[torsen] Re: [V8] differential/torque sensing

Andres Kroonmaa andre at online.ee
Mon Mar 31 07:20:07 EST 2003

 hi Keith,

 hope you have some time to drop few comments.

On 25 Mar 2003 at 9:37, Keith Maddock wrote:  

> For now I'm most concerned with the followign paragraph:  
> " IMO, actual friction value of metal surfaces is even irrelevant. It appears  
>  that what counts is force ratios against available friction surfaces. Thus  
> First, this disagrees with some paragraphs in the article on Torsen's site.  
> http://www.torsen.com/Traction_Control_Article.pdf   

 yes, I see what you mean. Maybe I'm wrong, thats why my claim shows off 
 some degree of uncertaintly. But let me explain why I reached that idea. 

> Top of Page 77, Column 2  
> "Completing the hardware complement are thrust washers used between each end  
> of each side gear, between side gears and the housing. Selection of thrust  
> washers is important in determining the operating characteristics for each  
> application. Proprietary Gleason models permit selection of components with  
> a high degree of accuracy with respect to vehicle characteristics."  

 Same paper, 4.1 Overall bias control: 
"The Torsen differential may be designed with different bias ratios ranging 
 from approximately '2.5:1' to '6:1' or higher. This may be accomplished by 
 varying the side gear helix angles, OR by altering the friction characteristics 
 for the primary components."

 Thats my startingpoint.

"In addition to providing a geared interconnection between drive axles which 
 permits the usual opposite relative rotation between the drive axles, the 
 gearing also distributes forces which may be generated to resist differentiation 
 over a large number of different surfaces within the differential. The surfaces 
 over which the Invex gearing distributes forces are designed with different 
 coefficients of friction, and the Invex gearing is designed to distribute 
 different loads between the surfaces. Collectively, the surfaces and the 
 gearing are designed to distribute wear evenly over the surfaces and to control 
 the overall amount of friction within the differential needed to achieve a 
 desired bias ratio." 

 This supports that indeed, in actual torsen implementation they opted to
 evenly distribute loads relieving forces acting upon worm meshes.

> If friction in the diff besides the actual gear meshes is NOT a factor as  
> you claim, why would selecting different thrust washers have such an effect  
> as Gleason claims??  

 yes, right, washers are important in university special. But for torsen
 as principle, they are not, in my opinion. 

 Of course, every moving part inside torsen has influence on friction.  
 Every frictional surface contributes to tweaking bias. Including journal 
 pins, ballbearings, everything. These thrustwashers are easiest parts for 
 finetuning forces, and perhaps strongest. Maybe I'm underestimating their 
 importance, but it seems to me that these washers are not of fundamental 
 importance to working principle. Maybe indeed they are important to actual 
 strength, wear and heat engineering..  

> Top of Page 78 Column 1  
> "Therefore, the maximum difference torque which  
> can be supported between drive axles is related to each of  
> the above-equated frictional torques as follows:  
> T1 - T2 = Tf1 + Tf2 + Tf3 + Tf4 + (R / Rc) x (Tf5 + Tf6)"  

> Seems that your explanation below is only considering the forces at the gear  
> teeth themselves, but you also have to consider that these forces also have  
> opposing reaction forces at their end faces, which also contribute heavily to  
> the locking effect.  

 Yes. There are 3 areas in the formula above. Tf5,6 we consider insignificant.  
 I also considered Tf3,4 as insignificant. Perhaps for actual actual unit this
 is error in the end, but for basic principle it seemed to turn focus away from
 the main point, function of wormgearing to cause force disbalance. Somehow I
 assumed that these washers are relatively well lubricated..

 Lets imagine that these washers have zero mu. Then they just oppose thrust  
 forces occuring from worm mesh, and as long as there is support force from  
 axle, applied force between worm teeth will go up, because now friction  
 between basket and sidegear washers does not transfer engine torque to
 axle, only that worm mesh teeths do.

 Remember, worm mesh locks, and although technically its not due to sliding 
 friction, it can be expressed in terms of friction. mu is ratio of applied 
 normalised force to resisting force. mu=Fn/Fr. Resisting force here in worm 
 mesh is function of traction on other axle.

 Note that whatever is actual coeff of friction of material, worm meshing 
 allows only one thing - all applied torque to basket is converted into 
 "frictional" torque to rotate axles. Worm surface mu could be high, or mu 
 could be low, resultant Tf would be same. It seems good to have teeth with
 low mu, to have less heat and wear when differentiation occurs. "Friction" 
 here is from inner molecular structural forces of metal (teeth) so to say.

