This paper presents a mathematical model to investigate a nonlinear vibration behavior of a rotor-bearing system due to combined localized defect of inner race and outer race. Here shaft-rotor bearing system is modeled as a seven degree of freedom. In the mathematical formulation, contacts between rolling elements and inner and outer races are considered as nonlinear springs as well as hysteretic damping is also taken into consideration. The governing equations of motion are formulated using energy approach. Contact force calculation having nonlinearity are solved by using Newton–Raphson method for n-unknown nonlinear simultaneous equations. Equations of motions are solved by implicit type numerical integration method by Newmark integration algorithm. A computer code is developed to simulate the results in the form of time domain and frequency domain. Results are obtained in the form of time domain and frequency domain. The analytical results are also compared with the experimental results.
SunnersjoCS. Varying compliance vibrations of rolling bearings. J Sound Vib1978; 58: 363–373.
2.
WhiteMF. Simulation and analysis of machinery fault signals. J Sound Vib1984; 93: 95–116.
3.
RahnejatHGoharR. The vibration of radial ball bearings. Proc IMechE, Part C: J Mechanical Engineering science1985; 202(199): 181–193.
4.
MatsubaraMRahnejatHGoharR. Computational modelling of precision spindles supported by ball bearings. Int J Mach Tools Manuf1988; 28(4): 429–442.
5.
AiniRRahnejatHGoharR. A five degrees of freedom analysis of vibrations in precision spindles. Int J Mach Tools Manuf1990; 30(1): 1–18.
6.
AiniRRahenjatHGoharR. Vibration modelling of rotating spindles supported by lubricated bearings. Trans ASME J Tribol2002; 124(1): 158–176.
7.
TiwariMGuptaK. Dynamic response of an unbalanced rotor supported on ball bearings. J Sound Vib2000; 238: 757–779.
8.
TondonNChaudharyA. An analytical model for the prediction of the vibration response of rolling element bearing due to a localized defect. J Sound Vib1997; 205: 275–292.
9.
TondonNChaudharyA. Theoretical model to predict the vibration response of rolling bearings in a rotor bearing system due to distributed defects under radial load. J Tribol2000; 122: 609–615.
10.
ChoudhuryATandonN. Vibration response of ball bearing in a rotor bearing system to a local defect under radial load. ASME J Tribol2006; 128: 252–261.
11.
AkturkNUneebMGoharR. The effect of number of balls and preload on vibration associated with ball bearings. J Tribol1997; 119: 747–753.
12.
AkturkN. Some characteristic parameter affecting the natural frequency of a rotating shaft supported by defect free bearings. Proc IMechE, Part K: J Multi-body Dynamics2003; 217: 145–151.
13.
GafariSHGolnaragiFIsmailF. Effect of localized faults on chaotic vibration of rolling contact bearing. Nonlinear Dyn2008; 53: 287–301.
14.
WangLCuiLZhengD. Nonlinear dynamics behavior of a rotor roller bearing system with radial clearances and waviness considered. Chin J Aeronaut2008; 21: 86–96.
15.
HarrisTA. Rolling bearing analysis, 4th ed. New York, NY: John Wiley & Sons Inc, 2001.
16.
UpadhyaySHHarshaSPJainSC. Analysis of nonlinear phenomenon in high speed ball bearing system due to Radial clearance and unbalanced rotor effects. J Vib Control2010; 16: 65–88.
17.
CaoMXiaoJ. A comprehensive dynamic model of double-row spherical roller bearing, Model development and case studies on surface defects, preloads, and radial clearance. Mech Syst Signal Process2008; 22: 467–489.
18.
GuptaTCGuptaKSehgalDK. Instability and chaos of a flexible rotor ball bearing system: An investigation on influence of rotating imbalance and bearing clearance. J Eng Gas Turb Power2011; 133: 1–22.
19.
ZhangXHanQPengZ. Stability analysis of a rotor-bearing system with time varying bearing stiffness due to finite number of balls and unbalanced force. J Sound Vib2013; 332: 6768–6784.
20.
WuHZhouQZhangZ. Vibration analysis on the rolling element bearing-rotor system of an air blower. J Mech Sci Technol2012; 26(3): 653–659.
21.
BaiCZhangHXuQ. Experimental and numerical studies on nonlinear behaviour of rotor system supported by ball bearing. J Eng Gas Turb Power2010; 132: 1–5.
22.
Patel Utkarshkumar A and Upadhyay SH. Theoretical model to predict the effect of localized defect on dynamic behaviour of cylindrical roller bearing at inner race and outer race. Proc IMechE, Part K: J Multi-body Dynamics 2014; 228(2): 152–171.
23.
LynaghNRahnejatHEbrahimiM. Bearing induced vibration in precision high speed routing spindles. Int J Mach Tools Manuf2000; 40: 561–577.
24.
VafaeiSRahnejatHAiniR. Vibration monitoring of high spindle using spectral analysis techniques. Int J Mach Tools Manuf2002; 42: 1223–1234.
25.
HuntKHCrosslyFR. Coefficient of restitution interpreted as damping in vibro impact. J Appl Mech1975; 7: 440–445.
26.
JohnsPMGoharR. Roller bearing under radial and eccentric load. Tribol Int1981; 14: 131–136.
27.
KabusSHansenMRMouritsenOØ. A new quasi-static multi degree of freedom tapered roller bearing model to accurately consider non Hertzian contact pressure in time domain simulations. Proc IMechE, Part K: J Multi-body Dynamics2014, pp. 228.
JonesAB. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. Trans ASME J Basic Eng1960; 82: 309–320.
30.
Harris TA and Kotzalas MN. Rolling bearing analysis. Boca Raton: Taylor & Francis, 2007.
31.
Laniado-Ja´comeEMeneses-AlonsoJDiaz-Lo´pezV. A study of sliding between rollers and races in a roller bearing with a numerical model for mechanical event simulations. Tribol Int2010; 43: 2175–2182.
32.
LundbergGPalmgrenA. Dynamic capacity of rolling bearings. Acta Polytech Mech Eng Ser1947; 1.
33.
EschmannP. Ball and roller bearings – Theory, design and application, New York: Wiley, 1985, pp. 342–355.
34.
GuptaPK. Advanced. dynamics of bearings, Berlin: Springer-Verlag, 1984.
35.
KramerE. Dynamics of rotors and foundations, Berlin: Springer, 1993.
36.
BatheKJ. Finite element procedures in engineering analysis, Englewood Cliffs, NJ: Prentice Hall, 1982. .
