Black & Tan 332iT

[Bry5on]

So I took another e46 friend's advice while I was under the car to swap out some parts.

First, I replaced the header exhaust clamps with a factory BMW part, because a bracket that is braced on both top and bottom of the pipes should be way stiffer than one that's just braced on the bottom. I used PNs 18307850435 and 18307850436 from the F80 M3 which has similar diameter pipes to the SSv1s. Here's what that looks like:





Then I took some measurements of the frequency response of the exhaust while smacking it. I did this in a not-great-but-probably-fine way by holding the iPhone to the exhaust and smacking it locally with my hand in the horizontal direction right next to where the phone was. I used the iPhone's internal accelerometer which only samples up to 50Hz. This produced some plots of oscillation frequencies at various points.

The muffler, as expected a very low frequency under 10Hz, this just is what it is, too low to damp:


The resonator, about 25Hz:


The cat(s), about 20Hz and just above 30Hz:

Then I decided that while I was double-bracketing things, I'd escalate the situation by doubling up the rear strap. This was pretty difficult to get in there, just in front of the cats, but what's done is done. For science.



Then I repeated the not-great-but-probably-fine test to see if there was a difference. Not much, and here are the plots:




I think that if there were another gain to be had, it would be by stiffening up the brace to the transmission and also attaching the brace to both pipes. There's not much room there so this will have to do.

And while we're on the topic of exhausts, I did another fun mini-experiment. I'd noticed that the rasp rpm seems to be lower on cold start than warm start, and I guessed that this was correlated with exhaust temperature. So I watched my EGT gauge while rasp happened and created a few data points:
- 2500rpm at 280*C EGT
- 2900rpm at 460*C EGT
- 3000rpm at 530*C EGT

The equation for the speed of sound is 331.3 * SQRT(1 + (Temp*C / 273.15) ). Let's plug in these temperature numbers and use the 280*C data point as our baseline. We get 471.5, 542.8 and 568.1 m/s. Well, 2900rpm is 16% higher than 2500rpm and 3000 is 20% higher. When you normalize the results of the speed of sound against that 280*C baseline, you see that 542.8 is 15% higher and 568.1 is 20% higher than 471.5 m/s. So, the rasp rpm increases as the temperature in the exhaust increases. I did some more math to see if I could simply correlate this with the difference in header lengths, but alas, nothing simple emerged in front of me. I thought at least it was a fun speed of sound experiment and validation.

[Bry5on]

Oh baby, we got it. Hypothesis #2 proves correct. So when I was calculating natural frequencies, I had considered two ways to perform the calculation. First, based on imbalance of the motor, was strictly with RPM. The second is based on the number of torque producing ignition events. So for a 4 stroke 6 cylinder motor, there are three ignition events per RPM. This means that if we wanted to figure out the excitation frequency of ignition events, we'd need to multiply the engine RPM by 3 before dividing by 60 to get a number in Hz. So let's do that - 1780rpm * 3 / (60 s/m) = 89Hz. What is the frequency of the middle damper in the non-m e46? 95Hz, which correlates to a 1900rpm excitation.

We also noticed last time that I could excite the first mode of the exhaust by hand, and contemplated a few different ways of measuring it (video and counting frames, strobe light, etc). Well, I think I found the easy way. Remove the damper and put a piece of metal to the side of the exhaust, then shake the exhaust by hand so that you're just able to get it to hit the metal and make a 'tink' noise. Do this constantly for 30s or so while exciting the natural frequency by shaking the tail pipes left to right. This is pretty easy to do since it's the low effort frequency to get the exhaust to displace enough to hit the metal. Then upload this video to ChatGPT and ask it to count the number of tink noises in the video and tell you the average number of tink noises per second. This is the exhaust's measured first mode. What did we measure? 4.7Hz - way lower than anything we'd been contemplating earlier. This is definitely not the frequency I'm feeling. Which means that the excitation frequency I'm feeling has got to be a second or third mode.

So this morning I made a trip to the junk yard to cut off a mounting bracket from a non-m e46 and take its 95Hz tuned mass damper. I figured the transmissibility of the damper probably has a wide enough range that it'll capture a few Hz to either end of its tuned frequency, so this might be enough to damp the vibration. Here's where damper is cut off:



And since I still don't have a stainless TIG setup, let's find a way to prove this theory first. What do I have? A second muffler bracket. Let's bend that to the right orientation and use some of the extra hose clamps I've got lying around to fix it in place.







And what's the verdict? This little vibration is nearly GONE. There's a tiiiny bit of it left around 1750Hz, so I'm going to order a 92Hz damper (PN: 18308639585) from the F12 6 series, which is the closest frequency I could find in the BMW catalog. That should kill it dead. Already I'm pretty confident saying that this has got to be the smoothest s54 powered BMW in existence under 4k or so until the airbox does its thing.

