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Old 04-20-2014, 06:41 AM
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Default Help me understand differential gear ratios

In most geared systems there is a ratio between the driven gear and the drive gear that is simply the ratio of the pitch circles. Increasing the ratio means the driven gear gets bigger and the drive gear gets smaller, (like changing cogs on a bicycle.) The centerline of each gear remains fixed and the contact point moves. The size of the gear teeth remains constant and the number of teeth on the gear changes.

How does this work in a differential? I can see how the pinion gear diameter changes by adding or removing teeth, but what happens to the ring gear? Does the diameter change? It canít get any bigger than the stock ratio because there isnít room in the housing. It could get smaller. Does that mean that the pinion shaft becomes longer, (and weaker) to mate with the ring gear? The ring gear thickness must change to keep the bearing centerlines and mate with the pinion. Is that why a 5.26 is weaker than a 3.7, because the backing of the ring gear is too thin? Are the teeth a constant size, or do they change with the ratio?
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Old 04-20-2014, 07:51 AM
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I'm not M.E., but the ring gear inside diameter can't change because it bolts to the differential carrier. So that's fixed. The pinion shaft length can't really change because the gear teeth centers must still align to the ring gear teeth centers. The diameter of the shaft itself is fixed practically because that sets the bearing and flange plates drive standardization. The diameter of the pinion gear circle can't change unless you change the thickness of the ring gear itself because the teeth centers still have to stay aligned. IOW, if you increased the diameter of the pinion the ring gear would have to get thinner to keep the teeth aligned.

In a word the pitch (or cone) circle of the gears I don't think changes (much) regardless of the ratio.

The ratio must therefore only be practically determined by the number of teeth on the pinion and ring gear. This means that the thickness and maybe the profile (e.g. the face width, addendum, dedendum, etc.) of the teeth will change to accommodate fewer or more teeth. The aspects of the teeth themselves need to be such that they mesh correctly, so that must then dictate the number that can practically fit on the ring and pinion. But I do know that there is a limit to what actually fits inside a case, so I assume that the outside ring diameter and maybe the ring gear thickness and tooth width might change.

The tooth count does change and there are some combinations that are better than others. Can't say about Cruisers but mini trucks with 8" diffs the 4.10 stock ratio is a 41 tooth ring and a 10 tooth pinion and is considered pretty much the strongest normal gear set in the 8" side while the 5.71 has a reputation for being weak. In a 8" diff when you go to a 3.73 is 41/11, 4.30 is 43/10, 4.56 is 41/9, 4.88 is 39/8, 5.29 is 37/7, 5.71 is 40/7. I think the reason 4.10 is stronger is the number of teeth fully or partially engaged is higher mainly more than anything else.

You'd expect as the tooth count goes down that they'd be thicker but it's probably marginal overall while you decrease the number of pinion teeth doing the work. So why a 5.29 is OK but a 5.71 is not doesn't make sense because it's usually the pinion that fails and these two ratios should be very close in configuration. I also wonder if it's a matter of factory set up vs. who knows aftermarket. Some diffs are set up perfectly and some are done poorly by shops while I would expect that the factory does what it does with less variance. There's Zuk who does a lot of mini truck (does he do Cruisers?) and he's pretty vocal that the there's nothing fundamentally wrong with 5.71 gears and he advocates that the 4.10 ratio is actually worse. It might come down to externals, most of the time guys running 5.71 gears do so in combination with 37" tires and double cases and there's a torque limit on a R&P that is just a matter of the amount of iron in the gears that's involved. OTOH the people saying 4.10 are good are running the same tires and drivetrains but are usually not driving on the highway, which is really the only reason you want to match tires and gearing. Not sure what conclusions you can draw really.

In a bike system the teeth and chain profile is fixed, so only the number of teeth changes. But the derailleur allows the dimensions of them to grow and shrink. There is a finite number of combinations based on the range the derailleur can accommodate and still tension the chain.
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Old 04-20-2014, 10:13 AM
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It's the number of teeth on the ring gear divided by the number of teeth on the pinion gear..... or so I always thought.

The O.D. of the ring gear becomes irrelevant if it can be made to spin faster/slower based on the number of teeth. The mathematics behind it are beyond my understanding.

