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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。
Taking the Lagrange polynomial as the basis function of DQ method, a dynamic model of sliding bearing based on local DQ-Lagrange method is established. On the basis of this research, a method is proposed to directly solve the static pressure and disturbance pressure simultaneously. The influence of node density, support domain size and boundary conditions on the solution is analyzed. The results show that the multi-point support domain model has high solution accuracy, which is equivalent to the high-order finite difference method. However, the DQ-Lagrange method is prone to numerical oscillations due to high-order interpolation when the number of interpolation nodes is large. The half-Sommerfeld condition and the Reynolds boundary condition The influence of the maximum pressure and the load on the bearing is small and the influence on the dynamic characteristic coefficient is great. The dynamic characteristic coefficient obtained by the Reynolds condition is generally greater than the semi-Sommerfeld’s condition.