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The Effect of a Viscous Coupling Used as a Front-Wheel Drive Limited-Slip Differential on Vehicle Traction and Handling
1 ABCTRACT
The viscous coupling is known mainly as a driveline component in four wheel drive vehicles. Developments in recent years, however, point toward the probability that this device will become a major player in mainstream front-wheel drive application. Production application in European and Japanese front-wheel drive cars have demonstrated that viscous couplings provide substantial improvements not only in traction on slippery surfaces but also in handing and stability even under normal driving conditions.
This paper presents a serious of proving ground tests which investigate the effects of a viscous coupling in a front-wheel drive vehicle on traction and handing. Testing demonstrates substantial traction improvements while only slightly influencing steering torque. Factors affecting this steering torque in front-wheel drive vehicles during straight line driving are described. Key vehicle design parameters are identified which greatly influence the compatibility of limited-slip differentials in front-wheel drive vehicles.
Cornering tests show the influence of the viscous coupling on the self steering behavior of a front-wheel drive vehicle. Further testing demonstrates that a vehicle with a viscous limited-slip differential exhibits an improved stability under acceleration and throttle-off maneuvers during cornering.
2 THE VISCOUS COUPLING
The viscous coupling is a well known component in drivetrains. In this paper only a short summary of its basic function and principle shall be given.
The viscous coupling operates according to the principle of fluid friction, and is thus dependent on speed difference. As shown in Figure 1 the viscous coupling has slip controlling properties in contrast to torque sensing systems.
This means that the drive torque which is transmitted to the front wheels is automatically controlled in the sense of an optimized torque distribution.
In a front-wheel drive vehicle the viscous coupling can be installed inside the differential or externally on an intermediate shaft. The external solution is shown in Figure 2.
This layout has some significant advantages over the internal solution. First, there is usually enough space available in the area of the intermediate shaft to provide the required viscous characteristic. This is in contrast to the limited space left in today’s front-axle differentials. Further, only minimal modification to the differential carrier and transmission case is required. In-house production of differentials is thus only slightly affected. Introduction as an option can be made easily especially when the shaft and the viscous unit is supplied as a complete unit. Finally, the intermediate shaft makes it possible to provide for sideshafts of equal length with transversely installed engines which is important to reduce torque steer (shown later in section 4).
This special design also gives a good possibility for significant weight and cost reductions of the viscous unit. GKN Viscodrive is developing a low weight and cost viscous coupling. By using only two standardized outer diameters, standardized plates, plastic hubs and extruded material for the housing which can easily be cut to different lengths, it is possible to utilize a wide range of viscous characteristics. An example of this development is shown in Figure 3.
3 TRACTION EFFECTS
As a torque balancing device, an open differential provides equal tractive effort to both driving wheels. It allows each wheel to rotate at different speeds during cornering without torsional wind-up. These characteristics, however, can be disadvantageous when adhesion variations between the left and right sides of the road surface (split-μ) limits the torque transmitted for both wheels to that which can be supported by the low-μ wheel.
With a viscous limited-slip differential, it is possible to utilize the higher adhesion potential of the wheel on the high-μsurface. This is schematically shown in Figure 4.
When for example, the maximum transmittable torque for one wheel is exceeded on a split-μsurface or during cornering with high lateral acceleration, a speed difference between the two driving wheels occurs. The resulting self-locking torque in the viscous coupling resists any further increase in speed difference and transmits the appropriate torque to the wheel with the better traction potential.
It can be seen in Figure 4 that the difference in the tractive forces results in a yawing moment which tries to turn the vehicle in to the low-μside, To keep the vehicle in a straight line the driver has to compensate this with opposite steering input. Though the fluid-friction principle of the viscous coupling and the resulting soft transition from open to locking action, this is easily possible, The appropriate results obtained from vehicle tests are shown in Figure 5.
