非定常短轴承油膜力公式的变分修正

Modified form of the unsteady oil-film force formula of short bearing by variational approach

本文采用了变分方法对非定常短轴承的油膜压力分布公式进行了修正 ,既保留了短轴承公式的简洁形式 ,又使其适用于大长径比轴承。得出了具有足够精度、适合轴颈大扰动情况下的有限长圆柱轴承非定常油膜力的解析公式。与差分充零算法相比 ,短轴承公式的结果在轴承长径比为 0 .6时 ,误差已经超过百分之二百 ,而本方法计算结果的误差小于百分之五。因此采用本方法既提高了短轴承油膜力公式的计算精度 ,又保持了油膜力公式的简洁形式 ,不失为进行转子

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.