New analysis model for rotor-bearing systems based on plate theory

doi:10.1007/s11465-019-0525-2

Front. Mech. Eng.

2019, Vol. 14

Issue (4) : 461-473 https://doi.org/10.1007/s11465-019-0525-2

RESEARCH ARTICLE

New analysis model for rotor-bearing systems based on plate theory

Zhinan ZHANG¹, Mingdong ZHOU²(

), Weimin DING³, Huifang MA⁴

¹. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
². State Key Laboratory of Mechanical System and Vibration, Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, Shanghai Jiao Tong University, Shanghai 200240, China
³. Ningbo Donly Co., Ltd., Ningbo 315000, China
⁴. AECC Commercial Aircraft Engine Co., Ltd. Shanghai 200240, China

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Abstract

The purpose of this work is to develop a new analysis model for angular-contact, ball-bearing systems on the basis of plate theory instead of commonly known approaches that utilize spring elements. Axial and radial stiffness on an annular plate are developed based on plate, Timoshenko beam, and plasticity theories. The model is developed using theoretical and inductive methods and validated through a numerical simulation with the finite element method. The new analysis model is suitable for static and modal analyses of rotor-bearing systems. Numerical examples are presented to reveal the effectiveness and applicability of the proposed approach.

Keywords rotor-bearing system rolling element bearing plate theory finite element analysis

Corresponding Author(s): Mingdong ZHOU

Online First Date: 09 October 2018 Issue Date: 02 December 2019

Cite this article:

Zhinan ZHANG,Mingdong ZHOU,Weimin DING, et al. New analysis model for rotor-bearing systems based on plate theory[J]. Front. Mech. Eng., 2019, 14(4): 461-473.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0525-2
https://academic.hep.com.cn/fme/EN/Y2019/V14/I4/461

Fig.1 Illustration of concentrated load applied to an annular plate [²⁷]. (a) Concentrated load is applied to the rigid shaft; (b) equivalent axial load; (c) equivalent radial load

Fig.2 (a) Illustration of the deformation of an annular plate; (b) illustration of an infinitesimal element

Fig.3 Deformation of the annular plate under (a) axial load and (b) radial load

Tab.1 Calculation of axial and radial deformation parameters

Fig.4 Application procedure for the proposed method [²⁷]

Fig.5 3D model of the rotor-bearing system in a water ring vacuum pump

Fig.6 Results of comparison of the first bending mode for the rotor bearing system. (a) Using the spring element-based approach; (b) using the plate theory-based approach

Tab.2 spring element-based approach and plate theory-based approach

Fig.7 Calculating displacement during acceleration

Fig.8 Comparison of the results of displacement during acceleration. (a) Using the spring element-based method; (b) using the plate theory-based method

Tab.3 Datasheet for displacement parameters

α

and

β

Fig.9 Flowchart for database development

Fig.10 Plate theory-based model and potential new models

Schematic of the coordinate system

Description	Diagram and maximum axial displacement w_max
A circular plate is subjected to evenly distributed load q with a simply supported boundary	$w max ? = q E 316 a 4 h 3 (1 − μ) (5 + μ)$ (In the formula, E is the elastic modulus of the slab, mis the Poisson’s ratio, and h is the thickness of the plate. The same applies to the formulas below.)
A circular plate is subjected to evenly distributed load q with a fixed boundary	$w max ? = q E 316 a 4 h 3 (1 − μ 2)$
A circular plate is subjected to evenly distributed load q of radius b with a simply supported boundary	$w max ? = q E 34 a 2 b 2 h 3 [3 − 2 μ − μ 2 − b 2 1 − μ 2 a 2 ln ? a b − b 2 4 a 2 (7 − 4 μ + μ 2)]$
A circular plate is subjected to evenly distributed load q of radius b with a fixed boundary	$w max ? = q E 34 1 h 3 (1 − μ 2) (a 2 + b 2 2 ln ? a b + 5 b 2 4)$
A circular plate is subjected to concentrated force P on the center of the plate with a simply supported boundary	$w max = P E 3 4 π a 2 h 3 (1 − μ) (3 + μ)$
A circular plate is subjected to concentrated force P on the center of the plate with a fixed boundary	$w max ? = P E 3 4 π a 2 h 3 (1 − μ 2)$
A circular plate is subjected to evenly distributed bending moment M₀ on its periphery with a simply supported boundary	$w max ? = M 0 E 6 a 2 h 3 (1 − μ)$
A circular plate with a hole is subjected to evenly distributed bending moment M₁ acting on the internal hole with a simply supported boundary	$w max ? = M 1 E 6 b 2 h 3 (2 a 2 1 + μ a 2 − b 2 ln ? b a − 1 + μ)$
A circular plate with a hole is subjected to evenly distributed bending moment M₁ acting on the periphery with a simply supported boundary	$w max ? = M 1 E 6 b 2 h 3 (1 − μ − 2 b 2 1 + μ a 2 − b 2 ln ? b a)$
A circular plate with a hole is subjected to evenly distributed load Q₀ acting on the inter hole with a simply supported boundary	$w max ? = Q 0 E 3 b h 3 [(μ 2 − 1) (a 2 + b 2) + 2 a 2 b 2 a 2 − b 2 (1 + μ) 2 (ln ? b a) 2 + a 2 − b 2 2 (1 − μ) 2]$

Table A1 Maximum axial displacement under different boundary conditions or loads

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