SIMPACK User Meeting 2004 Wartburg, Eisenach, November 2004 Development of a Spatial Track Module in SIMPACK and Application to a Simple Roller Coaster Example Klaus Schott, Jakub Tobolář klaus.schott@dlr.de, jakub.tobolar@dlr.de DLR Institute of Robotics and Mechatronics, Vehicle System Dynamics
Contents Introduction - Tracks in multibody simulation of vehicle dynamics Theory - Calculation concept for the spatial track - Kinematics of a body moving along the track - The clothoid loop Application example - Definition of the roller coaster example - Calculation results of the roller coaster example Summary and outlook RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 2
Tracks in multibody simulation of vehicle dynamics a) cartographic tracks in MBS package SIMPACK: - e.g. road and railway tracks - horizontal projection of path length as track parameter b) spatial tracks: - with vertical sections - e.g. roller coaster ride - actual path length s as track parameter RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 3
Calculation concept for the spatial track a) calculate a spatial curve r(s): - define input functions for curvature and torsion: - solve the Frenet equations: - and the tangent vector equation: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 4
Calculation concept for the spatial track b) calculate the orientation matrix A(s) of the track frame: - define the track roll angle derivative : - solve two additional differential equations: - calculate the orientation matrix: c) track module: - input: - output: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 5
a) body with one degree of freedom: - (body fixed frame) = (track frame), state vector : - body movement described by: - translatoric kinematic terms: Kinematics of a body moving along the track - rotatoric kinematic terms: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 6
b) body with six degrees of freedom: - state vector: Kinematics of a body moving along the track - translatoric kinematic terms: - rotatoric kinematic terms: c) wheel-rail constraints and friction forces: - used standard calculation procedures from SIMPACK RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 7
The clothoid loop - basic approach: path length -curvature: -torsion: continuous functions no steps in accelerations and forces RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 8
Definition of the roller coaster example different views of the track: perspective view parallel view side view top view RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 9
Definition of the roller coaster example input functions for the track definition: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 10
Calculation results of the roller coaster example video with contact force arrows: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 11
Calculation results of the roller coaster example video with friction force arrows: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 12
Calculation results of the roller coaster example velocity of the car: RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 13
contact forces on front wheels: Calculation results of the roller coaster example RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 14
contact forces on wheels: Calculation result for a wheelset in a circular loop RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 15
Summary - spatial track calculation by direct solution of the Frenet equations - movement of bodies with six degrees of freedom along the track - consideration of wheel/rail contact with friction force calculation - application example: roller coaster track with clothoid loop - simulation of a roller coaster ride, evaluation of forces and accelerations Outlook - optional input of discrete track points r i for track definition - implementation of side and/or under friction wheels RM-ER: Vehicle System Dynamics SIMPACK User Meeting 2004 16