Suspension suspense

[Arde]

If the lever is longer, you twist the bar less per unit of wheel movement, resulting in less force on the other lever. Here's a sway bar calculator from Circle Track - just click on the torsion/sway bar calculator link and you'll get linked to an xls file you can open and calculate to your heart's content.

http://www.circletrack.com/car_racing_calculators/torsion_bar_rate_calculator/viewall.html

Remember that the hole size can't be larger than the bar.

That is a shortcut because they have the other side of the bar fixed, but it helped me think about it right. Now I think about the body roll force applied as a pair of equal forces applied to the arms in opposite directions, and then all is clear. The sum of the forces times the arm length determines the angle (well you have include the spring forces as well, but I get it).

Thanks.

 

[kasbatts]

Sure, but the torsion bar connects to another arm of the same length on the other side, don't the leverages then cancel each other?

Exactly, and thus flattening the lean of the car.

When cornering, one side is getting twisted up as the car leans over, as it does the other ends wants to twist up as well, as the bar tries to flatten itself out.

It's all a bit hard to explain without waving my arms all over the place at the same time!

Go and bend a bit of thin wire into the shape of a sway bar and play with it, or find someone with a RC car, these usually have sway bars on them, they work exactly the same way, only smaller.


Good luck

 

[snj5]

Results

Picked up car today with the ST sway bars installed, as well as the Korman lowering springs and Biltiens. A very nice ride, can be a little stiff on potholed repaired roads, but very flat and responsive compared to stock. Terry Sayther even took it for a drive and commented how nice it is.
Although this may be a bit heretical, I am thinking of going back to the original springs as it may be a bit too low for everyday use.. Ideally, would like some stiffer springs at stock Euro ride height.

OBTW, the addition of the 265 five speed is terrific! It feels like it could sail all day down the freeway in 5th gear and cover some ground. Easy cruising at 72 mph at 3000rpm.

 

[Arde]

Although this may be a bit heretical, I am thinking of going back to the original springs as it may be a bit too low for everyday use.. Ideally, would like some stiffer springs at stock Euro ride height.

Wohooo, you just saved me that project.

 

[snj5]

Springs

Taking dQ's advice, I dialed up the Walloth website for springs. Indeed, it lists:

Front
coil spring, reinforced - 99 euros
progressive coil spring CSL -152 euros
Rear
coil spring standard version - 102 euros
coil spring rear progressive rate CSL - 125.40 euros

What does "reinforced" mean exactly?
Would the CSL progressives give a stock ride height, as my CSi is heavier?

thanks

 

[snj5]

Today the reinforced front and standard rear springs and rubber pads were ordered from W&N. The lowering springs were just to low for a daily driver, especially in the rear, although the ride was good. The new springs should be here in about a week or so. Will post side-by-side photos, and give a driving report.
The package will be the reinforced/stock W&N springs, large ST bars and Bilsteins using 16 staggered wheels and the standard 205/55 and 225/50 HD Contis.

And, off topic, but I've gotta say again the Getrag od 5 speed really adds to the enjoyment of the car. The car just feels like it could sail on forever down the highway.

 

[ScottAndrews]

Sure, but the torsion bar connects to another arm of the same length on the other side, don't the leverages then cancel each other?

Great Thread Arde.
The lever arm question seems interesting.

The spring rates on both sides of the car should be the same, so when the body rolls, the outside spring compresses. That pulls the outside bar lever down, and that in turn transfers the lever movement to the inside suspension, thereby also pulling down the inside lever and compressing that spring. The stiffer the sway bar, the more of this motion transfer.

If you consider an infinitely rigid bar, then the length of the lever arm is irrelevant from a motion transfer perspective. Where it IS relevant is that there needs to be enough lever arm length to not interfere with the motion of the suspension. If you had a super short lever with an infinitely rigid bar, then the bar and link would not allow the suspension to move at all. So the length of the lever must be sufficiently long to allow the bar to rotate freely over the full travel of the suspension.

