Active Rear Axle Kinematics

From E31Wiki
Jump to: navigation, search
Active Rear Axle Kinematics (AHK) indicator

Developed by BMW and Bosch Rexroth AG Active Rear Axle Kinematics (ARAK) or in German Aktive Hinterachskinematik (AHK) is a computer-controlled electrohydraulic four-wheel steering system. Whereas the earlier Anti-lock Braking System (ABS), Automatic Stability Control (ASC) and Automatic Stability Control Plus Traction (ASC+T) improve longitudinal stability during braking and acceleration, the Active Rear Axle Kinematics system improves lateral stability in high-speed maneuvers. The Active Rear Axle Kinematics system was not the first four-wheel steering stability system in passenger vehicles but it knew to impress press and drivers by its performance. The system could be ordered as optional equipment for the 850i in 1991 but would not be available until 1992 – the debut year of the 850CSi which had the Active Rear Axle Kinematics system as standard equipment. The 1993 M60 840Ci also offered the Active Rear Axle Kinematics system as optional equipment. The system was not available on USA-spec 8 Series. Despite offering vast stability improvements time rapidly caught up with the Active Rear Axle Kinematics system. In the 1994 M73 850Ci BMW, Robert Bosch GmbH and Continental Automotive Systems introduced Dynamic Stability Control (DSC) which heralded the end of the Active Rear Axle Kinematics system.

Although Active Rear Axle Kinematics abbreviates to ARAK, this abbreviation is rarely used and the system is commonly known by the German abbreviation of Aktive Hinterachskinematik – AHK.


For the Z1 BMW developed a brand new rear axle based on the multi-link suspension design. The rear axle was further refined and perfected in the BMW 850i and would become known as the Integral Rear Axle – also referred to as the Z-axle because of its shape. In 1989 the Z1 and 850i were the first BMW series production cars to be equipped with a multi-link rear axle. Despite the higher weight, complexity and cost over the (by then used) semi-trailing arm suspension, the Integral Rear Axle offered many advantages and performs as well as the double wishbone suspension used in high performance sports and racing cars but is far less space-consuming.

One of the novelties of the Integral Rear Axle is elasto-kinematics: Forces that act upon the suspension under cornering, acceleration and deceleration can change the suspension geometry to counteract the effects. To this end, kinematic and elasto-kinematic properties are designed into the rear axle and are calculated to provide a self-compensating response to force and spring action. This helps reducing roll, squat and dive behavior. The elasto-kinematic suspension geometry is also used to correct for the rear wheel's tendency to steer out of a curve: In most vehicles, when cornering at higher speeds, the rear wheels tend to steer slightly to the outside of the curve, which can reduce stability and make the vehicle more prone to oversteer. The Integral Rear Axle uses the lateral forces generated in a curve to steer the rear wheels a fraction into the curve. This stabilizing steering effect at the rear wheels improves the safety of the vehicle through the curve.

The 850i was designed to be a luxury gran turismo – the fastest and most powerful BMW car to date. Making a car faster is one thing – keeping it safe at those high speeds is another. The 850i was to set new standards in automobile safety. While the Integral Rear Axle was a clear step forward in safety over the previous suspension systems, BMW saw room for even more improvement. The passive rear-wheel steering of the Integral Rear Axle functions by a series of cause and effect: The steering front wheels force the vehicle to follow a different course. The change of direction causes a weight transfer in the vehicle. The weight transfer induces lateral forces on the rear suspension. Through elasto-kinematics these forces change the suspension geometry. The changed geometry finally steers the rear wheels into the turn... In other words, the relation between front-wheel and rear-wheel steering is not direct – a delay or phase shift arises. The Integral Rear Axle is always reacting to what just happened – not what is happening. In order to minimize the delay to the rear-wheel steering and to maximize its efficiency, the chain of actions must be shortened. Therefore BMW equipped the Integral Rear Axle with a computer-controlled electrohydraulic actuator unit which can actively steer the rear wheels – the Active Rear Axle Kinematics. By using the steering input and vehicle speed the computer logic can steer the rear wheels even before the lateral forces build up and at a greater angle than the passive Integral Rear Axle. AHK does not replace the elasto-kinematics of the Integral Rear Axle – AHK is an extension to the Integral Rear Axle and its effect comes on top of it. While the earlier ABS, ASC and ASC+T active safety systems improve longitudinal stability during braking and acceleration, AHK was the first active safety system in a BMW car to improve lateral stability in high-speed maneuvers.

