I don't want to get involved in this spitting match, however, you both are correct in your thinking, but not fully understanding what you are trying to say.
this should shine some light on it.
http://www.jedi.com/obiwan/jeep/misc/gearratio.html
cheers
snoranger has beat me to this....
I understand exactly what I'm trying to say, I just hadn't devoted an entire page of text to the nitty gritty details. Of course I'm assuming an open differential, but that's not any stretch to assume.
So, here's my understanding, and by some odd coincidence, it's exactly correct.
The mathematical and mechanical function of a differential is to drive the wheels, such that the
average speed of both wheels is equal to the ratio of the speed of the driveshaft. It doesn't care how fast or slow each individual wheel turns, but merely forces them to maintain that averaging relationship with each other.
Examples:
You're driving home from the parts store, straight down the road at 20mph. The drivers side wheel is turning at 20mph, the passenger's side wheel is turning at 20mph, the driveshaft is turning at that defined ratio to 20mph, and the vehicle is moving at 20mph. Simple math: the average of 20 and 20 is 20. As a side note, the spider gears aren't turning relative to the diff, and the ring gear and diff are spinning at that same 20mph axle speed.
Another: A block down the road you go around a fairly tight curve to the right. You maintain 20mph on the speedometer, so the truck itself is going 20mph and the driveshaft is still spinning that defined ratio which produces 20mph. The diff is also spinning at the same 20mph, but the right wheel (and axle and spider gear) are only turning at 15mph, and the left wheel (and axle and spider gear) are turning at 25mph. This is important because the left wheel has to travel a longer path than the right wheel, in the same amount of time, and thus
must be traveling faster. The average of 15 and 25 is once again 20. Another side note: The right spider gear is spinning slower than the diff, and the left faster, by the same amount, during this turn.
Third example: You pull into your driveway and turn off your truck, and put the rear axle on jackstands to install the brake shoes you bought at the store. Since both rear wheels are off the ground, you forego the parking brake and instead chock the front tires. You notice as you take off the lug nuts that spinning the left wheel backwards causes the right wheel to spin forwards at the same speed, and vice versa. You guess that you might be spinning the tire at 3mph, if it were on the ground. Now, the engine's stopped, so it's going 0mph, and the driveshaft is going 0mph too. One wheel's turning at 3mph, and the other at -3mph (because it's turning backwards). The average of 3 and -3 is 0. Even if you spin the wheel faster, maybe 5mph, the other turns at -5mph, and the average of 5 and -5 is still 0. In this case the diff itself is stopped, and the spider gears are turning at equal speeds in opposite directions.
Another note: Because of the way the spider gears mesh, and because they're all the same size, they
have to turn in opposite directions at equal speeds,
relative to the differential. (If they don't, they're broken.) In the second example, one wheel is 5mph faster than the diff, and the other is 5mph slower.
Fourth example: Big Jim M is stuck on the ice in a parking lot. One wheel's on really slick ice, and the other's on dry asphalt. He tries to pull out of the parking space but that one wheel slips and the truck doesn't move, although his engine revs up for a couple seconds and his speedometer reports 15mph, before he stops and gets out to pour a little ice-melt under the tire that's slipping. For that couple of seconds, his driveshaft was spinning at that known ratio to 15mph, his differential was spinning at 15mph, his one wheel was turning at 0mph, and the other wheel was spinning at 30mph. Inside, the one spider gear was stopped, thus moving 15mph
slower than the diff, while the other spider gear was moving 15mph
faster than the diff. The average of 0 and 30 is 15, which is what his engine and driveshaft were doing.
Final example: We're trying to find the drive ratio of a rear axle. We know that the ratio is the number of revolutions of the driveshaft divided by the number of revolutions of the
differential (regardless of what the axles may do), but we don't want to take the diff cover off in order to turn the differential directly. It would be really convenient if we could make the diff turn exactly one revolution, because then we don't have to do any division. So, we could emulate the first example above: if we turn both axles 1 revolution forward, the differential will also turn one revolution forward...but our arms aren't that long. This
would work because the average of 1 revolution and 1 revolution equals 1 revolution. Or, if we wanted to be silly, we could imitate the second example: we could turn one axle one-half turn forward, and the other one-and-one-half turns forward, knowing this will make the diff revolve once...but again we can't reach both axles at the same time, plus it's more confusing. This
would work because the average of 0.5 and 1.5 equals 1. So, instead we decide to follow the 4th example: we leave one axle stationary, and we turn the other twice. This makes the diff revolve exactly once, because the average of 0 and 2 equals 1, and we end up turning the drive shaft the number of revolutions corresponding to the gear ratio.
So, Angie, go ahead and tell me again that I don't understand, I dare you. I may not explain it wonderfully, and I may make invalid assumptions as to how the recipient comprehends it; but I certainly know what I'm talking about, and it's not hard to follow a statement like "Turn one axle twice while counting the revolutions of the driveshaft."
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