Dynamic performance of foil bearings with a quadratic stiffness model

Hydrodynamic foil bearings found various applications in high speed small turbomachinery due to several advantages compared with traditional oil lubricated bearing and rolling element bearings such as high speed, pollution free, high temperature, long service life, etc. Corrugated bump foils made of thin sheet metal is the most widely adopted foil structure used in many commercial foil bearings. However, due to various factors during manufacturing process of the foil structure and mounting methods of the foil structure on to the bearing sleeve, measured stiffness curves of the foil structure show very strong non-linearity. The non-linearity of the foil structure is often neglected in most simulation studies in the past, and single value of bump stiffness combined with appropriate structural loss factor were used in these simulation studies. Based on measured non-linear structural stiffness of entire foil bearing, a quadratic stiffness model of individual bump foil was derived and utilized in transient rotordynamic simulations in time domain by solving Reynolds equation, rotor equations of motion, and bump deflections together. The simulation results using the quadratic bump stiffness model were compared with those using linear bump stiffness models.