Suspension Preliminary Design

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Suspension Preliminary Design

• Dynamic ADAMS/View Model
• Driving Simulations, Vehicle Cornering Behaviour

Kai Bode, July 13th, 2006
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Full Vehicle Model in ADAMS/View

• Torque driver in each wheel, car running on a
  road
• (surface characteristics programmable)
• Incorporation of a full tire model
• (Pacejka 2002)

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Front and Rear Suspension
Double Wishbone Suspension at the Front
Multi Link Suspension at the Rear
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Vehicle Model Parameters

• Basic parameters as suggested by Dr. Lambert
  (May 2002)
• Total Mass 1130kg
• Length 1800mm
• Front Track 1275mm
• Rear Track 1350mm
• Other estimations
• Wheel Mass 20kg (tire, rim, rotor of motor)
• Motor Stator Mass 20kg (modeled as lumped
  masses)
• Body Inertia
• Ixx 240.625kgm2
• Iyy 240.625kgm2
• Izz 41.25kgm2

z
y
x
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Tire Model Pacejka 2002

• ADAMS/Tire calculates the forces and moments that
  tires exert on the vehicle as a result of the
  interaction between the tires and the road
  surface.
• The Pacejka 2002 Model is recommended for vehicle
  handling analyses.

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Tire Model Recommendations
Courtesy of MSC Software, Ann Arbor, MI
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Transient Behaviour Step Steering

• To analyze the vehicles transient behaviour, a
  steering step input can be simulated at a given
  forward speed.
• In particular, this excites the vehicles yaw
  motion, which can be approximated as a linear
  oscillator.
• The above shown equation is based on the bicycle
  model. Yaw natural frequency and yaw damping are
  functions of the forward speed.
• With estimated parameters, the bicycle model
  yields

r yaw rate D yaw damping rate O yaw
natural frequency d steering angle
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Step Steering 60km/h, 3 after 2s
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Step Steering 60km/h, 3 after 2s
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Step Steering 60km/h, 3 after 2s
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Step Steering Results

• The yaw rate shows a sharp rise, induced by the
  step input. It decreases due to the fact that no
  torque is applied to the wheels (throttle-off
  event).
• The tire lateral slip angles reach a peak of
  almost 4.5. They are different at each wheel,
  due to the uneven weight distribution.
• Body roll motion and tire slip angles are almost
  proportional to the lateral acceleration.
• The change in toe-in angles is as desired in the
  suspension design. They cause a slight understeer
  behaviour.
• At the front, the outer bumping wheel must get
  some toe-out angle and the inner wheel must be
  forced into toe-in.
• At the rear, the opposite behaviour is required
  to implement roll understeer effect.

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Steady-State Behaviour Skidpad Test

• The vehicle is driven in a circle at a constant
  forward speed. Torque is applied to each wheel,
  in order to maintain steady-state (to overcome
  friction).
• The turning radius at a given steering input
  gives evidence about the vehicles self-steering
  behaviour.

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Skidpad Test 35km/h, 8 after 2s
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Skidpad Test 35km/h, 8 after 2s
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Skidpad Test 35km/h, 8 after 2s
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Skidpad Test Results

• The vehicle drives along a circle, all parameters
  reach steady-state.
• From the bicycle model, a relationship between
  steering angle and turning radius is given.
• The first term is the theoretical steering angle,
  according to Ackermann.
• The second term describes additional steering
  input, necessary for a desired turn. Hence, it is
  a measure for under-/oversteer characteristic.

l wheel base R turning radius a distance
CM -gt front axle b distance CM -gt rear axle m
total vehicle mass cs tire cornering
stiffness ay lateral acceleration
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Skidpad Test Results

• Steering input and wheelbase are given. The
  turning radius is a result of the simulation. We
  can solve for the additional term.
• Since it is positive, we can conclude that the
  vehicle has a slight understeer behaviour.
• In the model, a b, so we would expect the term
  to be zero. But the bicycle model does not
  account for roll understeer. The value above is
  exactly the understeer characteristic induced by
  the change in toe-in angles.
• The first term is the theoretical steering angle
  according to Ackermann.
• The second term describes additional steering
  input necessary for a desired turn. Hence, it is
  a measure for under-/oversteer characteristic.

l wheel base a distance CM -gt front axle b
distance CM -gt rear axle m total vehicle
mass cs tire cornering stiffness ay lateral
acceleration
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Double Lane Change

• A test manoeuvre that shows the limits of a
  vehicles cornering capability is the double lane
  change.
• It is standardized in the norm ISO 3888 part 2,
  which describes a desired path, depending on the
  vehicle configuration.
• ADAMS allows simulations at different speeds and
  different road friction coefficients.

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Double Lane Change
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Double Lane Change
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Double Lane Change
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Double Lane Change Results

• The vehicle position shows that at a reasonable
  speed on a dry road, the vehicle can almost
  follow the desired path.
• On an icy road (µ 0.05), the car understeers
  significantly. The yaw rate is much lower than
  required for the turn.
• At 100km/h, the vehicle reaches the stability
  limit. It starts to skid and leaves the desired
  path.
• In order to allow such hard manoeuvres, a yaw
  rate control loop is required.