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

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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

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Outline

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

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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.

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Introduction ITC Transit
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Introduction Free Body Diagram

• Acceptable g-forces
• vertical 1 0.25 g
• longitudinal 0.16 g
• lateral 0.10 g

• Model designed to evaluate longitudinal g-force
  only

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Vehicle Model Structure Bondgraph Model
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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.

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Vehicle Model Structure Input Values (1)
Model Parameter Description Value Source
Controller_Sub_Constant Constant value to be subtracted from controller input 0 Assumed (non-resolved)
Distance_Frt2Rr Distance from the leg mounting point to the vehicle CG 5 Estimated
Leg_Extension_Controller Constant multiple for controller output 1 Assumed (non-resolved)
MagLev_Hor_Force Max Force applied by LIM-2300 Maglev motor 10000 (PowerSuper, 2006)
Nominal_Leg_Length Nominal length of each leg without extension or compression 1.2 Estimated
Pass_Dist_From_Rear Distance from the leg mounting point to the passenger assumed passenger standing at CG 5 Estimated
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Vehicle Model Structure Input Values (2)
Model Parameter Description Value Source
Pass_Fore_Aft_Damping Damping force acting at toes in the fore/aft direction represents biomechanical human body response 1240 (Fritz, 2000)
Pass_Fore_Aft_Spring Spring force acting at toes in the fore/aft direction represents biomechanical human body response (1/22,000 N/m) 4.5e-5 (Fritz, 2000)
Pass_Mass_Fore_Aft Mass of typical human used for modeling 75 (ISO, 1997)
Rr_Leg_Damper2Body Damping force of the attachments between the leg and the vehicle body 1000 Assumed
Rr_Leg_Ext_Friction Mechanical friction during the motion of leg extension 1000 Assumed
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Vehicle Model Structure Input Values (3)
Model Parameter Description Value Source
Rr_Leg_Ext_Spring Mechanical spring force of the motor/gears needed for leg extension 2.5e-5 Assumed
Rr_Leg_Gravity Gravitational force of quarter vehicle plus leg acting on leg (3,000 9.81) 29400 Calculated from estimates
Rr_Leg_Mass Mass of leg (756 kg for the motor plus mechanical structures) 1000 Estimated (PowerSuper, 2006)
Rr_Leg_Spring2Body Spring force of the attachments between the leg and the vehicle body 2.5e-5 Assumed
Veh_CG_From_Rear Distance between the leg and the vehicle body CG 5 Estimated
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Vehicle Model Structure Input Values (4)
Model Parameter Description Value Source
Veh_Horiz_Spring_Force Spring force to represent axial compression/expansion of the vehicle body used to eliminate differential causality in model assumed negligible 1e-10 Assumed
Veh_Vert_Spring_Force Spring force to represent vertical compression/expansion of the vehicle body used to eliminate differential causality in model assumed negligible 1e-10 Assumed
Vehicle_Air_Resistance Force of air resistance on the vehicle necessary to create a steady-state velocity varies with velocity2 Drag 1/2 Cd rho A V2 .9675 Calculated from Estimates
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Vehicle Model Structure Input Values (5)
Model Parameter Description Value Source
Vehicle_Mass_Horiz Inertial mass of the vehicle body (quarter) acting in horizontal direction 2000 Estimated
Vehicle_Mass_Vert Inertial mass of the vehicle body (quarter) acting in the vertical direction 2000 Estimated
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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

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Discussion Model Output
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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.

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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
• Dont procrastinate

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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 2631-11997,
  Mechanical Vibration and shock Evaluation of
  human exposure to whole-body vibration Part 1
  General Requirements.
• International Standard ISO 2631-42001,
  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 59822001, 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.