53 replies to this topic

[Lee200]

Much has been written over the years here at SRMZ about car differentials and how GPL models them.  The vast majority of this information has been good, but there have also been a few inaccuracies and some misunderstandings.  This post is an attempt to clear up some things.

1.  The purpose of the differential is simple--it permits two wheels on the same end of the car to rotate at different speeds.  This makes it easier for the two tires to negotiate different radius curves when the car is turning a corner.

2.  Several different types of differentials have been developed.

A.  Open--this type uses an ingenious set of gears that allows the two wheels to rotate at different speeds at all times as they are never locked together.  Consequently, it handles corners very nicely.  Its main drawback is that if one tire is slipping on a slick surface such as ice, torque is reduced so that the slipping tire spins while the other doesn't spin at all and the car won't move.  A similar situation occurs on race cars in a corner because the inside tire is less loaded and has less grip than the outside tire.  The open differential by itself is rarely seen on race cars although it is almost universally used on passenger cars.

B.  Locked--this type is the complete opposite of the open differential.  The two wheels are always locked together and rotate at the same rate.  It is commonly used on trucks, dragsters, and karts.  Locked differentials are seldom seen on race cars as they promote understeer.  However, the 1970s Porsche 917 Turbo CanAm cars used a locked differential as other differential types of that era could not handle the car's massive torque.

What is really needed for a race car is a differential that is open for entering the corners and locked for exiting the corners and maximum acceleration on the straights.  The limited slip differential (LSD) was developed to accomplish these goals.  An LSD has a mechanism that locks the two wheels together under certain conditions.  The two LSDs that apply to 1960s race cars and GPL are the Cam and Pawl and the Salisbury.

C.  Cam and Pawl LSD--this type uses a set of plungers (pawls) that extend into slots to lock the two wheels together completely when power is applied to the differential.  When power is removed, the plungers retract and the two wheels are free to rotate independently of each other.  The Cam and Pawl is one of the simplest forms of LSDs and is relatively cheap and reliable; however by its very nature, the plungers tend to wear quickly and have to be replaced often.  Also, the locking action is relatively quick so essentially it is either completely locked or completely open.

Cam and Pawl LSDs were used on all F1 cars of the 1960s.  Hewland in England and ZF in Germany manufactured their own versions of the Cam and Pawl LSD.  David Wright researched the subject and determined that the first use of a LSD other than the Cam and Pawl didn't occur until Ferrari used a Salisbury type LSD on their mid 1970s F1 cars.

This is all well and good, but strangely GPL does not model the Cam and Pawl LSD; rather, it models the Salisbury.

D.  Salisbury LSD--this type uses mechanical wedges (ramps) and a series of clutch plates to lock the two wheels together.  The advantage of the Salisbury is that the amount of lock is individually adjustable when the power is applied and when removed.  Also, the two wheels are locked together up to a certain point, then are free to rotate somewhat independently.  The locking action is more progressive than with the Cam and Pawl.  By all accounts, the Salisbury is a vast improvement over the Cam and Pawl.

3.  GPL Salisbury LSD Model:

A.  GPL models the Salisbury LSD fairly well.  The player setup menu contains settings for the ramp angles for "power" and "coast" and the number of clutches.  These settings are applied to a formula to determine a "locking percent".  GPL's code continually keeps both wheels/tires turning at the same rate by apportioning torque from one wheel to the other; however, when the torque difference reaches the locking percent limit, the two wheels begin to rotate independently of each other.

B.  The formulae for locking percent are:

Power Locking Percent = Cosine(Power Ramp Angle) * (Number of Clutches + 1) * 5%
Coast Locking Percent = Cosine(Coast Ramp Angle) * (Number of Clutches + 1) * 5%

Note that ramp angle and number of clutches both contribute to the locking percent calculation.  Therefore, it is possible to have the same locking percent by using different combinations of ramp angle and number of clutches.  The attached chart shows the locking percent for various combinations.

Note that the number of clutches affects both power and coast locking percent.

GPL Setup Manager displays locking percent according to these formulae.

C.  As best as I can determine from reviewing GPL's code, the car handles the same when using the same locking percent regardless of the ramp angle and number of clutches.  The ramp angle and number of clutches values are not used anywhere else in the code.

