An improved transfer-matrix method on steady-state response analysis of the complex rotor-bearing system
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ORIGINAL PAPER
An improved transfer-matrix method on steady-state response analysis of the complex rotor-bearing system Zhong Luo
. Zifang Bian . Yunpeng Zhu
. Haopeng Liu
Received: 20 May 2018 / Accepted: 9 September 2020 Springer Nature B.V. 2020
Abstract This paper proposes an improved transfermatrix method (TMM) for investigating the steadystate response of complex rotor-bearing systems. The internal damping of the shafts is considered to enhance the accuracy of the method. A transfer matrix of ball bearings with clearance and Hertzian contact is established. In addition, the incremental harmonic balance method is combined with the TMM to obtain the steady-state response of the rotor systems and simplify the investigation processes. The simulation results verify the superiority of this method in programming, reducing the order of system matrix,
Z. Luo (&) H. Liu School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, People’s Republic of China e-mail: [email protected] Z. Luo H. Liu Key Laboratory of Vibration and Control of AeroPropulsion System Ministry of Education, Northeastern University, Shenyang 110819, China Z. Bian College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China Y. Zhu (&) Department of Automatic Control and System Engineering, University of Sheffield, Sheffield S13JD, UK e-mail: [email protected]
and determining stability. Thus, this method is efficient in investigating the nonlinear dynamic characteristics of large-scale rotor-bearing systems. Keywords Transfer-matrix method Complex rotor-bearing system IHB Steady-state response
1 Introduction Ball bearings are common mechanical components, which are used in rotating machines, such as aeroengines and rocket turbopumps. The coupled nonlinearities in ball bearings, including bearing clearance, variable compliance, and ball–raceway Hertzian contact [1], strongly influence the dynamic response of rotor systems [2], especially under a high rotational speed [3], which therefore attract the interests of many researchers. Hou et al. [4] investigated the primary resonance of a dual-rotor system using the harmonic balance– alternating frequency/time domain (HB-AFT) method. Bonello et al. [5] proposed a whole-engine receptance harmonic balance method (HBM) to obtain the steady-state periodic vibration of aero-engine assemblies and formulated equations based on the receptance functions of the linear part of a structure. Researchers also studied other nonlinear factor effects on the rotor systems dynamic response, such as the
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shaft crack [6–8] and rotor/stator contact problems [9]. In these studies, the HBM was used to solve the nonlinear problem and obtain the approximate dynamic response of the rotor systems, which was more efficient than the numerical integral method. However, the solution procedure was complicated and entailed considerable computational costs beca
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