Global nonlinear dynamic characteristics of rod-fastening rotor supported by ball bearings

Abstract

Flexible rod-fastening rotor-ball bearing system (FRRBS) is usually adopted in aircraft engines. In this paper, a simplified model for the FRRBS is proposed, and the global nonlinear dynamic characteristics of FRRBS are investigated. The FRRBS has two kinds of special structural features: rods and interfaces. The circumferentially distributed rods are modelled as a constant stiffness matrix with an additional moment (when unequal pre-tightening occurs) without mass effect. The interfaces between disks are modelled as stiffness matrices with normal and tangential contact stiffness, which are determined by pre-tightening force. Then, the shaft is discretized by Timoshenko elements and supported by ball bearings with radial internal clearance. Periodic motions and bifurcation sets are obtained by shooting method. The result shows that the insufficient pre-tightening brings about abnormal vibrations through quasi-periodic instability in high speed region, and the unequal pre-tightening leads to severe vibrations in stable periodic operation state. Moreover, the mass eccentricity would be the most nonlinear source for the nonlinear instabilities. Generally, this paper presents a method for modelling a FRRBS to study the nonlinear dynamic characteristics of the FRRBS.

Keywords

Rod-fastening rotor contact interface bifurcation ball bearing clearance

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References

Day

. Active suppression of rotating stall and surge in axial compressors. J Turbomach Transact ASME 1993; 115: 40–47.

Porreca

Hollenstein

Kalfas

. Turbulence measurements and analysis in a multistage axial turbine. J Propul Power 2007; 23: 227–234.

Chiras

Evans

Rees

. Global nonlinear modeling of gas turbine dynamics using NARMAX structures. J Eng Gas Turbine Power Trans ASME 2002; 124: 817–826.

Camporeale

Fortunato

Mastrovito

. A modular code for real time dynamic simulation of gas turbines in simulink. Transact ASME J Eng Gas Turbine Power 2006; 128: 506–517.

El-Saeidy

FMA

Sticher

. Dynamics of a rigid rotor linear/nonlinear bearings system subject to rotating unbalance and base excitations. J Vibrat Control 2010; 16: 403–438.

Brancati

Rocca

Russo

. Journal orbits and their stability for rigid unbalanced rotors. J Tribol Transact ASME 1995; 117: 709–716.

Liao

Gasch

Kolk

. Stability improvement of motion of a rotor with an active control method. J Vibrat Control 2000; 6: 291–308.

Xiaoyao

Mei

. Effect of the seal force on nonlinear dynamics and stability of the rotor-bearing-seal system. J Vibrat Control 2009; 15: 197–217.

Alnefaie

. Start-up dynamic analysis of a rotor supported by fluid film bearings. J Vibrat Control 2010; 16: 879–896.

10.

Nelson

. A finite rotating shaft element using Timoshenko beam theory. J Mech Des Transact ASME 1980; 102: 793–803.

11.

Lynagh

Rahnejat

Ebrahimi

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

12.

Perret

. Elastiche spielschwingungen konstant belaster walzlger. Werkstatt und Betrieb 1950; 3: 354–358.

13.

Meldau

. Die Bewegung der Achse von walzlagern bei geringen Drehzahlen. Werkstatt und Betrieb 1951; 7: 308–313.

14.

Sunnersjo

. Varying compliance vibrations of rolling bearings. J Sound Vibrat 1978; 58: 363–373.

15.

Fukata

Gad

Kondou

. On the radial vibration of ball bearings: computer simulation, Tokyo, Japan: Japan Society of Mechanical Engineers, 1985.

16.

Mevel

Guyader

. Routes to chaos in ball bearings. J Sound Vibrat 1993; 162: 471–487.

17.

Sankaravelu

Noah

Burger

. Bifurcation and chaos in ball bearings. Nonlinear Stochastic Dynamics 1994; 78: 313–325.

18.

Aini

Rahnejat

Gohar

. An experimental investigation into bearing-induced spindle vibration. Proc IMechE, Part C: J Mechanical Engineering Science 1995; 209: 107–114.

19.

Yamamoto

. On the vibration of a shaft supported by bearings having radial clearances. Transact JSME 1955; 21: 182–192.

20.

Rahnejat

Gohar

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

21.

Tiwari

Gupta

Prakash

. Effect of radial internal clearance of a ball, bearing on the dynamics of a balanced horizontal rotor. J Sound Vibrat 2000; 238: 723–756.

22.

Tiwari

Gupta

Prakash

. Dynamic response of an unbalanced rotor supported on ball bearings. J Sound Vibrat 2000; 238: 757–779.

23.

Harsha

. Nonlinear dynamic response of a balanced rotor supported by rolling element bearings due to radial internal clearance effect. Mech Machine Theor 2006; 41: 688–706.

24.

Harsha

Sandeep

Prakash

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

25.

Greenwood

Williams

. Contact of nominally flat surfaces. Proc R Soc London Ser A: Math Phys Sci 1966; 295: 300–319.

26.

Krolikowski

Szczepek

. Assessment of tangential and normal stiffness of contact between rough surfaces using ultrasonic method. Wear 1993; 160: 253–258.

27.

Harris

Kotzalas

. Rolling bearing analysis, USA: Wiley, 1984.

28.

Matsubara

Rahnejat

Gohar

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

29.

Aini

Rahnejat

Gohar

. A 5 degrees of freedom analysis of vibrations in precision spindles. Int J Mach Tools Manuf 1990; 30: 1–18.

30.

Gao

Wang

. Influences of bearing housing deflection on vibration performance of cylinder roller bearing-rotor system. Proc IMechE, Part K: J Multi-body Dynamics 2013; 227: 106–114.

31.

Iooss

Joseph

. Elementary stability and bifurcation theory, Heidelberg: Springer-Verlag, 1989.