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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: email@example.com. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
Last month we considered the very unusual front-drive Nissan Nismo Le Mans car. I mentioned that it would be interesting to see if they could keep front brakes in it.
Evidently the designers were well aware of the issue, and they have addressed it by fitting brakes (at least on the front) that can be quickly changed on a pit stop. The rotor and caliper can be quickly swapped out, without even the need to re-bleed. Thereís a good interview with Chief Engineer Zack Eakin on Jay Lenoís Garage at https://www.youtube.com/watch?v=fw_2N3tGMEg.
Weíll see how many sets they go through.
LONGITUDINAL AXLE LOCATION WITH MUMFORD LINKAGE LATERAL LOCATION
All the photos Iíve seen of example cars with a Mumford/Mallock setup all seem to be four link. You also mentioned two trailing links at each end of axle with other requisite provisions regarding roll and wedge in braking (right side to bracket welded to rear housing and rotating birdcage on left carrying left brake caliper; with other description of instant centers of both link pairs at or near axle height; longitudinal location of both ICís same, etc.).
Can a three link (two lower and single upper) be configured for the Mumford AND provide for roll and wedge considerations?
Basically, any longitudinal locating mechanism can be used with any lateral locating mechanism, provided of course that nothing hits anything else and you donít run any joints out of travel. So yes, you can use three longitudinal links rather than four. With three links, the system will operate bind-free with any link angles. With four links, the two on each side have to be equal-length and parallel unless there is at least one birdcage, or compliance in the system, as from rubber bushings.
Regardless of the lateral locating mechanism, a simple three-link system can provide zero roll and wedge change in braking or under power, but not both from the same geometry. The fundamental problem is that driveshaft torque is present under power but not under braking. The choice of lateral locating mechanism does not affect this, however.
The usual approach is to either not attempt any compensation for driveshaft torque, or split the difference and provide partial compensation for driveshaft torque and accept a bit of wedge change in braking. Further help can be had from the fact that an offset top link will level out some when the rear suspension extends in braking.
Still, we cannot get perfect operation from such a simple system. It is best to provide some way for braking forces to be reacted differently from propulsion forces. There are many possible ways to do this, but all of them involve more complexity than just having three trailing links.
The main reason for using the Mumford linkage is that it can provide a lower rear roll center than other options, for a given set of packaging constraints. The main reason for wanting the low roll center is that we will then be using more elastic roll resistance (a/r bar and/or spring rate) at the rear, other things being equal. The reason we want more rear elastic roll resistance is that this diminishes the wedge changes we get when the longitudinal locating linkage cannot compensate for driveshaft torque and also react braking forces symmetrically.
So, a really good longitudinal linkage works just fine with a Mumford linkage for lateral location, but at least potentially, it eliminates the main reason for using the Mumford.
Well, okay Ė one might then ask: if a builder doesnít want to try to design a longitudinal linkage that compensates for driveshaft torque without creating a roll moment in braking, or just canít figure out how to, or is prevented under the rules Ė is it better to go with a three-link or a parallel four-link? Iíd go with the three-link, unless thereís some structural or packaging issue that makes it impractical. With a four-link, either we have no anti-squat or anti-lift, or we have roll steer, or we have compliant bushings in the system. With a three-link, we can have any anti-squat and anti-lift we want, with very little roll steer, and still use rod ends throughout with no bind.
How important is compensating for driveshaft torque, and how much does it help to have more elastic roll resistance at the rear? We can get some idea with a quick calculation. Suppose we have a 2,000 pound car and the rear tires are propelling it with 1,000 pounds of thrust. This would represent something like the limit of traction for a front-engined car on street tires. Suppose that the rear roll center is about at axle height and the front roll center is near ground level. For roughly equal amounts of load transfer at front and rear, the front suspension will then have around 80% of the elastic roll resistance. If the tires have a radius of a foot, and the car has a 4:1 axle ratio, the driveshaft torque is 250 lb ft. If the front suspension reacts 80% of that, and the track is five feet, the load change at the front wheels is 250 lb ft times 80%, divided by 5 ft, or 40 pounds. The right front and left rear gain 40 pounds of load each, and the other two wheels lose 40 pounds each.
