NOVEL SOLUTION TO REYNOLDS EQUATION FOR EXTERNALLY PRESSURISED GAS BEARINGS AS A COMBINATION OF THE SOLUTIONS OF TWO INITIAL VALUE PROBLEMS

This paper presents a novel method which generates the solution of Reynolds boundary value differential equation as a combination of the solutions of two initial value problems (IVP). By using the linearized PH theory, the results for the concentric Externally Pressurized Gas Bearing (EPB) were used to solve the case of a steady state eccentric EPB. The method was also used to investigate the influence of the feeding recess volume on the cylindrical whirl threshold ratio and bearing coefficients as well as for the calculation of the transition point between unchoked to choked flow. The results have engineering significance as the EPB coefficients are shown to vary considerably due to the interaction between the recces volumes and the journal vibration. Also, the transition from chocked to unchoked flow changes the gas bearing dimensionless flow and, as a result, the inlet pressure values.The Mathematica program used to implement the method has the advantage that it does not require grid spacing, or an estimated number of intermediate points. It employs standard Mathematica build-in functions, therefore easier to design and use for engineering applications. The calculated results and graphs are in fair agreement with available foundational experimental and theoretical published work.