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Helical Limited Slip Function and Torque Bias Ratio


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#1 JMortensen

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Posted 02 September 2011 - 09:00 AM

I was explaining helicals yesterday on another site and came up with what I think is my most concise and clear explanation to date, so I cleaned it up a bit and figured I'd repost it elsewhere.

Helical diffs work like this: two large side gears in the carrier are connected to the axles, and a bunch of worm gears drive off of each side gear and ride on each other in the center. The worm gears connect the two side gears together, so that when one side gear turns at a different speed than the other, all of the worm gears must also turn. When there is no load (no torque) and the unit is not preloaded (some are preloaded from the factory, some aren't), you can jack up the rear end and spin one side with one finger and the other side spins very easily in the opposite direction. There is probably even less resistance than a normal open diff and spider gears. When you put power to it though, the torque drives the side gears outwards into the case, and all the worm gears get driven inwards to the bottom of their machined pockets in the carrier. The force of these gears jammed up in all of their respective slots is what creates the resistance to differentiation. All of the gears also try to walk off of the gear they're riding on, so there is axial and radial friction between every gear and the case. If you try to spin one wheel at a different speed, it must turn all of the gears in the differential while they're loaded.

The amount of force produced here can be quantified by how much torque it can hold. This is what is called the Torque Bias Ratio. Really aggressive TBR's are 5:1, most common are ~3:1. This means that a 5:1 TBR can keep putting power to the wheel with less traction until it has 1/5 or 1/3 the traction of the other wheel and the torque applied does not exceed the traction of the inside tire. If you have less traction available or apply too much power so that you get wheel spin, then the gears inside lose some of their friction against the case. As the speed differential between the wheel speed and the car speed increases on the wheel that is unloaded, internal friction in the limited slip decreases and that tire spins more and more freely. If one wheel comes off the ground and there is no preload, all of the torque goes straight to the lifted tire. As soon as traction is restored, the diff resumes the task of limiting slip.

This definition that I've given is not typical, and I know it. Usually you see something like "the differential takes the torque at the wheel with less traction and transfers it to the wheel with traction" or "sends traction from the wheel that slips to the wheel that grips". You might see some math applied: "If the inside tire can put down 100 lb/ft of torque, the LSD will send 300 lb/ft to the outside tire." This is really not what is happening at all. It's more accurate to say that the helical LSD can lock the axles together to a certain degree by applying friction equally to both axles to prevent it, and once you go beyond the limits of the friction created by the diff or the traction available at the lesser tire and try to put torque down, you get wheel spin. There is no gear reduction mechanism in the diff, no mechanism to take power from one side and add it to the other. The limited slip acts uniformly on both sides. By way of contrast, traction control systems actually change the speed of one tire vs the other by applying the inside brake really do SEND the power from one side to the other by limiting drive to the spinning tire and applying more torque and power to the side with drive. Helical limited slips do not do this (no limited slip that I know of does).

We may truthfully say that the inside tire is putting 100 lbs of torque to the ground and the outside is putting 300 in a helical example, but the gears inside the diff are still applying the same amount of frictional force to both axles to resist differentiation. Limited slips allow wheel speeds to differentiate for corners and still maintain the ability to resist spinning one tire out of control, but they are not "sending power from the wheel that slips to the wheel that grips". LSDs are like sway bars in that respect. They attach to both axles of the car, so whatever effect they have is shared on both sides. The result of their equal effort can be quantified in terms of how much more power can go to the outside tire before the inside starts slipping, but the effect is not obtained by virtue of the diff transferring power to the outside tire, it occurs because the diff resists slipping and the fact that there is more traction at the outside tire.

If you have a clutch LSD shimmed really tight, it might have a TBR of 1000:1 or maybe it would even be locked up solid and be infinite like a spool. But that doesn't mean that a diff with an infinite TBR puts infinitely more power to the axle with traction. It means that it drives the axles EXACTLY EQUALLY and if one side has traction it does infinitely more work than the side that has none.

