轴承系统进行模型更新。通过两个案例验证了该方法的可行性。第一种情况是更新 2-DOF 轴承系统的接触刚度、间隙和偏心率等轴承参数，以便将预测的轴承响应与具有多值现象的强非线性中的测量响应相匹配。接下来是更新有限元 (FE) 转子轴承系统的左右轴承的赫兹接触参数以及圆盘偏心距。这些结果表明了该方法的有效性和优越性。