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Discussion Starter · #1 ·
Or, more exactly, is there a fixed relationship (or formula) that describes the rpm of the spider gears in an open differential?

There's lots of information available about how a differential works, and the rotational relationships between the ring gear (and attached differential case) and the side gears (going to the drive axles), but I haven't found anything relating to the rotation of the spider gears.

(I’m using the terminology set out here: OPEN DIFFERENTIAL PART IDENTIFICATION TERMINOLOGY | nomenclature, teardown, exploded diagram | NOMENCLATURO.COM )

Example: A regular, open, rear differential. When both wheels are going straight on the ground and neither slips, the wheels, side gears, differential case and ring gear all turn together. The spider gears transmit the force from the differential cage through the pinion shaft (goes across the case with the spider gears at each end) to the side gears, but they don't rotate on the center pinion shaft. No issue here.

If one wheel does not rotate while the other is free to turn, the free wheel will turn at twice the rate of the ring gear and differential case. (This is not in question.) At the same time the spider gears will rotate around both the side gears while also rotating on the pinion shaft. In this example, which is a "worst case" scenario for a differential, if the ring gear and case are turning at, say, 10 rpm, the free wheel will turn at 20 rpm. My question then is: How fast are the spider gears rotating on their center pinion shaft?

Reason for my question? The spider gears don't have bearings -- they are simply loose fit on the pinion shaft. There are washers between the back of the spider gears and the differential case. Because the spider gears, for the most part, normally don't rotate fast or constantly on the pinion shaft, they don't have to have the type of bearings and thrust controls that, say, the pinion drive gear or the side gears require. However, this design also assumes that both wheels will normally rotate at much the same speed, with minor variations for bumps and turns and the odd time a wheel loses traction. It can, conceivably, become a problem, however, if the two wheels/tires are not the same circumference (e.g., using the donut spare), or if one wheel is allowed to spin relative to the other for an extended time. There have been cases of differential failure in less than a minute in the latter case, such as when trying to go up an icy slope, or when one wheel is off the ground.

This raises a question about using the temporary "donut" spare, which is smaller than the normal tire. When using the donut spare, the spider gears must be rotating on the pinion shaft continuously, yet we are allowed to use it at limited speeds/distances. Presumably engineers have determined that there won't be any damage to the spider gears, but I wanted to get an idea of the magnitudes -- at what rate the spiders would rotate if one wheel is free to spin, and at what rate if the donut spare is used and the car is travelling at up to 50 mph.

Hope someone knows, or can refer me to a source of information about spider gear rotation rates.
 

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If they are the same size as the gears on the axle shafts, then at 'best' 1/2 the rotational speed difference of the 2 axles (wheels) assuming one wheel is spinning a bit slower than the carrier, and one a bit faster.

At worst, the same as the speed difference of the 2 axles.

At a guess, anyway.

To say how fast they spin with a spare tire on there, you have to decide what the difference in circumference is between the spare and the normal tire.
 

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Discussion Starter · #3 ·
Hi Dave

I'm at the guess level right now as well. I've been watching some animated videos of "how a differential works" to try to work this out subjectively, but I have a strong feeling there's a fixed relationship, somewhere.

I think I need only two (extreme) cases to determine the relationships for all others because the gears are always engaged and the same in all cases.

One case is when both wheels are turning at the same speed -- in this case, the spider gears don't rotate on the pinion shaft.

The other is where one wheel spins freely while the other is fixed. (This is a worst case -- they can't get any more different.) It's this case that I'm not clear about. Everything else is "in between". If I can determine the relationship, all other situations can be calculated.

I'm thinking there's a fixed formula/relationship that takes into account/relates the side gear (wheel) rotation speeds, the ring gear rotation speed, and the spider gears rotation speed (probably along with measures of gears, such as number of teeth.)

To say how fast they spin with a spare tire on there, you have to decide what the difference in circumference is between the spare and the normal tire.
Indeed, but that's no problem. It would also vary, of course, with vehicle/wheel speed.

Incidentally, the differential case and ring gear always turn at the average of the two side gears. When one wheel spins freely and the other doesn't the ring gear turns at 1/2 the speed of the turning wheel. Similarly, when cornering, one wheel speeds up and one slows down, while the ring gear continues to turn at the average which, if everything else (throttle, gear) remains the same, would be the same as it was when the car was going straight.
 

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Discussion Starter · #4 ·
Did more thinking about this and as it turns out, it's simpler than I had anticipated.

The spider gears rotate on the pinion shaft only when the two side gears rotate relative to one another. The rate at which the spider gear rotates on the pinion shaft will depend on the difference in side gear rotation and be in proportion to the gear ratio between the side gear and spider gear.

I had a look at the FSM diagram for the rear differential (my 07) and it looks as if the side gear has 12 teeth and the spider gear has 9. (I'm not sure if the diagram is meant to be accurate, or only a typical representation. I looked at quite a few internet photos of differentials, and as best as I could count the teeth, most had similar ranges. If someone has a 4.444 Subaru rear differential open and could count and report the number of teeth, that would be appreciated and might help ensure that what follows is "in the ballpark".)

