A comparative study of the preload effects on the stability performance of noncircular journal bearings using linear and nonlinear dynamic approaches

Abstract

In this work, the effects of preload factor on the stability performance of noncircular two and three lobe journal bearings with incompressible micropolar lubricant are presented based on the linear and nonlinear dynamic models. Assuming that the rotor is rigid, the governing Reynolds equation for the hydrodynamic lubrication of finite length lobed journal bearings has been modified using micropolar theory. Then, the linear and nonlinear dynamic models which include a certain harmonic disturbance and a time dependent trajectory of rotor center are applied to analyze the stability performance of the considered bearings. The generalized differential quadrature method and fourth-order Runge–Kutta technique have been used to solve the governing Reynolds equation and time-dependent dynamic equations of rotor motion, respectively. Finally, the numerical results for the critical mass parameter and the whirl frequency ratio of the rotor as the stability characteristics of the lobed bearings are obtained for different values of preload factor and are compared together. Results show that the dynamic stability of the noncircular bearings is enhanced by decreasing the preload factor i.e. increasing the amount of bearing noncircularity. These enhancements are in terms of increase of the critical mass parameter and decrease for the whirl frequency ratio. Also, by comparing the two dynamic analysis methods, it is seen that the results of linear model are more conservative in different investigated cases. The results of nonlinear analysis reveal that by changing the preload factor the dynamic responses of the lobed bearings appear in different manners. From the responses, it is observed that the type of dynamic trajectory of rotor center varies from stable fixed point to limit cycle periodic motions and also contact between rotor and bearing’s shell.

Keywords

Noncircular lobed journal bearings stability analysis linear and nonlinear dynamic approaches preload factor micropolar lubrication

Get full access to this article

View all access options for this article.

References

Scott

Suntiwattana

. Effect of oil additives on the performance of a wet friction clutch material. Wear 1995; 181–183: 850–855.

Balaram

. Micropolar squeeze films. Trans ASME J Tribol 1975; 97: 635–637.

Eringen

. Theory of micropolar fluids. J Appl Math Mech 1966; 16: 1–18.

Pinkus

. Analysis of elliptical bearings. ASME Trans J Basic Eng 1956; 78: 965–973.

Malik

. Comparative study of some two-lobed journal bearing configurations. ASLE Trans 1983; 26: 118–124.

Malik

Chandra

Sinhasan

. Design data for three lobe bearing. ASLE Trans 1981; 24: 171–178.

Huang

Weng

Chen

. Analysis of finite width journal bearings with micropolar fluids. Wear 1988; 123: 1–12.

Khonsari

Brewe

. Effect of viscous dissipation on the lubrication characteristic of micropolar fluids. Acta Mech 1994; 68: 57–68.

Rahmatabadi

Nekoeimehr

Rashidi

. Micropolar lubricant effects on the performance of noncircular lobed bearings. Tribol Int 2010; 43: 404–413.

10.

Rahmatabadi

Zare Mehrjardi

Fazel

. Performance analysis of micropolar lubricated journal bearings using GDQ method. Tribol Int 2010; 43: 2000–2009.

11.

Khonsari

. On the self-excited whirl orbits of a journal in a sleeve bearing lubricated with micropolar fluids. Acta Mech 1990; 81: 235–244.

12.

Khonsari

Chang

. Stability boundary of non-linear orbits within clearance circle of journal bearings. J Vib Acoust 1993; 115: 303–307.

13.

Das

Guha

Chattopadhyay

. Theoretical analysis of stability characteristics of hydrodynamic journal bearings lubricated with micropolar fluids. Proc IMechE, Part J: J Engineering Tribology 2004; 218: 45–56.

14.

Das

Guha

Chattopadhyay

. Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication. Tribol Int 2005; 38: 500–507.

15.

Chang-Jian

Chen

. Nonlinear dynamic analysis of a flexible rotor supported by micropolar fluid film journal bearings. Int J Eng Sci 2006; 44: 1050–1070.

16.

Prabhakran Nair

Sukamaran

. Static and dynamic analysis of elasto hydrodynamic elliptical journal bearing with micropolar lubricant. Tribol Int 2007; 40: 297–305.

17.

Chetti

. Micropolar fluids effects on the dynamic characteristics of four-lobe journal bearing. World Acad Sci Eng Technol 2011; 5: 497–501.

18.

Dhawan

Verma

. Analyzing micropolar lubrication in noncircular hybrid journal bearings. Tribol Trans 2014; 57: 182–189.

19.

Wang

Jang

Yeh

. Bifurcation and nonlinear dynamic analysis of a flexible rotor supported by relative short gas journal bearings. J Chaos Soliton Fractal 2007; 32: 566–582.

20.

Yang

Zhu

Wang

. On the non-linear stability of self-acting gas journal bearings. Tribol Int 2009; 42: 71–76.

21.

Zhang

Kang

Liu

. Numerical method and bifurcation analysis of Jeffcott rotor system supported in gas journal bearings. ASME Trans J Comput Nonlinear Dyn 2009; 4: 1–9.

22.

Rashidi Meybodi

Karami Mohammadi

Bakhtiari Nejad

. Preload effect on nonlinear dynamic behavior of a rigid rotor supported by noncircular gas-lubricated journal bearing systems. Nonlinear Dyn 2010; 60: 231–253.

23.

Rashidi Meybodi

Karami Mohammadi

Bakhtiari Nejad

. Numerical analysis of a rigid rotor supported by aerodynamic four-lobe journal bearing system with mass unbalance. Commun Nonlinear Sci Numer Simulat 2012; 17: 454–471.

24.

Zhang

Shi

. Numerical analysis method and bifurcation of gas-lubricated journal bearing-rotor system with gyroscopic effect. Adv Mater Res 2011; 230: 197–201.

25.

Zhang

Shi

. Nonlinear dynamic analysis of a rotor system with fixed-tilting-pad self-acting gas-lubricated bearings support. Nonlinear Dyn 2012; 69: 877–890.

26.

Zhang

Wang

Zhang

. Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects. Nonlinear Dyn 2013; 73: 751–765.

27.

Zhang

Hei

Lü

. Bifurcation and chaos analysis of nonlinear rotor system with axial grooved gas lubricated journal bearing support. Chin J Mech Eng (Engl Ed) 2014; 27: 358–368.

28.

Bellman

Casti

. Differential quadrature and long-term integration. J Math Anal Appl 1971; 34: 235–238.

29.

Malik

Bert

. Differential quadrature solutions for steady-state incompressible and compressible lubrication problems. ASME Trans J Tribol 1994; 116: 296–302.

30.

Zhang Q, Guo G and Winoto SH. Analysis of hydrodynamic journal bearing with GDQ method. In: Magnetic recording conference, Singapore, 2002, TU.P.06.01-02.

31.

Shu

Chen

. On optimal selection of interior point for discretized boundary condition in DQ vibration analysis of beam and Plates. J Sound Vib 1999; 222: 239–257.