Linear and nonlinear analysis of mount angle effects on the dynamic stability of micropolar lubricated hydrodynamic lobed journal bearings

Abstract

Journal bearings are one of the most widely used types of supporting devices for industrial machinery, especially for high-speed rotary systems. Considering the importance of mechanical systems ability to control vibrations and motion disturbances, the design of noncircular journal bearings has been one of the appropriate techniques used in recent years. In the present work, the effects of mount angle as a noncircularity unique feature on the dynamic stability of lobed journal bearings with micropolar lubricant are studied. For this purpose, modified Reynolds equation based on the linear and nonlinear methods is solved by generalized differential quadrature (GDQ) method. Then the static and dynamic characteristics of two-, three- and four-lobe bearings including load carrying capacity, whirl frequency ratio, critical mass parameter and rotor perturbation in terms of bifurcation diagram and Poincare map are presented for different values of mount angle. Nonlinear analysis results indicate that variation of mount angle can change the rotor response from limit cycle oscillations to convergent perturbation to static equilibrium point. Further, against plain circular journal bearings, choosing an appropriate orientation or mounting angle provides the optimal stability of noncircular lobed journal bearings. Also, the linear analysis results for the range of dynamic stability are more cautious than the nonlinear method in most of investigated cases.

Keywords

Noncircular lobed journal bearings dynamic stability micropolar lubrication mount angle linear and nonlinear analysis method bifurcation diagram GDQ method

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References

Eringen

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

Allen

Kline

. Lubrication theory for micropolar fluids. J Appl Mech 1971; 23: 646–650.

Prakash

Sinha

. Lubrication theory of micropolar fluid and its application to a journal bearing. Int J Eng Sci 1975; 13: 217–232.

Zaheeruddin

Isa

. Micropolar fluid lubrication of one dimensional journal bearing. Wear 1978; 50: 211–220.

Sinha

. The three-dimensional Reynolds equation for micropolar fluid lubrication bearings. Wear 1982; 76: 199–209.

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.

Das

Guha

Chattopadhyay

. Theoretical analysis of stability characteristics of hydrodynamic journal bearings lubricated with micropolar fluids. Tribol Int 2005; 35: 201–210.

Wang

Zhu

. Numerical analysis of journal bearing lubricated with micropolar fluid including thermal and cavitating effects. Tribol Int 2006; 39: 227–237.

10.

Yang

Wang

Zhao

, et al. A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings. Appl Math Model 2014; 38: 5239–5255.

11.

Pinkus

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

12.

Pinkus

. Analysis and characteristics of the thee-lobe bearing. Transact ASME J Basic Eng 1959; 1: 49–55.

13.

Kumar

Sinhasan

Singh

. Performance characteristics of two-lobe hydrodynamic journal bearings. J Lubricat Technol 1980; 102: 425–429.

14.

Malik

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

15.

Malik

Chandra

Sinhasan

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

16.

Rahmatabadi

Rashidi Meybodi

. Effect of mount angle on static and dynamic characteristic of gas lubricated noncircular journal bearings. Iran J Sci Technol Transact B 2006; 30: 327–337.

17.

Rahmatabadi

Nekoeimehr

Rashidi

, et al. Effects of bearing orientation on the static performance of micropolar lubricated lobe bearings. Proc IMechE, Part J: J Engineering Tribology 2012; 226: 3–13.

18.

Sharma

Rajput

. Stability of a constant flow value compensated multi-recess conical hybrid journal bearing operating with micropolar lubricant. Lubricat Sci 2014; 26: 347–362.

19.

Kushare

Sharma

. Nonlinear transient stability study of two lobe symmetric hole entry worn hybrid journal bearing operating with non-Newtonian lubricant. Tribol Int 2014; 69: 84–101.

20.

Zare Mehrjardi

Rahmatabadi

Rashidi Meybodi

. A study on the stability performance of noncircular lobed journal bearings with micropolar lubricant. Proc IMechE, Part J: J Engineering Tribology 2016; 230: 14–30.

21.

Zare Mehrjardi

Rahmatabadi

Rashidi Meybodi

. A comparative study of the preload effects on the stability performance of noncircular journal bearings using linear and nonlinear dynamic approaches. Proc IMechE, Part J: J Engineering Tribology 2016; 230: 797–816.

22.

Rashidi Meybodi

Zare Mehrjardi

Rahmatabadi

. Tilt angle effects on the performance of micropolar lubricated noncircular journal bearings. Industrial Lubricat Tribol 2017; 61: 536–549.

23.

Budheeja

Verma

. Nonlinear transient analysis of hole-entry journal bearing with constant flow of micropolar fluids. Proc IMechE, Part C: J Mechanical Engineering Science 2019; 233: 350–368.

24.

Bellman

Casti

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

25.

Malik

Bert

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

26.

Zhang Q, Guo G and Winoto SH. Analysis of hydrodynamic journal bearing with GDQ method. In: Digest of the Asia-Pacific Magnetic Recording Conference, Singapore, Singapore, 27–29 August 2002. IEEE.

27.

Shu

Chen

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