As noted earlier, when one wheel is fixed, the other is free to turn, and the ring gear turns one revolution, the free wheel turns two revolutions. At the same time, with the 12:9 ratio, the spider gear will have turned 1.333 revolutions on the pinion shaft. This relationship is fixed by the gears; consequently, if the two side gears turn one revolution relative to each other, then the spider gear turns about 0.66, or 2/3 of a revolution. So now there's a basis for assessing what this means.

(To put this in perspective, the tires on my car rotate about 750 times per mile. The "relative" difference being addressed here would appear if one wheel turned 750 and the wheel on the other side of the differential turned 749 or 751 revolutions.)

I have three examples: making a tight 90 degree turn; having one tire ¼-inch different in circumference; and, using the donut spare tire on one side.

Tight 90 degree turn:

Some years ago I calculated the difference between the path of the inner and outer wheels on my 07 to be equivalent to about 1.14 revolutions of the wheels. (Outer turns 1.14 revolutions more than the inner to complete the 90 degree turn.) Based on this, the spider gear will rotate about three-quarters of a revolution (1.14 X 0.667). Not much, and as the cornering will normally be at a slow speed, the EP gear oil that bathes the differential should be sufficient to protect the surfaces between the spider gear and the pinion shaft that it rides on from the related friction and heat over the life of the car. (Normal amounts of turning over the life a car would have been taken into account in the design.)

Straight travel with a 1/4 - inch difference in the tire circumferences:

Again, based on earlier calculations, and using the stock tires on my 07, over a mile of travel the slightly smaller wheel will turn 2.77 more revolutions than the larger tire. This would translate to the spider gear turning 1.8 revolutions on the pinion shaft. While this is notably more than if the two tires are the same (there will always be some rotation for small steering corrections, bumps etc), the slow rotation (it would make the 1.8 turns in about 1 minute at 60 mph) probably wouldn’t contribute to catastrophic wear of the contact surfaces between the spider gear and the pinion shaft and spacer washer provided the gear oil is performing properly, although some additional wear could be anticipated over the longer term.

Driving with the donut spare:

The donut spare on my car has a measured circumference of about 82.1 inches whereas the stock tires are nominally 84.5 inches in circumference. The difference in rotation over a mile of travel is 22 revolutions! That translates to the spider gear rotating about 15 times, per mile, or 15 times per minute at 60 mph. That seems a fair amount of turning relative to the other examples especially if the travel is for a long period and where, in this case, there’s no bearings (e.g., roller, ball) or special bearing surfaces other than the metals of the gear and pinion shaft. This is an additional reason why use of the donut spare should be limited in both distance and speed.

Worst case:

The worst case situation would be when one tire isn't turning and the other spins freely (e.g., on ice). Sustained spinning at high speed will cause the spider gears to rotate at speeds, and for lengths of time, that they are not designed for, and could lead to more significant wear of the contact surfaces. As noted earlier, there are reports of differential failures attributed to excess spinning of tires in this type of situation.

Perhaps not the most exciting issue to deal with on the forum, but I find the analysis and the results interesting and meaningful. Hope others will as well.
 

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Perhaps not the most exciting issue to deal with on the forum, but I find the analysis and the results interesting and meaningful. Hope others will as well.
This is of great relevance to all offroaders. Open axles crossed and lots of wheel spin is the perfect prescription for spider gear seizing on its shaft, subsequent shearing of the shaft and total failure of the diff. To be avoided at all cost :rolleyes:. This is not unheard in the R160 rear end even on street driven cars. Further, the resulting shock loads from loss of grip / grip is practically the only way to damage the front pinion / crown wheel in the 4EAT (in addition to the no oil condition after a service :eek:).

Tapani
former offroader :D
fan of TBDs at both ends :29: (Quaife rear / Modena front in a JDM VTD 4EAT)
 

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Discussion Starter · #6 · (Edited)
Tapani

Thanks for this interesting addition to thread

I wasn't aware that there were aftermarket "torque adjusting" front and rear differentials that could be installed in Subarus, but on reading your post I looked up the Quaife and Modena makes. However it looks as if their applicability is limited.

If I understand correctly, they are made to fit in the existing Subaru differential case. I presume the original pinion gear (coming from the transmission) is used and the crown gear is transferred from the old to the new differential (maintaining the same gear ratio); in other words, just the differential mechanism itself is changed.

[More info at: http://www.subaruoutback.org/forums/97-offroad-tech/41233-limited-slip-differential.html, and the links therein]

In any event, it must be awesome on snow and ice.
 

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However it looks as if their applicability is limited.

If I understand correctly, they are made to fit in the existing Subaru differential case. I presume the original pinion gear (coming from the transmission) is used and the crown gear is transferred from the old to the new differential (maintaining the same gear ratio); in other words, just the differential mechanism itself is changed.


In any event, it must be awesome on snow and ice.
Well, the Modena front can be used in any 4EAT (only 15 were ever made, though). Flatirons looked for interest in a 5EAT version in the LGT forum - none found. A bit pricey, but with a bit of torque from the turbo it's money well spent even in the SVX - not to mention a trailie OB. I do not know how much different the 4EAT and the 5EAT carriers are.

The Quaife should fit into all R160 cases. I had to grid just a bit off the case casting to fit into an originally open one. Just the CVs must match the side gears - there are two sets of grooves for the c-clips in the Torsen - the old style stubshafts with the long bolts (female CVJs) can not be used.

Br,

Tapani
 
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