Reported are the average steering-wheel torque Ts and the average corrective opposite steering input required to maintain a straight course during acceleration on a split-μtrack with an open and a viscous differential. The differences between the values with the open differential and those with the viscous coupling are relatively large in comparison to each other. However, they are small in absolute terms. Subjectively, the steering influence is nearly unnoticeable. The torque steer is also influenced by several kinematic parameters which will be explained in the next section of this paper.
4 FACTORS AFFECTING STEERING TORQUE
As shown in Figure 6 the tractive forces lead to an increase in the toe-in response per wheel. For differing tractive forces, Which appear when accelerating on split-μwith limited-slip differentials, the toe-in response changes per wheel are also different.
Unfortunately, this effect leads to an undesirable turn-in response to the low-μside, i.e. the same yaw direction as caused by the difference in the tractive forces.
Reduced toe-in elasticity is thus an essential requirement for the successful front-axle application of a viscous limited-slip differential as well as any other type of limited-slip differential.
Generally the following equations apply to the driving forces on a wheel
With Tractive Force
Vertical Wheel Load
Utilized Adhesion Coefficient
These driving forces result in steering torque at each wheel via the wheel disturbance level arm “e” and a steering torque difference between the wheels given by the equation:
△=
Where △Steering Torque Difference
e=Wheel Disturbance Level Arm
King Pin Angle
hi=high-μside subscript
lo=low-μside subscript
In the case of front-wheel drive vehicles with open differentials, △Ts is almost unnoticeable, since the torque bias () is no more than 1.35.
For applications with limited-slip differentials, however, the influence is significant. Thus the wheel disturbance lever arm e should be as small as possible. Differing wheel loads also lead to an increase in △Te so the difference should also be as small as possible.
When torque is transmitted by an articulated CV-Joint, on the drive side (subscript 1) and the driven side (subscript 2),differing secondary moments are produced that must have a reaction in a vertical plane relative to the plane of articulation. The magnitude and direction of the secondary moments (M) are calculated as follows (see Figure 8):
Drive side M1 =
Driven side M2 =
With T2 =
=
Where Vertical Articulation Angle
Resulting Articulation Angle
Dynamic Wheel Radius
Average Torque Loss
The component acts around the king-pin axis (see figure 7) as a steering torque per wheel and as a steering torque difference between the wheels as follows:
where Steering Torque Difference
WWheel side subscript
It is therefore apparent that not only differing driving torque but also differing articulations caused by various driveshaft lengths are also a factor. Referring to the moment-polygon in Figure 7, the rotational direction of M2 or respectively change, depending on the position of the wheel-center to the gearbox output.
For the normal position of the halfshaft shown in Figure 7(wheel-center below the gearbox output joint) the secondary moments work in the same rotational direction as the driving forces. For a modified suspension layout (wheel-center above gearbox output joint, i.e. negative) the secondary moments counteract the moments caused by the driving forces. Thus for good compatibility of the front axle with a limited-slip differential, the design requires: 1) vertical bending angles which are centered around or negative () with same values of on both left and right sides; and 2) sideshafts of equal length.
The influence of the secondary moments on the steering is not only limited to the direct reactions described above. Indirect reactions from the connection shaft between the wheel-side and the gearbox-side joint can also arise, as shown below:
Figure 9: Indirect Reactions Generated by Halfshaft Articulation in the Vertical Plane
For transmission of torque without loss and both of the secondary moments acting on the connection shaft compensate each other. In reality (with torque loss), however, a secondary moment difference appears:
△
With
The secondary moment difference is:
For reasons of simplification it apply that and to give
△
△ requires opposing reaction forces on both joints where . Due to the joint disturbance lever arm f, a further steering torque also acts around the king-pin axis:
Where Steering Torque per Wheel
Steering Torque Difference
Joint Disturbance Lever
Connection shaft (halfshaft) Length
For small values of f, which should be ideally zero, is of minor influence.
5．EFFECT ON CORNERING
Viscous couplings also provide a self-locking torque when cornering, due to speed differences between the driving wheels. During steady state cornering, as shown in figure 10, the slower inside wheel tends to be additionally driven through the viscous coupling by the outside wheel.
