Constant Radius

Understeer

Two desired vehicle behaviors underlie the concept of understeer: as the vehicle speed on a constant radius path increases the driver must increase the steer angle to follow the path, and when the speed increases to the point where the vehicle reaches its limit of lateral acceleration the vehicle drifts outward to a larger radius (yaw rate stops increasing) rather than spinning (increasing yaw rate). The latter behavior requires that the front tires lose adhesion before the rear tires. In front wheel drive vehicles one can induce excessive understeer by applying throttle so the front tires lose adhesion.

Neutral-Steer

For a neutral steer vehicle the steer angle required to follow a constant radius is constant independent of speed. However, the vehicle side-slip angle must increase with increasing speed to develop the necessary lateral force, requiring the driver’s careful manipulation of the steering and/or throttle to balance the vehicle and avoid a spin.

Oversteer

For an over-steer vehicle the steer angle required to follow a constant radius decreases with speed making the vehicle very difficult for a driver to control. Alternatively, a step steer input to an oversteering vehicle will cause the vehicle lateral acceleration and yaw rate to increase to the point where the vehicle spins. In contrast, a step-steer input to an understeering vehicle generates a limited lateral acceleration and yaw rate.

Vehicles with poorly designed suspensions and/or poorly chosen tires may show understeer but transition to oversteer for some combinations of speed, lateral acceleration and vehicle loading.

Computing Understeer

Understeer is the difference between the average front and rear tire slip angles. For a neutral steer vehicle the slip angles will be the same, for an understeering vehicle the front slip angles are of greater magnitude than the rear slip angles, while for an oversteering vehicle the rear slip angles are of greater magnitude than the front slip angles.

Here:

= Slip-angle: The angle in radians measured from the velocity vector to the tire heading looking downward from above the tire.

Figure 1.

In velocity control mode, the vehicle is driven at an increasing speed around the circular path, which results in an increase in lateral acceleration. Using the event form, you can control the driving time, constant radius, and end speed.

Figure 2. Constant Radius Event

Figure 3. Top View of a Constant Radius Path

Figure 4. Vehicle Model with Body Graphics

The event sequence is described in the table below:

Event Step

Description

Start

Vehicle begins driving in a straight line towards the constant radius circle tangent at the speed that will generate a Lateral Acceleration that was entered in the form.

Turn into Constant Radius Track

Vehicle enters the constant radius track. Turn direction is determined from the form entry (left or right). Steering is controlled by the steer controller. Speed is maintained by the drive torque controller. Lateral acceleration should be constant (because speed is constant).

Follow the Constant Radius

The vehicle follows the constant radius path for the time defined in the event.

End of Event

The event ends when the time in circular track time is met.

When the vehicle control is velocity, the vehicle drives around the track at a steadily increasing speed and as a result, an increasing lateral acceleration. This event provides a sweep of the lateral acceleration behavior of the vehicle (at increasing speeds). Left and right turn directions can be run and the time in the circle can be varied to provide a slower acceleration. The vehicle makes multiple loops around the circle if there is enough time. The event sequence is shown in the table below.

Event Step

Description

Start

The vehicle drives toward the tangent of the Constant radius path. The initial speed is determined from the Circle Radius and the desired initial Lateral Acceleration. Low accelerations result in lower initial speeds.

Turn into Constant Radius Path

The vehicle turns into the Constant radius path and begins to accelerate.

Follow Constant Radius Path

The vehicle drives along the Constant radius path and increases speed. The vehicle speed is increased from the initial speed to the final speed in the Time in circular track time. Use a longer time to minimize acceleration effects on the results.

Event End

The event ends after the Time in circular track time is complete.

Skidpad graphics are included to illustrate the path being driven, and are defined parametrically using the data in the Constant Radius event form. Skidpad graphics should never require editing unless the event is being fundamentally changed.

Figure 5. Skidpad Graphics

The numbers in the solver variable USER subroutine call are as follows:

Number

Description

5020

Branching ID. 5020 is a Constant radius event.

70000000

The ID of a solver array containing Driver Model Controller data. The array is in the steer controller system.

70000100

The ID of a Vehicle Data array containing vehicle information. The array is in the steer controller system.

30

The value of the circle radius.

The template for this event is shown below:

<ResOutput
     angle_type          = "YPR"
  />
  <ResOutput
     mrf_file            = "TRUE"
  />
  <ResOutput
     plt_file            = "TRUE"
  />
  <H3DOutput
     switch_on           = "TRUE"
     increment           = "1"
  />
  <ResOutput
     abf_file            = "TRUE"
  />
{if (tire_dataset.opt_omega.ival ==1)}
<!--Initial static analysis -->

<Simulate
	analysis_type = "Static"
	end_time      = "0.0"
/>	
{endif}


<Deactivate
	element_type = "MOTION"
	element_id = "{mot_frnt_wheel.l.idstring}"
/>
<Deactivate
	element_type = "MOTION"
	element_id = "{mot_frnt_wheel.r.idstring}"
/>
<Deactivate
	element_type = "MOTION"
	element_id = "{mot_rear_wheel.l.idstring}"
/>
<Deactivate
	element_type = "MOTION"
	element_id = "{mot_rear_wheel.r.idstring}"
/>
{if (tire_dataset.opt_omega.ival ==2)}
<!--Initial static analysis -->

<Simulate
	analysis_type = "Static"
	end_time      = "0.0"
/>	
{endif}
<Deactivate
	element_type = "JPRIM"
	element_id = "{j_clamp_1_body.idstring}"
/>
<Deactivate
	element_type = "JPRIM"
	element_id = "{j_clamp_2_body.idstring}"
/>

<Motion_Joint
     id                  = "{wh_motion.idstring}"
     expr                = "VARVAL({sv_str_path.idstring})"
/>


<Simulate
     analysis_type       = "Transient"
     end_time            = "{(pi*ds.radius.value*1000.0/2.0)/(447.04*ds.veh_vel.value)+ds.step_time.value+2.0}"
     print_interval      = "0.02"
  />
<Stop/>