D.  The power locking percent is used when the player's throttle is on by any amount.

E.  The coast locking percent is used only when the player's throttle is completely off!  This has a major implication for left foot brakers as they will be using the coast locking percent only if they completely remove their right foot from the throttle pedal.  It's all too easy to keep a slight amount of pressure on the throttle pedal which causes the power locking percent to be used inadvertently.

F.  Disregard any reference to what real world cars used for ramp angles and number of clutches.  They may or may not correlate to what GPL needs for a good handling car.  Years of practical experience with GPL has determined that power ramp angles between 60 to 85 degrees, coast ramp angles between 30 to 45 degrees, and number of clutches between 1 to 3 can be used depending on the car characteristics and the player's skill level.  These values correspond to locking percents of 1% to 10% for power and 7% to 17% for coast.

Note that some "alien" drivers may use locking percentages that are different than these.  If you are an alien, you probably don't need to be reading this in the first place.  

Attached Files

•  GPL Salisbury Differential Locking Percent.jpg   51.79K   50 downloads

Edited by Lee200, Dec 18 2018 - 09:03 PM.

[Tato]

Very good, clear and complete explanation. Many thanks!

[Robert Fleurke]

Thanks Lee, very interesting. A lot of stuff I was familiar with, but you always learn and pick up things.

Lee200, on Dec 13 2018 - 02:27 PM, said:

3.  GPS Salisbury LSD Model:

GPS=GPL ?

Lee200, on Dec 13 2018 - 02:27 PM, said:

D.  The power locking percent is used when the player's throttle is on by any amount.

E.  The coast locking percent is used only when the player's throttle is completely off!  This has a major implication for left foot brakers as they will be using the coast locking percent only if they completely remove their right foot from the throttle pedal.  It's all too easy to keep a slight amount of pressure on the throttle pedal which causes the power locking percent to be used inadvertently.

This is very important indeed for left foot brakers. Many guru's back in the day, and even members here on SRMZ have stated left footbrakers shouldn't use 45/60/1 or 30/85/1 since they will use the power angle all the time and could be using 45/45/1 or 30/30/1 as well. This can be easily debunked:

Funnily enough had a recent private discussion about this. The "secret" why very fast guys use 45/60/1 or more extreme 30/85/1 is they will use the coast angle late entry/midcorner for extra rotation, if needed, by completely lifting off. Often when you miss the line or carry slightly too much speed, or have understeer, this is a little trick to point the nose in the right direction. So there you have it, that is why fast left foot brakers use those coast angles

Edited by Robert Fleurke, Dec 13 2018 - 02:59 PM.

[Lee200]

Yes, GPS=GPL, a typo.  Fixed.

[SV3000]

Very detailed and important information, thanks very much Lee!
This is very helpful, as some of the information is very hard to find (i had only grasped limited idea about GPL's LSD from previous discussion on srmz, and info of Cam&Pawl LSD is also very little on the internet)

[gliebzeit]

Believe me, the last time someone put LSD in my Salisbury Steak ... I lost my grip!!

[Lee200]

SV3000, on Dec 13 2018 - 06:36 PM, said:

This is very helpful, as some of the information is very hard to find (i had only grasped limited idea about GPL's LSD from previous discussion on srmz, and info of Cam&Pawl LSD is also very little on the internet)

Yes.  I recall several years ago that one of our GPLers was able to get in contact with the design director of Hewland Engineering.  The question concerned esoteric stuff like the torque bias ratio of the old Hewland Cam and Pawl LSD.  The director admitted that Hewland itself had very little detailed information about how the LSD worked as they copied the design from elsewhere (probably ZF).  

Edited by Lee200, Dec 13 2018 - 09:04 PM.

[Lee200]

gliebzeit, on Dec 13 2018 - 07:47 PM, said:

Believe me, the last time someone put LSD in my Salisbury Steak ... I lost my grip!!

For the longest time, I thought it was a Saul's Berry LSD.  

Edited by Lee200, Dec 13 2018 - 09:11 PM.

[Alan Davies]

Interesting and a little easier to understand.
"Cam and Pawl LSDs were used on all F1 cars of the 1960s"  "the first use of a LSD other than the Cam and Pawl didn't occur until Ferrari used a Salisbury type LSD on their mid 1970s F1 cars"
"but strangely GPL does not model the Cam and Pawl LSD; rather, it models the Salisbury"

I thought GPL was accurately modeled! why did they put in LSD if it wasn't used in real life?