Figure 10: Tractive forces for a front-wheel drive vehicle during steady state cornering
The difference between the Tractive forces Dfr and Dfl results in a yaw moment MCOG, which has to be compensated by a higher lateral force, and hence a larger slip angle af at the front axle. Thus the influence of a viscous coupling in a front-wheel drive vehicle on self-steering tends towards an understeering characteristic. This behavior is totally consistent with the handling bias of modern vehicles which all under steer during steady state cornering maneuvers. Appropriate test results are shown in figure 11.
Figure 11: comparison between vehicles fitted with an open differential and viscous coupling during steady state cornering.
The asymmetric distribution of the tractive forces during cornering as shown in figure 10 improves also the straight-line running. Every deviation from the straight-line position causes the wheels to roll on slightly different radii. The difference between the driving forces and the resulting yaw moment tries to restore the vehicle to straight-line running again (see figure 10).
Although these directional deviations result in only small differences in wheel travel radii, the rotational differences especially at high speeds are large enough for a viscous coupling front differential to bring improvements in straight-line running.
High powered front-wheel drive vehicles fitted with open differentials often spin their inside wheels when accelerating out of tight corners in low gear. In vehicles fitted with limited-slip viscous differentials, this spinning is limited and the torque generated by the speed difference between the wheels provides additional tractive effort for the outside driving wheel. this is shown in figure 12
Figure 12: tractive forces for a front-wheel drive vehicle with viscous limited-slip differential during acceleration in a bend
The acceleration capacity is thus improved, particularly when turning or accelerating out of a T-junction maneuver ( i.e. accelerating from a stopped position at a “T” intersection-right or left turn ).
Figures 13 and 14 show the results of acceleration tests during steady state cornering with an open differential and with viscous limited-slip differential .
Figure 13: acceleration characteristics for a front-wheel drive vehicle with an open differential on wet asphalt at a radius of 40m (fixed steering wheel angle throughout test).
Figure 14: Acceleration Characteristics for a Front-Wheel Drive Vehicle with Viscous Coupling on Wet Asphalt at a Radius of 40m (Fixed steering wheel angle throughout test)
The vehicle with an open differential achieves an average acceleration of 2.0 while the
vehicle with the viscous coupling reaches an average of 2.3 (limited by engine-power). In these tests, the maximum speed difference, caused by spinning of the inside driven wheel was reduced from 240 rpm with open differential to 100 rpm with the viscous coupling.
During acceleration in a bend, front-wheel drive vehicles in general tend to understeer more than when running at a steady speed. The reason for this is the reduction of the potential to transmit lateral forces at the front-tires due to weight transfer to the rear wheels and increased longitudinal forces at the driving wheels. In an open loop control-circle-test this can be seen in the drop of the yawing speed (yaw rate) after starting to accelerate (Time 0 in Figure 13 and 14). It can also be taken from Figure 13 and Figure 14 that the yaw rate of the vehicle with the open differential falls-off more rapidly than for the vehicle with the viscous coupling starting to accelerate. Approximately 2 seconds after starting to accelerate, however, the yaw rate fall-off gradient of the viscous-coupled vehicle increases more than at the vehicle with open differential.
The vehicle with the limited slip front differential thus has a more stable initial reaction under accelerating during cornering than the vehicle with the open differential, reducing its understeer. This is due to the higher slip at the inside driving wheel causing an increase in driving force through the viscous coupling to the outside wheel, which is illustrated in Figure 12. the imbalance in the front wheel tractive forces results in a yaw moment acting in direction of the turn, countering the understeer.
When the adhesion limits of the driving wheels are exceed, the vehicle with the viscous coupling understeers more noticeably than the vehicle with the open differential (here, 2 seconds after starting to accelerate). On very low friction surfaces, such as snow or ice, stronger understeer is to be expected when accelerating in a curve with a limited slip differential because the driving wheels-connected through the viscous coupling-can be made to spin more easily (power-under-steering). This characteristic can, however, be easily controlied by the driver or by an automatic throttle modulating traction control system. Under these conditions a much easier to control than a rear-wheel drive car. Which can exhibit power-oversteering when accelerating during cornering. All things, considered, the advantage through the stabilized acceleration behavior of a viscous coupling equipped vehicle during acceleration the small disadvantage on slippery surfaces.
