Automotive Automotive differential problem

1. Jul 25, 2012

hexhamallstar

Hi there,

I'm currently doing some research into differentials and have been unable to find any indepth information on them. Every article I read covers the basics that one axle turns one direction relative to the diff casing and the other in the opposite direction so that the average of the 2 is always the casing speed.

However, I'm looking for some detail on the bevel gears inside the differential, and the effect that their gear ratio (between the planet bevel gears and sun bevel gears) has on the operation of the diff. This is with regards to a simple open diff, with 4 bevel gears on the interior of the differential.

I would also like to know the advantages of using 4 planet gears instead of just 2 (I have taken apart 2 differentials and one of them used 2 planet gears and one used 4).

I am not, I repeat, am not talking about the pinion and crown wheel, I know what effect that has!

Phil

Last edited: Jul 25, 2012
2. Jul 25, 2012

jack action

The differential is an epicyclic gear arrangement. On this site, you have all the math behind the concept.

On the previously linked site, the differential would be represented by example #2:

http://www.roymech.co.uk/images9/gear_epi3.gif [Broken]

The casing would rotate the planetary arm (L), one wheel is connected to the sun gear (S) and the other wheel is connected to the ring gear (A). In a car differential, NA would be equal to NS.

In the same example, you have this table:

Code (Text):

Rotation (CW= +ve) from action....................Nx = number of teeth
Action                          S       L        P               A
Fix L and rotate Sun 1 rev CW   1   0   - NS / NP   - NS / NA

Which, if NA = NS, gives the case where the casing is held fixed and one wheel rotates one way and the other rotates at the same speed in the reverse direction, or:

Code (Text):

Rotation (CW= +ve) from action....................Nx = number of teeth
Action                          S       L        P               A
Fix L and rotate Sun 1 rev CW   1   0   - NS / NP      - 1

Now, in real life, the casing is also rotating, so you have to add that rotation to the whole package as well. Say the casing rotates with a speed of 10 instead of 0, then you have to add this speed to the other gears as well:

Code (Text):

Rotation (CW= +ve) from action....................Nx = number of teeth
Action                          S       L        P               A
Add rotation L              1+10    0+10    - NS / NP      - 1+10

or:

Code (Text):

Rotation (CW= +ve) from action....................Nx = number of teeth
Action                          S       L        P               A
Add rotation L              11  10  - NS / NP        9

So S is faster than A and the speed of L is the average of the S and A.

When the differential is «inactive» (straight line), there is no rotation of P, so all gears rotate at the same speed:

Code (Text):

Rotation (CW= +ve) from action....................Nx = number of teeth
Action                          S       L        P               A
No speed difference         10  10       0               10

For planetary gears, only one is necessary for the differential to work, as shown in this picture:

The only gear ratio important is the one between the sun and ring gears (or the left and right wheels, in our case) which is always equal to 1 if you want the differential working properly. The planetary gears are only idlers and their speed has no effect on the output. I suspect that they're made with the smallest number of teeth as possible for them to work properly and thus, giving the smallest package possible.

Why use more than one planetary gear? To spread the load on many teeth. Remember that in a straight line, the gears don't rotate with respect to one another. The idler gear becomes some sort a «beam» locking both axle together and transmitting the torque through the gear teeth (which do not turn w.r.t. one another). The more idlers you have, the more «beams» you have, the stronger the differential.

Last edited by a moderator: May 6, 2017
3. Jul 26, 2012

hexhamallstar

Thanks for the excellent reply jack, this is exactly what I was after! I did think that the bevel gear ratio is irrelevant but it seems strange to me that such an important piece of kit has an arbitrary form.

Can anybody direct me to a textbook/website that explains how to find the smallest gear that can be used while still meshing properly?

Also, I was wondering about Torque in this case. Because the planet gears are attached to the casing they aren't meshing with the crown wheel so surely torque isn't transferred in the normal way (stepped down with size)? Does all of the torque in the crown wheel simply transfer to the sun gears via the mesh with the planet gears? Or does the ratio come into play here?

Thanks,

Phil

4. Jul 26, 2012

jack action

For gear design:

http://www.roymech.co.uk/Useful_Tables/Drive/Gears.html
http://www.roymech.co.uk/Useful_Tables/Drive/Bevel_Gears.html
http://viewmold.com/Products/Technical%20Reference%20Sheet/Gears/SPUR%20GEARS-BACKLASH%20UNDERCUT%20FORMULAS.pdf
http://www.akgears.com/pdf/direct_gear_design.pdf

For the torque, it is the same everywhere, so the force acting on the planetary gear(s) is proportional to the force acting on the ring gear, considering the radii where the forces are applied. Just like in the case of a stepped gear arrangement:

5. Jul 26, 2012