[Lee200]

We don't know why Papy used the Salisbury LSD instead of the Cam and Pawl LSD.  

[lore]

Interesting reading. Well done in many ways, but it looks to me as if some misunderstandings about LSD are still there (possibly just in my head, who knows...).

Let me try to explain my doubts with the help of some examples:

1) the two 1979 Ferrari drivers, Jody Scheckter and Gilles Villeneuve used to use 100% locked differentials on their cars (that's the reason Villeneuve could complete one entire lap of Zandvoort driving a car that very simply was missing one rear wheel). Both were famous (some times even infamous in fact, Scheckter a little bit earlier than Villeneuve, ca. 1973, Silverstone and Mosport for instance) for their mad oversteering and sideways skills.

2) I always recall the warnings written on the owners manual of my 1986 BMW 320i (e30) about its optional 40% LSD (very basically: "with an LSD the car will tend to rotate (to turn) with the throttle, specially on the wet, so watch out for oversteer");

3) my brothers Lotus 7 does have an LSD and it's literally oversteer prone;

4) I've driven go-karts (NO differential = 100% locked) and the first time I drove them it took me more than some laps to understand that I could have gone through many corners just flat out (BTW applying some "opposite lock") due to the amazing amount of oversteer they have.

With all that, the statement that "locked differentials promote understeer" looks to me incorrect. And I'm not saying "WRONG" just because I'm no engineer.
But, again, who knows...

Lorenzo

[Lee200]

Hi Lorenzo and thanks for your comments.  I'll try to clear up some things for you.

1. l don't doubt that Ferrari used locked differentials in 1979.  I was just saying that David Wright researched the use of limited slip differentials in F1 and found that the Cam and Pawl LSD was used until about the mid 1970s.  AFAIK, no one used a locked differential on 1960s F1 cars.  If you have a source that contradicts this, I'd like to see it.

2.  Just because a car is equipped with a LSD doesn't mean that you can't induce oversteer with throttle.  Even passenger cars with their limited power can oversteer in the wet or on ice if too much throttle is applied.

3.  Race cars, and the Lotus 7 is a good example of a low powered race car, can oversteer even with an LSD.  Again, it's all about how much throttle is applied and how the chassis suspension is set up.

4.  Your experience with carts is a good example of a locked differential.  I've never driven a cart, but my understanding of their cornering physics is that is important to set up the chassis so that the inside rear tire is lifted ("jacked") so that it's grip is reduced which also reduces the cart's inherent understeer from the locked differential.  This can be done by making the front end of the cart more flexible than the rear and by using a narrower track at the rear.

Race cars that have a locked differential do the same by using a larger rear roll bar.

5.  There is no doubt that locked differentials promote understeer as the two wheels turning at the same rate cause the car to want to go straight.  The literature is full of references that state this.  I've attached a good one for you to read (see the Spool section).

Attached Files

•  understanding_differentials.pdf   500.61K   22 downloads

[Robert Fleurke]

Very interesting thread. Keep it coming.

I always try to make a distinction between chassis/suspension induced oversteer and differential induced oversteer (rotation). Lee gives the example using a larger rear bar with locked differential. This will give you more oversteer balance, arguably compensating for the locked diff. But as I understand it in Lee's example, it's for jacking the inside rear tire so it's doesn't cause understeer, driving on the outside rear tire.

All in all, there's a lot for me still to learn and to understand...

Edited by Robert Fleurke, Dec 18 2018 - 07:25 AM.

[lore]

Thank you Lee for answering.

As said I'm no engineer. Yes, I know you're right about the literature. And one cannot onestly think that all that literature got it wrong.

Cheers


PS In a cart (at leas the ones I sat in, some 30 years old things by now) there is literally nothing you can set up in fact: no suspensions, no bars, nothing (maybe only play with tire pressure, but I've never gone that far). I guess the constructor already made the trick by keeping the chassis stiffer on the rear end and softer on the front end, for the good old rule of the mechanical grip.

Edited by lore, Dec 18 2018 - 08:56 AM.

[Lee200]

I'm not an engineer either Lorenzo so don't claim to be an expert.  I did spend two years studying engineering in college before changing to an easier major, drinking beer, and chasing girls which was a lot more fun.  In this I was successful as I'm now fat and have eight grandkids to show for it.  

Edited by Lee200, Dec 18 2018 - 09:09 AM.

