【正文】 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 windup. These characteristics, however, can be disadvantageous when adhesion variations between the left and right sides of the road surface (splitμ ) limits the torque transmitted for both wheels to that which can be supported by the lowμ wheel. With a viscous limitedslip differential, it is possible to utilize the higher adhesion potential of the wheel on the highμ surface. This is schematically shown in Figure 4. When for example, the maximum transmittable torque for one wheel is exceeded on a splitμ surface or during cornering with high lateral acceleration, a speed difference between the two driving wheels occurs. The resulting selflocking 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 lowμ side, To keep the vehicle in a straight line the driver has to pensate this with opposite steering input. Though the fluidfriction 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 steeringwheel torque Ts and the average corrective opposite steering input required to maintain a straight course during acceleration on a splitμ track 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 parison to each other. However, they are small in absolute terms. Subjectively, the steering influence is nearly 3 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 toein response per wheel. For differing tractive forces, Which appear when accelerating on splitμ with limitedslip differentials, the toein response changes per wheel are also different. Unfortunately, this effect leads to an undesirable turnin response to the lowμ side, . the same yaw direction as caused by the difference in the tractive forces. Reduced toein elasticity is thus an essential requirement for the successful frontaxle application of a viscous limitedslip differential as well as any other type of limitedslip differential. Generally the following equations apply to the driving forces on a wheel ?VT FF ? With ?TF Tractive Force ?VF 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: △ eT = ? ?loHhiH FFe ?? ??? ?c o s Where △ ?eT Steering Torque Difference e=Wheel Disturbance Level Arm ?? King Pin Angle hi=highμ side subscript lo=lowμ side subscript In the case of frontwheel drive vehicles with open differentials, △ Ts is almost unnoticeable, since the torque bias ( loHhiT FF ?? / ) is no more than . For applications with limitedslip 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 CVJoint, 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): 4 Drive side M1 = vv TT ?? ? tan/)2/ta n (2 ?? Driven side M2 = vv TT ?? ? tan/)2/ta n (2 ?? With T2 = dynT rF? ?T = ? ?systemJoTf in t,2 ? Where v? ?? Vertical Articulation Angle ? ??Resulting Articulation Angle dynr ??Dynamic Wheel Radius ?T ??Average Torque Loss The ponent ?cos2?M acts around the kingpin axis (see figure 7) as a steering torque per wheel and as a steering torque difference between the wheels as follows: ])t a n/2/t a n()s i n/2/t a n[(c o s 22 liwhiw TTTTT ?? ?????? ??????? ????? where ????T Steering Torque Difference W?? Wheel 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 momentpolygon in Figure 7, the rotational direction of M2 or ?T respectively change, depending on the position of the wheelcenter to the gearbox output. For the normal position of the halfshaft shown in Figure 7(wheelcenter below the gearbox output joint)