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Edited by JMortensen, 02 September 2011 - 09:11 AM.

Jon Mortensen, owner/operator www.petdoorstore.com


#2 Flexicoker

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Posted 13 October 2011 - 02:41 PM

That is a really good explanation. There is definitely no "magic" in the helical LSD's like people make it seem. Mathematically they operate the same as a clutch style LSD, there is a locking torque between the 2 axles that is proportional to input torque.

What you'll see looking at data from a racecar is that the outer wheel speed will be a little higher right before the apex (travelling a wider arc), and as soon as the driver applies power the inside tire will spin up a little (or a lot at high drive ramp angles). Then as the driver rolls on the throttle and straightens the steering, the vehicle weight transfers back to the inside and the wheel speed difference will start to reduce until there is an abrupt point where the diff locks and the inside tire slows down to match the outside. That point is where the clutch locking torque (proportional to input torque from the motor) exceeds the torque difference between the wheels. At zero input torque and zero preload, both diffs will be totally open. Although, off-throttle the motoring torque pushes against the coast ramp or pushes the planet gears in a Quaife in the opposite direction and create a locking torque.

Here is a good paper on differentials:
http://www.optimumg....BertaReport.pdf
Unlike women, a racecar is an inanimate object. Therefore it must, eventually, respond to reason.

#3 cygnusx1

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Posted 13 October 2011 - 02:49 PM

It's really simple when you take one apart and manually make it "work". Put torque into it, and the left and right output shafts get friction between them.

I had my dad apply torque to the input shaft with a wrench, I could feel the friction by turning the left and right output shafts opposite each other by hand. The more torque my dad applied, the more difficult it was to twist the side shafts opposite each other. When dad input no torque, or negative torque, the diff opened up...to it's pre load setting.

Edited by cygnusx1, 13 October 2011 - 02:50 PM.


#4 260DET

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Posted 13 October 2011 - 10:38 PM

That is a really good explanation. There is definitely no "magic" in the helical LSD's like people make it seem. Mathematically they operate the same as a clutch style LSD, there is a locking torque between the 2 axles that is proportional to input torque.

What you'll see looking at data from a racecar is that the outer wheel speed will be a little higher right before the apex (travelling a wider arc), and as soon as the driver applies power the inside tire will spin up a little (or a lot at high drive ramp angles). Then as the driver rolls on the throttle and straightens the steering, the vehicle weight transfers back to the inside and the wheel speed difference will start to reduce until there is an abrupt point where the diff locks and the inside tire slows down to match the outside. That point is where the clutch locking torque (proportional to input torque from the motor) exceeds the torque difference between the wheels. At zero input torque and zero preload, both diffs will be totally open. Although, off-throttle the motoring torque pushes against the coast ramp or pushes the planet gears in a Quaife in the opposite direction and create a locking torque.

Here is a good paper on differentials:
http://www.optimumg....BertaReport.pdf


Wouldn't a helical diff work smoother than a clutch type though, particularly at the point when the clutch type breaks and begins to slip? Even more so when the clutch type is adjusted up so much that most of the time it stays locked. As an amateur driver I like the smooth operation of the helical, like all good things you don't know its there, in contrast to most clutch types.

#5 JMortensen

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Posted 14 October 2011 - 09:28 AM

Wouldn't a helical diff work smoother than a clutch type though, particularly at the point when the clutch type breaks and begins to slip? Even more so when the clutch type is adjusted up so much that most of the time it stays locked. As an amateur driver I like the smooth operation of the helical, like all good things you don't know its there, in contrast to most clutch types.

Why would the helical be somehow inherently smoother? When you describe smoother as "not knowing it's there" that means that you want an LSD so weak that you can't feel it working. If you had a clutch limited slip with no preload and had the clutches setup to minimize friction (stack them plate plate plate disk disk disk for example so that there is only one plate face working on one disk face) what would make the friction that it generates feel different than a helical's friction?