Suppose the ideal was for the bar to rotate a maximum of 45 degrees (probably a lot more than it actually does rotate). If the lever arm is 100 mm long, then the vertical travel of the sway bar link is 100sin(45)=70.71 mm (2 3/4"). That's not much suspension travel. If the arm was, say 250 mm, then the vertical travel would be 250sin(45)=176mm (7 inches). That's probably way more than needed, but it illustrates the point.

Once that length is determined, then the stiffness of the bar will determine how much motion gets transferred. Since the longer lever arm results in more torque applied to the bar, you can determine, based on the weight of the car (at that corner) the amount of relative motion transfer (bar twist) you want, and the shear strength of the bar material, what the torsion modulus of the bar isl, and from that, the desired diameter of the bar.

In reality, I suspect the bigger the bar the better, but the bigger the bar, the more difficult it is to fit, and the heavier it is. So the result is a compromise.

 

[bavbob]

My question to Arde is how he likes the Dinan's on his E24. I put them in mine here in Ma and I love the stance but the ride is killer on our roads. I seriously think of switching back when I have the time to do it.

 

[Arde]

My question to Arde is how he likes the Dinan's on his E24. I put them in mine here in Ma and I love the stance but the ride is killer on our roads. I seriously think of switching back when I have the time to do it.

I love that suspension setup, I do not drive on harsh roads to be fair, and I have not gone to low profile tires, so I can't complain. It is harder than the e9 suspension but in general the E24 seems optimized for driving 20-30 MPH above the E9 optimal speed.

 

[JFENG]

I suspect the bigger the bar the better

Don’t forget that too much weight transfer can overload the availble grip on the outside tire. If on the front outside the car will become more responsive to steering inputs, but understeer more as you approach the limit. If on the rear outside then the rear will lose grip and result in oversteer as you approach the limit. This can be pretty exciting in the wet or on other lower mu surfaces.

I use the standard ST front/rear bar setup and set the rear on the softest position (combined with Carl Nelson’s springs). For me this gives a more crisp turn in without too much tail happiness in the wet or at the limit. It’s also nice because it compensates for the stiffer front bar (that increases understeer).

For the record. I never drive more than 6-7/10ths on public roads. Would love to try the coil overs fromVSR1, but that comes after the big jobs.

 

[ScottAndrews]

Don’t forget that too much weight transfer can overload the availble grip on the outside tire. If on the front outside the car will become more responsive to steering inputs, but understeer more as you approach the limit. If on the rear outside then the rear will lose grip and result in oversteer as you approach the limit. This can be pretty exciting in the wet or on other lower mu surfaces.

Interesting point. By pulling the inside wheel down the normal force on the outside tire goes down, thereby reducing its friction on the road. But then the weight on the inside tire is going up, increasing the inside tire friction. So, somewhere in there is an optimal distribution of weight and traction on both tires.

This also makes clear why the rear bar has different settings. These change the effective lever arm, and thus how much weight is transferred for a given bar stiffness. Could probably do that up front as well...but there isn't a lot of room there (or maybe the effect on the rear is more noticeable).

Once the lever arms are long enough to allow full suspension travel, then the stiffness of the bar and the lever arm length will affect the degree of weight transfer.

So the minimum lever length is fixed by suspension travel, and then the combination of bar stiffness and any additional lever length determine the handling.

I have a 29 mm ST bar on the front of my E24, and a thinner bar (can't recall the diameter) on the rear. I always wondered about the three holes on the back bar. I noticed the other day that the bar struts are onthe middle setting, but they are slightly canted forward at the top. I think I'll try moving them to the front (softer) setting. Running ST springs and Bilstein Sport shocks on this setup. Ride is pretty hard, but handling is great! Drives like a giant Go-Kart!

 

[JFENG]

By pulling the inside wheel down the normal force on the outside tire goes down,

IMHO, anti-roll bars transfer weight from the inside to the outside, which is the opposite of your description.

W/o a bar, the inside suspension will extend to keep the inside tire pressed against the road.

With a bar, the inside suspension is lifted/compressed due to the compressed outside suspension. This reduces the pressure of the inside tire onto the road.

 

[JFENG]

when the body rolls, the outside spring compresses. That pulls the outside bar lever down,

On an E9, suspension compression (outside) pushes the end of the anti roll bar end up not down.