 Normalized force here is force from axle, multiplied by wormmesh ratio. 
 Resisting force here is Trg/2 if axle torque split is 50/50. Because Trg
 is the only source for torque, it occurs that normal force and resisting
 force cannot be too much different, and depend on worm ratio only. If we
 just conjecture that the ratio is 2.0, we'll get that effective mu is 2.0.
 So, resultant effective mu is very high, and so is "frictional torque".
 Effective mu = (T1 x ratio)/Trg1

 On other axle, if there is less traction, normal force is lower, and that 
 causes effective worm friction to go down, causing effectively "frictional 
 torque" disbalance between axles, and that difference is cause for torque
 split. Point where sliding becomes possible if when normalised force
 becomes equal to resisting force, or less. For one worm axle, it means
 reduction of axle force by 2.0 ratio. Because axle force is directly
 related to engine force on gripping worm, their relation doesn't change,
 its only defined by worm ratio, not by torque applied there. But because
 of interaxle gearing, there is additional freedom of movement, and that
 translates into reduced torque force (Trg1) on gripping axle worm aswell
 (when slip occurs on other axle).
 That doesnt change mu on gripping wormgearing. mu changes only on slipping
 axle where axle isn't able to support force transferred to it from Trg2.
 Ratio of resisting force and normal force goes down below 1.0 and movement 
 begins. Any remaining traction force is multiplied by gear ratio, and
 countered to both Trg and opposite axle equally. From here its apparent
 that other axle can transfer no more torque than slipping axle's remaining
 traction times wormgear ratio.

 So, there is direct relation between worm ratio and torque split. Worms 
 work effectively as frictional interface. I suppose that its increasingly 
 difficult to make strong small worms with higher ratios, therefore they
 stop at about 2..3 (+/-). The rest for TBR is achieved through additional
 frictional surfaces like washers. To engage them they use that reaction 
 thrust created by worm mesh. Picking washers, they can finetune TBR up 
 (but not down) from hardcoded wormratio based TBR to any desired value,
 limited only by mu of washers and reactional forces extracted from worm
 mesh. So they can ship same physical torsen based on requirements with
 different TBRs by only swapping washers.

 In formula above, this means that Tf3,Tf4 are purely frictional, while 
 Tf1,Tf2 are not, they are combinational from worm lock effects and plain
 friction, and latter is least important there. In my view, you could make
 Tf3,4 very low, and even though worms are very well lubricated, Tf1,2
 would still be possible to make quite high. So I think that plain
 simple rotational friction isn't absolutely necessary. Its magnitude
 depends on worm locking forces anyway, and if there is no support from
 slipping axle, that friction goes towards zero with any mu unless there
 is some preloading. Therefore it seems that actual surface friction mu
 is of no fundamental importance, giving only additional kick to TBR.

 You could have worms with higher ratio, and you get higher TBR without 
 additional frictional interfaces. Probably they utilise washers for 
 technological reasons, washers are simpler, they don't change shape with 
 wear, and its easier to make large surface, and being attached to housing, 
 this makes it easier to remove heat from system. If all the torque were 
 to be taken by element gears, they'd simply get roast. 

 So, I still stand by my claim that actual friction is not fundamentally
 important. I stand corrected that in actual torsen washers have quite
 notable portion of locking friction. But even though that seemingly
 discredits abit my view, it is not that much. Thrust forces against
 washers are still exactly proportional to wormgearing ratios and traction.
 They occur only when forces act upon wormgearing, and that can occur only
 when washers are free to rotate. If friction of washers would be upped
 too much, they'd lockup and that would reduce forces upon worms that
 are source of thrust for washers (basket would be locked to axles).
 Thus, max frictional torque from washers is directly correlated to max
 frictional torque from worms, and I would dare to bet that they are equal.
 This also explains why torsen can never fully lock even in theory.

 From here I conclude that max TBR of torsen can be approx 2 times of
 that derived from pure wormgearing. What they do to get requested TBR,
 is make worms delivering TBR/2 or slightly more, and then pick washers
 to finetune up to required TBR. This also means that TBR in reverse
 gear can be no worse than that created by pure wormgearing, or no
 less than forward TBR/2.

 Whats interesting about worm mesh, is that its locking effect is not
 that much dependant on surface friction value, but on the ratio of
 forces. Locking effect of worms is overcome when torque at wormwheel
 is ratio times larger than at wormgear. And that part is independant
 from any actual surface friction, which only offsets that unlock point
 to higher required torque difference. Thus even worms with hypotetically
 zero surface mu would still offer minimally effective mu equal to
 wormgear ratio. In torsen such mesh would offer locking effect and
 TBR even if there is absolutely no friction resisting slip.

 In regards to torsen TBR forward vs reverse, I still can't see any
 other source for TBR difference than in friction of washers. I really
 wonder if due to very rare engagement washers used in reverse might
 get covered by excess oil, and simply doesn't engage quickly enough,
 especially if there is very little traction and thus low thrust forces.
 Maybe after applying brakes and letting that shit burn out, torsen
 would behave exactly the same in forward vs reverse? Although every
 engine braking should make those washers work..

 Andres Kroonmaa <andre at online.ee>
 CTO, Microlink Data AS
 Tel: 6501 731, Fax: 6501 725
 Pärnu mnt. 158, Tallinn
 11317 Estonia

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