机车非线性横向稳定性分析的数值分叉方法

THE NUMERICAL BIFURCATION METHOD OF NON-LINE ARLATERAL STABILITY ANALYSIS OF A LOCOMOTIVE

本文给出了一种２７个自由度的三轴转向架六轴机车非线性横向稳定性的数学模型，建立了数值分叉方法作为非线性横向稳定性的分析方法，引入分析稳定性的一组判别原则，指出为了得到机车横向稳定性的完整图像，必须获得亚临界Ｈｏｐｆ分叉速度Ｖ＿ｎ及脱轨速度Ｖ＿ｄ。最后对东风＿９型客运内燃机车进行了非线住板向稳定性分析。作者优选采用Ｎｅｗｍａｒｋ预测－校正积分法以求解运动微分方程组；开发了求解运动微分方程组的数值积分程序，以及处理计算结果的绘图程序。在机车非线性横向稳定性的数学模型中，考虑了轮轨接触几何学非线性、弹性滑动饱和非线性、悬挂非线性以及电机转矩对机车稳定性的影响。其研究结果可以有效地适用于新型机车的性能预测，新型机车设计的多数选择、调整，以及定型机车性能的检验及旧型机车的技术改造。对该模型略作修改，整个分析可适用于二轴转向架四轴机车和二轴转向架四轴客车的非线性横向稳定性问题。

This paper gives a model of twenty-seven degrees of freedom for a six-axle locomotive with three-axle bogies,sets up the numerical bifurcation method as the method ofnonlinear lateral stability analysis of a locomotive,and derives criteria of stabillity analysis.This paper indicates that the subcritical Hopf bifurcation speed V_n and the derailing speed V_dmust be obtained in order to describe a complete picture of the lateral stability of a locomotive.However,the critical speed V_c is not the most important index of locomotive stability. At the end of this paper,the diesel locomotive DF_9 has been analyzed for nonlinear lateral stability.To solve the locomotive equations of motion about nonlinear lateral stability, the papergives preference to Newmary′s predictor-corrector integration scheme as an integration algorithm,and sets up the numerical integration programs using FORTRAN language.At thesame time,the after treatment programs have been set up.Nonlinear geometry,changing contact areas,nonlinear suspension,nonlinear creep forcesand driving motor moment are taken into account in the model.The result of analysis may beused to choose a new-type locomotive′s parameter and predict a new-type locomotive′s performance as well as remake an old-type locomotive.The analysis will be suitable for a four-axle locomotive with two-axle bogies and a four-axle passenger car with two-axle bogies bydoing a little revision to the model.