 

[ScottAndrews]

On an E9, suspension compression (outside) pushes the end of the anti roll bar end up not down.

You are correct about the direction of movement of the bar levers. I was describing it from the perspective of the wheels. As the outer bar lever gets pushed up, the inner lever moves up, thereby compressing the spring and causing the inner wheel to move down toward the GROUND, not down from the BODY.

I am not convinced that the weight transfer is as you describe. You stated: "With a bar, the inside suspension is lifted/compressed due to the compressed outside suspension. This reduces the pressure of the inside tire onto the road." I think this last part is incorrect.
First off, if the bar reduces the weight onthe inside wheel, as you state, then more cornering will reduce the weight more, and the inside wheels will lift of the ground, which is exactly what the bar is trying to prevent.

Yes, the bar compresses the inside wheel suspension, but unless the car CG is so high that there is no weight on the inside wheels the compressed inside suspension will cause the body to roll back toward the inside, thereby increasing the weight on the inside wheels, and reducing the weight on the outside wheels.

It is not as if the weight gets transferred one way and then the other. Instead it is a dynamic thing. As the car tries to roll, the roll force pushes the bar up and this then compresses the inside suspension, thereby REDUCING the weight shift to the OUTSIDE. Sort of a dynamic feedback system.

Note too, that if the CG is such that the inside tire lifts off the ground, then the bar will just lift the inside wheels, but if there is no restoring force, then compressing the inside springs and lifting the inside wheels toward the body will do nothing to cause the car to roll back toward the inside. Either the car will drive circus style, on two wheels, or it will roll over. The bar only works because the CG is usually lower than the roll center, so left to its own devices, the car will roll so as to keep all of the wheels on the ground.

 

[ScottAndrews]

Too cold to work on my E24, so I spent some time looking at the physics of the roll bar. Under no lateral load the chassis and forces look like this:

Here, RC is the roll center, GC is the gravitational center, Ho is the distance between RC and GC, and Xo is the distance between the center of the vehicle and the top of each spring (yes, this is a somewhat simplified suspension). Notice that the weight of the vehicle is split evenly between each wheel, and the deflection of the springs (YR and YL) is based on the spring constant and half the weight of the car.
Here is a car without any roll bar, when exposed to a lateral force Fc. This force acts on the GC, and since the GC is above the RC, it applies a torque Tc to the body. This torque is the lateral force Fc times the distance Ho between RC and GC. This torque then applies a downward force on one spring and an upward force on the other. These forces are equal and opposite, and are just the lateral force translated (via the torque equation) out to the part of the body pressing on the springs. To avoid a bunch of vector jazz, I simplified this by assuming the distance from the roll center to the spring is the same as the distance from the center of the car to the spring, and that the roll force is directly downward on the spring. So, roughly, the force on the spring is given by Fc(Ho/Xo). Note, because the body is free to roll, it does so, causing the lower arms to assume some angular relationship with the body, and, because of the forces, one spring compresses and the other extends. I have obviously exaggerated things here to show the effect.

Note that the force WL on the ground on the left side is now increased by The force applied to the spring, and the force WL on the left side is decreased by this same amount. Note too, as a cross check, that the sum of these forces equals the weight of the car, which it must, since the car is being held up by the ground and it is neither going through the ground, nor is it floating away.

Note too that while the force FC comes from the lateral cornering force applied to the GC, this force is carried by the deflection of the springs, which is proportional to the applied force. This is important, since this deflection is what the roll bar is going to control, and the amount of force it applies to the system depends on the deflection of the spring by the bar, and the spring constant Ks.

Now, let's introduce the roll bar. The roll bar is attached to the body, so it tries to roll with the body. In doing so, the lever end on the left side is deflected upwards as the angle between the body and the lower arm changes. This deflection is a result of the link (shown in green) having a fixed length, so wjhenm the arm moves the link moves and the arm must deflect. This deflection is translated to the right side of the car by the (here infinitely stiff) roll bar. So the roll bar pulls up the lower arm by the same amount the left arm was deflected.
Here is how this looks.

