Improved Lateral Dynamics through Optimized Torque Distribution

GKN Automotive presents in this article a comparative analysis of four axle torque distribution concepts commonly used in vehicles with an electric rear axle: open differentials, electrically controlled limited-slip differentials, torque splitter differentials and twin-motor drivetrains. The study focuses on the performance criteria of traction, stability, and agility. Simulation studies are used to support the evaluation.

The distribution of axle torques can be realized in different ways for vehicles with an electric rear axle. Four concepts are frequently used in this area: open differentials, electronically controlled Limited-Slip Differentials (eLSDs), torque splitter differentials and dual-motor drivetrains. These technology options each offer advantages and disadvantages, which are described and evaluated below.

Open Differential

The open differential is a fundamental drivetrain technology that has been widely utilized in both conventional internal combustion engine vehicles and Battery Electric Vehicles (BEVs). Its simplicity and cost-effectiveness have made it a popular choice in various automotive applications. The open differential's limitations become apparent when it comes to optimizing vehicle performance. One of the main drawbacks is the limited ability to efficiently distribute torque to the wheels, especially in situations with different coefficients of friction (µ-split) where traction and grip for both wheels is limited by the lower µ level. During low-traction scenarios, such as driving on wet or icy roads, the open differential may struggle to direct power effectively to the wheels with the most grip. As a result, especially high powered BEVs may experience wheel spin, reduced traction, and compromised acceleration.

Electronic Limited- slip Differential

One of the key strengths of the eLSD is its ability to improve traction compared to the conventional open differential. During high-torque situations, such as accelerating from a standstill or challenging road surfaces, the eLSD can partially lock the wheels together. This feature allows it to distribute torque more effectively between the rear wheels, ensuring that power is sent to the wheel with better grip. As a result, the eLSD minimizes wheel slip and provides enhanced traction, especially in µ-split scenarios like on wet or icy roads.

With an electric rear axle drive, where the electric motors deliver instantaneous torque, managing the power distribution to the wheels becomes critical to optimize performance and energy efficiency. The eLSD's ability to control wheel slip ensures that the available torque is utilized efficiently, improving overall vehicle performance. Moreover, the capability to influence torque distribution between the wheels contributes to improved stability and agility - especially BEVs with a higher vehicle load do profit here. During cornering, the eLSD mitigates understeering tendencies by sending more power to the outer wheel due to its higher dynamical wheel load and traction potential. Locking the eLSD during oversteering situations reduces slip angles and hence stabilizes the vehicle. The combination of both features enables balanced and predictable handling when cornering.

Twin-clutch Torque-vectoring

One of the key features of torque-vectoring systems is their ability to distribute torque independently with the support of a friction clutch to each wheel. This allows for efficient power delivery, optimizing traction, agility, and stability in various driving conditions. When a vehicle accelerates from a standstill or navigates challenging terrains, torque-vectoring systems can intelligently direct torque to the wheel with the most grip, reducing wheel slip and improving overall traction. By managing torque distribution in real time, the system ensures that the vehicle remains stable and responsive, even during high-torque situations. During cornering, the system can actively send more power to the outer wheel to help the vehicle turn and reduce understeer tendencies. These capabilities ensure improved overall performance similar to eLSD systems and a heightened sense of control and safety in challenging driving environments.

Dual-motor Drivetrain

Dual-motor drivetrains use individual electric motors for each wheel, providing precise and independent torque distribution. The capability of dual-motor drivetrains to deliver exceptional traction and stability has made them a potential choice for high-end electric vehicles. Both dual-motor drivetrains and torque-vectoring systems share the ability to distribute torque to each rear wheel independently, maximizing traction and improving handling during cornering.

While both drivetrain technologies contribute to improved handling and stability, they achieve this through different mechanisms. Dual-motor drivetrains leverage separate motors for each wheel, allowing them to actively control both speed and torque distribution precisely. In contrast, other torque-vectoring systems employ clutches to redirect torque between the wheels to improve agility and stability.

Traction Performance Evaluation

The importance of traction lies in its direct impact on acceleration, braking, and cornering capabilities of the vehicle. Optimal traction ensures efficient power delivery, enhancing acceleration as well as overall safety and reducing energy wastage. In high-performance vehicles, traction is crucial for precise handling that gives the driver confidence and control during demanding maneuvers.

