軌道車輛懸吊與軌道線形之量測分析

Measurement Analysis of Railway Vehicle Suspensions and Track Alignments

邱錫斌(Ship-Bin Chiou)

指導教授 ： 顏家鈺

國立臺灣大學/工學院/機械工程學研究所/博士(2018年)

https://doi.org/10.6342/NTU201800913

摘要

軌道車輛之主懸吊和次懸吊，是為確保良好乘車品質基本要件，本研究仔細探討懸吊零件採購規格，建立車輛橫切斷面模型，運用拉格朗日方程式(Lagrange equation)推導各運動方程式，於實際運轉軌道系統，比較該懸吊規格之模擬和實測結果，等效軌道剛性和阻尼亦予以推導；研究結果顯示，懸吊剛性將隨車輛載客荷重而改變，次懸吊剛性之變化可由採購規格查悉，而在滿座乘客時，主懸吊剛性比採購規格之最高剛性再提升26%；依維修工作說明書，車廂振動量測值係經由7赫茲之低通濾波後做判讀，建議該截止頻率至少增至9赫茲，以含括懸吊缺陷之分析；另運用智慧型手機，其內含傳感器，亦可量測車廂振動，當取樣率設為100赫茲時，可得到滿意的量測結果，確為一種有效且迅速之振動分析量測方法。
軌道維修常見的工項，是透過一條長弦進行軌道橫向和垂向正矢值量測，本研究針對橫向之左軌和右軌正矢值提出精準計算，並精確推導垂向正矢值函數，依推演結果，建立可供查詢垂向正矢值之線圖，呈現與斜率差值及曲線長度之比例關係，進而推導垂向正矢值近似方程式，並探討非對稱弦長之量測方法；研究結果顯示，當以10米弦長量測半徑小於300公尺之橫向圓曲線時，內側軌和外側軌之正矢值差異宜予以考量，在軌道設計標準內，由拋物曲線形成之垂向正矢值，以10米弦長量測最高可達30公釐，以5米弦長量測最高可達7.5公釐，軌道線形之容許偏差應基於該等正矢值，以正確執行軌道檢查。
為分析道岔在岔心附近軌道線形，本研究提出V形、U形、和S形函數，而翼軌和鼻軌之間隙，則得以方槽、單斜槽、或雙斜槽不平整函數描述，考量車輪之尺寸以進行軌跡分析，鼻軌之磨損和研磨亦予以詳述，模擬車輛行經該函數建模道岔之車輛垂向振動，研究結果顯示，將S形軌道線形函數和雙斜槽模型函數組合，可適用於岔心區域之道岔幾何分析。

關鍵字

軌道車輛 ； 懸吊參數 ； 振動量測 ； 軌道線形 ； 正矢值量測 ； 道岔 ； 車輪軌跡

並列摘要

To ensure satisfactory ride quality, primary and secondary suspensions are essential in railway vehicles. In this study, the specifications of suspension components were discussed in detail by referring to the component procurement documents. These specifications were compared with those obtained from simulations and measurements of an operational railway system through a transverse vehicle model using the equations of motion derived from the Lagrange equation. The equivalent rail stiffness and damping were also derived. Results showed that the stiffness should be altered according to the vehicle’s load, i.e., the number of passengers on board. The secondary suspension stiffness could be determined based on the specification. The primary suspension stiffness was 26% higher than the upper limit of the specification with a load of full seated passengers. According to the maintenance instructions, a 7-Hz low-pass filter (LPF) was used for car body vibration measurements. It’s suggested that the cutoff frequency of the LPF had to be increased to 9 Hz at least for suspension defect diagnoses. Furthermore, a smartphone with a gravity sensor could also be used for measuring car body vibrations. A sampling rate of 100 Hz could obtain the desired results, which could be an effective and efficient method for vibration analyses.
The chord method is commonly used in rail maintenance for horizontal and vertical versine measurements. In this study, the horizontal versines of the left and right rails were precisely calculated, and the vertical versine functions were exactly derived. According to the inferences, the line charts used for determining the vertical versine were created, to demonstrate the proportional relationship with the grade difference and the curve length. The equations for proximate vertical versine calculations were therefore derived. The asymmetrical chord measurements were introduced as well. The results indicated that the versine difference between the inner and outer rails had better to be considered when measuring the horizontal circular curve with a radius less than 300 m using a 10-m chord. According to the design criteria, a maximum vertical versine of 30 mm formed by the parabolic curves could be measured using a 10-m chord or a maximum versine of 7.5 mm could be measured using a 5-m chord, which should be considered as the essential versines. The deviation tolerance should be based on these values for accurate rail inspections.
In this study, three functions including the ‘V’, ‘U’, and ‘S’ shapes were considered for the analysis of alignment around the turnout in the frog area. The gap between the wing and nose rails was presented as an irregularity function that could be illustrated as a rectangular, single-slope, or double-slope trough model, and the dimension of the wheel of the vehicle was taken into account for the trajectory analysis. The wear and grinding of the nose rail were also demonstrated in detail. The vertical vibrations of the vehicle were simulated as passing through the functional model of the turnout. The results showed that the combination of an S-shaped alignment and a double-slope trough model could be suitable for the analysis of the turnout geometry in the frog area.

並列關鍵字

railway vehicle ； suspension parameters ； vibration measurement ； track alignment ； versine measurement ； railway turnout ； wheel trajectory

參考文獻

[1]TRTC, EMU Type 321/341: Operation and Maintenance Manual, Taipei Rapid Transit Corporation, Taiwan, 2000.

[2]TRTC, Rolling Stock: Maintenance Training Material, Taipei Rapid Transit Corporation, Taiwan, 2011.

[3]T.S. Wang, Study on Particular Technical Specification for Mass Rapid Electrical Multiple Units, PhD Thesis, National Taiwan University of Science and Technology, Taiwan, 2002.

[4]Y.T. Fan, Dynamic Analysis of Railway Vehicles and Its Verification through Field Test Data, PhD Thesis, National Taiwan University, Taiwan, 2005.

[5]S.K. Chang, Dynamic analysis of the rail vehicle structure system, Taiwan Railw. J., Vol. 321, pp. 1-35, 2005.