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I know that the differential gearbox is providing a torque to the wheels; as the relation in the figure indicates : Tw (wheel torque) = Td (differential torque) × (ηd×nd). Where nd:is the differential gear ratio and η:is the effeciency of the differential gearbox. Now this torque at wheels (Tw), which is provided by the differential , is also = Rw×Fx (torque from road friction ) . My question is : Won't the torque from (Fx) on the wheels accelerate (increase) the wheel's rotational speed(ωw) ? If this is the case;now ωw is increasing. And since (ωd=nd×ωw); then ωd(differential or driveshaft rotational speed) should also increase to maintain the gear ratio (nd) constant. So how would this differential/drive shaft rotational speed (ωd) increase to maintain this gear ratio (nd) constant ?

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  • $\begingroup$ Why would the gear ratio be constant? the whole point of having gears is to match engine speed to road speed. Also will the torque be shared equally to both wheels? $\endgroup$
    – Solar Mike
    Jun 1 at 14:20
  • $\begingroup$ So you are obviously saying that the gear ratio is not constant ; the gear ratio is teeth ratio of the input gear to the output gear . And of-course number of teeth will not change unless there was some magic happening in the gear-box $\endgroup$ Jun 1 at 14:28
  • $\begingroup$ Based on this: So how would this differential/drive shaft rotational speed (ωd) increase to maintain this gear ratio (nd) constant $\endgroup$
    – Solar Mike
    Jun 1 at 14:34
  • $\begingroup$ And there are gear drives with varying ratios… $\endgroup$
    – Solar Mike
    Jun 1 at 14:35
  • $\begingroup$ @SolarMike Let's assume it the first gear ratio... $\endgroup$ Jun 1 at 14:38

2 Answers 2

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Interesting question! I think that the driveshaft would increase its speed from the engine itself as a response to the increase of the wheel's rotational speed.

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  • $\begingroup$ What do you mean? the engine will increase itself's speed as a response ? how would the engine feel that response and on what basis will the engine speed increase? Please provide some logical evidence to your answer $\endgroup$ Jun 1 at 14:40
  • $\begingroup$ @JesseFlynn cars can gain speed without throttle when going downhill. Easy. $\endgroup$
    – Solar Mike
    Jun 1 at 16:06
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The engine, transmission, differential and wheel are all essentially locked together in a traditional transmission. There are other ways to connect the four, but let's assume they are locked. If the engine supplies more torque than required to keep the vehicle at a constant speed, the vehicle speeds up, and all the rotational speeds go up. This is strictly a function of engine load versus throttle position (or throttle position sensor input). Gear ratios have nothing to do with it, and remain constant. If we are in a turn and the wheels are spinning at different rates, the difference in speed of the two wheels is seen in rotation of the differential plentary gear.

A modern continuously variable transmission will monitor engine load and speed and change the gear ratio to maximize performance and economy. The differential gear ratio will remain constant.

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