Helical Limited Slip Function and Torque Bias Ratio by JMortensen

6 minute read

Helical Limited Slip Function and Torque Bias Ratio

Compliments of JMortensen @ hybridz.org

9-2-2011

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.