wheel power distribution by differential in a turn

[JAlberts]

I need a bit of assistance in identifying a reference that specifically address the fact that when an automobile is in a turn that the differential acts to redistribute power from the inside wheel to the outside wheel. This is an obvious result of the differential allowing the outside wheel rpm to increase and the inside wheel rpm to slow while maintaining equal torque on both wheels; and, is obvious from the power formula for a differential drive.

P in = P1 out + P2 out = T1 * RPM1 + T2 * RPM 2 with: T1 =T2
One form of the power equation being: P = T * rpm

I am having a problem convincing someone of this simple correspondence, and he is demanding a "reliable" reference stating this fact.
At first I thought that would be simple to find, but unfortunately every online reference about auto differentials, except one by an MIT student, is focused on the fact "that the differential allows the two wheels to rotate at different speeds" without including any mention of the corresponding power transfer.
Any identified references that address the power transfer element will be much appreciated.

[jboggs]

Add the term "limited slip" to your search. Differentials were invented to account for the difference in wheel speed in a turn. I visualize their working principle as this: the average of the speeds of the inner and outer wheel equals the speed of the input shaft. Of course, if one wheel were spinning freely with no limit to its speed, like in mud, the other wheel could lock up. The speed equation would be satisfied but zero torque would be transmitted. Limited Slip differentials were created overcome that difficulty by limiting the speed difference between the wheels.

[Kelly_Bramble]

Here's a video on How Automobile Differentials Work.


Watch the whole video - the first part is a little corny..

[JAlberts]

Kelly, thanks, entertaining but unfortunately does not address my specific issue. What does illustrate is that the technology is so old that finding any serious engineering discussions on the design and operation of the differential is probably going to require a trip to Rice University's archived documents area.

[Kelly_Bramble]

Kelly, thanks, entertaining but unfortunately does not address my specific issue. What does illustrate is that the technology is so old that finding any serious engineering discussions on the design and operation of the differential is probably going to require a trip to Rice University's archived documents area.

So, you're looking for an equation that defines the power transferred? I'm confused..

[JAlberts]

No, I know what the equation is but I am dealing with an individual who refuses to accept the equation is valid “strictly on my say so”; and, is demanding that I provide a "reliable reference" supporting the equation.
The ironic part is that I have not at this point decided or declared that the solution I have proposed is fully developed; but, in my process of working on it, I was reminded of the fact that not only did a differential allow interchange of rpm's between two wheels, which he seems to accept, but that this clearly validates a similar exchange of Power (P = T * rpm).
The problem is that if the equation P t = P r + P l with P t and T being specified constants is valid (as it clearly is) then it invalidates his presented solution that he is fully convinced "is absolutely correct".
Obviously, this encounter has gotten clear off base; and, because the problem being addressed is not of a critical nature, I am actually considering dropping out of the whole project, but as a matter of integrity, I hate for his erroneous solution to stand for no other reason than that I have decided to walk way rather than deal with the situation.

[surfmase]

You have assumed that T1=T2, can you prove this? If so, then maybe this is the proof you need for your colleague. Could it not be that the slower wheel is delivering more torque than the faster wheel in proportion to the speed differential such that P1=P2?