A new modified Reynolds equation for ultrathin film gas lubrication

2020

Micromachines

Temperature rise and elastic deformation are unavoidable issues occurring in high-speed gas microbearings due to the dominant small-scale fluid dynamics in rarefied gas flow applications. In this paper, thermo-elasto-aerodynamic analysis requires simultaneously solving the modified Reynolds equation, modified energy equation, temperature–viscosity relationship and the elasticity equations for predicting the lubrication characteristics of microbearings. A thermo-elasto-aerodynamic lubrication is systematically investigated by using the partial derivative method, finite difference formulation and the finite element approach. The results indicate that, compared with rigid microbearing which has a constant viscosity gas lubricant, the temperature effect increases the load capacity, friction coefficient and stiffness coefficients, and it decreases the attitude angle and damping coefficients of the microbearing. The flexibility of the bearing pad also leads to the increase in load capacity and direct stiffness coefficients, while it remains to further decrease the direct damping coefficients on the basis of thermo-aerodynamic performance. The present study is conducive to accurately analyze the microscopic flow properties in a microbearing-rotor system.

Section: Methodsmentioning

confidence: 99%

Thermo-Elasto-Hydrodynamic Characteristics Analysis of Journal Microbearing Lubricated with Rarefied Gas

2020

Micromachines

“…For the slip correction factors in rarefied gas flows under ultra-low spacing, the dimensionless Poiseuille flow rate between rotor and bearing surfaces with the gas thickness h is given as [30] QP=12μ∂p∂xh3(b⋅Dc+aπ2D+16)−h32μD⋅∂p∂x=b⋅Dc+1+aπ2+D6…”

Section: Numerical Model and Solution Methodsmentioning

confidence: 99%

Interactive Effects of Rarefaction and Surface Roughness on Aerodynamic Lubrication of Microbearings

2019

Micromachines

The aerodynamic lubrication performance of gas microbearing has a particularly critical impact on the stability of the bearing-rotor system in micromachines. Based on the Duwensee’s slip correction model and the fractal geometry theory, the interactive effects of gas rarefaction and surface roughness on the static and dynamic characteristics were investigated under various operation conditions and structure parameters. The modified Reynolds equation, which governs the gas film pressure distribution in rough bearing, is solved by employing the partial derivative method. The results show that high values of the eccentricity ratio and bearing number tend to increase the principal stiffness coefficients significantly, and the fractal roughness surface considerably affects the ultra-thin film damping characteristics compared to smooth surface bearing.

“…The above Equations (15)- (20) are solved simultaneously by using the finite element method and relaxed iterative algorithm, and P E and P θ are obtained. According to the coordinate system as shown in Figure 1, the stiffness coefficients K ij and damping coefficients D ij of gas microbearing are given by the following formula.…”

Section: Of 18mentioning

confidence: 99%

“…Subsequently, a number of approaches, based on the kinetic theory, to the practical analysis of rarefaction effects on micro fluidic systems have been reported that have created discussion. Hwang et al [20] proposed a new modified Reynolds equation which includes three adjustable coefficients in the velocity boundary conditions, and the results showed that the model produces good approximation to the Boltzmann model for a wide range of Knudsen numbers. Kang et al [21] extended the databases of Poiseuille flow rate and Couette flow rate by introducing new terms into system equations at track recording head/disk interface in hard disk drives by using the Bhatnagar-Gross-Krook kinetic equation.…”

Section: Introductionmentioning

confidence: 99%

Research on Static and Dynamic Characteristics of Gas-lubricated Microbearings for Microfluidic Devices

2020

Applied Sciences

Aerodynamic journal microbearings with microtribological phenomena significantly influence the operating stability of microfluidic devices. The modified Reynolds equations including different rarefaction models are derived and are solved by the partial derivative method and relaxation iteration algorithm. The effects of Knudsen number and bearing parameters on the static and dynamic characteristics of microbearings are investigated in detail. The results show that the rarefaction effect plays a crucial role in the ultra-thin gas film lubrication. The maximum film pressure of Fukui–Kaneko (FK) model is lowest and the result in Boltzmann model is largest in small Knudsen number regions. As the Knudsen number increases further, the curve of FK model is coincident with that of the Boltzmann model in the transition regime. The direct stiffness coefficients of Boltzmann model increase with the increase of eccentricity ratio and aspect ratio, whereas the effect of Knudsen number on the damping coefficients yields a relatively complicated trend.