Black & Tan 332iT

[Bry5on]

+1

I'll join the "SSV1 slip joint modification" party if you end up doing it. Should also V-Band section 1 -> section 2 and section 2 -> section 3 for even easier removal/reassembly.

Also, I know you already sent the part to be manufactured, but did you consider bolting it to the muffler body by sandwiching it between the nuts for the hangers and the muffler mounting tabs?

No mounting tabs or bolts on my conversion muffler - I've got metal rod "J" tabs that the stock hangers thread through then the hanger bolts to the chassis floor. I don't think there's room in there either in any case, it kinda had to be where it landed.

[heinzboehmer]

If I'd have known better, I would be using SS v2 cats instead of v1, forum 'wisdom' be damned.

+1

I'll join the "SSV1 slip joint modification" party if you end up doing it. Should also V-Band section 1 -> section 2 and section 2 -> section 3 for even easier removal/reassembly.

Also, I know you already sent the part to be manufactured, but did you consider bolting it to the muffler body by sandwiching it between the nuts for the hangers and the muffler mounting tabs?

[Bry5on]

I also have a ZHP muffler and another M3 section 2 here that total 18lbs lighter and the muffler has a 32Hz damper attached, but I'd really like to see this project through before swapping mufflers to experience the effect of change. For science

will likely do the ZHP exhaust setup eventually, for the weight savings, ground clearance and power at the expense of some additional exhaust noise in the cabin.

Plus I can re-make the shittily toleranced SS exhaust pipes to center the exhaust while I'm in there. Hell, maybe even replace the shitty SS slip joint with a joint that will actually seal section 1 to section 2 too. If I'd have known better, I would be using SS v2 headers instead of v1, forum 'wisdom' be damned.

[Bry5on]

Well I picked up another cold on my way home from overseas, so I decided to pick up another project that I can mostly knock out on my computer.

So we've moved the natural frequency of the exhaust up away from idle speed when we affixed the exhaust to the transmission. This helped greatly with idle smoothness and eliminated some oscillations during shifting and clutch takeup from idle. There's still one very narrow frequency range which presents a small seat of the pants vibration between 1760 - 1800 rpm. Now that the tune is dialed in, I find this to be one of my more common engine speeds to drive in and pass through. The hypothesis is that this is the exhaust's new first mode and its natural frequency.

Practically speaking, we can't raise the natural frequency of the exhaust any higher as the transmission is the last thing to affix it to, and there's no real way to increase its area moment of inertia due to packaging constraints under the car. So we're left with having to apply some different physics, tuned mass dampers. Each of us has at least one tuned mass damper in the car attached to the front of the crankshaft that is preventing your crank from splitting in two at its natural frequency.

The way a natural frequency works is that when something is shaken (linearly in the case of the exhaust, rotationally in the case of the engine) at exactly the right frequency, it will KEEP shaking or even INCREASE shaking until failure.

The way a tuned mass damper works is the opposite. Using a combination of materials, one that is usually heavy, and another that has elasticity and inherent damping (typically rubber), you can create a tuned mass damper. By varying the properties of the damping material and the weight of the mass, you can create a material that will arrest vibration at a specific frequency, but otherwise sit idly at other frequencies.

The engineers who design cars all know this, and the BMW engineers who designed the e46 knew it too. That's why the non-m cars feature a tuned mass damper attached to the front end of the muffler (32Hz as it turns out). Too bad the e36 didn't use one and I'm using an e36 muffler..

Enter the project. So first let's convert that motor rpm into a frequency in Hz = 1780rpm/60 = 29.67 rps = 29.67 Hz. This is very close to the BMW specced 32Hz muffler damper, which shows we're on the right track. Let's just do a quick hand wavy first principles check. My exhaust is attached to the motor and transmission in roughly the same place as the non-m, so we can isolate our analysis to transmission-backward. Well the length of the exhaust-back is the same as the non-m, the pipe diameter is very close, so we should have roughly the same 'spring' stiffness from the pipes, with the M3 exhaust being stiffer, raising the natural frequency a bit higher than a non-m would be, probably a few Hz. Then I've got the e36 M3 muffler, which is about 5/3 the weight of the non-m muffler. This will bring the natural frequency down, likely more than the stiffer pipes brought it up. Cool, so this brings us somewhere below 32Hz. Empirically we've discovered that 29.67 Hz is right, and the math agrees in a hand wavy way.

