Torque Vectoring

Torque Vectoring Systems (TVS) form a very large topic with a complex amount of mathematics behind it. This section will try to cover the more tangible and practical aspects of design.

Introduction

Torque vectoring essentially exists to:

• • damp yaw acceleration (usually for safety)

  • induce yaw acceleration (usually for performance)

Correctly designed torque vectoring reduces the conflict between:

• • good stability

  • fast response

Influence on yaw rate

Response to a rapid manoeuvre is dictated by the fact that tyres take time to build up lateral forces.

At high vehicle speed, vehicle yaw rate will have some delay, then can overshoot and oscillate.

Within chassis and suspension design criteria, any increase in stability is usually at the expense of vehicle agility.

In simplistic terms, a given vehicle will typically have a natural balance that is dictated by what is called the cornering stiffness of the tyres in relation to the mass on each axle. It is natural that at different speeds, the vehicle behaviour will tend to vary depending on the tyre construction.

When running simulations we can calculate that:

TurnRadius = Wheelbase/SteerAngle + UndersteerGradient*v^2/SteerAngle

In order to create an agile vehicle, we may choose the control strategy to give a Neutral-steer kind of vehicle response. We can thus aim to achieve a desired Yaw Rate, but must enforce a limitation given by the tyre maximum allowable grip with the asphalt (for example if the friction coefficient changes).

Influence on tyre grip

It is very important to understand that with torque vectoring it is often possible to better distribute longitudinal and lateral grip within the tyre traction ellipse. Therefore the overall lateral force per axle that can be generated with TVS is higher than with a conventional mechanical torque differential device. This allows the system for example to alter the under/oversteer characteristics at different speeds.

Methods of torque control

Torque vectoring it is not simply a case of distributing torque based on steering angle because this would achieve excessive yaw response and reduce stability. The system requires a more accurate setpoint (target) and output control system. There are two main ways of achieving this:

• • feedback control

  • model based control

Model based control can give faster response than a pure feedback control (which is affected by signal noise). In order for this to work, the model needs to be a good approximation of the inverse of the actual vehicle.

Many (but not all) drivers would feel comfortable with a "linear" response between steering rate and yaw rate. This would produce a plot with a straight line. A production system will need testing and calibration to provide the level of control that is most natural for a typical human driver. If the vehicle were autonomously driven, then the controller implementation might be different.

Electric vehicles with four electric motors can achieve total wheel torque and yaw moment with some different torque distributions. Hence the criterion for allocating individual torque may be that of Energy Efficiency.

Literature & resources

This is how Global Formula Racing (Oregon+Ravensburg) have implemented their controller: MATLAB and Simulink Racing Lounge: Torque Vectoring

Control of Torque Vectoring for EVs with Induction Motors