Development of AHK started in the late eighties. Some early articles about the 850i suggest the system was to debut together with the 850i but it would take until 1991 before the system could be ordered by customers and another year before it was finally available. 1992 was also the year the 850CSi was introduced which had AHK as standard equipment so the AHK introduction is often linked to that of the 850CSi although this is not entirely correct. AHK could be ordered for the 850i, M70 850Ci and M60 840Ci as part of option 237 Dynamic Drive Package, and was standard equipment on the 850CSi. Option 237 also included 214 Automatic Stability Control Plus Traction (ASC+T), 216 Servotronic, 223 Electronic Damper Control (EDC), and 245 Electrical Steering Column Adjustment. Note that EDC was not available on the 850CSi or when option 704 M Sport Suspension was chosen. AHK was also not offered on the later M73 850Ci and M62 840Ci, nor was it available on any USA-spec E31.


Sideslip angle without and with AHK
Effect of the sideslip angle on the steering input in a slalom maneuver

Under high-speed cornering conditions, a car develops a greater lateral velocity than is indicated by the direction in which the wheels are pointed: the car's longitudinal axis tends to move away, yaw, from the direction of motion. The angle between the car's longitudinal axis and direction of motion is the sideslip angle. If the longitudinal axis is pointing outwards the turn, the vehicle is said to understeer. If the longitudinal axis is pointing inwards the turn, the vehicle is said to oversteer. The sideslip angle has a negative impact on the steering response of a vehicle and the steering effort that is required to change direction: If a driver decides to change direction in a curve while the vehicle is subject to oversteer and turns the steering wheel, because of the sideslip angle the vehicle's longitudinal axis has to cross the current direction of motion first before the vehicle body actually changes direction. In other words, there's a delay between the steering input from the driver and the actual change of direction. The negative effect of the sideslip angle is very evident in a high-speed slalom maneuver. The sideslip angle causes the vehicle's longitudinal axis to make a greater angle with the direction of travel axis of the slalom course than is strictly required for the maneuver. This greater angle must be overcome on each change of direction. In other words, a much greater steering effort is required from the driver due to the sideslip angle.

Understeer is a dynamically stable condition, meaning that if control is lost, the vehicle continues to point and travel in the direction that it is already pointing and traveling in. Oversteer on the other hand is dynamically unstable. The sideslip points the vehicle's longitudinal axis towards the inside of the curve, amplifying the steering angle of the front wheels on the direction of motion. The car will steer harder into the turn. This on its turn increases the lateral acceleration and sideslip angle, amplifying the steering even further. In oversteer the sideslip angle amplifies itself ultimately ending in a spin. Recovering from oversteer requires proper application of opposite lock steering. Therefore oversteer is considered an unsafe condition for inexperienced and panicking drivers. It's obvious that minimizing the sideslip angle improves stability and vehicle safety. It reduces the risk of a spin, makes the car more responsive and predictive to steering input from the driver, and lessens the required steering effort – the vehicle is easier to control near the physical limits.

Steering the rear wheels into the curve forces the car's rear back towards the inside of the curve and moves the longitudinal axis back towards the direction of motion, reducing the sideslip angle. The passive rear-wheel steering from the Integral Rear Axle provides up to 0.2 degrees compensation for the rear wheels tendency to steer to the outside of a curve but it is nowhere as effective as the active rear-wheel steering from the Active Rear Axle Kinematics. AHK can steer the rear wheels far beyond what is possible with passive systems and because AHK does not rely on the build-up of forces acting upon the suspension and vehicle body but uses computer calculations based on the vehicle speed and steering angle instead, the system can counteract even before the sideslip angle is actually built-up. This makes AHK capable of preventing the build-up of sideslip up to an extent. At low speeds the sideslip angle is negligible and thus is AHK not active. AHK increases the rear-wheel steering progressively at speeds greater than 40 km/h (25 mph) and with moderate to high lateral accelerations. At the highest lateral accelerations, near the physical limit, AHK reaches its maximum rear-wheel steering angle of 2 degrees – ten times more than the passive steering provides! AHK can reduce the sideslip angle from 4.5 degrees (without AHK) to well below 1 degree. AHK provides maximum sideslip angle correction up to speeds of 220 km/h (137 mph). AHK continues to reduce the sideslip angle at even higher speeds but because it cannot steer the rear wheels beyond 2 degrees the sideslip angle correction gradually decreases.

