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The Dynamic Performance Analysis of a Low-Floor Tram Hydraulic Anti-Kink System Based on Multidisciplinary Collaboration

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The Dynamic Performance Analysis of a Low-Floor Tram Hydraulic Anti-Kink System Based on Multidisciplinary Collaboration energies Article The Dynamic Performance Analysis of a Low-Floor Tram Hydraulic Anti-Kink System Based on Multidisciplinary Collaboration Xiaokang Liao 1 , Zili Chen 2,*, Yiping Jia 3 and Jianhui Lin 4 1 School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611730, Sichuan, China; [email protected] 2 School of Mathematics, Southwest Jiaotong University, Chengdu 611730, Sichuan, China 3 Sichuan Aerospace Industry Group Co., Ltd., Chengdu 610100, Sichuan, China; [email protected] 4 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610036, Sichuan, China; [email protected] * Correspondence: [email protected]; Tel.: +86-139-8005-0975 Received: 5 August 2020; Accepted: 18 August 2020; Published: 21 August 2020 Abstract: According to the basic principle of the hydraulic anti-kink system and flow continuity equation, this paper takes the low-floor tram as the research object and the four vehicles as the research carrier. Based on the correlation parameters between the vehicle subsystem and the hydraulic subsystem, a co-simulation platform of a low-floor tram with hydraulic an anti-kink system is built. The co-simulation results show that the anti-kink system can well maintain the relative yaw angle consistency between the vehicle body and bogie. The anti-kink system restrains the maximum yaw angle and excessive lateral displacement of the vehicle body effectively. The consistency between the experiment results and the simulation results shows the accuracy of the model. The co-simulation model of the low-floor tram with hydraulic anti-kink system can be used to research the dynamic performance when it passes through curve line. Keywords: hydraulic anti-kink system; low-floor tram; co-simulation; dynamic performance 1. Introduction With the continuous expansion of the city boundary, the traffic problems inside the city are becoming increasingly serious. As an efficient means of transportation, urban rail transit has been paid more and more attention by urban decision makers. Among them, the low-floor tram has been widely used in many cities because of its economic and environmental protection, energy saving, and other characteristics [1,2]. The low-floor tram is composed of three motor vehicles Mc1, M, Mc2, and a trailer T. The overall structure of a low-floor tram is shown in Figure1. Mc1 and T form a unit and M and Mc2 form another unit. The two units are connected by a single hinge joint, and only two vehicles are allowed to yaw around the hinge center in the horizontal plane [3]. Because this kind of tram adopts the structure of one bogie for each vehicle, the yaw angle of the vehicle body relative to the bogie in the plane is larger when crossing the curve. When the train passes through the curve, the bogie and articulated device will bear a certain torque, which can cause the relative rotation of the vehicle body and the lateral force on the wheel flange to increase. The excessive torque may even cause the train derailment. The installation of a hydraulic anti-kink system can restrain the yaw angle of the vehicle body relative to the bogie and greatly reduce the lateral force on the wheel flange [4]. Therefore, it is essential to research the curving performance and running stability of the low-floor tram. Energies 2020, 13, 4335; doi:10.3390/en13174335 www.mdpi.com/journal/energies Energies 2020, 13, 4335 2 of 19 Energies 2020, 13, x FOR PEER REVIEW 2 of 19 FigureFigure 1.1. OverallOverall structurestructure ofof low-floorlow-floor tram.tram. UhlUhl T.T. etet al.al. [5[5]] researchedresearched thethe structuralstructural dynamicdynamic characteristicscharacteristics ofof thethe low-floorlow-floor tramtram byby experimentalexperimental method,method, includingincluding thethe strainstrain measurementmeasurement atat thethe hingehinge jointjoint andand somesome motionmotion devicesdevices inin thethe vehiclevehicle body.body. TheyThey usedused aa non-contactnon-contact sensorsensor toto measuremeasure thethe displacement,displacement, yawyaw angle,angle, andand somesome mutualmutual characteristicscharacteristics describingdescribing vehiclevehicle dynamics.dynamics. ZhangZhang X.X. etet al.al. [[6]6] establishedestablished thethe dynamicdynamic modelmodel ofof aa low-floorlow-floor tram,tram, determineddetermined thethe innerinner andand outerouter wideningwidening amountamount ofof low-floorlow-floor tramtram whenwhen runningrunning onon thethe curve.curve. TheyThey analyzedanalyzed thethe dynamicdynamic performanceperformance indexindex ofof low-floorlow-floor tramtram withwith oror withoutwithout anan anti-kinkanti-kink system.system. However, theirtheir