Optimal Control in Thermal Engineering pp 529-581 | Cite as

# Optimization of One Dimensional Slider Bearings

## Abstract

Optimal slider bearing profiles for maximum bearing load are studied by using direct constrained optimal control techniques. Technological constraints such as the maximum lubricant pressure and temperature and the minimum lubricant film thickness are included into the model. The realistic problem considered here yields optimal bearing profiles which are much more complex than the classical Rayleigh step bearing profile. Several bearing design and operation parameters, such as bearing length, inlet height, sliding velocity and lubricant inlet pressure and temperature, have been considered. They all have complex influence on the optimal bearing profile.

## Keywords

Lubricant Film Abrupt Decrease Constant Height Slider Bearing Lubricant Film Thickness## References

- Badescu, V.: Optimal pro fi les for one dimensional slider bearings under technological constraints. Tribol. Int.
**90**, 198–216 (2015)CrossRefGoogle Scholar - Bayrakceken, H., Yurusoy, M.: Comparison of pressure distribution in inclined and parabolic slider bearings. Math. Comput. Appl.
**11**, 65–73 (2006)zbMATHGoogle Scholar - Betts, J.T.: Practical Methods for Optimal Control Using Nonlinear Programming. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2001)Google Scholar
- Bonnans, F., Giorgi, D., Grelard, V., Maindrault, S., Martinon, P.: BOCOP—The Optimal Control Solver, User Guide, April 8, 2014. http://bocop.org; accessed 10 December 2014
- Brewe, D.E.: Slider Bearings. Chap. 27 in Modern Tribology Handbook, p. 35. CRC Press LLC (2001)Google Scholar
- Bruckner, R.J.: Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings. PhD Thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, Ohio (2004)Google Scholar
- Buscaglia, G.C., Ausas, R.F., Jai, M.: Optimization tools in the analysis of micro-textured lubricated devices. In: Colaco, M.J., Orlande, H.R.B., Dulikravich, G.S. (eds.) Inverse Problems, Design and Optimization. E-papers Publishing House, vol. II, pp. 181–190. Rio de Janeiro, Brazil (2005)Google Scholar
- Chang, L.: A baseline theory for the design of oil-lubricated centrally pivoted plane-pad thrust bearings. J. Tribol.
**132**, 041703.1–041703.6Google Scholar - Cupillard, S.: Thermohydrodynamics of Sliding Contacts with Textured Surfaces. Doctoral Thesis, Lulea University of Technology, SwedenGoogle Scholar
- Dobrica, M.B., Fillon, M.: Thermohydrodynamic behavior of a slider pocket bearing. J. Tribol.
**128**, 312–318 (2006)CrossRefGoogle Scholar - Farmer, D.G., Shepherd, J.J.: Slip flow in the gas-lubricated rayleigh step-slider bearing. Int. J. Appl. Mech. Eng.
**11**, 593–608 (2006)zbMATHGoogle Scholar - Garcia, A., Alder, B., Alexander, F.J.: Direct simulation Monte Carlo for thin film bearings. Phys. Fluids
**6**, 3854–3860 (1994)CrossRefzbMATHGoogle Scholar - Garcia, A., Huang, W., Bogy, D.B.: Three-dimensional direct simulation Monte Carlo method for slider air bearings. Phys. Fluids
**9**, 1764–1769 (1997)CrossRefGoogle Scholar - Glavatskih, S.B., De Camillo, S.: Influence of oil viscosity grade on thrust pad bearing operation. Proc. Inst. Mech. Eng. part J, J. Eng. Tribol.
**128**, 401–412 (2004)CrossRefGoogle Scholar - Knežević, D., Savić, V.: Mathematical modeling of changing of dynamic viscosity, as a function of temperature and pressure, of mineral oils for hydraulic systems. Facta Univ. Ser. Mech. Eng.
**4**, 27–34 (2006)Google Scholar - Li, H., Braun, M.J.: The lubricant flow structure and pressure generation in a journal bearing with diamond-knurled stator surface, In: Proceedings of the ASME Turbo Expo 2007—Power for Land, Sea, and Air, vol. 5, pp. 1005–1015 (2007)Google Scholar
- Lin, J.-R., Lu, Y.-M.: Steady-state performance of wide parabolic-shaped slider bearings with a couple stress fluid. J. Marine Sci. Technol.
