【正文】 the secondary moments work in the same rotational direction as the driving forces. For a modified suspension layout (wheelcenter above gearbox output joint, . v? negative) the secondary moments counteract the moments caused by the driving forces. Thus for good patibility of the front axle with a limitedslip differential, the design requires: 1) vertical bending angles which are centered around 0?v? or negative ( 0?v? ) with same values of v? 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 wheelside and the gearboxside 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 vdvw ?? ? both of the secondary moments acting on the connection shaft pensate each other. In reality (with torque loss), however, a 5 secondary moment difference appears: △ WDDW MMM 12 ?? With ??? ?TTT WD 22 The secondary moment difference is: ?DWM ? ? VWWVWWVDVDW TTDTwTT ???? ??? tan/2/tans i n/tan 22/2 ???? For reasons of simplification it apply that VVWVD ??? ?? and ??? TTT WD ?? to give △ ? ?VVVDW TM ???? tan/1s i n/12/tan ???? △ DWM requires opposing reaction forces on both joints where LMF DWDW /?? . Due to the joint disturbance lever arm f, a further steering torque also acts around the kingpin axis: LfMT DWf /c o s ????? ? ?loloDWhihiDWf LMLMfT //c o s ?? ????? Where ??fT Steering Torque per Wheel ???fT Steering Torque Difference ??f Joint Disturbance Lever ??L Connection shaft (halfshaft) Length For small values of f, which should be ideally zero, fT? is of minor influence. 5． EFFECT ON CORNERING Viscous couplings also provide a selflocking 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 frontwheel 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 pensated 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 frontwheel drive vehicle on selfsteering 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: parison between vehicles fitted with an open differential and viscous 6 coupling during steady state cornering. The asymmetric distribution of the tractive forces during cornering as shown in figure 10 improves also the straightline running. Every deviation from the straightline 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 straightline 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 straightline running. High powered frontwheel drive vehicles fitted with open differentials often spin their inside wheels when accelerating out of tight corners in low gear. In vehicles fitted with limitedslip 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 frontwheel drive vehicle with viscous limitedslip differential during acceleration in a bend The acceleration capacity is thus improved, particularly when turning or accelerating out of a Tjunction maneuver ( . accelerating from a stopped position at a “T” intersectionright or left turn ). Figures 13 and 14 show the results of acceleration tests during steady state cornering with an open differential and with viscous limitedslip differential . Figure 13: acceleration characteristics for a frontwheel 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 FrontWheel 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/sm while the vehicle with the viscous coupling reaches an average of 2/sm (limited by enginepower). 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, frontwheel 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 fronttires due to weight transfer to the rear wheels and increased longitudinal forces at the driving wheels. In an open loop controlcircletest this can be seen in the drop of the yawing speed (yaw rate) after starting to accelerate (Time 0 in 7 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 fallsoff more rapidly than for the vehicle with the viscous coupling starting to accelerate. Approximat