David Roggenkamp April 19, 2006

1. E579 Final Project:A Study of the Influence of Adjustable Support Legs on Passenger-Experienced g-forces During Acceleration of a Maglev Train Using a Bondgraph Simulation Model David Roggenkamp April 19, 2006

2. Outline • Objective • Introduction • Vehicle Model Structure • Bondgraph Model • Model Assumptions • Input Values • Model Validation • Discussion • Lessons Learned • References

3. Objective • The objective of this project was to use a bondgraph model representation of a maglev train car concept to study the influence of adjustable ‘legs’ of the train on the g-forces experienced by a passenger. Specifically, it was desired to understand the maximum acceleration rate that could be achieved while maintaining acceptable g-force loads to the passenger with a given amount of leg height adjustment.

4. Introduction: ITC Transit

5. Acceptable g-forces: vertical: 1 ± 0.25 g longitudinal: 0.16 g lateral: 0.10 g Introduction: Free Body Diagram • Model designed to evaluate longitudinal g-force only

6. Vehicle Model Structure: Bondgraph Model

7. Vehicle Model Structure: Model Assumptions • Floor angle is small relative to distance between legs so that distance remains relatively constant and the angle can be estimated as a simple numeric difference between the rise and the run. • Very stiff springs were added to the model to eliminate differential causality of the vehicle mass for both the horizontal and vertical directions. The model would not solve with differential causality in either bond. • Moment effects of the vehicle center of mass not being aligned with the axis of applied loads are neglected. It was assumed that the physical model would be rigid and the moment effects would be small relative to the translation force. • Air resistance of the vehicle legs is negligible and/or can be lumped into the vehicle body air resistance. • Atmospheric conditions and, hence, air resistance remain constant over time. • The airgap created and maintained by the maglev motor and corresponding magnets remains constant with no spring or damper forces acting on the vehicle. • The model assumed that a simple proportional controller was adequate to adjust the leg length. This appears to be an invalid assumption but has not been resolved at this time.

8. Vehicle Model Structure: Input Values (1)

9. Vehicle Model Structure: Input Values (2)

10. Vehicle Model Structure: Input Values (3)

11. Vehicle Model Structure: Input Values (4)

12. Vehicle Model Structure: Input Values (5)

13. Model Validation • Model has not been validated since no reasonable, logical output has been generated from the model • It was intended to use basic mathematical expressions to validate the steady-state model results but since no steady-state model results are available…

14. Discussion: Model Output

15. Discussion: Known Issues • Air resistance is proportional to the square of the velocity. When the equation for that resistance was modified, the model stopped working as expected. • The controller is not working appropriately to adjust the leg length based upon passenger-experienced g-force. Tried PID controller but could not get to work. Needs to be reconfigured so that the leg length returns to nominal value when acceleration is zero. • Current controller ‘error’ term is derived from force on passenger, not acceleration. Tried putting in d/dt calculation but model did not function that way.

16. Lessons Learned • Waited for ‘real’ data on the vehicle • Too much time spent on research looking for precise input values • Sometimes it is difficult to find (research) something that you think should be easy • More time should have been allocated to create and debug the simulation model • No matter how well I thought I understood what needed to be done, it has been many times more difficult than I anticipated • Don’t procrastinate

17. References • Fritz, Martin, “Simulating the response of a standing operator to vibration stress by means of a biomechanical model”, Journal of Biomechanics, 2000, 33, 795-802. • International Standard ISO 2631-1:1997, “Mechanical Vibration and shock – Evaluation of human exposure to whole-body vibration – Part 1: General Requirements”. • International Standard ISO 2631-4:2001, “Mechanical Vibration and shock – Evaluation of human exposure to whole-body vibration – Part 4: Guidelines for the evaluation of the effects of vibration and rotational motion on passenger and crew comfort in fixed-guideway transport systems”. • International Standard ISO 5982:2001, “Mechanical Vibration and shock – Range of idealized values to characterize seated-body biodynamic response under vertical vibration”. • Interstate Traveler Company, LLC Website, http://www.interstatetraveler.us/, accessed March 12, 2006. • Karnopp, D. C., Margolis, D. L. and Rosenberg, R.C., System Dynamics: Modeling and Simulation of Mechatronic Systems, John Wiley & Sons, 2000. • Power Superconductor Applications Corporation Website, “Class 1 Single-sided Linear Induction Propulsion Motor Schedule 2 Specifications,” http://www.powersuper.com/limspec2.html, accessed April 17, 2006. • U.S. Department of Transportation, “Colorado Maglev Project, Part 2 – Final Report”, Federal Transit Administration Report Number FTA-CO-26-7002-2004, June 2004.