The nice part about clutch LSDs in my view is that the clutch stack arrangement is a more efficient friction generation mechanism so you can generate a much higher torque bias ratio than you can in a helical, and you can also tailor it to suit your particular car/driving style. While we don't have different ramp angles and pressure rings from Nissan, if someone were inclined they could make their own. In fact I believe Ron Tyler did this at one point. You can add more clutches and put more surface area to work, or you can stack them so as to minimize the surface area. With the helicals you can change the pitch of the gears to increase or decrease friction as well, but they don't seem to have the capability to get the TBR near as high as a clutch type can.

Thanks for the article Flexicoker. Interesting stuff in there.

Jon Mortensen, owner/operator www.petdoorstore.com


#6 RTz

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Posted 14 October 2011 - 06:17 PM

...I believe Ron Tyler did this at one point.


Jon is half right. I didn't make one, but I did re-cut the ramps of an E30 M3 diff. It's do-able, but you've gotta want it. Trying to keep the tangential intersects intact takes a little forethought and respect for what you're doing. Also, I threw a fairly expensive carbide end mill in the garbage.

I violated this particular diff for my own car. It was worth it. I had the corner exit bite of a more aggressive diff, but I hadn't lost drive-ability in slippery conditions (it occasionally rains in the Pacific NW).

If I were to do it again, I would consider making a pair from scratch. Jon would know better than I, but I'm guessing a quality case harden would probably be up to the task. If so, an ambitious guy could spend a great deal of time tuning his car via the diff.

Sorry for the hi-jack, Jon. I haven't yet come to terms with the helical diff. Not because it can't work, but because if it doesn't, I'm not experienced with them enough to deal with it. A CLSD, on the other hand, is very tunable, as you know.
Regards, Ron

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#7 JMortensen

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Posted 14 October 2011 - 06:30 PM

Jon is half right. I didn't make one, but I did re-cut the ramps of an E30 M3 diff. It's do-able, but you've gotta want it. Trying to keep the tangential intersects intact takes a little forethought and respect for what you're doing. Also, I threw a fairly expensive carbide end mill in the garbage.

I violated this particular diff for my own car. It was worth it. I had the corner exit bite of a more aggressive diff, but I hadn't lost drive-ability in slippery conditions (it occasionally rains in the Pacific NW).

If I were to do it again, I would consider making a pair from scratch. Jon would know better than I, but I'm guessing a quality case harden would probably be up to the task. If so, an ambitious guy could spend a great deal of time tuning his car via the diff.

Sorry for the hi-jack, Jon. I haven't yet come to terms with the helical diff. Not because it can't work, but because if it doesn't, I'm not experienced with them enough to deal with it. A CLSD, on the other hand, is very tunable, as you know.

I don't know much about metallurgy, hardening, or machining, so I have stuck with changing the clutch stack around and shimming for my own vehicles. On the different LSD's that my business sells, there are different springs and clutches, but nobody gets into ramp angles and that sort of thing either. I think to get that far into it you have to be a pretty hardcore road racer or autoxer. Most of my stuff is geared towards 4wds, where it's all about increasing lockup, and that is relatively easy to do.

Judging by your response it sounds like you made a 2 way LSD into a 1.5. Is that right?

Jon Mortensen, owner/operator www.petdoorstore.com


#8 260DET

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Posted 15 October 2011 - 01:01 AM

Why would the helical be somehow inherently smoother? When you describe smoother as "not knowing it's there" that means that you want an LSD so weak that you can't feel it working. If you had a clutch limited slip with no preload and had the clutches setup to minimize friction (stack them plate plate plate disk disk disk for example so that there is only one plate face working on one disk face) what would make the friction that it generates feel different than a helical's friction?

