基于X射线断层扫描的钢轨滚动接触疲劳裂纹形状建模方法
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摘要
为建立钢轨滚动接触疲劳裂纹真实形状数学模型,采用X射线断层扫描技术,获得了钢轨轨距角-轨肩处的滚动接触疲劳裂纹的真实形态点云数据,提出栅格算法确定裂纹尖端和开口的边界点、三次B样条曲线拟合裂纹尖端、裂纹面与钢轨轨面相交确定裂纹开口的钢轨滚动接触疲劳裂纹形状建模方法。研究发现:栅格算法提取的裂纹边界特征点比凸包算法提取的裂纹边界特征点多,代表裂纹边界特征的凸点和凹点都识别,使得裂纹边界失真度更小;随着栅格边长减小,栅格算法提取出的裂纹边界点数量增加,减少了凸包算法的漏点问题。将提取好的裂纹尖端边界点分别用最小二乘法、Bezier曲线、三次B样条曲线等方法进行曲线拟合,发现三次B样条曲线拟合得到的裂纹尖端与真实裂纹最为接近,其数据拟合的偏差最大值和标准差均最小,由此获取了真实裂纹的尖端形状数学模型。
In order to establish the true shape mathematical model of the rail rolling contact fatigue(RCF) crack,the true shape point cloud data of the RCF crack at the rail gauge-rail shoulder was obtained by X-ray tomography.A method was proposed to model the shape of rail RCF crack by using the grid algorithm to determine the boundary point of crack tip and opening,fitting crack tip with cubic B-spline curve and using intersection of crack surface and rail surface to determine the shape of crack opening.It was found that the number of crack boundary feature points extracted by the grid algorithm was more than that extracted by the convex hull algorithm.Both the bumps and the concave points representing the crack boundary feature were identified by the grid algorithm and the crack boundary distortion was smaller.As the length of the grid was gradually reduced,the number of crack boundary points extracted by the grid algorithm was further increased and the missing point problem of the convex hull algorithm was solved.The extracted crack tip boundary points were fitted by the least square method,Bezier curve and cubic B-spline curve.It found out that the crack tip obtained by the cubic Bspline curve fitting was the closest to the real crack and the maximum deviation and standard deviation of data fitting with the cubic B-spline curve were both the smallest and the mathematical model of the true crack tip shape was obtained.
In order to establish the true shape mathematical model of the rail rolling contact fatigue(RCF) crack,the true shape point cloud data of the RCF crack at the rail gauge-rail shoulder was obtained by X-ray tomography.A method was proposed to model the shape of rail RCF crack by using the grid algorithm to determine the boundary point of crack tip and opening,fitting crack tip with cubic B-spline curve and using intersection of crack surface and rail surface to determine the shape of crack opening.It was found that the number of crack boundary feature points extracted by the grid algorithm was more than that extracted by the convex hull algorithm.Both the bumps and the concave points representing the crack boundary feature were identified by the grid algorithm and the crack boundary distortion was smaller.As the length of the grid was gradually reduced,the number of crack boundary points extracted by the grid algorithm was further increased and the missing point problem of the convex hull algorithm was solved.The extracted crack tip boundary points were fitted by the least square method,Bezier curve and cubic B-spline curve.It found out that the crack tip obtained by the cubic Bspline curve fitting was the closest to the real crack and the maximum deviation and standard deviation of data fitting with the cubic B-spline curve were both the smallest and the mathematical model of the true crack tip shape was obtained.
引文
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[12]张熙胤,陈兴冲,王常峰,等.最小二乘法曲线拟合在桥梁施工应力监控中的应用[J].中外公路,2015,35(4):138-141.
[13]于佳琳,言勇华,王嘉宁.基于改进Bezier拟合算法的工业机器人轨迹规划[J].机电一体化,2016(2):12-18.
[14]李卫东,侯丽虹.基于三次B样条曲线拟合的列车定位方法研究[J].控制工程,2017,24(1):135-140.
[15]周宇,邝迪峰,郑晓峰,等.基于三维重构的钢轨滚动接触疲劳裂纹扩展预测[J].机械工程学报,2018,54(4):158-166.
[2]FLETCHER D,HYDE P,KAPOOR A.Modelling and full-scale trials to investigate fluid pressurisation of rolling contact fatigue cracks[J].Wear,2008,265(9/10):1317-1324.
[3]GARNHAM J E,FLETCHER D I,DAVIS C L,et al.Visualization and modelling to understand rail rolling contact fatigue cracks in three dimensions[J].Journal of Rail and Rapid Transit,2011,225(2):165-178.
[4]ZHOU Y,WANG S F,WANG T Y,et al.Field and laboratory investigation of the relationship between rail head check and wear in a heavy-haul railway[J].Wear,2014,315(1-2):68-77.
[5]NICHOLSON G L,KOSTRYZHEV A G,HAO X J,et al.Modelling and experimental measurements of idealized and light-moderate RCF cracks in rails using an ACFM sensor[J].NDT&E International,2011(44):427-437.
[6]NAEIMI M,LI Z L,QIAN Z W,et al.Reconstruction of the rolling contact fatigue cracks in rails using X-ray computed tomography[J].NDT and E International,2017(92):199-212.
[7]ZHOU Y,ZHENG X F,JIANG J N,et al.Modeling of rail head checks by X-ray computed tomography scan technology[J].International Journal of Fatigue,2017(100):21-31.
[8]姜俊楠.基于三维重构和轮轨蠕滑的钢轨疲劳裂纹扩展分析[D].上海:同济大学,2015:19-34.
[9]CASEY J,JOHAN A,LARS H,et al.3D characterization of rolling contact fatigue crack networks[J].Wear,2016(366-367):392-400.
[10]GRAHAM R L,YAO F F.Finding the convex hull of a simple polygon[J].Journal of Algorithms,1983(4):324-331.
[11]王炳军,肖洪天,岳中琦.半无限横观各向同性介质中多裂纹相互作用分析[J].岩土力学,2012,33(8):2527-2535.
[12]张熙胤,陈兴冲,王常峰,等.最小二乘法曲线拟合在桥梁施工应力监控中的应用[J].中外公路,2015,35(4):138-141.
[13]于佳琳,言勇华,王嘉宁.基于改进Bezier拟合算法的工业机器人轨迹规划[J].机电一体化,2016(2):12-18.
[14]李卫东,侯丽虹.基于三次B样条曲线拟合的列车定位方法研究[J].控制工程,2017,24(1):135-140.
[15]周宇,邝迪峰,郑晓峰,等.基于三维重构的钢轨滚动接触疲劳裂纹扩展预测[J].机械工程学报,2018,54(4):158-166.