Advanced Materals Research Vol. 4 (0) pp 7-80 Onlne avalable snce 0/Dec/0 at www.scentfc.net (0) Trans Tech Publcatons, Swtzerland do:0.408/www.scentfc.net/amr.4.7 Knematcs and Dynamcs Smulaton Research for Roller Coaster Mult-body System Genng Xu a, Huun Xn b, Fengy Lu c,mnglang Yang d School of Mechancal Engneerng, Tayuan Unversty of Scence and Technology, Tayuan 03004, Chna a xugenng@3.com, b xnhuun9@.com, c lufengy3@sna.com, d 535075@qq.com Key words: Roller coaster, Constrants, Knematcs and dynamcs smulaton Abstract: To assess the roller coaster mult-body system securty, t s need to extract the runnng process of knematcs, dynamcs, load spectrum and other features, as bass dates of the roller coaster structural desgn. Based on Soldworks/moton software and n the 3D model, the calculaton formula of the carryng car velocty and acceleraton s derved, and the fve rsk ponts of the roller coaster track secton are found by smulaton n the runnng, and the smulaton results of roller coaster axle mass center velocty are compared wth theoretcal calculaton results, whch error s less than 4.%, ndcatng that the calculaton and smulaton have a good ft and provdng the evdence for the roller coaster structure desgn analyss. Introducton The roller coaster, because of ts hgh speed and stmulate, has become an essental amusement park rdes. It s loved by young. But gven ts hgh, fast hazardous characterstcs, roller coaster comes nto natonal specal equpment management. There are strct requrements for ts desgn, nstallaton and operaton of the securty. Vrtual technology wth powerful functon and ntutve vsual make the desgn of roller coaster change from the tradtonal manual calculaton desgn to computer smulaton desgn. Based on Soldworks software establshed the roller coaster model, the resstance and constrant s mposed, and to realze the roller coaster knematcs and dynamcs smulaton. Track the each of structure ont velocty and acceleraton curves are obtaned by smulaton, and then the rsk ponts of the roller coaster track secton are found. Based on the energy conservaton theorem, the calculaton formula of the velocty and acceleraton s derved. The smulaton results of rsk ponts velocty are compared wth theoretcal calculaton results,t s ratonal and prepare for the roller coaster structure research. Roller Coaster Model Constrants Roller Coaster Model Hypothess. Manly by the roller coaster track, carrage, headstock, tal car, axle, wheel stand, draw-bar, htch yoke, tal connector, pulleys and other components, and the track by one vertcal rng and two spral rngs. As the roller coaster devce s very complex, so t requred model assumptons before the smulaton (Roller coaster the whole space model shown n Fgure )[]. Fg. Roller coaster the whole space model All rghts reserved. No part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of TTP, www.ttp.net. (ID: 30.03.3.75, Pennsylvana State Unversty, Unversty Park, USA-0/03/5,0:5:4)
Advanced Materals Research Vol. 4 77 Carryng car model hypothess: people-char model smplfed to such qualty rectangular; mport sx carryng car model, to ensure complete data acquston (carryng car assembly model shown n Fgure )[]. Fg. Smulaton Constrants. Knematcs and dynamcs smulaton s carred out n Soldworks plug-n moton. In the moton, the roller coaster model has been assembled could be drectly nto Soldworks/moton, and the orgnal assembly relatonshps map drectly to moton constrants[3]. In addton, the roller coaster needs to be added some necessary constrants to ensure that carryng car to be able smoothly along the track to complete a crcle. Specfc constrants defned as follows: The smulaton envronment s mposed gravtatonal feld that s carryng car by gravty. The carryng car s mposed tracton when t s on clmbng stage. To enable t can clmb to the hghest pont, and to obtan the correspondng potental energy. It s dffcult to acheve complete cooperaton n the vew of the pulley and the track. So here assumed that a pont on the axle along the track loftng contour curve moton to complete the cycle path, and to mprove the accuracy. The track and the ponts on the axle are establshed resstance constrants. Contact materals were based on the actual stuaton s defned as steel and dry nylon. The roller coaster s not mposed the resstance to stop when t back to the platform after the end of the smulaton. The dynamc smulaton of the anmaton frame s defned per second 5. Velocty and Acceleraton Vector Calculaton Carryng car assembly model Carryng Car Velocty Calculaton. Accordng to the carryng car energy conservaton theorem, the carryng car velocty at any pont and arrve at the pont + s calculated[4]: Calculatng pont : Knetc energy: Potental energy: Ed = mv () E = mgh () p = Where: m s qualty sngle car, and there are altogether vehcles(=, ); speed calculaton pont, ts unt s m / s ; g s acceleraton of gravty, and s the calculaton pont, and the vehcle heght, ts unt s m. Calculatng pont + : Knetc energy: v s the tran g = 9.8m / s ; H E+ d = mv + (3)
78 Advanced Desgn Technology, ICAMMP 0 Potental energy: E = mgh (4) + p +, = Gravty frcton loss: E, + g = mg ( cosγ+ cosγ+, ) fs, +, (5) = Centrpetal force frcton loss: v v+ E, + n = m + f s, +, = () R R+, Where: v + s the tran speed calculaton pont +, ts unt s m / s, and there are altogether vehcles(=, ); H +, s the calculaton pont +, and the vehcle heght, ts unt s m ; cosγ, s the drecton cosne n the calculaton pont, and the vehcle normal (vertcal track); γ s the drecton cosne n the calculaton pont +, and the vehcle normal (vertcal cos +, S, track);, + s the center of gravty traectory arc length n the calculaton pont and + of the vehcle, ts unt s m ; R s the center of gravty traectory curvature radus n the calculaton pont, ts unt s m ; R +, s the center of gravty traectory curvature radus n the calculaton pont +, ts unt s m. Accordng to the prncple of energy balance, obtaned: mv + mgh = mv + mgh mg + = v v+ m + fs = R R+, The formula (7) smplfy to obtan v + : v = + = +, ( cosγ cosγ ) +,, +,, +, v + g ( H H+, ) + g( cosγ + cosγ +, ) + fs, +, = = R + = fs, +, = R +, Carryng Car Curve Segment Acceleraton Calculaton. fs v (7) (8) a = v / R (9) + + + Where: a + s the acceleraton n pont + ; v + s the velocty n pont + ; R + s the curvature radus n pont +. The roller coaster velocty and acceleraton at any pont can be obtaned by formula (8) and (9).
