空气轴承节流器阵列气膜压强的等效电路建模

对于空气轴承中气膜的复杂湍流运动,无法直接用解析法求解其雷诺方程。针对计算流体力学(Computational fluiddynamics,CFD)方法计算大规模节流器阵列气膜压强分布所需时间较长的问题,提出一种结合节流器单元气膜等效电路建模与分段非线性插值的气膜压强分布解析计算方法。在CFD仿真得到单元气膜压强分布的基础上,建立以线性电阻网络表示的多端口单元气膜稳态等效电路模型,确定了其中的模型参数。通过对单元气膜进行区域划分,借助PSpice电路仿真得到的关键点电位数据,确定气膜压强的分区段插值函数,从而计算得到单元气膜承载力,与CFD仿真结果相比误差为3.7%。通过16个单元的互联建立4 4阵列等效电路模型,可快速计算出阵列气膜的承载力。与CFD仿真相比,4 4阵列等效电路模型的计算误差为8.74%,而计算速度提高三个数量级以上。

Equivalent Circuit Modeling of Film Pressure in Air Bearing with Orifice Array

For the turbulent flow in the air bearing,the Reynold’s equation has no closed-form solution.Computational fluid dynamics(CFD) simulation is time-consuming for large scale orifice arrays.An approximate analytical model for the pressure distribution of the air film in orifice arrays is proposed,which combines equivalent circuit modeling and segmented nonlinear interpolation.Based on the pressure distribution of the air film derived from CFD simulation,a multi-port equivalent circuit model for the steady-state pressure distribution of an orifice unit is established by using linear resistor network,and the resistances in the network are determined.The air film of an orifice unit is subdivided into multiple regions,and a nonlinear segmented interpolation function is fitted by using the PSpice circuit simulation data.The load capacity of an orifice unit is calculated from the interpolation function with an error of 3.70% as compared with the CFD results.The equivalent circuit model for a 4?4 orifice array is obtained by interconnecting 16 orifice units,and the load capacity of the orifice array can be calculated efficiently.As compared with the CFD simulation,the error of the equivalent circuit model for the 4?4 orifice array is 8.74% in terms of load capacity while the computational speed is improved by over 3 orders of magnitude.