As one of the most important components in a rotor-bearing system, journal bearings provide proper support and damping to the rotor so that it can run both smoothly and efficiently and keep stable under different working conditions. As the rotating speed of the rotor growing faster and load getting heavier, the traditional cylinder journal bearing can no longer meet the demand of stabilizing the rotor, so different kinds of non-circular journal bearings were invented, such as elliptical bearing, multi-lobe bearing, wave bearing and etc., to provide better stability and greater load capacity. However, these kinds of non-circular bearings were mostly designed by experience of the engineers, and also the current hydrodynamic bearing design methodology still depends on empirical design. There lacks of corresponding theoretical foundation. In order to develop a theoretical method for bearing designing, an innovative analyzing approach needs to be carried out to explore the mechanism of the bearings and its performance. In this paper, a new approach is presented focusing on the profile of each bearing and their film thickness. A universal mathematical expression for different types of non-circular bearings has been put forward based on the Fourier series theory. The influence of periodic harmonics of film thickness on the static performance of non-circular bearings of finite length is studied for incompressible lubricant. The results show that the film thickness can always be expanded into a Fourier series, and the harmonic components of film pressure can be obtained by solving the Reynolds equation. Finally, the relation between the k-th order harmonic component H0,k and the corresponding static pressure component P0,k is established. This new investigation can be used to improve the non-circular bearing designing methodology with theoretical guidance.

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