Improved finite difference method for pressure distribution of aerostatic bearing

一类改进的气体静压轴承压力场分布有限差分算法(英文)

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

针对传统的静压气体轴承压力分布算法效率较低或收敛性较差等问题,提出了一类改进的有限差分计算方法.以小孔节流式的径向静压气体轴承的压力分布为对象,采用有限差分法求解非线性雷诺气体润滑方程;根据流量平衡原理,提出了一种新型变步长逐步逼近迭代算法,用于修正迭代过程中的供气口出口压力,提高算法的效率和收敛性;基于Matlab工具,开发了一套通用的径向静压气体轴承的压力场分布计算软件.算例结果表明:所提出的改进有限差分法计算效率高,稳定性好,收敛快;对于小间隙(小于2μm)气膜,此方法仍然有效并快速收敛.