A Technical Review on Multi Lobe Journal Bearings

A Technical Review on Multi Lobe Journal Bearings

S. Udaya Bhaskar1, M. Manzoor Hussain2, Md. Yousuf Ali3

1Associate Professor, AHCET, Chevella, 2Principal, JNTUH CES, Medak, 3Principal, NSAKCET, Malakpet

Abstract

Fluid film bearings are machine elements to produce smooth motion between solid surfaces in relative motion and to generate a load support for mechanical components. The lubricant used between the surfaces may be a liquid or gas. Fluid film bearings are designed to support static and dynamic loads, and consequently, their effects on the performance of rotating machinery are of great importance. In the design of high speed rotary machinery, consideration of surface roughness is important to predict the steady state characteristics and stability analysis of the hydrodynamic journal bearings.

1. Introduction

   Bearings play a vital role in the performance of rotor bearing system. Though the plain cylindrical journal bearing is generally used in the rotating machinery it does not satisfy the stability requirements of high speed machinery. In such specialized cases plain circular bearings are replaced by non-circular journal bearings. Multilobe journal bearings are widely used to suppress instability under lightly loaded conditions. Bearings with two lobes, three lobes and four lobes are widely used to support the rotating machinery.

2. Literature survey

   O. Pinkus [1], [2] and [3] was one of the first study multi lobe bearing, static characteristics of two lobe and three lobe bearings were predicted for different aspect ratios.

   Falkenhagen et al. [6] did the analysis of stability characteristics and general transient motion of the finite width three lobe bearings. Reynolds equation was solved by time transient procedure. The linearized stiffness and damping coefficients were computed by evaluating the changes in hydrodynamic forces caused by small perturbation about the steady state position. Threshold speed o stability was determined. The influence of rotor unbalance above and below the stability threshold was investigated.

   S.T.N Swamy et al. [9] calculated the stiffness and damping coefficients of finite journal bearings and their application to find the stability prediction. The Reynolds equation is solved using the over relaxation scheme. First the steady state equilibrium performance is calculated next a small change in the eccentricity ratio and attitude angle which is a function of time gives the stiffness and damping coefficients. Characteristic equation is solved using the stiffness and damping coefficients to find the stability curves.

   Flack et al. [12] and [13] did an experiment and theoretical investigation of pressure distributions in four lobe bearings. Theoretical pressure disturbances were obtained by using variational approach to solve the Reynolds equation. Both half Sommerfeld and Reynolds boundary conditions were used separately and theoretical results obtained by both conditions were compared with experiment results.

   Leader et al. [13] tested a pair of preloaded (factor 0.7 and 0.77) four lobe bearings with simple flexible rotor for the instability threshold analysis. Experiment results were compares with the theoretical results obtained by finite element analysis. In the analysis, half Sommerfeld boundary condition was used for Reynolds equation.

   Li et al. [14] determined the linearized stability threshold for multi lobe bearings (elliptical, offset, three-lobe and four-lobe). Reynolds equation was solved by using series solution based on variational principle. Stability of these bearings for different load conditions are discussed. The analysis was done for L/D =0.5 and preload factor of 0.5.

   Ghosh et al. [13] studied the stability of a rigid rotor supported on a rough surface journal bearing. By using a first order perturbation method, the time dependent Reynolds equation was linearized and the steady-state and dynamic pressure were obtained. The stability characteristics were evaluated for various roughness heights, eccentricity ratios, and L/D ratios and

   roughness parameters. By using stochastic models for isotropic roughness.

   A. Raj et al. [17] applied the stochastic theory for the analysis of dynamically loaded short rough journal bearing which have striations transverse to the direction of motion. Instead of Gaussian function an approximate polynomial is used to represent the roughness profile. To make the analysis applicable to the real lubrication situations, it is assumed that the standard deviation of the roughness heights and the minimum film thickness are of the same order.

   J. Ramesh et al. [22] investigated the stability of a rigid rotor supported by finite oil rough journal bearings with the use of non linear time transient analysis. The effects of the various surfaces roughness parameters composite surface roughness parameters, roughness orientation parameters, variance ratio on the stability is presented in the form of centre trajectories.

   H. Hashimoto [25] described an applicability of modified Reynolds equation considering Reynolds equation considering the combined effects of turbulence and surface roughness. In the numerical analysis of modified Reynolds equation, the non-linear simultaneous equations for the turbulence correction coefficients are greatly simplified to save the computational time with a satisfactory accuracy under the assumption that the shear flow is superior to the pressure flow in the lubricant films.

