German Aerospace Center (DLR) The Foundation of the DLR RailwayDynamics Library: The Wheel-Rail Contact A. Heckmann, A. Keck, I. Kaiser, B. Kurzeck Institute of System Dynamics and Control Oberpfaffenhofen www.DLR.de • Chart 1 > Wheel-Rail Contact > A. Heckmann > Modelica 2014
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German Aerospace Center (DLR)
The Foundation of the DLR RailwayDynamics Library: The Wheel-Rail Contact A. Heckmann, A. Keck, I. Kaiser, B. Kurzeck Institute of System Dynamics and Control Oberpfaffenhofen
www.DLR.de • Chart 1 > Wheel-Rail Contact > A. Heckmann > Modelica 2014
Content
- Motivation
- Theoretical Background
- The Reference
- Evaluation Scheme
- Geometrical Problem
- Normal Contact Problem
- Tangential Contact Problem
- Application Examples
- The Free Wheelset
- The Scaled Roller Rig
- Conclusions and Outlook
www.DLR.de • Chart 2
Motivation: DLR‘s Next Generation Train Project www.DLR.de • Chart 3
- 10 DLR institutes contribute to the NGT project.
- Very high speed train in double deck configuration and lightweight design
- New type of running gear with active control
- Nonlinear Modelica Models for - Observer (see Brembeck et al. : Nonlinear State Estimation with Extended FMI 2.0 Co-
Simulation Interface, Modelica 2014)
- Control
Multi-Body Simulation animated by Autodesk® Maya
The Reference: The Nonlinear Rolling Contact [Kalker 1982]
− Highly elaborated but much too expensive for vehicle dynamics simulations
− Several assumptions allow to tackle the problem in sequential steps.
www.DLR.de • Chart 4
Exemplary normal stresses Exemplary shear stresses
running direction running direction
Evaluation Scheme Implemented in Modelica www.DLR.de • Chart 5
Search for Contact Point
Evaluate Tangential Contact
Evaluate Geometry of Normal Contact Ellipse
Evaluate Kinematics of Wheel w.r.t. Rail
Profile Geometry (Splines)
Normal force and its direction
Tangential force and torque
Tim
e In
tegr
atio
n
Kinematic Loop
Geometrical Problem
Normal Contact Problem
Tangential Contact Problem
Theory: The Geometrical Problem I
- Contact formulated as kinematical constraint
www.DLR.de • Chart 6
Theory: The Geometrical Problem: II
- Quasielastic formulation: [Arnold, Netter 96]:
www.DLR.de • Chart 7
Theory: The Normal Contact Problem
- The Hertz assumption
- Geometry of contacting surfaces ≈ elliptic paraboloids
⇒ contact patch is a plain ellipse
www.DLR.de • Chart 8
For comparison: Kalker‘s nonelliptical contact
Theory: The Tangential Contact Problem www.DLR.de • Chart 9
normal stress field
max. shear stresses
adhesion region
slip region
leading edge trailing edge
running direction
- Nonlinear analytical formulation [Polach 2000]:
- Converges against Kalker‘s linear theory for vanishing slip
- Is in particular tailored for high traction forces
Application: The free Wheelset www.DLR.de • Chart 11
Application: the free Wheelset www.DLR.de • Chart 12
- Beyond critical speed: limit cycle behavior
[Polach 2010]
Application: the scaled roller rig www.DLR.de • Chart 13
− Experimental environment for validation and research on control
− Actual wheel-rail profile in use here is comparable simple.
− Assembled with force / torque – sensors
− Modelica simulation is approx. 2 times faster than real time.
animated by DLR Visualization Library see youtube-video
Application: the scaled roller rig
www.DLR.de • Chart 14
Application: the scaled roller rig
- Measurements versus simulation
www.DLR.de • Chart 15
Normal contact forces
Longitudinal contact forces
Lateral contact forces
Conclusions and Outlook
- The wheel-rail contact for several geometries has been implemented.
- The final goals are
- observer development
- feed-forward control
- feed-back control
www.DLR.de • Chart 16
Funded by BMBF 011S12022G in conjunction with ITEA2 project
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