To compare the traction performance of the four aforementioned technologies an acceleration scenario under µ-split condition is considered, Figure 1. The simulated vehicle accelerates with a constant axle torque of 3000 Nm at the rear axle in a simplified open-loop configuration. The virtual driver tries to keep the vehicle driving straight in a closed-loop control of the steering angle. In case of eLSD, twin-clutch torque vectoring (GKN Twinster), and dual-motor, the traction torque is distributed by constant values.

Figure 1

µ-split vehicle simulation: concept (© GKN)

The results of the µ-split acceleration show significant differences in particular between open differential and the three other concepts, Figure 2. In case of the open differential, the inertia of the left wheel due to the low friction value leads to a short torque deviation between left and right wheel. After that the acceleration of the vehicle is limited by the low friction of the left wheel resulting in a high steering angle demand towards the side with the higher friction value.

Figure 2

µ-split vehicle simulation: results (© GKN)

The dual-motor configuration shows instant acceleration while the torque-vectoring system as well as the eLSD require time to engage the respective clutches leading to a slight delay. Nevertheless, after full locking torque is applied the three configurations show almost equal behavior resulting in significantly higher vehicle acceleration. The variations in acceleration in case of the eLSD results from driveline windup because of open-loop inputs. This can easily be solved by a closed-loop control.

In general, it can be concluded that eLSD, torque-vectoring, and dual-motor show very similar behavior, resulting in improved mean vehicle acceleration by a factor of 2 compared to an open differential. By applying closed-loop optimum slip control the acceleration performance can be improved even further.

Agility Performance Evaluation

Highly agile vehicles respond promptly to driver inputs, allowing for quick lane changes and evasive maneuvers, which is essential for avoiding potential accidents and ensuring road safety. Improving agility is particularly important for manufacturers of performance oriented vehicles, where customers are looking for a dynamic driving experience.

The comparison of agility performance is based on simulation results of an acceleration in a curve, Figure 3. The simulated vehicle accelerates with constant axle torque of 3000 Nm at the rear axle in a constant corner radius of 50 m. The steering angle is controlled in a closed loop to keep the vehicle on the corner radius until the vehicle begins to oversteer. The rear axle acceleration, which is open-loop operated to avoid influences of the control algorithms on the simulation results. For the three concepts with torque distribution capability, the traction torque is distributed by constant values, again to avoid influence of closed-loop control algorithms. Electronic stability control or other brake control systems are not considered in this scenario to allow a fair comparison of all four concepts, although these can be expected to significantly improve the vehicle behavior under real-world conditions.

Figure 3

Accelerated cornering vehicle simulation: concept (© GKN)

The simulation results show that in general the steering angle demand with the eLSD and the dual-motor system in the linear range is in general lower than with the open differential and eLSD, Figure 4. Until a lateral acceleration about 6m/s² is reached, the steering angle demand of open differential and eLSD are equal. At this point, the clutch torque of the eLSD can be increased for this specific scenario and the locking torque can support the yaw operation of the vehicle.

Figure 4

Accelerated cornering vehicle simulation: result (© GKN)

The three mechatronic concepts, limited-slip differential, torque-vectoring, and dual-motor, allow significantly higher maximum lateral acceleration before the vehicle starts to enter the oversteer event, due to their capability to distribute torque between outer and inner wheel. It can be expected that for all concepts the behavior can be further improved by applying a proper control strategy on vehicle level instead of a constant torque distribution.

Stability Performance Evaluation

Stability is a crucial performance criterion that directly impacts vehicle safety, comfort, and handling characteristics. High stability minimizes body roll as well as vibrations and promotes predictable and controlled handling even in unfavorable road conditions. This is essential for manufacturers to provide reliable and enjoyable driving experiences while ensuring road safety.

The simulation scenario for comparison of stability performance is based on a double lane change, Figure 5. The simulated vehicle drives on a straight road at about 90 km/h, approaching an obstacle. A late and fast reaction of the driver prevents a collision by going off-throttle and quick steering. The virtual driver catches and stabilizes the vehicle on the right lane. Again, for the three concepts with torque distribution capability, the traction torque is distributed by an open-loop characteristic to avoid influence of closed-loop control algorithms on the comparison.