   J. Ramesh et al. [26] considered the effect of surface roughness on the stability of submerged oil elliptical journal bearings under unidirectional constant and unidirectional periodic load. The non linear transient simulation taking the oil film history into account has been used to predict the threshold of various parameters, they are composite surface roughness, roughness orientation pattern and variance ratio on stability has been studied.

   Ram Turaga et al. [27] considered the surface roughens pattern significantly influence the steady state and dynamic characteristics of hydrodynamic journal bearings. The effect of surface roughness pattern on bearing with different b/d ratios has also been studied. However the influence of surface roughness parameter which is a ratio of half of the total ranges of random film thickness variable to the radial clearance on the performance of hydrodynamic journal bearings.

   Cheng et al. [29] analyzed the combined effects of the surface roughness and flow rheology on the linear

   stability of a rigid rotor supported on the short length journal bearing. The modified equation and the rotor motion equation are linearized about the equilibrium position and the fluid film is modelled as a spring and damping elements. By using the characteristic equation, the instability threshold is then obtained with various surface roughness parameters, flow rheology and eccentricity ratios.

   Guha [30] deals with the concept of stochastic process to solve the problem of isotropic steady state characteristics if hydrodynamic journal bearings with finite width, considering two types of misalignment axial and twisting, using a finite difference method, the steady state film pressures are obtained by solving a Reynolds type equation based on the principle of isotropic roughness pattern, with the help of steady state film pressure, the steady state performance characteristics, in terms of the load carrying capacity, attitude angle, leakage flow rate, friction coefficient and misalignment moment of a journal bearing with the slenderness ratio of unity are obtained for various values of isotropic roughness parameter, eccentricity ratio and degree of misalignment.

   Cheng-Hsing Hsu et al. [33] theoretically predicted the combined effects of the couple stresses and surface roughness on the lubrication performance of the journal bearing systems. To take account of the pressure of both the surface roughness of the bearings and the couple stresses effects due to the lubricant containing the polar suspensions, the generalized stochastic non- Newtonian lubricant smooth bearing case, the couple stress effects and longitudinal roughness improve the load carrying capacity, and thus decrease the attitude angle and frictional parameters.

3. Conclusion

Surface appreciably effects the lubrication of surfaces if the film thickness is same order as the roughness. By using the first order perturbation method, the time dependent Reynolds equation was linearized and the steady state curves were obtained. The importance of roughness in predicting bearing performance has gained considerable attention in tribology. All previous developments were based on stability analysis of hydrodynamic bearings.

References

1. O.Pinkus, Power loss in elliptical and three lobe bearings, Transactions of the ASME, vol. 78, 1956, pp. 894- 904.

2. O.Pinkus, Experimental investigation of resonant whip Transactions of the ASME, Vol. 78. 1956, pp. 975-983.

3. O.Pinkus, Analysis and characteristics of three- lobe bearings Transactions of the ASME, Vol. 81, 1959, pp. 49-55.

4. S.T Tzeng and E Saidel, On the effects of surface roughness in the hydrodynamic lubrication theory of a short journal bearing Wear, Vol.10, 1967, pp. 179- 184.

5. P Shelley and C Ettles, A tracable solution for medium length journal bearings, Wear, Vol.12, 1970, pp. 221-228.

6. G. L. Falkenhangen, E. J Gunter, and F.T. Schuller, Stability and transient motion of vertical three lobe bearing system Journal of engineering for industry, May 1972, pp. 665-677.

1. J Prakash and Prawal Sinha, Theoretical effects of solid particles on the lubrication of journal bearing considering cavitation, Wear, Vol.41, 1977, pp. 233- 249.

2. S.T.N Swamy, B.S Prabhu and B.V.A Rao, Stiffness and damping characteristics of finite width journal bearing with non-Newtonian film and their application to instability prediction, Wear, Vol.32, 1975, pp. 379-390.

3. S.T.N Swamy, B.S Prabhu and B.V.A Rao, calculated load capacity of non-Newtonian lubricants in finite width journal bearings, Wear, Vol.31, pp.277- 285, 1975.

4. C. Rajalingham, B.S Prabhu and B.V.A Rao, The steady state performance of a hydrodynamic journal bearing with non-Newtonian lubricant, Wear, Vol.55, 1979, pp. 107- 120.

5. M.E Leader, R.D Flack and D.W Lewis, an experimental determination of the instability of a flexible rotor in four lobe bearings, Wear, Vol.58, 1980, pp. 35-47.

6. R.D Flack, M.E Leader, and P.E Allaire, An experimental and theoretical investigation of pressure in four lobe bearings Wear, Vol.61, 1980, pp. 233- 242.

7. D.F Li, K.C Choy, and P. Allaire, Stability and transient characteristics of four multi lobe journal bearing configurations, Journal of lubrication technology, Vol. 102, 1980, pp. 291-299.

