Pressure distribution for multi-lobe bearings using Fourier analysis

During the past decades, researchers have focused a great deal of attention on the lobe bearings because of their superior stability. In this paper, a comprehensive methodology for determining the performances of bearings is developed based on the Fourier analysis. The advantage of this method is no longer to treat each lobe as an individual partial bearing like before, but to take into account the inherent relevance and coupling effects among lobes, etc. This article firstly puts forward universal frameworks of mathematical procedure, within which two multi-lobe journal bearings, namely, three- and four-lobe bearing are investigated. For the bearings with similar topology structure, the results show that the Fourier expansions of oil-film thickness are composed of the same family of harmonic basis functions. And those functions are merely related to the number of bearing lobes N. The results also show that both the oil-film profile and pressure field of the whole bearing completely inherit the periodicity from the periodic bearing structure and own the same period 2π/N commonly. Again, the simulated results construct the corresponding relationship between the expanded terms of oil-film thickness and pressure field. Further, quantitatively analyzing the variations of the pressure component indicates that as the order increases, the maximum of the pressure component decreases gradually. That provides a more convenient approach to obtain a satisfied prediction of the performance of the bearings just by using finite Fourier harmonic terms.