Advanced Materals Research Vol. 4 79 Smulaton Results and Analyss It spends 83 seconds Roller coaster smulaton from start to fnsh n a tme of. Carryng car began to moton to the track bottom of the ramp by ts own gravty from the platform, and moton to the track hghest by the ncrease tracton force, then back to the platform to complete a workng cycle n gravty. Roller coaster front axle mass center velocty-ampltude and acceleraton-ampltude curve are obtaned by the roller coaster dynamc smulaton. They are shown n Fgure 3. Fg. 3 Roller coaster front axle mass center velocty and acceleraton-ampltude curve Fg. 4 The 5 rsk ponts of the roller coaster track secton As the velocty-ampltude curve n Fgure 3 (black lne) shows, the carryng car began to moton o n ntal stage by ts own gravty, and velocty ncrease, then turned 80 to track bottom along the track. In 0~s process, the velocty frst gently, after the rapd ncrease. In the s, when t suddenly reduced to m/s, ths s due to the carryng car overcome resstance to down moton, and the velocty s reduced to the fxed value by tracton on the ramp after carryng car through the track turn. In the s~54s process, the carryng car unform upward moton by tracton on the ramp. Therefore, n the fgure here the velocty curve s a straght lne, the velocty s m/s, and the acceleraton s 0 m/s. In the 4s~77s process, the carryng car s through respectvely one vertcal rng and two spral rngs, and the velocty curve shows 5 peaks, the maxmum s 9.5 m/s, the mnmum s.97 m/s. Roller coaster axle mass center acceleraton ampltude s expressed by blue lne n Fgure 3. The acceleraton s 0 m/s when the roller coaster velocty and the haulng chan velocty are at the same tme on the ramp. There s maxmum peak acceleraton n the 4s, t s g. Other department the maxmum acceleraton s 3g. Consderng the 5g~g for human body lmts and the g s duraton of only 0.0s, so the transent feel s lttle or no. The acceleraton s n the body wthn an acceptable range.
80 Advanced Desgn Technology, ICAMMP 0 As can be see from Fgure 3, the 5 rsk ponts of the roller coaster track secton are reflected by velocty and acceleraton, and they are marked n Fgure 4 (the two lowest ponts at vertcal rng and the three lowest at spral rngs). In addton to parts and components of the calculaton and the 5 rsk ponts of the roller coaster track secton n Fgure should also be calculated about structural to ensure ther stffness, strength and stablty n the subsequent structure calculaton. The velocty whch derved from formula (8) s nto the formula (9), the acceleraton n the 5 rsk ponts of the roller coaster track secton can be obtaned n the course of a workng cycle. The smulaton results of rsk pont s velocty are compared wth theoretcal calculaton results as the Table: Table Roller coaster axle mass center velocty about the calculaton and the smulaton comparson table condton 3 4 5 axle mass center velocty calculaton smulaton [ m / s ] the error of calculaton and the smulaton /% 8.753 9.5 8.34 8.805 8.0 7.83 7.83.97 7.48 7.047 4..4-4. -4.0 -.5 As the Table shows, The smulaton results of roller coaster axle mass center velocty are compared wth theoretcal calculaton results, ts error s less than 4.%, ndcatng that the calculaton and smulaton have a good ft and the smulaton results has reference value. Concluson Based on Soldworks/moton software establshed the roller coaster mode, the resstance and constrant s assumed and mposed, to realze the roller coaster knematcs and dynamcs smulaton. The roller coaster varous parts of the velocty and acceleraton curves are obtaned n the course of a workng cycle by the dynamc smulaton. The 5 rsk ponts of the roller coaster track secton can be found after analyze the velocty and acceleraton curves. Ths provdes reference for the next step on the roller coaster desgn optmzaton and the parts calculaton. The calculaton formula of the carryng car velocty and acceleraton s derved, and the smulaton results of velocty are compared wth theoretcal calculaton results, and ths smulaton has reference value. A new reference method s provded for Mechancal system dynamc smulaton research. References [] L. Chen and W. Guan: Chnese Journal of Constructon Machnery, Vol. 8 (00) No 4, pp.400-403. [] J.R. Zheng and H.Q. Wang: Journal of Machne Desgn and Research, Vol. 0 (004) No, pp.74-77. [3] H. Jang, L.F. Lu and Z. We: Soldworks Anmaton and Moton Analyss Example Analyss (Machnery Industry Press, Chna 00). [4] General Admnstraton of Qualty Supervson, Inspecton and Quarantne of the People s Republc of Chna: GB8408-008 Amusement Devce Safety Code (Standards Press of Chna 008).
Advanced Desgn Technology, ICAMMP 0 0.408/www.scentfc.net/AMR.4 Knematcs and Dynamcs Smulaton Research for Roller Coaster Mult-Body System 0.408/www.scentfc.net/AMR.4.7