Steady-State Hydrodynamic Lubrication Modeled With the Payvar-Salant Mass Conservation Model

Steady-state smooth surface hydrodynamic lubrications of a pocketed pad bearing, an angularly grooved thrust bearing, and a plain journal bearing are simulated with the mass-conservation model proposed by Payvar and Salant. Three different finite difference schemes, i.e., the harmonic mean scheme, arithmetic mean scheme, and middle point scheme, of the interfacial diffusion coefficients for the Poiseuille terms are investigated by using a uniform and nonuniform set of meshes. The research suggests that for the problems with continuous film thickness and pressure distributions, the results obtained with these numerical schemes generally well agree with those found in the literatures. However, if the film thickness is discontinuous while the pressure is continuous, there may be an obvious deviation. Compared with both the analytical solution and other two schemes, the harmonic mean scheme may overestimate or underestimate the pressure. In order to overcome this problem artificial nodes should be inserted along the wall of the bearings where discontinuous film thickness appears. Moreover, the computation efficiency of the three solvers, i.e., the direct solver, the line-by-line the tridiagonal matrix algorithm (TDMA) solver, and the global successive over-relaxation (SOR) solver, are investigated. The results indicate that the direct solver has the best computational efficiency for a small-scale lubrication problem (around 40 thousand nodes). TDMA solver is more robust and requires the least storage, but the SOR solver may work faster than TDMA solver for thrust bearing lubrication problems. Numerical simulations of a group of grooved thrust bearings were conducted for the cases of different outer and inner radii, groove depth and width, velocity, viscosity, and reference film thickness. A curve fitting formula has been obtained from the numerical results to express the correlation of load, maximum pressure, and friction of an angularly grooved thrust bearing in lubrication.

[1]  J. F. Booker,et al.  A Finite Element Cavitation Algorithm , 1991 .

[2]  Minel J. Braun,et al.  Cavitation formation and modelling for fluid film bearings: A review , 2010 .

[3]  A. Gosman,et al.  Entrainment and Inlet Suction: Two Mechanisms of Hydrodynamic Lubrication in Textured Bearings , 2007 .

[4]  Chih Lin,et al.  Mixed Lubrication of Coupled Journal-Thrust-Bearing Systems Including Mass Conserving Cavitation , 2003 .

[5]  Tadashi Nimura,et al.  On Aerodynamic Characteristics of a Hybrid-Sail with Square Soft Sail , 2003 .

[6]  F. Shi,et al.  An Implicit Finite Element Cavitation Algorithm , 2002 .

[7]  A. O. Lebeck,et al.  Principles and Design of Mechanical Face Seals , 1991 .

[8]  Philippe Dupont,et al.  Numerical Prediction of the Cavitation in Pumps , 2002 .

[9]  P. K. Goenka,et al.  Dynamically Loaded Journal Bearings: Finite Element Method Analysis , 1984 .

[10]  Fanghui Shi.  A deterministic mixed-elastohydrodynamic lubrication model and analysis of lip seal performance , 1999 .

[11]  van Hj Harry Leeuwen,et al.  Upstream pumping of radial lip seals by tangentially deforming, rough seal surfaces , 1996 .

[12]  Dominique Bonneau,et al.  EHD Analysis, Including Structural Inertia Effects and a Mass-Conserving Cavitation Model , 1995 .

[13]  Richard F. Salant,et al.  A Computational Method for Cavitation in a Wavy Mechanical Seal , 1992 .

[15]  Jih-Ping Peng,et al.  A Finite Element Scheme for Determining the Shaped Rail Slider Flying Characteristics With Experimental Confirmation , 1995 .

[16]  The Thermoelastic Behavior of Thrust Washer Bearings Considering Mixed Lubrication, Asperity Contact, and Thermoviscous Effects , 2008 .

[17]  Hugh Spikes,et al.  ‘Inlet suction’, a load support mechanism in non-convergent, pocketed, hydrodynamic bearings , 2006 .

[18]  Guy Bayada,et al.  Micro-Roughness Effects in (Elasto)Hydrodynamic Lubrication Including a Mass-Flow Preserving Cavitation Model , 2006 .

[19]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[20]  A. Lubrecht,et al.  MultiLevel Methods in Lubrication , 2013 .

[21]  H. Elrod.  A Cavitation Algorithm , 1981 .

[22]  Mihai Arghir,et al.  The finite volume solution of the Reynolds equation of lubrication with film discontinuities , 2002 .

[23]  Theo G. Keith,et al.  Numerical prediction of cavitation in noncircular journal bearings , 1989 .

[24]  Roberto F. Ausas,et al.  A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation , 2009 .

[25]  Claudia M. Woods,et al.  The Solution of the Elrod Algorithm for a Dynamically Loaded Journal Bearing Using Multigrid Techniques , 1989 .

[26]  Fanming Meng,et al.  On elastic deformation, inter-asperity cavitation and lubricant thermal effects on flow factors , 2009 .

[27]  M. Fesanghary,et al.  A Modification of the Switch Function in the Elrod Cavitation Algorithm , 2011 .

[28]  A. Cameron,et al.  The Full Journal Bearing , 1949 .

[29]  Theo G. Keith,et al.  Development and evaluation of a cavitation algorithm , 1989 .

[30]  Richard F. Salant,et al.  A mixed soft elastohydrodynamic lubrication model with interasperity cavitation and surface shear deformation , 2000 .

[31]  Shuangbiao Liu.  On boundary conditions in lubrication with one dimensional analytical solutions , 2012 .

[32]  Farshid Sadeghi,et al.  Groove Effects on Thrust Washer Lubrication , 2001 .

[33]  O. Pinkus,et al.  Theory of Hydrodynamic Lubrication , 1962 .