analysisanalysis lackedlacked thethe statestate quantityquantity calculationcalculation ofof thethe hydraulichydraulic system,system, whichwhich hadhad certaincertain limitations.limitations. AccordingAccording toto thethe flowflow continuitycontinuity equationequation andand forceforce balancebalance equation, equation, Huang Huang Y.P. Y.P. et al.et [al.7] established[7] established the dynamic the dynamic model mo ofdel the hydraulicof the hydraulic anti-kink anti-kink system ofsystem the tram of the and tram analyzed and analyzed the dynamic the dynamic response response characteristics characteristics of the hydraulic of the hydraulic anti-kink anti-kink system. Theirsystem. results Their showed results thatshowed the forcethat ofthe the force hydraulic of the hydraulic cylinder controlled cylinder controlled by the anti-kink by the systemanti-kink is disystemfferent, is anddifferent, the force and ofthe the force hydraulic of the hydrauli cylinderc cylinder near the near guide the wheel guide of wheel the front of the vehicle front vehicle is the largest.is the largest. Zhu W.L Zhu et W.L al. [8 et] established al. [8] established the models the mo of thedels control of the control subsystem, subsystem, air brake air subsystem, brake subsystem, electric brakeelectric subsystem, brake subsystem, and brake and execution brake execution subsystem subsystem by using by multidisciplinary using multidisciplinary collaborative collaborative analysis method.analysis Theirmethod. results Their provided results theoretical provided basis theo forretical the development basis for andthe design development optimization and of design brake system.optimization Li J. et of al. brake [9] established system. Li the J. damping et al. [9] mathematical established the model damping which amathematicalffected the lateral model damping which functionaffected ofthe the lateral anti-kink damping system function by analyzing of the anti-k the principleink system of by the analyzing anti-kink the system. principle They of analyzed the anti- thekink influence system. ofThey throttle analyzed valve the and influence pressure of limiting throttle valve valve in and the pressure buffer valve limiting group valve on the in the damping buffer characteristics.valve group on The the simulationdamping characteristics. curve of damping The characteristicssimulation curve was of in damping good agreement characteristics with the was test in curve.good agreementWang Y.Q. with et al. the[10 ]test designed curve. Wang two sets Y.Q. of theet al. hydraulic [10] designed anti-kink two system,sets of the which hydraulic can satisfy anti- thekink operation system, which state of can anti-kink satisfy systemthe operation in normal state mode, of anti-kink fault mode, system and in anti-kink normal mode, mode. fault They mode, took theand articulated anti-kink mode. Mc1 and They vehicle took the T as articulated their research Mc1 objects.and vehicle The T two as their sets ofresearch anti-kink objects. system The were two simulatedsets of anti-kink under normalsystem were operation simulated mode under by AMESim normal software, operation they mode obtained by AMESim the displacement software, they of vehicleobtained Mc1’s the maindisplacement control cylinder of vehicle and Mc1’s vehicle main T’s main control control cylinder cylinder and piston. vehicle Ding T’s W.S. main et al.control [11] basedcylinder on piston. the establishment Ding W.S. et of al. a corresponding[11] based on the mathematical establishment model of a andcorresponding analyzed the mathematical formation principlemodel and of combinedanalyzed the damping. formation The principle influence of of combined the design damping. parameters The of influence the buffer of valve the groupdesign onparameters the damping of the characteristics buffer valve wasgroup further on the analyzed. damping Their characteristics results showed was thatfurther the combinationanalyzed. Their of throttleresults showed valve and that pressure the combination limiting valve of throttle in the buvafflveer valveand pressure group forms limiting the valve damping in the characteristics buffer valve ofgroup multi forms segment the parabola damping combination characteristics with of multi multi inflection segment points. parabolaLiu X.combination et al. [12] established with multi a lateralinflection dynamic points. curve Liu X. negotiation et al. [12] established model of a suspension lateral dynamic rail vehiclecurve negotiation bogies based model on of the suspension coupling systemrail vehicle of rubber bogies tire based and on ground. the coupling They analyzed system of the rubber lateral tire and and yaw ground. motion They dynamics analyzed of wheelthe lateral set structureand yaw with motion rubber dynamics tire and groundof wheel coupling, set structur the displacemente with rubber and tire acceleration and ground response
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