Understanding Lockup Part 1
Lockup is a little understood phenomenon, which is made more difficult to grasp due to the volume of misinformation on the web. Here is some more. Actually this information is based entirely on the manufacturer's original specifications in the data sheet from 1984 when hot chips were 20c. 0% of this information is made-up, unlike much of the other information found on reputable websites where you can buy strange 5-clutch builds, and 2-clutch LSDs with 80% lockup.
For cost and simplicity reasons most vehicles had a simple
2-clutch LSD unit. They feel smooth and remain quiet and tight for a long time because
they have two belleville springs installed at each end. One large pair compresses the
clutch plates, and will keep them under compression even with considerable
internal wear. The second set of belleville springs compresses the floating differential
assembly (splined gears, spider gears, thrust bars). They typically have 45
degree angles cut into the thrust plates. One or both of these angles can be
changed to any angle between 45 degrees and 30 degrees. Lockup will increase as
the angle approaches the maximum 30 degrees. Angles less than 30 degrees are
not specified by the manufacturer. I believe that internal stresses on the LSD capsule would be too great with angles less than 30 degrees.
This graph demonstrates the lockup curve by plotting the thrust angles versus the lockup percentage. You can roughly work out what angles you would cut to achieve the desired lockup for a 2-clutch unit. For example 30 degrees = 40% lockup, 35 degrees = 35% lockup, 40 degrees = 28% lockup. Below is an example of a thrust plate with factory 45 degree ramps on one side and 30 degree ramps on the other.
It becomes apparent that there is only one angle worth grinding and that is: 30 degrees. The lockup increases slowly as we approach 30 degrees. Considering all of the surface grinder work, lathe work, heat treating and blasting, the 30 degree angle is the only choice which represents value for money. This machine work raises the lockup by 15 percentage points. The 2-clutch LSD becomes a good performer with this ramp angle change, for only a small investment. Rebuilds are inexpensive as there are only 2 clutch plates and 2 steel plates to replace. This configuration is very popular.
For improved performance, some BMWs had a 4-clutch LSD installed as OEM equipment. These were rare fitment, and had comparable lockup to a 2-clutch unit at just 40% on drive. Unlike the OEM 2 clutch units, these did not have the large belleville springs to compress the clutch plates. Due to their "unsprung" design they had little to no preload, and may show close to zero ft/lbs breakaway torque. For some drivers the improved turn-in is advantageous. Though the low break-away torque makes it more difficult to ascend uneven driveways and other uneven surfaces where one wheel may lift. The unsprung configuration reacts quickly and feels direct. Most drivers would prefer this. Though the lack of springs means that if the LSD is custom built with for example 60 ft/lbs of breakaway torque, it will degrade down to zero ft/lbs over time. For race vehicles, this is the price to pay for the unsprung build. The use of one spring instead of two gives something in between, depending on how much the spring is compressed. Measurements need to be taken very carefully in this case, because the entire stack is being pushed in one direction, and this could put pressure on the splined gears which should be floating, and never touching a thrust plate.
There are a few different custom 4 clutch options which all have relatively high lockup starting at 45%. The graph below plots the angles in degrees versus the lockup as a percentage.
Using this graph, it is possible to determine custom lockup angles for any amount of lockup between 45% and 75% for custom BMW LSDs.