Research On Calculation Method In Existing Railway Curve Realignment By Optimization Theory And Its Application

The railway after a long time operation and repair, the plane position is prone to misplace and deformation. This deformation and misplaced is more serious in the curve section, the shape of curve is easy to change, causing the irregularity of curve Track, curve Track directly affect the safe and stable of the train. To ensure the safe and stable operation of the train, the curve of direction must be regularly checked to restore a smoother curve when it is necessary. It is very import to study the optimization method of existing railway curve realignment to ensure train safe, stable and continuous operation.There are three main methods of existing railway curve realignment: string method, deflection method and coordinate method. In this paper, the conversion formula between the three methods is derived by the theory of calculation, combined with a large number of field data to analyse. Because string method and deflection method are based on the principle of involute, so the result of two methods after conversion calculations is very closed, the calculated error is increasing as the declination angle. But the involute theory is an approximate calculation, the Application of the Theory have a certain scope. The conclusion is that the calculated error of involute method is increases as the curve angle by analysing the data of deflection method and coordinate method after conversion calculations. As the curve angle of CWR track, when it is no more than one radian, the result of involute method is accurate. When it is greater than a radian, the calculation error of involute method is aside from the increasing curve radius, but with increasing curve angle, the calculation error be maximum when the curve angle close to 180 degrees.The optimization of curve realignment is to choose the best curve which is the most closed with the existing curve, so that the move distance of each measuring point is minimum. In this paper, study of the optimization of curve realignment by optimization theory, using the integral optimization methods, the square of move distance of each measuring point is minimum as the objective function, deduced the formula of gradient of the deflection method and coordinate method. Combined with a large number of field data, make the optimization analysis with string method, deflection method and coordinate method. In the optimization of curve realignment, the calculation results of various optimization methods are very similar, the results of multiplication method as constrained optimization is very similar with other optimization methods, but it is relatively complicated. As can be seen, if initial value selected with Linear fitting, the unconstrained optimization method also can be used to the optimization of curve realignment, the calculated results are very similar with constraints optimization method, and its optimal results is very similar with grid method. When using 10 m string method to optimize of incidental curve realignment, the optimization variables only have curve radius. Through optimized can significantly reduce the total move distance of incidental curve.Combining with characteristics of Excel, introduced the calculation Method of string method, deflection method and coordinate method and the optimization of curve realignment using Excel Solver. And through a large number of field data verified, the optimal results with Excel Solver is a high degree of compliance with the result of procedures, and all the results are almost identical with the grid method. Through optimized can significantly reduce the total move distance of curve. Based on the optimal results with Excel Solver, the total move distance of curve can be further reduce by fine adjustment with plan versine(-0.5mm-0.5mm), which reduces the workload of maintenance and repair.