Research on Electronic Differential for electric racing

Chunyun Fu Reza Hoseinnezhad Simon Watkins Reza Jazar What is a differential?

 Problems with the absence of differentiation

 Wheel slips occurs; much energy loses in friction and heat; severe wear appears.

 Much harder to initiate a turn, once the turn is started the driver has to continually fight under-steer. (the inside rear wheel is trying to turn the back to a straight line)

 Drawbacks of conventional open differentials

 Inherent equal-torque characteristic

 On a ‘split-μ’ condition road, maximum propelling torque is restricted to twice the limiting torque at the driving wheel with poorer adhesion Torque Sensing (Torsen) Differential

 Torsen differential

 Much higher torque bias ratio, normally kd =T2/T1=2.5~4.5  When one wheel loses traction and attempts to spin, it transmits drive to the other wheel with better traction before spinning starts

 Popular in racing applications Torque Sensing (Torsen) Differential

 Drawbacks of Torsen differential in racing application

 Transfer torque from the outer wheel to the inner wheel when cornering. However the inner wheel will be considerably unloaded during a turn, thus significantly impair the effect of torque bias

 The torque bias ratio is invariable during a race, in other words, it’s not adaptive to the variable racing conditions Electronic Differential

 What is e-differential?

 An electronic differential, is a torque and wheel speed control system for managing multiple driving motors

 it supervises the distribution of torques and speeds between driving wheels in accordance with the states of the vehicle and driver’s commands.

 Usually an e-differential has the configuration of twin-rear mounted motors (e.g. RMIT R11E Car) or all-in-wheel motors Electronic Differential

Throttle Pedal Steering Angle Wheel Speed Gyroscope & Sensor Sensor Sensors Accelerometer

Micro-control Unit (MCU)

Inverter Inverter

Left Right Right Left Gear Gear Driving Driving Driven Driven Reducer Reducer Wheel Motor Motor Wheel

Schematic diagram of a proposed electronic differential Existing ED Control Algorithms

 The equal torque strategy

 It’s the easiest control strategy for e-diff, it always applies even torque to driven wheels regardless of the driven wheel speeds, emulating the behavior of a mechanical differential. Its schematic is shown below [1].

 The speed differentiation is achieved naturally by the reaction forces and moments exerted on the contact patch. Existing ED Control Algorithms

 Independent motor control structure using the Ackerman steering condition

 Based on the Ackerman steering geometry, this method uses the vehicle speed and steering angle as inputs and calculates the desired inner and outer wheel speed.

 When the electric car enters a corner, the electronic differential acts immediately on the two motors, reducing the angular speed of the inner wheel while increasing that of the outer wheel to their desired values. Existing ED Control Algorithms

 Independent motor control strategy based on vehicle dynamic models Normally, a vehicle planar model is used to derive the desired yaw rate which is expressed as follows:

where K is called the “stability factor” given by: Research Questions

 Most e-differential strategies reported so far focus on maintaining the vehicle stability as the first and dominant priority. They work on the basis of keeping the vehicle states (such as slip ratio) in a “safe region” .  With racing cars however, the priority of e-differential, with the vehicle stability being pushed to its margins (yet maintained), is the swiftness and accuracy of following the driver’s commands. Therefore, keeping the car in neutral-steer becomes our control goal. Research Questions

1. How the torque generated by each driving affects the stability of the electric car, in general, and its steerability, in particular? 2. How can an efficient electronic differential system be designed in such a way that perfect, or close to perfect steering performance is achieved? 3. How the novel, mathematically formulated control methods for electronic differential perform in numerical simulations and simulated test drives? 4. How the new electronic differentials perform on board a real electric racing car? 5. How robust are the new electronic differential designs to variations in vehicle dynamic parameters? How can the robustness be improved? The Proposed Algorithm

 Equation of motion [2] in the local coordinate frame The Proposed Algorithm

 Vehicle dynamics after adding one additional torque on the rear axle The Proposed Algorithm

 The steady-state motion is governed by the following equation

Yaw rate response:

From the yaw response equation, we find out that the steady-state yaw rate of the race car can be directly

controlled by Fad. The Proposed Algorithm

 The desired yaw rate for a neutral steer car is

Control goal: The Proposed Algorithm

 Block diagram of the control system The Proposed Algorithm

 Simulink model of the proposed e-differential 521.5

Left Fz 0.02845 Env Driveline Left Wheel Slip Environment1 318.8 phi omega Fx4 Vx Fx4 596.8 Initial Condition delta slip Fx3 69.34 Fz Vy TL delta Left Tire Dynamics p Left Tire Inertia Fx4 phi Fx3 Vehicle State Variables TL+TR r 0.5 T Vx Vehicle Dynamics Gain -1.043 Left Motor Torque Vx throttle yaw rate Sine Wave Throttle TL+TR 0.5 T phi omega -0.02017 Tire Angular Speeds Gain1 Right Motor Torque Vx Fx3 roll angle 0.01803 delta slip 130.7 Right Wheel Slip 1333 Fz Yaw Rate Comparison TR 278 Right Tire Dynamics Right Fz Right Tire Inertia Actual Fad Env error TL-TR Driveline Environment 304.8 Controller Vx desired Fad

Initial Condition1 Desired Fad delta desired y aw rate

Derised Fad -1.03

Desired Yaw Rate Simulation Result

 The figure shows a close-to-neutral steering performance of the race car (while maintaining its stability) in challenging steering scenarios.

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 C. Fu, R. Hoseinnezhad, S. Watkins, and R. Jazar, “Direct torque control for electronic differential in an electric racing car,” in Proceedings – 4th International Conference on Sustainable Automotive Technologies 2012, ICSAT 2012, Melbourne, Australia, 2012, pp. 177-183. References

1. G. A. Magallan, et al., "A neighborhood with electronic differential traction control," in 34th Annual Conference of the IEEE Industrial Electronics Society, IECON 2008, Orlando, FL, United states, 2008, pp. 2757-2763. 2. R. N. Jazar, Vehicle Dynamics : Theory and Application: New York ; London : Springer, 2008. Contribution to knowledge in this area

 My research on the electronic differential will solve a problem that automotive engineers have been chasing for years, namely achieving desired steering characteristic in changing dynamic conditions, which is impossible to achieve with conventional differentials.

 The proposed control strategies can lead the research on electronic differential to a new scope where not only should the vehicle stability be considered, but also the steering response needs to be taken into account.