Effects of the slip velocity boundary condition on the characteristics of microbearings

During the application of results obtained by Pan et al (1999 J. Micromech. Microeng. 9 270), several issues have arisen about the flow and load characteristics in coaxial microbearings of finite length. In this paper, the analytical solutions of Pan et al are modified to obtain more reasonable results. Some further investigations are made concerning the effects of the slip coefficient β (representing the slipping extent of gas flow) on the characteristics of microbearings. Diverse parts of microbearings have various velocity alterations with different slip coefficients. Especially at the ends of the journal, a sharp upturn of the velocity is observed as the slip coefficient increases. The corresponding turning point of slip coefficient β_v depends on the length, gap and journal radius of the microbearings. In addition, direct comparisons of moment distributions on the journal of microbearing between the work of Pan et al and our work show that the moment at the two ends of the journal upturns at β_m = 0.0035 for L/a = 10, instead of at β_m = 0.01 in Pan et al. The corresponding turning point β_m depends only on, and is approximately linear with, the ratio L/a of microbearing length to journal radius. Moreover, the boundary conditions at the two ends only influence the velocities of flow field and moments near the ends, while having little effect on the moment distributions of inner flow. In this paper, the slip coefficient only ranges from 0 to 0.4 since the characteristics of microbearings essentially change little for β > 0.4.