A few weeks back, as part of a project with heinzboehmer to retrofit the driver's side euro dash cubby to the US cars, I went hunting and found a 30Hz mass damper attached to an e46. Curiously, this value is not specced for the e46 according to realoem, but it's bang on the frequency I need to tune out my remaining vibration. Here's what that looks like covered in a glove to keep my hands clean:



Sweet. Now we need to attach it to the muffler somehow. I have some scans of the underbody of the car from the suspension project, so let's use one of those to design a bracket. And since I only have a MIG for non-stainless steel and the exhaust is stainless, and I'd like to keep it rust-free, let's bolt it on instead of welding it on. Now I know what you're thinking, time for more of my favorite exhaust clamps! Unfortunately, the pipes are so close together that those clamps won't fit. So we'll need to use a few stainless steel hose clamps (bummer) until I can find a local friend with a nice TIG welder setup. Here's what that looks like:



And with the order placed with sendcutsend, we now wait a week or so until install time.

[Bry5on]

Did I miss it? Are you trying to fit an E39 rear subframe on E46 for multi link or otherwise? Couldn't this affect how Ackerman behaves as like, a line between the outer tie rod pivot point & front rotational axis (FCA outer ball joint) need to align with a specific spot of the rear suspension?

Yep, I’d like to make an integral link e46 rear suspension to correct for the inherent jacking problem and provide bump compliance without sacrificing toe control.

i don’t expect the rear suspension to have any effect on Ackerman as the rear axle locations and static toe won’t be changing. I do expect toe control will be better, so less unwanted rear steer, particularly to help with on-center steering feel and immediacy.

[YoitsTmac]

Did I miss it? Are you trying to fit an E39 rear subframe on E46 for multi link or otherwise? Couldn't this affect how Ackerman behaves as like, a line between the outer tie rod pivot point & front rotational axis (FCA outer ball joint) need to align with a specific spot of the rear suspension?

[Bry5on]

Well, some disappointing news. The e46 fuel tank lump on the passenger side that I was concerned about is in direct interference. And also the spring perch is a couple inches rearward on the e39.

All is not lost, there are options still. It’s just not easy now.

[Bry5on]

And we have our first scan of the e39 touring rear suspension on the ground: https://s.digital3dcloud.com/space/f...lang=en&loop=1

I managed to get the full LCA, both diff output flange locations, lower shock mount location, sway bar position, and spring pad location. Packaging in the touring was unfortunately too tight for me to get the upper control arms completely in the scan - I think I'll need to scan a subframe removed from a car to really get it.

[Bry5on]

Ok screw it, let’s just cover the hand wavy math:

Maximum G of 21.5” (546mm) CG before 100% load on outside tire. Sum moments about the tire:
0 = 1G * track width/2 - xG * CG height
xG = (1G*1525mm/2)/(546mm)
= 1.4G

Outside tire load is then, let’s assume it’s linear for simplicity:
50% @ 0G, 100% @ 1.4G

Let’s now assume that the tire cornering force relationship is linear with its vertical force, which is close enough for a first order approximation. Let’s now calculate the lift for 1G of cornering load using all the numbers:

1G = 86% load on outside tire, 24% on inside tire (total is 1700)
Outside cornering load = 1462lb
Inside cornering load = 408lb
Outside jacking = .855"
Inside jacking = -0.24"
Total jacking = 0.62"

And contrast this with the front, where at 1G we’ll see almost no jacking given the same load. If you’re lowered, you’re actually likely to be jacking DOWN! The worst of all.

[Bry5on]

Okay, jacking. Let's do some quick math.

Let's assume that the car weighs 3400lb with 50/50 weight distribution and for the sake of simplicity, it's cornering with 1G and 100% of the load on the outside tires. So 1700lb load on each of the two tires. We'll also assume bushings behave like ball joints, which is close enough for this analysis. Also for this analysis, we're going to assume that the suspension isn't moving, which isn't accurate but again, close enough for a first order approximation.

For axes, x will be left-right, y will be forward-aft and z will be up-down.
The lower control arm is 11.2 degrees from horizon
The upper control arm is 6.4 degrees from horizon
Both control arms are ~25 degrees looking down
Lower outer ball joint is 162mm high
Upper outer ball joint is 404mm high

Given that the angle of the rear control arms are in 3 dimensions, and each link can only take force along its axis we need to break this into a couple trigonometry calculations.

