Multigrid Multilevel Methods Research Articles

Theoretical Investigation of Surface under Soft Mixed Lubrication

This paper presents the effect of surface roughness in line contact under isothermal soft mixed lubrication with non-Newtonian based on Power law viscosity model. The time independent modified Reynolds equation, elasticity equation and the load capacity of asperities equation were numerically solved using finite different method, Newton-Raphson method and multigrid multilevel methods to obtain the film pressure profiles, film thickness profiles and contact pressure in the contact regions. The simulation results showed that the the amplitude of surface roughness has a significant effects on the film pressure, film thickness and surface contact pressure in the contact region. The minimum gap between surface, friction coefficient and asperity load increase when the amplitude of surface roughness increases. For increasing surface velocity, the minimum gap between surface increases but asperity load decreases.

Effect of Solid Particle on Rough Thermo-Elastohydrodynamic Lubrication with Non-Newtonian Lubricant

This paper presents the performance characteristics of rough thermo-elastohydrodynamic lubrication (TEHL) with non-Newtonian liquid–solid lubricant based on a Power law viscosity model. The time independent modified Reynolds equation, elasticity equation and energy equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel methods were used to obtain the film pressure profiles and film thickness in the contact region. The effects of amplitude of surface roughness and concentration of solid particles are examined. The simulation results showed surface roughness has rapidly effect on film pressure and film temperature. The effect of solid particle can be increases film thickness and decreases friction coefficient.

Rough Air-Soft Elastohydrodynamic Lubrication

This paper presents the effects of rough surface air-soft elastohydrodynamic lubrication (EHL) of rollers for soft material under the effect of air molecular slip. The time independent modified Reynolds equation and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel methods were used to obtain the film pressure profiles and film thickness in the contact region. The effects of amplitude of surface roughness, modulus of elasticity and air inlet temperature are examined. The simulation results showed surface roughness has effect on film thickness but it little effect to air film pressure. When the amplitude of surface roughness and modulus of elasticity increased, the air film thickness decreased but air film pressure increased. However, the air inlet temperature increased when the air film thickness increased.

Transient Air-Soft EHL of Rough Surface with Impact Sudden Load

This paper presents the effects of transient rough surface air-soft elastohydrodynamic lubrication (EHL) of rollers for soft material. The time independent modified Reynolds equation, and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel method to obtain the film pressure profiles and film thickness in the contact region. The effects of overload, surface roughness and time period are examined. The simulation results show surface roughness has effect on film thickness. The impact of sudden load condition is that the air film pressure increases but film thickness decreases. The minimum film thickness decreases when the amplitude of surface roughness increases. Increasing of impact from sudden loads resulted in minimal film thickness decrease.

Theoretical Investigation of Transient Lubrication in Spur Gear

This paper presents performance characteristics of transient thermo-elastohydrodynamic lubrication (TEHL) in line contact with Newtonian fluids. The time-dependent modified Reynolds equation, energy equation and elasticity equation with initial conditions were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel method for an involutes spur gear to obtain the film pressure profiles, film thickness profiles, film temperature and friction coefficient in the contact region. In this analysis, the load is applied on either two pairs or one pair of gear teeth. The simulation results show that at approach point, the film thickness is minimized and film temperature rapidly increases. Film temperature and friction coefficient were suddenly increase when the transition from two pairs to one pair and vice versa are modeled as a step variation of load. The friction coefficient and film temperature were occurrence at pitch point. Film temperature and friction coefficient increase but film thickness decreases when applied load increases. For increasing of speeds, film thickness and film temperature increase but friction coefficient decreses.

Effect of Al<sub>2</sub>O<sub>3</sub> Nanoparticles Additives on Thermo-Elastohydrodynamic with Newtonian Lubricant

This paper presents the effect of Al2O3nanoparticles additives on thermoelastohy-drodynamic with Newtonian lubricant. The modified Reynolds equation and energy equation have been formulated and solved numerically with initial conditions using multi-grid multi-level method. Simulation results show the operating with Al2O3nanoparticles blended particularly with SAE-90 lubricant. The maximum pressure and temperature decreases, as compared to SAE-90 oil without nanoparticles additives.

Transient Thermo-Elastohydrodynamic Lubrication of Rough Surface in Soft Material

This paper presents the effects of transient rough surface thermo-elastohydrodynamic lubrication (TEHL) of rollers for soft material with non-Newtonian fluid base on power law model. The time independent modified Reynolds equation, energy equation and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel method to obtain the film pressure profiles, film thickness profiles and friction coefficient in the contact region. The simulation results show surface roughness has effect on film thickness but its effect on film temperature is insignificant. The minimum film thickness decreases while the coefficient increases when the amplitude of surface roughness increases. Meanwhile, increasing applied loads causes the friction coefficient to decrease.

Effect of Solid Particle on TEHL under Line Contact with Solid-Liquid Lubricant

The two infinitely long surfaces in line contact under thermoelastohydrodynamic lubrication with solid-liquid lubricants were investigated. The time-dependent modified Reynolds equation elasticity equation and the adiabatic energy equation have been formulated and solved numerically with initial conditions using multi-grid multi-level method with full approximation technique. The characteristics of the two surfaces in line contact under thermoelastohydrodynamic lubrication were presented as; film pressure, film temperature and oil film thickness profiles. The results of solid-liquid lubricants with micro-particle and nano-particle under thermal elastohydrohynamic lubrication were compared with the case of pure liquid lubricant.

Stability analysis of rough journal bearings under TEHL with non-Newtonian lubricants

The combined effects of surface roughness and lubricants rheology on stability of a rigid rotor supported on finite journal bearing under thermal elastohydrodynamic lubrication have been investigated using the transient method. The newly derived time dependent modified Reynolds and the adiabatic energy equations were formulated using a non-Newtonian Carreau viscosity model. The simultaneous systems of modified Reynolds equation, elasticity equation, energy equation, and the rotor motion equation with initial conditions were solved numerically using multigrid multi-level method with full approximation technique. From the characteristic equation, the instability threshold is then obtained with various surface roughness parameters and the elastic modulus of the bearing liner materials. The results show that stability of the bearing system deteriorates with decreasing both the power law exponent and the elastic modulus of bearing liner material. The rough surface journal bearing with transverse pattern under TEHL regime exhibits better stability when compared with the rough surface journal bearing with longitudinal pattern.

Analysis of EHL Circular Contact Start Up: Part I—Mixed Contact Model With Pressure and Film Thickness Results

In this paper a model is presented to investigate the start up condition in elastohydrodynamic lubrication. During start up the lubrication condition falls into the mixed lubrication regime. The transition from solid contact to lubricated contact is of importance when investigating the start up process and its effects on bearing performance. The model presented uses the multigrid multilevel method to solve the lubricated region of the contact and a minimization of complementary energy approach to solve the solid contact region. The FFT method is incorporated to speed up the film thickness calculation. An iteration scheme between the lubrication and the solid contact problems is used to achieve the solution of the mixed lubrication contact problem. The results of start up with smooth surfaces are provided for the case when speed increases from zero to desired speed in one step and the case when speed is linearly increased to desired speed. The details of the transition from full solid contact to full lubricated contact in EHL start up are presented. The change of pressure and film thickness as well as contact forces and contact areas are discussed.