Equivalent Stiffness Calculation of a Journal Bearing by Analytical Approach for Vibrational Modeling

More equipment which is used in the mechanical industry has rotating shafts. In the design of the rotating shaft, vibration prediction of the system is very important to reduce and prevent vibrations of the system. One of the important elements that have a more efficacy on the results of the vibration simulation of the rotating shaft is modeling of the bearings. The journal bearings are of great importance in the industries. In this study, firstly, the pressure equation of the lubricant film is derived in any position (angle) using Reynolds hydrodynamic theory for one-dimensional flow. Then using the definition of stiffness and its relationship with the force and pressure, the equivalent stiffness of the journal bearing lubricant film is calculated based on the angle by an analytical approach. Finally, with the solution of governing equations, equivalent stiffness is calculated for a sample journal bearing. Also, the calculated stiffness is validated and error factors of the results are studied. The obtained analytical equations can be helped the designer of the journal bearings to understand the stiffness behavior of the journal bearing versus the angular position and also system parameters of the bearing. The obtained results show that the journal bearing stiffness is directly related with the lubricant viscosity, the angular velocity, the length, and the second power of the journal radius. Also, the journal bearing stiffness is inversely related with the third power of the radial clearance of journal bearing.