In linear rotor dynamics, the oil-film forces of bearings are generally treated as the well-known model of eight dynamic coefficients at the equilibrium state. This linear and steady model fails to analyze the nonlinear dynamic behaviors of a rotor-bearing system. So short bearing model is frequently used in the nonlinear rotor-bearing system because of its concise form. However, the error may be significant when the length to diameter ratio of the bearing is not small enough. Thus if we want to analyze the nonlinear phenomena of a rotating machine correctly the hydrodynamic forces of the bearing has to be solved numerically. That is, Reynolds equation needs to be solved by the discrete methods such as the finite difference method or the finite element method step by step following the nonlinear dynamic analysis process of rotor-bearing system. The oil-film pressure solution of the short bearing is improved to be a new form with few of parameters. The formulae of these parameters are obtained by the variational method. Thus, a modified form of the unsteady oil-film force of the short bearing is obtained. The modified formulae not only hold the concise form of the short bearing, but also adapt to the bearings with the large length to diameter ratio. These formulae of oil-film forces have a high precision even the journal motions largely in the bearing. Compared with the finite differential method (set-zero algorithm), the error of the results computed by the short bearing formula is as high as 200% when the length to diameter ratio of the bearing equals to 0.6, however this error decreases to only about 5% if the modified formulae are used. So the modified method is an effective way for the nonlinear analysis of a rotor-bearing system, since it improves the oil-film force precision of short bearing model greatly and still has the concise analytical form.

基于自由边值理论和凸集上的变分方法,提出一种求解当轴颈大扰动时实际轴承瞬态油膜力的近似公式.公式中引入一个参数来模拟油膜破裂自由边界(雷诺边界条件),则凸集上的泛函极值问题就转换为求此参数的代数极值问题.对椭圆轴承在轴颈作大范围扰动情况下的计算结果表明,这一方法达到了很高的精度,可用于转子-轴承系统的非线性动力分析,能大量降低数值计算瞬态油膜力所需的计算量.