Minimizing the sideslip does not only improve safety in curves. During the development of AHK at BMW, people from BMW Motorsport GmbH (in 1993 renamed to BMW M GmbH) who were developing the 850CSi at that time, were given the opportunity to drive a test vehicle equipped with AHK on the Nürburgring Nordschleife circuit. The drivers had the feeling the car with AHK did not allow them to exactly hit the brake and acceleration points they were used to and complained they could not hit the proper racing line and apex in curves. Despite that and much to their surprise, the lap times of the test vehicle equipped with AHK were consistently noticeably faster. The reason is again with the sideslip angle: The car without AHK develops sideslip in a curve which is still present at the exit of the curve. The car with AHK on the other hand minimizes sideslip making it much more stable on the corner exit. This allowed the drivers to apply throttle much sooner and gaining higher speeds at the straights. Because of the performance edge AHK provided, BMW Motorsport GmbH decided to make AHK standard equipment on the 850CSi.

Case study: high-speed lane-change maneuver

AHK does improve overall handling making the car a bit quicker around the track, but its primary function and reason of development is to increase vehicle safety on the road. In racing the driver is deliberately pushing the car towards its limits and anticipates for crossing these limits, but on the road a driver may be caught totally off guard in an emergency situation. An example is an unprepared high-speed lane-change maneuver. A vehicle is traveling at high speed when the driver suddenly notices an obstacle in his path and needs to perform an emergency evasive maneuver to avoid colliding with it. An idealized version of the situation is shown in the picture below.

High-speed lane-change maneuver: Ideal driving line

The image shows three graphs below the driving line visualization. The steering wheel angle graph shows the travel the steering wheel makes throughout the whole maneuver. The lateral acceleration graph shows the magnitude of the lateral force acting on the rear axle induced by the weight of the car. The sideslip angle graph indicates the angle the vehicle makes with the current direction of travel.

  • Point 1: The driver commences the evasive maneuver by steering hard left. At time 0 no lateral force works on the car but it quickly grows as the steering angle increases.
  • Point 2: The steering wheel reaches its maximum angle for this maneuver. At this point the car makes the tightest corner and moves fastest away from the original course. The lateral acceleration maxes out but has no effect in this idealized situation. After this the driver begins returning the steering wheel to the center position.
  • Point 3: As the driver ends the first half of the maneuver and initiates the second half, the steering wheel crosses the center position. For a short moment the car drives straight ahead – albeit in a different direction than the original direction of travel – with no lateral force working on it. The second half of the maneuver is exactly the opposite of the first half.
  • Point 4: Once again the steering wheel reaches its maximum angle for this maneuver, but this time in the opposite direction.
  • Point 5: The steering wheel returns to the center position and the car continues to travel straight ahead in the original direction of travel. A collision with the obstacle has been successfully avoided.

Logic says the above is a correct and adequate reaction of the driver to the emergency. However, it is only valid for a low-speed lane-change maneuver where the maximum lateral acceleration is low! As seen earlier, at high speed the lateral force acting on the rear axle pulls the rear of the car towards the outside of the corner. This causes the vehicle to be angled to the actual direction of travel – the sideslip angle. The higher the lateral acceleration becomes, the larger the sideslip angle grows. The image below shows what happens when a driver performs exactly the same reaction in a real world car.

High-speed lane-change maneuver: Driving line without AHK

Despite having exactly the same steering input as the idealized car, the resulting driving line is completely different!

  • Point 1: The driver commences the evasive maneuver by steering hard left. Due to inertia the actual turn-in is slowed down a bit compared to the idealized situation. As soon as the lateral force builds up it pulls the car's tail outwards – the sideslip angle increases and the vehicle points more and more towards the inside of the turn, slightly increasing the steering effect of the front wheels.
  • Point 2: The steering wheel reaches its maximum angle for this maneuver and the driver begins turning back to the center position – lessening the turning radius. However the sideslip angle compensates this partially, slowing down the speed with which the vehicle returns to driving straight ahead.
  • Point 3: The steering wheel crosses the center position. Despite the fact the front wheels point straight ahead the car still points to the inside of the turn – the sideslip angle forces it to continue turning left. Even when the front wheels begin to steer right the car continues the left turn. The car moves slightly sideways! This should not be regarded as drifting: The lateral acceleration does not exceed the rear tires' grip level and the sideslip angle is still relatively small.
  • Point 4: The sideslip angle and lateral force finally return to 0 and the vehicle ends the left turn. For a moment the car drives straight ahead but the front wheels steer right at the maximum angle for this maneuver. Despite the driver steers equally to each direction it is as if the right turn commences far more aggressively! This increases the build-up of the lateral force and sideslip angle.
  • Point 5: The steering wheel returns to the center position but the momentum from the aggressive turn-in keeps the lateral force and sideslip angle growing, forcing the car to continue the right turn. The lateral force grows so large the grip level of the rear tires is exceeded.
  • Point 6: The car is drifting through the turn.
  • Point 7: The momentum of the turn wears off. The lateral force and sideslip angle decrease and the rear tires regain traction, pushing the car forward in the direction it is currently pointing at.
  • Point 8: The lateral force and sideslip angle return to 0 and the car finally exits the evasive maneuver, albeit in a different direction of travel than before entering the maneuver. A collision with the obstacle was avoided but the car followed a completely different path than what the driver may have expected.

