Numerical analysis on the static–dynamic coupling influences of parallelism flaw in disc-rod rotor ball bearing system

Abstract

The static–dynamic coupling influences of parallelism flaw are investigated in the disc-rod rotor ball bearing system. Three-dimensional finite element method and a contact solving method are combined to analyze the statics of flawed disc-rod rotor. This analysis shows that parallelism flaw causes mass eccentric and rotation-dependent rotor bow. When these dynamic factors are involved, parallelism flaw promotes the nonlinear complexity in high speed and reduces global stability areas for the flawed disc-rod rotor. Unstable motions are more likely to happen when rotating speed exceeds the critical speed when rotor has a parallelism flaw. The spectrums of flawed rotor are composed of rotating frequency, subharmonic frequency, and their linear combinations. Flawed rotor has a larger bow deformation and orbit size than the ideal rotor. Dynamic stress performs the same property with vibration curves which enables rotors to have the first-order bow deformation. Dynamic stress of flawed rotor is much higher than that of ideal rotor. This paper presents a numerical analysis method to study the static-dynamic features of disc-rod rotor ball bearing system with parallelism flaw.

Keywords

Parallelism flaw ball bearing static–dynamic coupling nonlinear dynamics

Get full access to this article

View all access options for this article.

References

Gao

Yuan

et al.

Effects of bending moments and pre-tightening forces on the flexural stiffness of contact interfaces in rod-fastened rotors. ASME J Eng Gas Turbines Power 2012; 134: 102503–102503.

Liu

et al.

Investigation on the stability and bifurcation of a rod-fastening rotor bearing system. J Vib Control 2015; 21: 2866–2880.

Liu

Wang

et al.

Nonlinear dynamic characteristics of a three-dimensional rod-fastened rotor bearing system. Proc IMechE Part C: J Mechanical Engineering Science 2015; 229: 882–894.

Lynagh

Rahnejat

Ebrahimi

et al.

Bearing induced vibration in precision high speed routing spindles. Int J Mach Tools Manuf 2000; 40: 561–577.

Rahnejat

. Computational modelling of problems in contact dynamics. Eng Anal 1985; 2: 192–197.

Matsubara

Rahnejat

Gohar

. Computational modelling of precision spindles supported by ball bearings. Int J Mach Tools Manuf 1988; 28: 429–442.

Sarangi

Majumdar

Sekhar

. Stiffness and damping characteristics of lubricated ball bearings considering the surface roughness effect. Part 1: theoretical formulation. Proc IMechE Part J: J Engineering Tribology 2004; 218: 529–538.

Ueda

Mitamura

. Mechanism of dent initiated flaking and bearing life enhancement technology under contaminated lubrication condition. Part II: effect of rolling element surface roughness on flaking resulting from dents, and life enhancement technology of rolling bearings under contaminated lubrication condition. Tribol Int 2009; 42: 1832–1837.

Harsha

Sandeep

Prakash

. Non-linear dynamic behaviors of rolling element bearings due to surface waviness. J Sound Vib 2004; 272: 557–580.

10.

Bai

. Dynamic model of ball bearings with internal clearance and waviness. J Sound Vib 2006; 294: 23–48.

11.

Gao

Wang

et al.

Influences of bearing housing deflection on vibration performance of cylinder roller bearing–rotor system. Proc IMechE Part K: J Multi-body Dynamics 2012; 227: 106–114.

12.

Pang

Liu

et al.

Influence of misalignment on nonlinear dynamic characteristics for matched bearings-rotor system. Proc IMechE Part K: J Multi-body Dynamics 2014; 228: 172–181.

13.

Lee

. Modelling and vibration analysis of misaligned rotor-ball bearing systems. J Sound Vibration 1999; 224: 17–32.

14.

Liu

Shao

Zuo

. The effects of the shape of localized defect in ball bearings on the vibration waveform. Proc IMechE Part K: J Multi-body Dynamics 2013; 227: 261–274.

15.

Liu

Shao

. A numerical investigation of effects of defect edge discontinuities on contact forces and vibrations for a defective roller bearing. Proc IMechE Part K: J Multi-body Dynamics 2016; 230: 387–400.

16.

Patel

Upadhyay

. An analytical model (7 D.O.F.) for the prediction of the vibration response of cylindrical roller element bearings due to a combined localized defect. Proc IMechE Part K: J Multi-body Dynamics 2015; 229: 383–406.

17.

Zhou

et al.

Dynamic analysis of an unbalanced rotor-water pump-bearing system considering varying compliance effect and localized defects on bearing races. Proc IMechE Part K: J Multi-body Dynamics 2015; 229: 424–438.

18.

Simo

Laursen

. An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 1992; 42: 97–116.

19.

Bathe

. Finite element procedures, Englewood Cliff, New Jersey: Prentice-Hall, 2006.

20.

Rahnejat

Gohar

. The vibrations of radial ball bearings. Proc IMechE, Part C: J Mechanical Engineering Science 1985; 199: 181–193.

21.

Harris

Kotzalas

. Rolling bearing analysis, New York, USA: Wiley, 1984.

22.

Van De Vorst

ELB

Fey

RHB

De Kraker

et al.

Steady-state behaviour of flexible rotor-dynamic systems with oil journal bearings. Nonlinear Dyn 1996; 11: 295–313.