Integrated numerical model for thermohydrodynamic analysis of bump-type foil bearings

This investigation presents a thermohydrodynamic (THD) analysis for bump-type foil bearings. Two basic equations, the generalized Reynolds equation and the energy equation, are simultaneously solved for the air pressure and generated heat due to the viscous shearing action in the air film. The compliant foil strip is described as a link-spring structure. The calculated foil deflection is coupled into the solution of the two basic equations to account for its effect on the film thickness. This model accounts for heat convection in the air film region and the material property variations of the lubricant air due to the temperature rise, heat convection with the cooling air, heat conduction between the solid components, heat transfer at the surface of the solid components, and thermal expansion of the bearing components as well as change in the bump foil elasticity. The airflow within the air film is a distinctive characteristic of bump-type foil bearings (BTFBs) compared to normal oil bearings because the top foil detaches at sub-ambient regions. The unique airflow is also taken into consideration in this model to modify the thermal boundary condition of the air film. Data from a published experimental investigation is used to validate the mathematical model. The predicted bearing temperatures, as well as the bearing load, agree well with the experimental data. The effects of ambient temperature on BTFB performance are discussed with the THD model. With increased ambient temperature, the influence of the bearing clearance changes, because the thermal growth of the bearing components is more significant than the decrease of the foil elasticity. Therefore, the thermal expansion coefficients of the bearing components should be considered during bearing design. The temperature profile within the foil bearing is predicted and compared with published tested temperature values. The calculated temperature correlates well with the experimental data at most of the positions. The deviation between the two values at the bearing-load position is demonstrated to be less than 10.3%.