Transcript E579 Final Project: A Study of the Influence of Adjustable

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
Outline
Objective
Introduction
Vehicle Model Structure
• Bondgraph Model
• Model Assumptions
• Input Values
Model Validation
Discussion
Lessons Learned
References
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.
Introduction: ITC Transit
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
Vehicle Model Structure:
Bondgraph Model
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.
Vehicle Model Structure: Input
Values (1)
Model Parameter
Description
Value
Source
Controller_Sub_Constant
Constant value to be
subtracted from controller
input
0
Assumed (nonresolved)
Distance_Frt2Rr
Distance from the leg
mounting point to the
vehicle CG
5
Estimated
1
Assumed (nonresolved)
Leg_Extension_Controller Constant multiple for
controller output
MagLev_Hor_Force
Max Force applied by LIM2300 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
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
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
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 steadystate velocity – varies with
velocity^2
Drag = 1/2 * Cd * rho * A * V^2
.9675
Calculated
from
Estimates
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
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…
Discussion: Model Output
model
40
Vehicle Velocity
30
20
10
0
-10
Floor Angle
1.5
1
0.5
0
0.15
Passenger Feet Fore/Aft
0.1
0.05
0
0.15
Passenger CG Fore/Aft
0.1
0.05
0
0
1
2
3
4
5
time {s}
6
7
8
9
10
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.
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
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.