基于局部微分求积-拉格朗日法的滑动轴承动力特性求解模型

Journal Bearing Dynamic Characteristics Calculation Model Based on the Local Differential Quadrature-Lagrange Method Based on Lagrange Interpolationmethod

以拉格朗日(Lagrange)多项式作为微分求积(the differential quadrature method,DQ)方法的基函数,建立了基于局部DQ-Lagrange方法的滑动轴承动力特性求解模型。并在此研究基础上,提出了将静态压力及扰动压力同步直接求解的方法。分析了节点密度、支持域大小、边界条件等对求解的影响。结果表明:多点的支持域模型求解精度高,相当于高阶有限差分法,但插值节点较多时,DQ-Lagrange方法易出现高阶插值引起数值振荡现象;半Sommerfeld条件与Reynolds边界条件对滑动轴承最大压力及载荷求解影响较小,对动力特性系数影响较大,Reynolds条件求出的动力特性系数普遍大于半Sommerfeld条件。

The paper set up a local differential quadrature-Lagrange method based on Lagrange interpolation （DQ-Lagrange） to solve the journal bearing dynamic characteristics. Based on the research above, both the static pressure and perturbed pressure were solved in the same time. This paper analyzed the influence of the mesh density, the size of the support domain and the boundary condition treatment method on the accuracy of the calculation. The calculation results show that the multipoint support domain model has high accuracy, which is equivalent to high order finite difference method. It may cause numerical oscillation when support domain has too much nodes. The half-Sommerfeld boundary condition and the Reynolds boundary condition have more influence for the dynamic characteristic coefficients to the maximum pressure and load. The dynamic characteristic coefficients solved by the Reynolds boundary condition are usually bigger than those by the half-Sommerfeld boundary condition.