It's obvious the sideslip angle has a very negative impact on the handling of the car throughout the maneuver. The sideslip angle slows down the steering input. It's causing a delay between input and output making it more difficult for the driver to control the vehicle. In the example the driver completed the steering maneuver in two seconds but it took the car twice as long to complete it and the result is quite different from what the steering input suggests.

A problem with the driving line of the car without AHK is that it may quickly run out of road. Avoiding the obstacle is one thing but not running into something else is another. The key to improving the handling and stability in high-speed maneuvers is minimizing the sideslip angle. This is exactly what AHK does.

High-speed lane-change maneuver: Driving line with AHK

The driving line of the vehicle with AHK is much closer to that of the ideal car than that of the car without AHK.

  • Point 1: The driver commences the evasive maneuver by steering hard left. The microprocessor of the AHK system detects the steering input immediately and steers the rear wheels accordingly even before the lateral force builds up. The parallel steering rear wheels push the car's tail towards the inside of the turn – opposing the lateral force.
  • Point 2: The steering wheel reaches its maximum angle for this maneuver and the lateral force maxes out. AHK minimizes the sideslip angle although it cannot eliminate sideslip entirely.
  • Point 3: The steering wheel crosses the center position. There is a small sideslip angle remaining which prolongs the left turn, but far less dramatic as for the non-AHK vehicle.
  • Point 4: The lateral force returns to 0 and the car commences the second half of the maneuver, almost immediately after the driver initiated it.
  • Point 5: Once again the steering wheel reaches its maximum angle, but this time in the opposite direction. AHK keeps the sideslip angle small.
  • Point 6: The steering wheel returns to the center position as the driver ends the maneuver. The car continues the right turn for a little longer due to the small remaining sideslip angle.
  • Point 7: The lateral force and sideslip angle return to 0 and the vehicle exits the maneuver. A collision with the obstacle has been successfully avoided. The driving line is not exactly the same as in the ideal situation, but it is very close – the exit course is almost exactly what the driver would expect.

The difference in trajectory between the vehicle with and without AHK is startling. The effect of the lateral force on the sideslip angle is much lower for the vehicle with AHK. Due to a limited degree of correction the sideslip angle is not entirely neutralized by the AHK system; a small delay between steering input and output remains but the delay is very small. This keeps the car stable and the steering very responsive throughout the whole maneuver. AHK makes the car more nimble and it's this effect that gives the driver the impression the car weighs a lot less than it actually does, seemingly defying the laws of physics.

Naturally it is possible for the non-AHK car to complete the lane-change maneuver without going very wide or exiting in a different direction but this requires a skilled driver applying proper opposite lock steering and earlier initiation of the maneuver. However there is no earlier in a sudden emergency situation and an unprepared or panicking driver may not be able to apply proper opposite lock steering.

It should be clear AHK improves the high-speed stability and handling, adding to the safety of the vehicle.


The Active Rear Axle Kinematics system received most attention in the 850CSi which was received very well by press and drivers praising the improved handling over the 850i. However along with AHK the 850CSi also had suspension, braking, steering and engine power improvements. Since AHK cannot be disabled by the driver, judging its effect is somewhat difficult.

Nevertheless the 850CSi scored very well in tests which can be attributed mostly to AHK. In a series of tests performed in 1996 by the German Auto Motor und Sport Magazine the 850CSi put up a remarkable performance in the 36 meter (39 yard) slalom, only beaten by the Porsche 911 Carrera and Turbo and the Ferrari F350 sports cars. In the 110 meter (120 yard) moose test the 850CSi beat all other cars despite weighing over 500 kg (1100 lb) more than the other cars in the top 5.

At the E31 8 Series meeting in Munich 2007, organized by the ClubE31 Worldwide Owners Group e.V., Dr.-Ing. Edmund Donges, General Manager CA Methods and Processes in Chassis Engineering of BMW and responsible for the development of AHK, said a test vehicle equipped with AHK was noticeably faster around the Nürburgring Nordschleife circuit than without. Because of the smaller sideslip angle in curves the test vehicle equipped with AHK was more stable on corner exits allowing the driver to apply throttle much sooner and gaining higher speeds on the straights. While primarily designed for safety AHK stretches the vehicle's physical limits with better track performance as a bonus.