Note that the infinitely stiff bar has caused the deflection on theft side to be translated to the right side, and since the car must still sit on both wheels, the deflection (not the roll, but the deflection, of the lower arms) is about half of what it was with no roll bar. More importantly, the infinitely stiff bar means that the deflection on the right must be the same as the left, so all of the body roll is eliminated. What is really happening here is that the lateral force causing the torque on the body has been re-directed to deflect the springs on both sides of the car, causing the car to actually lower itself by an amount related to the spring rates and the lateral force on the car. Weird, but logical.. Note too that the weight on the left is different from the right by the difference between the roll induced force on the spring and the deflection of the bar times the spring constant. So, while there's still more weight on the left wheel, that increased weight, that would have occurred with no bar, is reduced by the force from the bar deflecting the spring (the KsYbar term), and the weight on the right wheel is increased by that same amount And, as must be the case, the total weight is still the weight of the car.

Now, obviously we do not have infinitely stiff roll bars, so in reality, the bar twists slightly, and not all of the body roll force is converted into lowering the car against its springs. The stiffness of the bar and the length of the bar levers determines how much roll feedback the system has.

 

[Arde]

Good perspectives. From the above, and what I learned since the thread start, Mike Goble is right that the stiffness increases with the fourth power of the sway bar diameter, that is helpful when choosing what bar to use starting from stock... I learned that the arms forces do not cancel each other, the force is inversely proportional to the arm's lengths...
Finally, the oversteer/understeer is not determined by the rear bar stiffness per se, but rather by the ratio between the front and rear bars. That explains why there is no real need to adjust the front, you can just adjust the rear to control the ratio.
Overall sway bars reduce body roll, and create the illusion of higher spring rate during cornering, which are both good.
This is all E9 1970s stuff, looks like nowadays there are active sway bar systems. Fat chance I will let firmware control the forces applied to my suspension during cornering . Gravity and torsion always work, even when power and the computer are out...

 

[Arde]

Too cold to work on my E24, so I spent some time looking at the physics of the roll bar. Under no lateral load the chassis and forces look like this:
View attachment 174349
Here, RC is the roll center, GC is the gravitational center, Ho is the distance between RC and GC, and Xo is the distance between the center of the vehicle and the top of each spring (yes, this is a somewhat simplified suspension). Notice that the weight of the vehicle is split evenly between each wheel, and the deflection of the springs (YR and YL) is based on the spring constant and half the weight of the car.
Here is a car without any roll bar, when exposed to a lateral force Fc. This force acts on the GC, and since the GC is above the RC, it applies a torque Tc to the body. This torque is the lateral force Fc times the distance Ho between RC and GC. This torque then applies a downward force on one spring and an upward force on the other. These forces are equal and opposite, and are just the lateral force translated (via the torque equation) out to the part of the body pressing on the springs. To avoid a bunch of vector jazz, I simplified this by assuming the distance from the roll center to the spring is the same as the distance from the center of the car to the spring, and that the roll force is directly downward on the spring. So, roughly, the force on the spring is given by Fc(Ho/Xo). Note, because the body is free to roll, it does so, causing the lower arms to assume some angular relationship with the body, and, because of the forces, one spring compresses and the other extends. I have obviously exaggerated things here to show the effect.

View attachment 174350
Note that the force WL on the ground on the left side is now increased by The force applied to the spring, and the force WL on the left side is decreased by this same amount. Note too, as a cross check, that the sum of these forces equals the weight of the car, which it must, since the car is being held up by the ground and it is neither going through the ground, nor is it floating away.

Note too that while the force FC comes from the lateral cornering force applied to the GC, this force is carried by the deflection of the springs, which is proportional to the applied force. This is important, since this deflection is what the roll bar is going to control, and the amount of force it applies to the system depends on the deflection of the spring by the bar, and the spring constant Ks.

Now, let's introduce the roll bar. The roll bar is attached to the body, so it tries to roll with the body. In doing so, the lever end on the left side is deflected upwards as the angle between the body and the lower arm changes. This deflection is a result of the link (shown in green) having a fixed length, so wjhenm the arm moves the link moves and the arm must deflect. This deflection is translated to the right side of the car by the (here infinitely stiff) roll bar. So the roll bar pulls up the lower arm by the same amount the left arm was deflected.
Here is how this looks.