Throttle-off reactions during cornering, caused by releasing the accelerator suddenly, usually result in a front-wheel drive vehicle turning into the turn (throttle-off oversteering ). High-powered modeles which can reach high lateral accelerations show the heaviest reactions. This throttle-off reaction has several causes such as kinematic influence, or as the vehicle attempting to travel on a smaller cornering radius with reducing speed. The essential reason, however, is the dynamic weight transfer from the rear to the front axle, which results in reduced slip-angles on the front and increased slip-angles on the rear wheels. Because the rear wheels are not transmitting driving torque, the influence on the rear axle in this case is greater than that of the front axle. The driving forces on the front wheels before throttle-off (see Figure 10) become over running or braking forces afterwards, which is illustrated for the viscous equipped vehicle in Figure 15.
Figure 15:Baraking Forces for a Front-Wheel Drive Vehicle with Viscous Limited-Slip Differential Immediately after a Throttle-off Maneuver While Cornering
As the inner wheel continued to turn more slowly than the outer wheel, the viscous coupling provides the outer wheel with the larger braking force . The force difference between the front-wheels applied around the center of gravity of the vehicle causes a yaw moment that counteracts the normal turn-in reaction.
When cornering behavior during a throttle-off maneuver is compared for vehicles with open differentials and viscous couplings, as shown in Figure 16 and 17, the speed difference between the two driving wheels is reduced with a viscous differential.
Figure 16: Throttle-off Characteristics for a Front-Wheel Drive Vehicle with an open Differential on Wet Asphalt at a Radius of 40m (Open Loop)
Figure 17:Throttle-off Characteristics for a Front-Wheel Drive Vehicle with Viscous Coupling on Wet Asphalt at a Radius of 40m (Open Loop)
The yawing speed (yaw rate), and the relative yawing angle (in addition to the yaw angle which the vehicle would have maintained in case of continued steady state cornering) show a pronounced increase after throttle-off (Time=0 seconds in Figure 14 and 15) with the open differential. Both the sudden increase of the yaw rate after throttle-off and also the increase of the relative yaw angle are significantly reduced in the vehicle equipped with a viscous limited-slip differential.
A normal driver os a front-wheel drive vehicle is usually only accustomed to neutral and understeering vehicle handing behavior, the driver can then be surprised by sudden and forceful oversteering reaction after an abrupt release of the throttle, for example in a bend with decreasing radius. This vehicle reaction is further worsened if the driver over-corrects for the situation. Accidents where cars leave the road to the inner side of the curve is proof of this occurrence. Hence the viscous coupling improves the throttle-off behavior while remaining controllable, predictable, and safer for an average driver.
6. EFFECT ON BRAKING
The viscous coupling in a front-wheel drive vehicle without ABS (anti-lock braking system) has only a very small influence on the braking behavior on split-μ surfaces. Hence the front-wheels are connected partially via the front-wheel on the low-μ side is slightly higher than in an vehicle with an open differential. On the other side ,the brake pressure to lock the front-wheel on the high-μ side is slightly lower. These differences can be measured in an instrumented test vehicle but are hardly noticeable in a subjective assessment. The locking sequence of front and rear axle is not influenced by the viscous coupling.
Most ABS offered today have individual control of each front wheel. Electronic ABS in front-wheel drive vehicles must allow for the considerable differences in effective wheel inertia between braking with the clutch engaged and disengaged.
Partial coupling of the front wheels through the viscous unit does not therefore compromise the action of the ABS - a fact that has been confirmed by numerous tests and by several independent car manufacturers. The one theoretical exception to this occurs on a split-μ—surface if a yaw moment build-up delay or Yaw Moment Reduction(YMR) is included in the ABS control unit. Fig
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