Wheel Physics, and Multiphysics Problems

CS 493/693 Lecture, Dr. Lawlor

Traction Forces

Along the axle: An unpowered wheel can only apply sustained forces in the direction along the axle: dot(appliedforce,axledir)*axledir.  Forces in other directions, along the wheel's rim, just cause the wheel to rotate.  Projecting the ground/car relative velocity into forces along the axle direction allows a totally unpowered set of front wheels to reliably steer a rear-wheel drive car.

Across the axle: Engine torque turns the tires, or brakes stop the tires, both of which use the tire to apply forces to the ground perpendicular to the axle.  Since a single car's tire forces don't cause the planet to move very much, we can quite accurately treat the axles themselves as a source of thrust, rather like jet propulsion.

One element that should be accounted for is the coefficient of friction between the tire and ground.  Depending on how much downward pressure the car's chassis is applying to the wheel (and this can be zero when approaching a rollover event), there is a limit to how much force the wheel can apply to the ground before contact breaks loose and the car begins to slide.  The coefficient of dynamic friction is normally much smaller than that of static friction: dry concrete on soft warm clean rubber has a coefficient of friction near 1.0; wet ice on frozen rubber has a coefficient of friction (static or dynamic) near zero, as anybody on an icy road can attest.  Currently bunnyracer does not explicitly account for the coefficient of friction.

Finally, wheels only apply traction forces when in contact with the ground.  This sounds trivial, but determining whether the wheels are contacting the ground must be an explicit check, and can be different for each wheel during rollover events.

Stability

As we saw in class, simulation stability problems are common when joining multiple independent physics together.  In particular, we found:
• A longer axle can more easily support the wheel's torques, especially dynamic torques during ground collisions.  In particular, Ben suggested using the excellent old model-car trick of running the axles straight across the frame, so you have two long axles at front and back instead of four shorter ones for each tire.  This led to dramatically increased stability, and some crash resilience.
• The dynamic interplay between tire forces and solid tet simulation is surprisingly complex.  I ended up tweaking the bunny model several times to provide more supporting tets over the axles, since skinny parts can easily fold up on themselves.  This is a situation where our simple spring-based tetrahedra are much less robust than a more complex solid formulation.
• Adding a short gap between the height where traction forces apply, and the height where we enforce the vertical boundary condition, led to more stable operation.  Changing both a particle's position and net force at exactly the same spot (when the wheel contacts the ground) is an excellent way to drive the particle into oscillations; while applying the same changes separately results in no oscillation.