View attachment 174352
Note that the infinitely stiff bar has caused the deflection on theft side to be translated to the right side, and since the car must still sit on both wheels, the deflection (not the roll, but the deflection, of the lower arms) is about half of what it was with no roll bar. More importantly, the infinitely stiff bar means that the deflection on the right must be the same as the left, so all of the body roll is eliminated. What is really happening here is that the lateral force causing the torque on the body has been re-directed to deflect the springs on both sides of the car, causing the car to actually lower itself by an amount related to the spring rates and the lateral force on the car. Weird, but logical.. Note too that the weight on the left is different from the right by the difference between the roll induced force on the spring and the deflection of the bar times the spring constant. So, while there's still more weight on the left wheel, that increased weight, that would have occurred with no bar, is reduced by the force from the bar deflecting the spring (the KsYbar term), and the weight on the right wheel is increased by that same amount And, as must be the case, the total weight is still the weight of the car.

Now, obviously we do not have infinitely stiff roll bars, so in reality, the bar twists slightly, and not all of the body roll force is converted into lowering the car against its springs. The stiffness of the bar and the length of the bar levers determines how much roll feedback the system has.

Good analysis. Explains why zero body roll and deflection is half of the no sway bar case. Surprising that the weight is still uneven but makes sense because the lateral force is causing that, and FC is an external force that is still there doing its thing regardless of sway bar. You cannot make it disappear.

I am intrigued by the role of the shock absorbers, as the system cannot be just springs (as anybody who had the E9 shock tower fail can tell). I assume shook absorbers apply forces related to the derivative of the displacement bit not the displacement? At the onset of cornering it is all about the derivative, not a static force case, right?

 

[ScottAndrews]

I am intrigued by the role of the shock absorbers, as the system cannot be just springs (as anybody who had the E9 shock tower fail can tell). I assume shook absorbers apply forces related to the derivative of the displacement bit not the displacement? At the onset of cornering it is all about the derivative, not a static force case, right?

Yes. Technically the shocks will only have any effect in transient operation. That is, when the forces are changing over time (the derivative of which you speak! ). Imagine the figure above in super slow motion. That would not require any damping. But try that in real time and the car would jiggle and bounce all over with every turn. In addition, a car with just springs would encounter all sorts of resonances and "ringing" (that is, continued oscillations after every transient input). The shocks also slow down the roll effect, both by damping the roll itself, and by damping the reaction of the springs.

Here is a good example the effect of damping.

 

[ScottAndrews]

I'm sure there are plenty of ME graduate theses dealing with the subtleties of suspension dynamics. The lateral cornering force is parallel tot he ground, and this is not orthogonal to the car body as the body rolls, so part of that force acts to lift the body up and out from the center of the turn. The springs and shocks are not vertical. The force imparted to the springs may not be orthogonal to the springs, the lower arms are not usually horizontal at rest, the roll causes the lower arms to move the wheels inward and outward from the body, changing the camber, and we have not considered the effects of caster and camber, just to list a few simplifications.

It would be fun to develop an accurate Matlab model of the E9 suspension and better understand these things. Maybe I'll do that when I finally retire!!!

As for electrically controlled suspension...I agree about the reliability of gravity and torsion!
As part of my work as a technical expert on car systems for patent litigation, I had the opportunity to drive a Bentley Bentayga. That car is based on the Audi Q7 platform, except among other things, they have a fully dynamic suspension. The dampers, and maybe even the spring rates are electronically controlled. So under some operating conditions the suspension has super compliance. For example when rock crawling, (which I'm sure any self respecting Bentley owner is likely to do every day crossing the moors to the castle!), the suspension is compliant and flexible, allowing huge wheel travel. At highway speeds on good pavement, the car is solid as a rock, and handles like it weighs 3.5K pounds instead of the 5K or so it actually weighs. The 626 hp 640 lb-ft torque W12 engine is nice too!

 

[JFENG]

compressing the spring and causing the inner wheel to move down toward the GROUND, not down from the BODY.

Did you mean, “UP from the ground, “ and not down from the body?