UIC University of Illinois at Chicago

Transcription

1 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago FINITE ELEMENT/ MULTIBODY SYSTEM ALGORITHMS FOR RAILROAD VEHICLE SYSTEM DYNAMICS Ahmed A. Shabana Department o Mechancal and Industral Engneerng Unversty o Illnos at Chcago VEHICLE/TRACK DYNAMICS 1

2 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago CONTENTS 1. Background 2. Goals and Approaches 3. Wheel/Ral Contact Formulatons 4. Flexble Body Dynamcs 5. MBS Sparse Matrx Implementaton 6. Summary VEHICLE/TRACK DYNAMICS 2

3 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago BACKGROUND 1. Ralroad vehcles are examples o multbody systems (MBS); large rotatons (nonlneartes), and algebrac equatons (constrants). 2. General purpose MBS codes have DAE s solver, can beused to develop more dtld detaled models, can handle more general smulaton scenaros, do not employ lnearzaton, and can be used or advanced lexble body nvestgatons. 3. In order to correctly capture nonlnear eects n exstng tran models and uture hgh speed ral systems, t s necessary to use MBS codes. VEHICLE/TRACK DYNAMICS 3

4 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago GOALS AND APPROACHES 1. Develop new general, 3-D ully nonlnear wheel/ral contact ormulatons that can be mplemented n MBS algorthms (no lnearzaton, no look-up tables, creep orces). 2. Develop ral module (SAMS/Ral) that can be lnked to exstng general purpose MBS codes (such as SAMS/2000) that have advanced lexble body modelng capabltes (track and ral lexblty, car body lexblty, etc). 3. Develop accurate methods or track geometry descrpton (ANCF, B-Splnes, curvature, super-elevaton, elevaton grade). VEHICLE/TRACK DYNAMICS 4

5 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago WHEEL/RAIL CONTACT FORMULATIONS 1. In contact constrant and elastc ormulatons, ve equatons are used. 2. Normal wheel/ral contact t orce s used wth creepages n the calculatons o the creep orces (huntng). 3. Hgher dervatves wth respect to the surace parameters must be evaluated. R. Yakoub, D. Valtorta, K. Zaazaa Z Y Z Body Y S1 S2 Z r n n S1 Y S2 Body r 0 T t T t 2 0 Z Y Z w Y w Z w Y VEHICLE/TRACK DYNAMICS 5

6 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago FLEIBLE BODY DYNAMICS Floatng Frame o Reerence (FFR) Large translaton and rotaton Systematc couplng o FE/MBS codes 2 Use o modal analyss or coordnate reducton Implemented n general purpose MBS codes 1 3 R O r 2 1 u u o u P Flexble Ral Model (Integraton o Geometry 3 and Analyss) Geometry: Isoparametrc ANCF representaton or the ral surace s used to determne hgher dervatves o the geometrc vectors. FFR/FE deormaton analyss: Detaled track models can be developed by ntegratng FE/MBS algorthms (cross tes, asteners, ballasts, etc.). O VEHICLE/TRACK DYNAMICS 6

7 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago MBS SPARSE MATRI IMPLEMENTATION (SAMS/2000) SAMS/2000 s desgned to solve systems that consst o rgd bodes (q r ), lexble bodes (q r, q ), and very lexble bodes (q a). All the system constrants, ncludng contact constrants, are satsed at the poston, velocty and acceleratonlevels. e eve The user has access to all elements o the equatons o moton. M. Berzer JH J.H. Seo System Coordnates q q q q s T T T T r a Constrants Cq ( r, q, qa, s, t) 0 r a C q C q C q C s Q q r q q a s c T Augmented Equatons T Mrr Mr 0 0 Cq r q r Qr T M r M 0 0 Cq q Q T 0 0 Maa 0 C q a a a Q q T C s 0 s c Cq C r q C q C a s 0 Q G. Sanborn VEHICLE/TRACK DYNAMICS 7

8 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago SUMMARY 1. MBS algorthms that employ DAE s solver and sparse matrx technques are necessary or accurate vrtual prototypng o ralroad vehcle systems. 2. Several three-dmensonal wheel/ral contact ormulatons are mplemented n SAMS/Ral. The locatons o the contact ponts are predcted dtdonlne. 3. The track geometry s dened usng ANCF nte elements that allow or accurate calculatons o the poston coordnates and geometrc vectors at the wheel/ral contact ponts. 4. Flexble body FE/MBS algorthms are ntegrated to study the track, car body and vehcle component deormatons. VEHICLE/TRACK DYNAMICS 8

9 DSL Dynamc Smulaton Laboratory UIC Unversty o Illnos at Chcago Thank You! Australa, November 28, 2003; 48 cars. Cause; heat-induced track buckle. VEHICLE/TRACK DYNAMICS 9