Calculating Torque Distribution in 4WD Vehicles

[RJ01]

How would I calculate what % of torque is transferred to front and rear wheels in a 4WD?
The split happens at the lay shaft. Crown pinion(CP) attached to rear end and 4WD attached to front end on lay shaft. I have calculated toques as shown:
For Rear wheel, Torque = gear box ratio * Rear CP ratio / 2 * Final reduction
For Front wheel, Torque = gear box ratio * 4WD ratio * Front CP ratio / 2 * Bevels reduction ratio
I have split CP shaft torques into 2 while transferring to wheels but for lay shaft where it was CP and 4WD gears attached on either ends, I have not split the torques.
I suppose it has to be split but I am not sure in what ratio as CP rear ratio and 4WD ratio are different.
Can anyone help me on this split?
Regards,
RJ

 

[jack action]

You have a very confusing terminology. Trying explaining your 4WD system with images and terminology used by Wikipedia (there are other pages about differentials and such too).

 

[RJ01]

Dear Jack,
Please check the image if it helps in understanding
https://commons.wikimedia.org/wiki/File:Drivetrain.png

 

[jack action]

If I understand correctly, there is no center differential in the gearbox.

A differential splits the torque 50/50 (some design can alter this ratio) on both sides and splits the power (by adjusting the rpm) to whatever each side needs.

With no differential, the rpm is the same on both sides and the power split is done by adjusting the torque to whatever each side needs. For example, if an axle has both wheels on the ground with the same grip on both tires, the torque split will be 50/50. But if one wheel is in the air, this wheel has no grip, hence zero torque, so the split will be 100/0. With different levels of grip on each side, the split can be anything between 50/50 and 100/0. With the split in your central gearbox, it is the same thing, you only need to replace torque from left and front wheels by torque from front and rear axles.

In summary, with a differential, the power split depends on whatever the output rpms will be and torque split is always 50/50. With no differential, the power split depends on the load you put on the output shafts and their rpm is always the same. In any case, power is always torque times rpm.

 

[jim hardy]

Please check the image

ahhh, that's worth a thousand words.

jack nailed it

in this picture you linked

front and rear differentials are driven by opposite ends of "lay shaft" so must turn at same speed.

with no center differential
torque to front wheels is whatever keeps the wheels turning at engine speed X gear ratios
torque to rear wheels is whatever keeps them also turning at engine speed X gear ratios
torque splits between front and rear according to slipperiness of their wheel to ground contact and those may not be the same.
If there's no wheel slip , sum of torques is whatever is required to move the vehicle. How it divides front to rear is random, determined by gear backlash. You could assume 50/50 but it's a guess.

If front and rear tires are of different diameters, front and rear torques have opposite sign because one axle pushes the vehicle forward and other pushes it backward.
That's why you disengage 4wd on hard surface road, so as to not drive one set of gears against the wrong side of its teeth..
Full time 4wd has provision for different speed of front and rear axles, jack's 'center differential' . It'd go in the middle of your 'lay shaft' to allow different speed at its ends.

old jim

 

[RJ01]

Thanks Jack and Jim. I have almost arrived at the ratios. Adjusted gear ratios on front and rear to keep approximately the same speed on wheels, the front was tuned to have 3% lead now which was acceptable in earlier designs. I am not using central diff, looks to be a good option though. Thanks again.
Regards,
RJ

 

[jim hardy]

Hey sorry i missed the different ratios on those intermediate gearboxes front to rear.

I'd think for in the mud a bit of lead on front could be desirable for steering , so rear isn't tying to get ahead of front.
But for thinking purposes
consider the ground as an outside set of gears coupling front and rear axles at ratio of the wheel diameters
that's where the unequal reduction in internal gears gets corrected, and if it doesn't get corrected something's going to slip.
3% lead ? I guess they intended for the front to drag the rear along, like a rudder ?

I learned something --- Thanks !

 

[RJ01]

Not a problem. Yes, it is likely that the lead helps to rev and steer the vehicle through the mud which is very much required for this application.

 

[JBA]

The speed bias may also be based upon the vehicle's forward weight bias (i.e. vehicle forward cg bias) due to the front engine weight so as to insure the max pulling force at the heaviest end of the vehicle in the mud.

 

[Cynthiamyra Kaelyn]

Nice work, Thanks for sharing it with us.