Bergamo University Italy 12 th -14 th June 2012. Lecture 7- Full Vehicle Modelling. Professor Mike Blundell Phd , MSc, BSc ( Hons ), FIMechE , CEng. Contents. Underlying Theory (Bicycle Model Approach) Understeer and Oversteer
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12th-14th June 2012
Professor Mike Blundell
Phd, MSc, BSc (Hons), FIMechE, CEng
“Confidence” (Consistency/Linearity to Inputs)
“Fun” (High Yaw Gain, High Yaw Bandwidth)
“Fluidity” (Yaw Damping Between Manoeuvres)
“Precision” (Disturbance Rejection)
Courtesy of www.drivingdevelopment.co.uk
“Inertia Match” is the relationship between the CG position, wheelbase and yaw inertia.
At the instant of turn in:
w= Cafaf a t / Izz
v = Cafaf t / m
Combining these velocities gives an
“instant centre” at a distance c behind the CG:
c = Izz/ ma
Noting that Izz = mk2
Thus if c is equal to b then
1 = k2 / ab
k2/ ab therefore describes the distance of the centre of rotation
with respect to the rear axle.
Lateral Acceleration (Ay )
Forward Speed (Vx)Vehicle Handling – Understeer and Oversteer
For pure cornering (Lateral Response) the following outputs are typically studied:
Typical lateral responses measured in vehicle coordinate frame
Centre of Mass
Centre of TurnCornering at Low-Speed
Assuming small steer angles
at the road wheels to avoid
scrubbing the wheels
The average of the inner and
outer road wheel angles is
Known as the Ackerman Angle
Centre of TurnSteady State Cornering (continued)
The bicycle model can be described by the following two equations of motion:
Ffy + Fry = m ay
Ffy b - Fry c = 0
Neutral Steer Path
Disturbing force (e.g. side gust)
Acting through the centre of massUndersteer and Oversteer
Olley’s Definition (1945)
OversteerUndersteer and Oversteer
33 mThe Constant Radius Test
The constant radius turn test procedure can be use to define
the handling characteristic of a vehicle (Reference the British
ay = V2 / R
K = Understeer Gradient
Lateral Acceleration (g)Understeer Gradient
Lateral Acceleration (g)
Vehicle Speed (kph)Limit Understeer and Oversteer Behaviour
Fy= m ay
Where ay is the centripetal acceleration acting towards the centre of the corner
Fy - m ay = 0
Where –m ay is the d’Alembert Force
Representing the inertial force as a d’Alembert force consider the forces acting on the roll stiffness model during cornering as shown
FFIzForces and Moments Acting at the Roll Axis
ΔFFzM = component of weight transfer on front tyres due to roll moment
ΔFRzM = component of weight transfer on rear tyres due to roll moment
bForces and Moments (continued)
Consider again a free body diagram of the body roll axis and the components of force acting at the front and rear roll centres
Δ ApproachFFzL = component of weight transfer on front tyres due to lateral force
Δ FRzL = component of weight transfer on rear tyres due to lateral force
DFFzLForces and Moments (continued)
Taking moments again for each
of the front and rear axles gives:
FFIzForces and Moments (continued)
FFIz = FFSz - DFFzM – DFFzL
FFOz = FFSz + DFFzM + DFFzL
FRIz = FRSz - DFRzM - DFRzL
FROz = FRSz + DFRzM + DFRzL
Lateral Force ApproachFy
Vertical Load FzLoss of Cornering Force due to Nonlinear Tyre Behaviour
Increase front weight transfer - Understeer
Increase rear weight transfer - OversteerThe Effect of Weight Transfer on Understeer and Oversteer
LUMPED MASS MODEL
SWING ARM MODEL
ROLL STIFFNESS MODEL
The following are typical of the tests which have been performed on the proving ground:
(i) Steady State Cornering - where the vehicle was driven around a 33 metre radius circle at constant velocity. The speed was increased slowly maintaining steady state conditions until the vehicle became unstable. The test was carried out for both right and left steering lock.
(ii) Steady State with Braking - as above but with the brakes applied at a specified deceleration rate ( in steps from 0.3g to 0.7g) when the vehicle has stabilised at 50 kph.
(iii) Steady State with Power On/Off - as steady state but with the power on (wide open throttle) when the vehicle has stabilised at 50 kph. As steady state but with the power off when the vehicle has stabilised at 50 kph.
(iv) On Centre - application of a sine wave steering wheel input (+ / - 25 deg.) during straight line running at 100 kph.
(v) Control Response - with the vehicle travelling at 100 kph, a steering wheel step input was applied ( in steps from 20 to 90 deg. ) for 4.5 seconds and then returned to the straight ahead position. This test was repeated for left and right steering locks.
(vi) I.S.O. Lane Change (ISO 3888) - The ISO lane change manoeuvre was carried out at a range of speeds. The test carried out at 100 kph has been used for the study described here.
(vii) Straight line braking - a vehicle braking test from 100 kph using maximum pedal pressure (ABS) and moderate pressure (no ABS).
Following the guidelines shown performing all the simulations with a given ADAMS vehicle model, a set of results based on recommended and optional outputs would produce 67 time history plots. Given that several of the manoeuvres such as the control response are repeated for a range of steering inputs and that the lane change manoeuvre is repeated for a range of speeds the set of output plots would escalate into the hundreds.
This is an established problem in many areas of engineering analysis where the choice of a large number of tests and measured outputs combined with possible design variation studies can factor the amount of output up to unmanageable levels.
MANOEUVRES - Steady State Cornering, Braking in a Turn, Lane Change, Straight Line Braking, Sinusoidal Steering Input, Step Steering Input,
DESIGN VARIATIONS - Wheelbase, Track, Suspension, ...
ROAD SURFACE - Texture, Dry, Wet, Ice, m-Split
VEHICLE PAYLOAD - Driver Only, Fully Loaded, ...
AERODYNAMIC EFFECTS - Side Gusts, ...
RANGE OF VEHICLE SPEEDS - Steady State Cornering, ...
TYRE FORCES - Range of Designs, New, Worn, Pressure Variations, ...
ADVANCED OPTIONS - Active Suspension, ABS, Traction Control, Active Roll, Four Wheel Steer, ...
30 m Approach
A - 1.3 times vehicle width + 0.25m
B - 1.2 times vehicle width + 0.25m
C - 1.1 times vehicle width + 0.25mDouble Lane Change Manoeuvre
Roll Moment (Nmm) FRONT SUSPENSION
Roll Angle (deg)
Steering motion applied at joint Approach
Revolute joint to vehicle body
Translational joint to vehicle body
suspensionModelling the Steering System
Motion on the steering system is ‘locked’ during the initial static analysis
Downward motion of vehicle body and steering rack relative to suspension during static equilibrium
Connection of tie rod causes the front wheels to toe outModelling the Steering System
COUPLER initial static analysis
COUPLERModelling the Steering System
REV initial static analysis
Dummy transmission part located at mass centre of the body
WHEELSModelling a Speed Controller
Vehicle Ballast Conditions:
ADAMS Quadrifiler Simulation:
Driving on Wet Basalt
Proving Ground Results