8. W.A Crosby, The stability of a rigid rotor in ruptured finite journal bearing, Wear, Vol.80, 1982, pp. 333-346.

9. M. Malik, A comparative study of two-lobed journal bearing configurations ASLE Transactions, Vol.26, 1983, pp. 118-124.

10. A Raj and P Sinha, Transverse roughness in short journal bearings under dynamic loading Tribology International, Vol.5, 1983, pp. 245-251.

11. R Pai and B.C Majumdar, Stability of a submerged oil journal bearing under dynamic load Wear, Vol.146, 1991, pp. 125-135.

12. Bernard J Hamrock, Fundamentals of fluid film lubrication, NASA Reference Publication 1255, 1991.

13. R Sinhasan and K.C Goyal, Transient response of a circular journal bearing lubricated with non- Newtonian lubricants Wear, Vol.156, 1992, pp. 385- 396.

14. D.V Taylor, G.J Kostrezewsky, and R.D Flack, Measured performance of highly preloaded three lobe journal bearing part-I: static characteristics, Vol.38, 1995, pp. 507-516.

15. J Ramesh and B C Majumdar, Stability of rough journal bearing using nonlinear transient method ASME Journal of Tribology, Vol.117, 1995, pp. 691- 695.

16. D.V Singh, R Sinhasan and A Kumar, A variational solution of two lobe bearing Mechanism and machine theory, Vol.12, 1997, pp. 323-330.

17. C.M Muller-Karger, L.E Barrett, and R.D Flack, Influence of fluid film non-linearity on the experimental determination of dynamic stiffness and damping coefficients for three lobe bearing STLE Tribology Transactions, Vol.40, 1997, pp. 49-56.

18. H. Hashimoto, Surface roughness effects in high speed hydrodynamic journal bearing, ASME Journal of Tribology, Vol.119, 1997, pp. 776-780.

19. J. Ramesh, B.C Majumdar, and N.S Rao, Stability characteristics of rough submerged oil elliptical bearing under dynamic load, Tribology International, Vol.30, 1998, pp. 857-863.

20. Ram Turaga, A.S Sekhar and B.C Majumdar, The effect of roughness parameter on the performance of hydrodynamic journal bearing with rough surfaces, Vol.32, 1999, pp. 231-236.

21. K. Raghunandana, and B.C Majumdar, Stability of journal bearing system using non-Newtonian lubricants: a non-linear transient analysis Tribology International, Vol.32, 1999, pp. 179-184.

22. Cheng-I Weng, Chein-Ru Chen Linear stability of short journal bearings with consideration of flow rheology and surface roughness. Journal of Tribology international, Vol. 34, October 2000, pp. 507-516.

23. S.K Guha, Analysis of steady state characteristics of misaligned hydrodynamic journal bearings with isotropic surface roughness effect Tribology International, Vol.33, 2000, pp.1-12.

24. J.Y Jang and M.M. Khonsari, Thermo elastic instability with consideration of surface roughness and hydrodynamic lubrication ASME Journal of Tribology, Vol.122, 2000, pp.725-732.

25. T.V.V.L.N. Rao, S.Biswas and K.Athre, A methodology for dynamic coefficients and non-linear response of multi lobe journal bearings STLE Tribology Transactions, Vol.40, 2001, pp. 111-117.

26. Cheng-Hsing Hsu, Jaw-Ren Lin, and Hsiu-Lu Chaing, Combined effects of couple stresses and surface roughness on the lubrication of short journal bearing, Industrial Lubrication and Tribology, Vol.55, 2003, pp. 233-243.

27. Bernard J Hamrock, Lubrication fundamentals, NASA TM 81762.

28. B C Majumdar and D.E. Brewe, Stability of rigid rotor supported on oil film journal bearings under dynamic load, NASA TM 102309.

29. M.M. Khonsari, D.E Brewe, On the performance of finite journal bearings lubricated with micro polar fluids, NASA TM 100293.

30. Sumit Singhal, A simplified thermo hydrodynamic stability analysis of the plain cylindrical hydrodynamic journal bearings, M.S Thesis, Louisiana state university and agricultural and mechanical college, August 2004.

31. Bernard J. Hamrock, Steven R Schmid and Bo O Jacobson, Fundamentals of fluid film lubrication second edition.

32. J. Frene, D. Nicolas, B. Degueurce, D. Berthe, M. Godet, Hydrodynamic lubrication, Tribology series, 33, Elsevier.

33. Michal M. Khonsari, E Richard Booser, Applied Tribology bearing design and lubrication.

34. Bharat Bhusan, Modern tribology hand book

volume one.