Download - Basic Vehicle Performance Modeling
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Basic VehiclePerformance Modeling
Prof. R.G. Longoria
Spring 2004v.1
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Overview
Basic 2 axle vehicle model
Review typical road loads
Example modeling for performance
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Performance Modeling
Performance usually relates to longitudinal motion of a vehicle,
and is constrained by one of two limits.
The first is a power plant limitation, which tends to be especially critical
at high speed. The second limitation is traction, which tends to dominate at low speeds.
In both cases, the impact on acceleration or deceleration is of
particular interest. Some common needs might be:
Finding torque and power for a given application (e.g., to go up a hill,
drawbar)
Selecting a power plant
Development or evaluation of cruise, braking, traction, or engine control
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Basic Model 2 axle vehicle
From Wong, Chapter 3, Fig. 3.1
xx x
dvp m m a F
dt= = =
Along the longitudinal (x) axis:x
z
Tractive force Road LoadsxF =
,
,
tractive effort on front and rear
aerodynamic resistance force
rolling resistance on front and rear
drawbar load
grade resistance sin
x f r a rf rr d g
f r
a
rf rr
d
g s
F F F R R R R R
F
R
R
R
R W
= +
=
=
=
=
= =
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8/13/2019 Basic Vehicle Performance Modeling
5/18
ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Basic Model 2 axle vehicle
From Wong, Chapter 3, Fig. 3.1
x z
0
0
zz z
y
y y y
dvp m Fdt
dh I T
dt
= = =
= = =
Use equilibrium conditions in thevertical direction and about the y
axis.
Need to:
1. Find loads on the axles2. Use knowledge of road adhesion
and other vehicle parameters to
determine tractive effort (TE)
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Dissipative Loads
Recall, any dissipative forces take the form of effort vs. flow.
For translation: force (F) velocity (V) plots
For rotation: torque (T) (angular) speed () plots
orF T
orV
( or )V forbidden
forbidden
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8/13/2019 Basic Vehicle Performance Modeling
7/18
ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Aerodynamic Forces and Moments
Aerodynamic effects can affect vehicular dynamics in several
ways.
Refer to Wong, Section 3.2 or Gillespie, Ch. 4, for a detailed discussion of aerodynamic
effects.
From Gillespie (1992)
MomentForceDirection
Yawing
moment
Lift forceVertical,
positive
upward
Pitchingmoment
Side forceLateral,positive right
Rolling
moment
Drag forceLongitudinal,
positive
rearward
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Tire Force and
Moment ConventionsGillespie (1992)
Wong (1993/2001)
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8/13/2019 Basic Vehicle Performance Modeling
9/18
ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Rolling Resistance Primarily caused by hysteresis in tire materials due to deflection of the
carcass while rolling.
Others factors that might contribute to RR in tires: friction in sliding, air
circulation, fan effect of rolling tire.
Dominant load at low speeds; dependent on speed.
Example: loads on tire at 80-95 mph
(90-95% hysteresis, 2-10% friction, 1.5-3.5% air resistance)
For free-rolling tire, a horizontal force is introduced to balance the rollingresistance moment, which arises when pressure shifts to leading half due to
carcass deflection.
Ratio of rolling resistance to normal load is the coefficient of rolling
resistance, which incorporates all the complicated and interdependent
physical properties of tire and ground.
Aerodynamics become equal to rolling at about 50 or 60 mph.
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8/13/2019 Basic Vehicle Performance Modeling
10/18
ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Typical Road LoadsFrom Steeds, Mechanics of Road Vehicles (1960)
Generally, we assume that
aerodynamic effects can
be ignored for low groundspeeds.
Rolling resistance and
grade dominate until
about 50 to 60 mph.
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Estimating Rolling Resistance
7 20.0136 0.4 10rf V
= +
Ex. Radial-ply passenger car tires under rated loads and inflation
pressures on a smooth road (Wong, Ch.1),
From Automotive Handbook (SAE)
with V in km/h.
Total force is estimated on all
wheels,r rf rr r F F F f W
= + =
where Wis the total weight on the
vehicle.
In some cases, can approximate with
average values, as given the table
shown.
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Additional Estimates
0.01(1 /100), ( in mph)rf V V= +
Speed dependence of rolling resistance
For low speeds:
At higher speeds: ( )2.5
3.24 , ( in mph)100
basic coefficient
speed coefficient
r o S
o
S
Vf f f V
f
f
= +
=
=
From Automotive Handbook (SAE)
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8/13/2019 Basic Vehicle Performance Modeling
13/18
ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Vehicle on an Incline 1
From Wong (2001)
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Vehicle on an Incline 2
These equations can be
formulated to solve for the 3
unknowns:
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Vehicle on an Incline 3
14. 036deg=Ftm axfv( ) W cos ( )
b h frv( )+( )
L h +( ):=Ftmaxrv( ) W cos ( )
a h fr v( )( )
L h ( ):=
atan 1
4
:=
Fa v( ) 1
2 Cd Af v( )
2:=fr v( ) A B v( )
2+:=Fg ( ) W sin ( ):=
r 33 cm:=
b L a:= 0. 8:=
1.23kg
m3
:=
B 0.4 10 7
1
km
hr
2:=a 127 cm:=
mvW
g:=
Cd 0.45:=h 50.8cm:=
A 0.0136:=Af 2.32m
2:=L 279. 4cm:=W 4500lbf :=
Data for Proble m 3.1 from Wong (1993)
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Vehicle on an Incline 4
RWD11182674
FWD10574843
RWD6982742FWD6074931
TypeV (m/s)Ftmax (N)Pt.
Check out the power delivery.
Line 2 = 571 kW! (766 hp)
Graphically extracted results
Does this seem reasonable?
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8/13/2019 Basic Vehicle Performance Modeling
17/18
ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
Summary Road Loads
This overview of road loads illustrates the largeamount of information available related to predictingand controlling typical road loads.
Basic analysis can be conducted to determineacceleration performance on grades underaerodynamic loading, including the effect of rolling
resistance. Later, we will examine how power plant and
transmission effects play a role in longitudinal
performance.
First, we will study tire-ground interaction in moredetail to understand braking and traction applications.
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8/13/2019 Basic Vehicle Performance Modeling
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ME 379M/397 Prof. R.G. Longoria
Vehicle System Dynamics and ControlDepartment of Mechanical Engineering
The University of Texas at Austin
References1. Steeds, W., Mechanics of Road Vehicles, Illiffe and Sons, Ltd., London,
1960.
2. Gillespie, T.D., Fundamentals of Vehicle Dynamics, SAE, Warrendale, PA,
1992.
3. Wong, J.Y., Theory of Ground Vehicles, John Wiley and Sons, Inc., New
York, 1993 (2nd) or 2001 (3rd) edition.
4. W.F. Milliken and D.L. Milliken, Race Car Vehicle Dynamics, SAE,
Warendale, PA.