First, sum moments about lower link:

(404-162)*upper reaction_x = 162*Load
Upper reaction_x = 162/242*1700lb
Upper reaction_x  = 1,138.0165 lb tension

Sum moments about upper link:

Lower reaction_x =404/242*1700lb
Lower reaction_x  = 2,838.0165 lb compression

Check your math with som of forces in x:

2838 - 1138 = 1700 - check

Now we convert the loads from x to loads in xy. These are all increasing because math.

cos(25) = 2838/Lower_reaction_xy
Lower_reaction_xy = 3131lb
Upper_reaction_xy = 1256lb

Then we add the vertical component of the loads:

Lower reaction_xyz = 3131/cos(11.2)
Lower reaction_xyz = 3192lb
Upper reaction_xyz = 1256/cos(6.4)
Upper reaction_xyz = 1264lb

Now let’s make it easier to understand and normalize the forces for every 100lb of cornering force on the tire:

Lower/100lb = 188lb compression
Upper/100lb = 74lb tension

Now, finally, let’s perform jacking calculations. Both numbers add to jacking because of the angle from horizontal of each arm. Nice.

Jacking_lower/100lb = 188*sin(11.2)
Jacking_lower/100lb = 36.5lb
Jacking_upper/100lb = 74*sin(6.4)
Jacking_upper/100lb = 8.2lb

And sum them together:

Jacking/100lb = 44.7lb

So for every 100lb of cornering load on the outside tire, the e46 suspension is applying 45lb of jacking force to the chassis. That’s kinda nuts.

And now let’s turn this into displacement. Stock springs are 380lb/in (there are two of them)

Displacement/100lb = Jacking/100lb / Spring Rate = .06in

So finally, for every 100lb of cornering load on the tire (this is not much), the outside tire will increase rear ride height by 1/16”

We’ve ignored the opposing force from the inside tire, which counteracts some of the jacking, but its effect is much smaller because the load on that tire is much lower.

If you do some other hand wavy math that I’ll skip, a first order approximation of rear suspension lift due to jacking in the rear is .5-.75” at about 1G, which is about what you can expect from your tires. Yep, you’ll feel that. Twinkle toes rear suspension.

[Bry5on]

No worries. The same general concept applies, correct? Datalog and make iterative changes to the appropriate maps. I purchased a HTE tune so should be able to adjust part throttle response from there if i’m on the right track.

Mike

Kinda - you really need an engine dyno to get the cam angles correct with custom cams unfortunately. There’s really no replacement for that. More thorough than what I’ve been doing for sure.

[nuc1]

Realistically pretty unlikely. Either an engine dyno and a lot of time, or I’d need to daily that setup and iterate for several months. Sorry!

No worries. The same general concept applies, correct? Datalog and make iterative changes to the appropriate maps. I purchased a HTE tune so should be able to adjust part throttle response from there if i’m on the right track.

Mike

[heinzboehmer]

Pulling what I wrote in from the sister e46f thread:


So instead of just projecting the upper and lower control arms to a point and assuming that’s roughly where the IC is, I’m projecting those arms to a point, and using that point to define a line that extends outward to define the IC (and in turn, roll center). Very hard to describe in words, I can show you with a model open some time.

Worth noting that jacking is still an issue with the suspension design due to that lower control arm angle, and with the added fore/aft angle I’d been ignoring, jacking looks like it’s even worse. So the butt isn’t lying but it’s not from the roll center itself, just the placement of the members.

Aah I see. Think I got it, but down to peek at your models sometime.

[Bry5on]

Thank you! Instant buy. There's also a guy building a cybertruck vehicle of sorts (channel Project66). He did a phenomenal video talking about building optimal suspension setups, but I feel what's optimal depends on your weight distribution and where your CG is. Another great guy talks about building suspension but leaves the details out - still a great watch (channel XF Motorsports). He's absolutely unhinged and lets his dreams steer his engineering. Very cool stuff

Definitely will be pulling up some of those channels, thanks!

[Bry5on]

What changed in the way you were calculating roll center?

Pulling what I wrote in from the sister e46f thread:

The instant center is basically an imaginary point that defines the roll center when combined with the tire location and track width. It is an important part of handling characteristics. In previous posts I’d estimated the instant center location as the virtual point that the upper and lower control arms make, this was an error as I hadn’t considered the true angle of the upper and lower control arms when looking up/down on the car. As a result, the instant center is significantly farther outboard, which means the roll center is much lower and more reasonably placed than I had originally thought. I’ll have to redo the roll center calculation and update my suspension geometry/roll calculator. I’m disappointed in myself for missing this!

So instead of just projecting the upper and lower control arms to a point and assuming that’s roughly where the IC is, I’m projecting those arms to a point, and using that point to define a line that extends outward to define the IC (and in turn, roll center). Very hard to describe in words, I can show you with a model open some time.

Worth noting that jacking is still an issue with the suspension design due to that lower control arm angle, and with the added fore/aft angle I’d been ignoring, jacking looks like it’s even worse. So the butt isn’t lying but it’s not from the roll center itself, just the placement of the members.