Figure 5

Double lane change vehicle simulation: concept (© GKN)

The steering action can be separated in three main phases:

• 1. quick steer to the left hand to avoid collision

• 2. quick counter-steer to change back to right lane

• 3. stabilizing phase to catch the vehicle.

The different drivetrain concepts can be compared based on the simulation results of Phase 3. Also in this scenario, no brake or stability control intervention is considered.

The simulation results in Figure 6 show the steering angle in the three above mentioned phases. The simulated vehicle with open differential shows the highest steering angle demand and the driver requires almost 5 s to stabilize the vehicle after the initial maneuver. Dual-motor and torque-vectoring system show almost similar, compared to the open differential much better, behavior with slightly lower steering angle demand of the dual-motor concept. Also, the eLSD shows significantly lower steering angle demand than the open differential with almost equal stabilization time compared to torque-vectoring and dual-motor.

Figure 6

Double lane change vehicle simulation: result, driver input (© GKN)

Furthermore, the analysis of the resulting yaw rates shows that the stabilizing performance of the four drivetrain concepts vary significantly, Figure 7. While for the open differential no yaw damping is possible, the dual-motor concept shows superior performance due to the fact that negative torque can be applied on the outer and positive torque on the inner wheel. Almost similar performance can be achieved with the torque-vectoring system, which allows to distribute more negative torque to the outer wheel, resulting in still excellent yaw damping performance even without the capability to actively apply positive torque on the inner wheel. Yaw damping capability of the eLSD is still very significant through the locking function of the system resulting in intermediate yaw rate levels and the abovementioned equal stabilization time compared to the much more complex torque-vectoring and dual- motor systems.

Figure 7

Double lane change vehicle simulation: result, yaw rate (© GKN)

Cost

When evaluating systems for vehicles, where affordability, total cost of ownership, and sales margins play a prominent role, component costs must be analyzed alongside with technical criteria, Figure 8.

Figure 8

Cost and complexity of different drivetrain types (© GKN)

Open differentials offer the smallest feature set but at the same time show lowest complexity and serve as the technical as well as cost baseline. In this simplified view the open differential is considered to consist of ring gear and differential case with bevel gears. The eLSD adds a friction clutch with a mechatronic actuation mechanism to the open differential, which is adding complexity and costs but also increases the feature set significantly.

The torque-vectoring system replaces the function to compensate for differences in wheel speed, realized in a differential by cage and gears, by two friction clutches including mechatronic actuation systems. As costs for a second clutch can be considered much higher than differential cage and gears, the resulting total costs are significantly above the level of an eLSD.

Costs for a dual-motor drivetrain must be measured on a different scale, and in total are almost a magnitude higher than the considered torque-vectoring system. Nevertheless, it must be acknowledged that for all other concepts, costs for the other electric drivetrain components like e-motor, inverter, and reduction gear set have not been considered. Independent of that, the dual-motor concept can be considered to be the most expensive solution, with total costs in the range of almost twice as high as a standard electric drivetrain.

Another cost driver is the technical safety concept along with the higher functionality and therefore increasing complexity of the different drivetrains.

Conclusion

The twin-clutch torque-vectoring and dual-motor concepts show their strength to control wheel torques individually resulting in superior performance in all three analyzed categories, Figure 9. This performance also comes at a significantly higher cost level than the other analyzed concepts.

Figure 9

Performance and cost comparison of the four systems discussed (GKN)

The opposite end of the analyzed spectrum is the open differential. With lowest complexity and consequently costs it represents the benchmark in these categories. Although suitable for a majority of applications in the field, it shows the lowest technical performance of the concepts in focus of this paper.

Electronic limited-slip differentials appear to be a compromise of the beforementioned concepts. They show good results in all performance criteria and are able to reach similar levels as torque-vectoring and dual-motor concepts in some categories. At same time, eLSDs offer this performance at reasonable costs.

It can be concluded that all four concepts with their respective strengths and weaknesses have their niche in the market. While open differentials will remain the mainstream for the majority of applications, vehicles with high performance or specific use-cases are creating demand for more complex systems like torque-vectoring or dual-motor drivetrains. The eLSD seems to be the best compromise in terms of value for money, showing a significant performance improvement compared to a standard open differential offered at reasonable costs.