The change in crossweight is then 80 pounds, or 4%. On racing slicks, the forces could be as much as half again as great. The change in crossweight could then be 6%.
If the rear roll center is nearly as low as the front one, so that the rear has 50% of the elastic roll resistance, the load transfer at the front is only 25 pounds and the crossweight changes by 50 pounds, or 2.5%. In other words, by using a Mumford and a stiff anti-roll bar at the rear rather than a Panhard bar at axle height, we can reduce torque wedge by somewhere between a quarter and a half. This is a worthwhile improvement, but not as good as having linkage that compensates for driveshaft torque.
DIFFERENTIALS FOR FSAE
In the December 2014 newsletter, I mentioned that I would like to discuss differentials for FSAE cars at greater length.
I have at least some experience with the following options, in chain-drive FSAE cars:
1. Worm gear diff (Quaife, Zexel)
2. Clutch pack diff (Drexler)
3. Viscous diff (adapted from Mazda Miata)
4. Face cam diff (Suretrac, from a Honda ATV)
The problem with the worm gear design is that it doesnít provide much locking effect when the inside rear wheel is very lightly loaded. This can be helped some by preloading the gears, but the preload is highly wear-sensitive. The result is that when cornering near the limit, the car cannot be throttle steered. The inside wheel spins, and the tail stays planted.
The Drexler can be preloaded. It comes preloaded. When the preload is right, the car can put enough torque through the diff to get some further locking, even with the inside wheel very light. There is, however, an inevitable compromise between torque transfer when itís needed and the tendency of the preload to produce understeer. In the 2015 UNC Charlotte FSAE car, the team found it best to reduce preload torque to about half the value the unit had as supplied.
It should be noted that this car was a very light single-cylinder car with ten-inch wheels. The car, with driver, is around 500 pounds, compared to more like 650 for a typical four-cylinder car. The tires have about an 18 inch outside diameter, versus about 21 for a typical thirteen-inch tire. This means that for a similar effect on car behavior, that car would theoretically need the preload reduced by a factor of (18/21)(500/650), or to about 2/3 as much, compared to a four-cylinder car on 13ís. The amount of preload reduction actually used was the result of cut-and-try.
The team had a car with an adapted Mazda Miata viscous limited-slip. This type of diff has the advantage of having negligible locking torque when there is little speed difference, and still
generating locking torque when one wheel spins, even if the wheel thatís spinning is transmitting very little torque. It is entirely velocity sensitive.
The UNCC car with the viscous didnít perform as well as hoped. I attribute this to two factors. First, there was no way to adjust the aggressiveness of the viscous unit. Second, the team insisted on using traction control. The viscous unit works by allowing some wheelspin but generating a locking torque roughly proportional to the square of the amount of wheelspin, and also related somewhat to temperature. When the engine management wonít allow any significant wheelspin, the viscous diff canít work as intended. According to the students responsible for tuning the ECM, the abruptness of traction control intervention could be adjusted, but the trigger point, in terms of slip value where intervention began, could not.
The face cam unit remains a bit of a mystery to me, even after reading an SAE paper about it (#930672). It appears to me to be a kind of soft locker, rather than a true differential. That is, it will allow one wheel but not both to either overrun or underrun the carrier, and the average of the two output shaft speeds will not necessarily equal the carrier speed. The paper referenced does not include information relating locking torque to input or output torque. The team used this unit because it seemed promising, was able to put some power down with one wheel very light, and was available at a much lower price than a Drexler. I am not sure what degree of success the team had with this unit, but they went to a Drexler for the next car.
One car had a spool. A car with a spool requires a driver who can deal with its properties. Drivers with go kart experience tend to be good candidates. This particular car never was developed to the point where it was reliable. One problem was that it kept breaking driveshafts.
I still think somebody should try a locker Ė either a face dog locker like a Detroit locker or a roller clutch locker like the Weismann. Iíd appreciate hearing from anybody who is aware of anything like either of these being tried in FSAE.