While AHK was developed to increase vehicle safety, incorrect steering of the rear wheels could have disastrous results. For this reason the AHK system is built almost entirely redundant and enters a failsafe mode on even the slightest malfunction.

  • The vehicle speed is determined by a speed sensor on the differential and by calculating the average speed between both front wheels using the ABS pulse sensors.
  • The steering angle of the front wheels is determined by a double steering angle sensor on the steering column spindle and additionally by calculating the speed difference between both front wheels using the ABS pulse sensors.
  • The steering angle of the rear wheels is determined by a double position sensor on the AHK actuator unit.
  • The rear wheel steering can be locked in a fixed position by both a hydraulic lock and a mechanical lock. The system is designed to lock automatically in case of both hydraulic and electric failure.
  • The control module contains two separate processing units that have both access to all inputs and can operate both locks. Both processing units compare their outputs and can decide independently to lock the rear wheel steering when the outputs differ. The locks can only be released when both processing units agree.

Vehicle safety is not compromised when the rear wheel steering is locked. The vehicle will behave exactly like the same vehicle without AHK. The passive steering of the Integral Rear Axle remains in effect. In the event of a failure during heavy cornering it is possible the rear wheels are locked at a slight angle causing a very mild crab crawl driving line but otherwise not affecting the vehicle's stability and safety.

End of AHK

AHK was not long-lived. In 1994 BMW and Bosch introduced Dynamic Stability Control (DSC) which basically meant the end of AHK – only a few years after its introduction. DSC is an evolution of the Anti-lock Braking System (ABS) and Automatic Stability Control Plus Traction (ASC+T). By omitting the expensive and complex rear-wheel steering and sharing most components with ABS and ASC+T, Dynamic Stability Control could be implemented at a relatively low cost. DSC can measure speed of all four wheels independently and uses yaw rate and lateral acceleration sensors to accurately recognize instability like understeer and oversteer. DSC controls stability entirely by means of smart independent braking and limiting engine power. AHK on the other hand guesses oversteer by parameterized steering angle and vehicle speed input. The system controls oversteer by increasing the vehicle's physical limits. A skilled race driver would find DSC having a negative impact on lap times whereas AHK results in better lap times. Although the AHK steering rear axle offers a degree of stability control for oversteer DSC cannot match, DSC is clearly the most cost-efficient technology of both. This opened the doors to a rapid adoption of Dynamic Stability Control throughout the BMW vehicle range and ultimately the demise of AHK. The 1994 M73 850Ci was along with the E38 750i and 750iL the first BMW vehicle equipped with DSC – AHK was no longer an option although AHK remained standard for the 850CSi and optional for the M60 840Ci. There are signs BMW had plans to combine AHK and DSC although no such cars were ever built. When the last 850CSi rolled of the production line in late 1996, the final curtain fell on AHK. In total only 1732 vehicles were equipped with AHK.

Due to the rarity of AHK, dealers lack knowledge about the system. In case of problems – even simple ones – they usually resort to replacing the very expensive actuator, accumulator and control unit. This forced several owners to disable the AHK system entirely because they couldn't afford the high repair costs. Frequent causes for failures are the use of incorrect hydraulic fluid and leaks in the high-pressure hydraulic piping due to corrosion and lack of maintenance.

Future of four-wheel steering

The coming of Dynamic Stability Control made it possible to improve high-speed stability at a much lower cost than four-wheel steering. While this meant the end for AHK in the E31 8 Series it doesn't mean there are no other applications for four-wheel steering in modern vehicles. With the ever-growing size and wheelbase length of luxury vehicles it becomes more difficult to maintain a small turning radius. Steering the rear wheels opposite from the front-wheels – even at only a small angle – can considerably reduce the turning radius and make parking and or taking short corners easier.

In 2008 BMW presented the new F01 and F02 7 Series. Amongst the options was Integral Active Steering (IAS) – the return of four-wheel steering, albeit a completely different design from AHK. AHK is a complex electrohydraulic system developed to improve high-speed stability whereas Integral Active Steering is a simpler electromechanical system developed to improve the low-speed turn radius, although it improves high-speed stability as well. The simpler construction does not necessarily imply worse performance, but it should keep the cost down while increasing reliability. IAS is also available on the F07 5 Series Gran Turismo and F10 and F11 5 Series.