The nice part about clutch LSDs in my view is that the clutch stack arrangement is a more efficient friction generation mechanism so you can generate a much higher torque bias ratio than you can in a helical, and you can also tailor it to suit your particular car/driving style. While we don't have different ramp angles and pressure rings from Nissan, if someone were inclined they could make their own. In fact I believe Ron Tyler did this at one point. You can add more clutches and put more surface area to work, or you can stack them so as to minimize the surface area. With the helicals you can change the pitch of the gears to increase or decrease friction as well, but they don't seem to have the capability to get the TBR near as high as a clutch type can.

Thanks for the article Flexicoker. Interesting stuff in there.


As an illustration of what I was getting at re unobtrusiveness Jon, compare doing slow tight parking lot type turns with the two types. Invariably the clutch type chatters and shunts the transmission while the helical type is quiet and smooth. My Z is set up for the helical type and it never causes a loss of rear grip in dry conditions, it just does it's job so well I do not know it's there. Personal preference no doubt comes into it, all I can comment on is my own experience.

#9 RTz

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Posted 16 October 2011 - 02:07 PM

Judging by your response it sounds like you made a 2 way LSD into a 1.5. Is that right?


That's correct, but I didn't really say anything to give it away. If my rain comment threw you, sorry. I'll say it differently... with more aggressive ramps, you should get a higher TBR at the same preload setting. I was able to get good lock up under accel, without running the excessively high preloads that can cause a car to push on turn-in, particularly in lower traction conditions.

If you shallow out all the ramps to the same degree, the accel/decel bias should remain unchanged. In my case, I only shallow'd out the ramps that are active under acceleration. That changed the bias. I'm not sure if it technically became a 1.5, but it should tilt it in that direction.
Regards, Ron

HybridZ; Some diligence required.

#10 heavy85

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Posted 16 October 2011 - 04:06 PM

I'm always confused when people say helical last forever as there are no wear parts. It seems to me the whole thing is a wear item due to the way it works?

PS: I used to run the factory LSD out of an ~88 300ZX with unknown preload. Had a lot of problems putting the power down on corner exit without the rear end stepping out. This year I switched to an OBX helical. The damn thing looks like it was machined with a blow torch and was fully locked up when I got it due to manufacturing quality issues but after a nominal amount of work I got it in working order. I REALLY like it much better than the old clutch LSD. It allows me to plant my foot and hold it there much earlier in a turn without stepping the back end out. I think I can hear the gears working in the on slow tight turns but hasn't caused any known problems. Again I dont know the settings of the factory diff I was using but the helical for me performs comparatively mooch betta.

Cameron

#11 puretone

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Posted 21 April 2014 - 08:04 PM

A Helical & TorSen differential is nearly similar in operation, no?
I've been involved with some Toyota Celica fan-boy boards for a while. Some of the sportier SS3 Gen 5 & 6 Gen Celicas were delivered with Helical LSDs that for whatever reason at times displayed open-diff characteristics.

Perhaps it should be mentioned that the amount of "bite" a clutch-type LSD has, can be "adjusted" to an extent by virtue of different viscosity & additives found in various diff fluids.

#12 johnc

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Posted 22 April 2014 - 05:13 AM

Helical diffs require a torque load at each axle or the diff will go open. It's inherent in the design and can be band-aided by increasing preload.

A better option is to reduce roll stiffness at the driven end of the car to keep from picking up a wheel. You also need to be careful curb hopping. Getting a wheel in the air, having it spin up as it goes open, and then slamming it back to ground has been known to destroy helical diffs.
----- John Coffey, Fabricator at Benton Performance, LLC

#13 260DET

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Posted 11 August 2016 - 11:15 PM

Vale johnc.

 

In my experience he nails the point about helical diffs, they work great while both wheels are on the deck otherwise go the clutch type. As for tuning the clutch type that's well beyond most of us amateurs I suggest, at least with the helical you know that the suspension has to be set up so both drive wheels will stay on the deck. Get that right and you have the basis of a nice, fast, drivable package. 






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