**12**, 239–246 (2004)Google Scholar - Lin, J.-R., Hung, C.-R.: Analysis of dynamic characteristics for wide slider bearings with an exponential film profile. J. Marine Sci. Technol.
**12**, 217–221 (2004)Google Scholar - Mcallister, M.N., Rohde, S.M., Mcallister, G.T.: Constructive solution of the 1918 problem of Lord Rayleigh. Proc. Am. Math. Soc.
**76**, 60–66 (1979)MathSciNetCrossRefzbMATHGoogle Scholar - McCarthy, D.M.C.: Sliding Bearings for Hydropower Applications—Novel Materials, Surface Texture and EALs. Doctoral Thesis, Lulea University of Technology, Sweden (2008)Google Scholar
- Miller, B., Green, I.: Constitutive equations and the correspondence principle for the dynamics of gas lubricated triboelements. J. Tribol.
**120**, 345–352 (1998)CrossRefGoogle Scholar - Nocedal, J., Wright, S.J.: Numerical Optimization. Springer-Verlag, New York (1999)CrossRefzbMATHGoogle Scholar
- Oladeinde, M.H., Akpobi, J.A.: A comparative study of load capacity and pressure distribution of infinitely wide parabolic and inclined slider bearings. In: Proceedings of the World Congress on Engineering, 30 June–2 July 2010, vol. II, pp. 1370–1377, London, U.K. (2010)Google Scholar
- Ozalp, A.A., Ozel, S.A.: An interactive software package for the investigation of hydrodynamic-slider bearing-lubrication. Comput. Appl. Eng. Educ.
**11**, 103–115 (2003)CrossRefGoogle Scholar - Ozalp, A.A., Umur, H.: Optimum surface profile design and performance evaluation of inclined slider bearings. Curr. Sci.
**90**, 1480–1491 (2006)Google Scholar - Rahmani, R., Mirzaee, I., Shirvani, A., Shirvani, H.: An analytical approach for analysis and optimisation of slider bearings with infinite width parallel textures. Tribol. Int.
**43**, 1551–1565 (2010)CrossRefGoogle Scholar - Rayleigh, L.: Notes on the theory of lubrication. Phylosophical Mag.
**35**, 1–12 (1918)CrossRefGoogle Scholar - Rohde, S.M.: A demonstrably optimum one dimensional journal bearing. J. Tribol.
**94**, 188–192 (1972)Google Scholar - San Andrés, L.: Modern lubrication theory. Notes 2. Classical lubrication theory, Appendix. In: One Dimensional Slider Bearing, Rayleigh (Step) Bearing and Circular Plate Squeeze Film Damper. Texas A&M University, College Station TX; http://rotorlab.tamu.edu/me626/DEFAULT.HTM, Accessed 10 December 2014
- Savić, V., Knežević, D., Lovrec, D., Jocanović, M., Karanović, V.: Determination of pressure losses in hydraulic pipeline systems by considering temperature and pressure. Strojniški vestnik—J. Mech. Eng.
**55**, 237–243 (2009)Google Scholar - Sharma, R.K., Pandey, R.K.: an investigation into the validity of the temperature profile approximations across the film thickness in THD analysis of infinitely wide slider bearing. Tribol. Online
**1**, 19–24 (2016)CrossRefGoogle Scholar - Shyu, S.-H., Jeng, Y.-R., Chang, C.-C.: Load capacity for adiabatic infinitely wide plane slider bearings in the turbulent thermohydrodynamic regime. Tribol. Trans.
**47**, 396–401 (2004)CrossRefGoogle Scholar - Valkonen, A.: Oil film pressure in hydrodynamic journal bearings. Doctoral Dissertation, Helsinki University of Technology, Faculty of Engineering and Architecture, Department of Engineering Design and Production, TKK Dissertations 196 (2009)Google Scholar
- Wachter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program.
**106**, 25–57 (2006)MathSciNetCrossRefzbMATHGoogle Scholar - Walther, A., Griewank, A.: Getting started with ADOL-C. In: Naumann, U., Schenk, O. (eds.) Combinatorial Scientific Computing. Chapman-Hall CRC Computational Science (2012)Google Scholar
- Yurusoy, M.: A study of pressure distribution of a slider bearing lubricated with Powell-Eyring fluid, Turkish. J. Eng. Env. Sci.
**27**, 299–304 (2003)Google Scholar