轨道交通超高顺坡率变化的缓和曲线盾心平面坐标计算及盾心曲线拟合方法
朱礼佳
Planar Coordinate Calculation and Curve Fitting Method for Transition Curve Shield Center of Variable Superelevation Slope in Rail Transit
ZHU Lijia
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作者信息:上海市政工程设计研究总院(集团)有限公司， 200092， 上海
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Affiliation:Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., 200092, Shanghai, China
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关键词:
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Key words:
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DOI:10.16037/j.1007-869x.2023.08.026
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中图分类号/CLCN:U212.3
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栏目/Col:研究报告
摘要:
目的：当缓和曲线的超高顺坡率变化时，不能采用常规的缓和曲线盾心坐标计算方法。此外，利用三次抛物线对此类缓和曲线盾心坐标拟合的精度通常也难以满足设计要求。因此需研究超高顺坡率变化的缓和曲线盾心平面坐标计算及曲线拟合方法。方法：基于超高顺坡率变化的缓和曲线，构建等效缓和曲线模型，设置虚拟的曲线段轨道超高值，进而计算曲线段上任意点的盾心偏移平面坐标。通过优化既有盾心缓和曲线拟合模型来提升曲线拟合精度，使之满足设计要求。引入校正决定系数对拟合曲线方程的精度进行准确评价，给出了超高顺坡率变化的缓和曲线盾心坐标拟合方程的拟合优度，并进一步给出了相应的拟合优度判断区间。以上海轨道交通崇明线为例，对拟合方程进行优化。结果及结论：利用等效缓和曲线可精确地计算出超高顺坡率变化缓和曲线上任意点的盾心坐标；适当增加拟合阶数，可较好地满足拟合精度的设计要求。
Abstracts:
Objective: When transition curve superelevation varies along with slope, conventional methods for calculating transition curve shield center coordinates are insufficient. Additionally, the fitting accuracy of such transition curve shield center coordinates using cubic parabolas often fails to meet design requirements as well. Therefore, it is necessary to investigate the calculation of shield center planar coordinates and curve fitting methods for transition curves with variable superelevation slopes. Method: An equivalent transition curve model is constructed based on the transition curve with variable superelevation slopes. Virtual curve segment track superelevation values are set for calculating the shield center offset planar coordinates at any point on the curve segment. The accuracy of curve fitting is improved by optimizing existing models for shield center curve fitting, ensuring compliance with design requirements. The coefficient of determination is introduced to accurately evaluate the accuracy of the fitting curve equation. The goodness of fit for the transition curve shield center coordinate fitting equation with variable superelevation slopes is determined, and the corresponding goodness of fit intervals are provided. The fitting equation is optimized using the example of Shanghai Rail Transit Chongming Line. Result & Conclusion: The shield center coordinates at any point on the transition curve with variable superelevation slopes can be accurately calculated using the equivalent transition curve. Increasing the fitting order appropriately can better meet the design requirements for fitting accuracy.
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