Looking forward to someone giving a better explanation. Subscribed.
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Last edited by Fishy; 04-20-2014 at 10:15 AM. Reason: posting to subscribe to thread.....
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Old 04-20-2014, 10:34 AM
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The outer diameter is not irrelevant because it has to fit into the opening of axle housing. My rear axle has a small notch where the ring gear passes through, which is I think common to all axle housings. The inner diameter and bolt circle of the ring gear is fixed by the differential carrier. If the O.D. grows any more and you increase the notch depth you lose surface for the seal and potentially material for the stud/bolt, so this is the practical outer diameter limit of the ring gear. You can shrink it at the expense of tooth size in theory, but there is no reason to do that.

Ultimately the question is what is the functional limitation of the tooth profile with respect to the total working surface area and cross section of the fully and partially engaged teeth.
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Old 04-20-2014, 10:42 AM
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So you're saying I can take a ring gear out of a F350 and bolt it on the carrier in my 100 and change my gear ratio?

It's irrelevant in terms of gearing on one specific vehicle. It still has to fit the carrier. It's relevant in terms of "mathematical gear ratio", but not in this text.
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Old 04-20-2014, 11:08 AM
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Quote:
Originally Posted by Fishy View Post
So you're saying I can take a ring gear out of a F350 and bolt it on the carrier in my 100 and change my gear ratio?
Yes, if:
  • you used the matching pinion so the tooth profiles matched,
  • the bolt circle matched the carrier,
  • the I.D. and O.D. worked functionally,
  • the matching pinion shaft was the right diameter and length to work and,
  • therefore, the pitch cone was the same
Quote:
It's irrelevant in terms of gearing on one specific vehicle. It still has to fit the carrier. It's relevant in terms of "mathematical gear ratio", but not in this text.
I agree, it's only irrelevant if you assume it's not fixed by specification. The profile of the teeth will change depending on ratio but the tooth width of the ring gear shouldn't. The main difference in ring gears would seem to be the tooth width, fewer teeth equals thicker teeth since it's just the circumference equally divided by the number of teeth. But the tooth-to-tooth dimension must match the pinion while at the same time not changing the gear cone.
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Old 04-20-2014, 11:28 AM
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Quote:
Originally Posted by DaveInDenver View Post
Yes, if:
  • you used the matching pinion so the tooth profiles matched,
  • the bolt circle matched the carrier,
  • the I.D. and O.D. worked functionally,
  • the matching pinion shaft was the right diameter and length to work and,
  • therefore, the pitch cone was the same
.
But, they don't. Which makes it irrelevant in this context. Your knowledge on mechanical and electrical far exceeds mine. So much so that I have a hard time following you most of the time. I'm just not smart enough.

I'm thinking simple and you're thinking complex: Here's what I have, (in my case a 100) and I want to change the gear ratio, in theory I could get there a number of ways. My way would be to change the ring gear and pinion gear to another one made the same size as the one I currently have, but with a different number of ring gear teeth relative to number of teeth on the pinion gear. Your way would be to build an entire new drivetrain from scratch.

I effectively changed the gear ratio on my 100 by going from 32's to 35's.
I could not swap the ring gear from a F350 onto the carrier of my current set up. It doesn't fit. Therefore, the size of that ring gear is irrelevant.

This thread is way off from where it started, so I will defer to your knowledge here. It's already over my head.
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Old 04-20-2014, 11:30 AM
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I am definitely beyond what little I picked up in cross-discipline classes studying for the F.E. test. So enough to be irritating to someone who actually knows.

What I'm trying to say is the dimensions of the pinion axis and drive axles are fixed as are the I.D. and O.D. of the ring. So any change to the number of ring gear teeth impacts the cross sectional width and maybe the center-to-center dimension, which must match the pinion.

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So the pitch cone can only change w.r.t. the physical size of the pinion gear? This would be limited by the space available and how the face of the pinion engages and moves across the face of the ring. Obviously the fewer teeth on the pinion the faster it travels and less material involved.

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What I wonder, then, is whether or not the ring gear is the same across a similar gear set. IOW is a 41-tooth ring the same on a 3.73 and 4.10 ratios with the pinion changing to match? I totally have no idea.
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Old 04-20-2014, 12:35 PM
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^ I don't believe it is. Because you're dividing the number of teeth on the ring gear to the number of teeth on the pinion gear. You couldn't get to the same number on your equation above.

In simple terms, differential gear ratios are calculated and changed by the number of teeth. The angle of the teeth would/could obviously change too.

Correct?
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Old 04-20-2014, 01:49 PM
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^ yes.

Here is a sloppy FBD that I copied out of my machine design text from college. Unless were planning on designing our own Landcruiser diffs, I think that you are correct
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