Flow and load characteristics in a coaxial microbearing of finite length

Abstract

An analytical solution of the velocity field in a microbearing of finite length is derived based on a slip-flow model. Flow characteristics, such as velocity and friction torque for different slip coefficients are investigated in detail. The results show that the flow and load characteristics inside the microbearing depend on not only the magnitude of the slip coefficient but also the boundary conditions at both ends of the microbearing. It is found that when the slip coefficient decreases from 0.4 to 0.01, the friction torque exerted on the rotating shaft increases, and the effect of bearing ends becomes larger and larger. At = 0.01, the torque near the ends of the bearing rises to four times that in the middle of the rotating shaft. As the slip coefficient continues to decrease from 0.01, the friction torque in the middle of the shaft remains unchanged, while the distribution characteristic of the torque near the shaft ends approaches that in a macrobearing.

Inverted velocity profiles in rarefied cylindrical Couette gas flow and the impact of the accommodation coefficient

“…Two fundamental cylindrical Couette flow cases are considered: a stationary outer cylinder and a rotating inner cylinder ͑case I͒; and, second, a stationary inner cylinder and a rotating outer cylinder ͑case II͒. Previous analytical studies 1,2,5,6 have generally assumed that the accommodation coefficients at the inner and outer cylinder walls are identical. In contrast, the present study considers the influence of both the inner and outer accommodation coefficients.…”

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

“…The Knudsen number, which reflects the degree of rarefaction of a gas, is defined as the ratio of the molecular mean free path to the significant characteristic dimension of the flow field. Various criteria are proposed with some disagreement and the criterion adopted in this paper is followed by Pan et al [6]. The regimes of continuum flow, slip flow, transition flow and free molecule flow correspond to Kn 0.001, 0.001 < Kn < 0.1, 0.1 < Kn < 10 and Kn 10, respectively.…”

“…The departure from the continuum flow occurs when the gas layer adjacent to the surface does not satisfy the no-slip velocity boundary condition. Some researchers have made experimental and theoretical analyses on the characteristics of microbearings and film lubrication [3][4][5][6]. Harley et al [4] demonstrated the existence of non-zero wall velocity in microchannels and showed the contribution of non-zero slip velocity to the mass flow.…”

“…Maureau et al [5] analyzed the characteristics of eccentric microbearings of infinite length. Considering the effects of bearing ends, Pan et al [6] solved the simplified governing equation and obtained some results on the characteristics inside a finite size microbearing. However, some problems arise in the application of these results.…”

“…We discuss velocity variations in different positions of the journal and axle housing with slip coefficients, which represent the slipping extent of gas flow. The moments of Pan et al [6] and of our work in microbearing journal under different slip coefficients are compared and further analyzed. Also, investigations are made of velocity and moment distributions of microbearings at different boundary conditions.…”