Thermohydrodynamic lubrication analysis of micro gas bearing with journal misalignment
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摘要:
基于能量守恒原理推导计入气体稀薄效应的修正能量方程及其有限差分表达式，并通过偏导数法和有限差分法联立求解修正Reynolds方程、修正能量方程、气体黏温关系和气膜厚度方程，详细研究了微型气体轴承静动态性能随结构参数、轴颈倾斜方位角和黏温热效应的变化规律。结果表明：气膜热效应提高了微型气体轴承的承载能力、摩擦因数和动态刚度系数，而降低了直接阻尼系数，轴颈倾斜误差对微型气体轴承的静、动态性能均产生不利影响，计算结果可为提高微型气体动压轴承⁃转子系统的稳定性提供重要理论依据。
Abstract:Due to the ultra‑thin gas film of microbearing and various loads caused by the high‑speed rotation of micro rotor，the effects of gas rarefaction，viscosity‑temperature relation and journal misalignment on the lubrication characteristics of micro gas bearing cannot be neglected.The modified energy equation and its finite difference expression considering rarefaction effect were derived based on the energy conversation，and the modified Reynolds equation，modified energy equation，gas viscosity‑temperature relationship and film thickness equation were solved simultaneously by partial derivative method and finite difference method.The influences of structural parameters，misalignment angle and thermal effect on static and dynamic performance of microbearings were investigated in detail.Results showed that the load capacity，friction coefficient and dynamic stiffness coefficient of gas microbearing were improved by the gas film temperature，while the direct damping coefficient was reduced.The journal misalignment had an adverse influence on the static and dynamic performance of microbearing.Therefore，the results can provide an important theoretical basis for improving the stability of gas microbearing‑rotor system in microfluidic devices.
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图 1 微型稀薄气体润滑轴承结构示意图
Figure 1. Schematic illustration of rarefied gas⁃lubricated hydrodynamic microbearing
图 3 考虑气体稀薄效应和热效应的气膜压力分布对比
Figure 3. Comparison of gas pressure distribution with considering gas rarefaction and thermal effects
图 5 轴颈倾斜角和转动角速度对考虑黏温热效应微型气体轴承承载系数的影响
Figure 5. Load carrying capacity of gas microbearings considering viscosity‑temperature effect for various rotation speed and misalignment angle
图 7 扰动频率和轴颈倾斜角对考虑黏温热效应微型气体轴承动态刚度系数的影响（ε=0.7,ω=7×104 rad/s,B/Djo=0.1）
Figure 7. Influence of perturbation frequency and misalignment angle on dynamic stiffness coefficients （ε=0.7,ω=7×104 rad/s,B/Djo=0.1）
图 8 扰动频率和轴颈倾斜角对考虑黏温热效应微型气体轴承动态阻尼系数的影响（ε=0.7,ω=7×104 rad/s,B/Djo=0.1）
Figure 8. Influence of perturbation frequency and misalignment angle on dynamic damping coefficients （ε=0.7,ω=7×104 rad/s,B/Djo=0.1）
图 9 偏心率和轴颈倾斜角对考虑黏温热效应微型气体轴承动态系数的影响（Ω=4,ω=5×104 rad/s,B/Djo=0.1）
Figure 9. Influence of eccentricity ratio and misalignment angle on dynamic coefficients（Ω=4,ω=5×104 rad/s,B/Djo=0.1）
图 10 轴颈转速和轴颈倾斜角对考虑黏温热效应微型气体轴承动态刚度系数的影响（Ω=4,ε=0.7,B/Djo=0.1）
Figure 10. Influence of rotation speed and misalignment angle on dynamic stiffness coefficients （Ω=4,ε=0.7,B/Djo=0.1）
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