[Lee200]

Even though GPL doesn't model the Cam and Pawl LSD, it's still interesting to see how it works.  This drawing depicts the Hewland style Cam and Pawl LSD.

When power is applied to the differential, the rotating set of cams (item 9) forces the pawls (item 10) to extend into the set of slots (item 11).  This locks the two wheels together.  When power is removed, the cams relax their force allowing the plungers to retract from the slots and the two wheels rotate independently.  Pretty simple actually.

Attached Files

•  Hewland Cam and Pawl LSD.gif   19.5K   37 downloads

Edited by Lee200, Dec 18 2018 - 08:41 PM.

[Lee200]

Just FYI for those who care and to finish up this discussion, here is more detailed information about how the Salisbury LSD works.

The Salisbury LSD is much more complicated and expensive than a Cam and Pawl LSD, but is vastly superior for reasons mentioned before.  It is based on a standard open differential, but modifies it to lock the two wheels together under specified conditions.

A standard open differential contains a set of four planetary (sometimes called spider) gears whose spin axles are rigidly fixed inside a cage.  However, the Salisbury differential splits the cage vertically into two halves which are then free to slide in and out relative to the two wheels.  When the cage half moves outward, it compresses a series of clutch disks.  Half of the clutch disks are locked to the differential's output gear while the other disks are locked to the wheel's half shaft.  As the clutch disks are pressed together, their increasing friction begins to lock the differential's output gear and wheel's half shaft together.  As a result, both wheels progressively lock and rotate together too.

Usually, a small amount of clutch disk friction is always desired so a small spring is added to compress the disks a bit.  The spring's force is called preload.  A Belleville type spring washer is normally used for this purpose.  GPL does not model preload.

Figure 1 is a diagram of a typical Salisbury differential.  The Belleville spring washer is labeled Item 2 "Belleville Clutch Plate".  The planetary gears are labeled Item 4 "Planet Pinions".  The planetary gear axles are labeled Item 5 "Cross Pins".  The output gear is labeled Item 6 "Sun Pinion".  The cage half is labeled Item 7 "Sun Pinion Ring".  The clutch disks are labeled Item 8 "Splined Clutch Plates".  The wheels and their half shafts aren't shown.

The inside edge of each cage half has angled slots (ramps) in which the planetary gear axles can slide fore and aft.  Figure 2 shows a real world cage half on its side with the ramps on the top edge.

When the throttle is on and engine torque is applied, the gear axle rotates rearward which forces the cage halves apart along the "power" ramp.  When the throttle is off, engine braking torque rotates the planetary gear axle in the forward direction and the cage halves are forced apart along the "coast" ramp.

Figure 3 shows a real world cage looking at the end of one of the planetary gear axles.  The  planetary gear itself is underneath and can't be seen.  The ramps on the inside edges of the two cage halves are clearly shown.  Note that the power and coast ramps have different angles.

Figure 4 depicts how the two cage halves are forced apart by planetary gear axle movement during throttle on acceleration.

By using different combinations of ramp angles and number of clutch disks, the differential designer can control how much the two wheels lock together under power on and off conditions.  It is possible to achieve complete lock which effectively is a locked differential, no lock which effectively is an open differential, or any amount of lock in between.  In the last case, the two wheels can still rotate at different rates if the reactive torque difference from the two tires exceeds the locking friction.

There are three ways for classifying Salisbury differentials.  The classification depends on the power and coast ramp angles:

1.0 Way--the coast ramp angle is 90 degrees.  This classification operates as an open differential when the throttle is off.
1.5 Way--the power and ramp angles are not the same.  This classification provides different locking for throttle on and off.  GPL models this classification.
2.0 Way--the power and ramp angle are the same.  This classification provides the same locking for throttle on and off.

Attached Files

•  Figure 1 Salisbury Differential Diagram.jpg   56.15K   30 downloads
•  Figure 2 Cage Half With Ramps.jpg   78.43K   26 downloads
•  Figure 3 Planet Gear Axle Between Ramps.jpg   44.8K   18 downloads
•  Figure 4 Acceleration Lock.jpg   47.08K   12 downloads

[leon_90]

Thanks Lee for the in-depth explanation

[JonnyA]

Yes, thanks Lee.

[Bob Catly]

Does a cam and pawl diff use clutches?  Or is it 100% locked whenever it's locked?