[Bry5on]

Bracket showed up already and went in - needed a little clearancing as it was too close to the subframe mount washer. I've only done one test drive in the rain, and I haven't really driven the car much in three weeks, so a bit hard to tell if/where there's a change, but it didn't kill the resonance around 1780rpm, so I've got to keep chasing that one. It does seem smoother under 4-5krpm, particularly during rev matching, and I think I'm noticing that there's less clutch engagement feel and that it's a lot harder to shift poorly and upset the drivetrain (meaning shifts are smoother, even when I'm ham-footed). Time will tell! And maybe I need that second damper as well.

[Bry5on]

I was basically saying that if there was a 1ft long tube, you could weld like a 0.25” thick metal sheet perpendicular to the pipe to increase the rigidity of the pipe at the 6” mark. Could I not just use a microphone to record the frequency to understand what length pipes I'd want to add?

And with modern M cars, the exhaust is hanging and not having any rigidity outside of the pipe thickness, right? You're referring more to a coupling effect, right? If the exhaust was hard mounted to the chassis, I could understand what you're saying in terms of rigidity, but it's hanging.

You can definitely increase rigidity in-plane by welding a sheet along the length of the tube, yep. That'll bring the natural frequency higher in the left-right direction if the sheet is horizontal. This would be a similar effect to having a dual exhaust where the pipes are spread further from each other but re-connected at the ends (engine, muffler, resonator) like you see in the more modern M cars. The modern M cars are suspended mostly just like the e46 M3 (well the e9x bolts to the tranny, so it's closer to the non-m). The rigidity comes all from the shape of the exhaust itself and the resulting stiffness of having the pipes spaced apart. Area moment of inertia is the technical engineering term for understanding the stiffness of different types of members. You'll note that the modern non-m cars with single tube exhausts still have dampers because they do not have the benefit of two pipes spaced far apart.

Placing a microphone (your phone would work for this) in the car and recording the FFT or frequency signature of the noise should show a peak at some frequency. This would be the target frequency for your Helmholtz resonator. Plug that frequency and an exhaust temperature of 600F or so into a calculator and you can turn that frequency into a wavelength. Divide that wavelength by 4 and that would be the target length of your pipe to cancel out the annoying drone frequency you've got.

Finally getting some time to go through your journal and look at all this PDC retrofit stuff.

Super interesting with disassembling the switch center and looking at how the board identifies various buttons.


Even on the standard M3 switch sender that has all the buttons except the rear power sunblind... When you disassemble the switch center, there's an empty socket still available. Couldn't we still use that instead of having to get the more expensive variant with the sunblind button?

Also, very curious when you added the PDC button that sends the 12 volt signal and you added the additional white wire on the board... I couldn't tell from the pictures of the text, but does that mean you ended up hijacking a spare empty unused pin slot on the switch center plug receptacle so that the pdc harness could be wired into the main switch center plug for a plug and Play solution?

This is the kind of stuff I used to do before I had kids lol now three kids later I'll hardly have time to even diagnose my own problems.

I love the solution of using the f10 sensors so I'll save those part numbers. Since I'm using the M3 front bumper that doesn't have the bumper strip, I like the idea of using the f10 sensors with the brackets for a more flush solution. It sucks that I can't hide them in a bumper strip like on the non-M bumpers.

The switch center circuit board is the same on both of those switch center versions you identified, but you need the front panel with the final hole to fit the button into. You could router this hole or something, but then you'd need to deal with the soft touch plastic that we all know and love.

Adding the PDC button - yes the wires added mean that I hijacked empty pins 8 and 9 in the switch center plug. The plug is the same on the e39, etc and pins 8 and 9 are the pins that are used for the PDC function. Kinda neat that the pin assignment ended up following the factory numbers without messing with the e46 existing functionality. It's plug and play. Hope that makes sense.

The F10 sensors work great in the bumper (not the strip) too, as you can see I did that for the rear bumper inner sensors by punching holes through the painted part and purchasing F10 style paint-matched PDC sensors. Really barely visible on a black car.

It was an involved project! Took time both on the planning and execution fronts, and I'm not sure I'd do it again but it was fun.

[nextelbuddy]

That was more work than I expected. It turns out the sport button gets a GROUND signal from the DME, where the PDC sends a 12V signal. Also the button needed some serious trimming, epoxying, etc on the back side to fit. Thanks heinzboehmer for buying another M3 and letting me pillage it the day after you picked it up!

Regardless, perseverance paid off. It’s ready for the PDC harness

Finally getting some time to go through your journal and look at all this PDC retrofit stuff.

Super interesting with disassembling the switch center and looking at how the board identifies various buttons.


Even on the standard M3 switch sender that has all the buttons except the rear power sunblind... When you disassemble the switch center, there's an empty socket still available. Couldn't we still use that instead of having to get the more expensive variant with the sunblind button?

Also, very curious when you added the PDC button that sends the 12 volt signal and you added the additional white wire on the board... I couldn't tell from the pictures of the text, but does that mean you ended up hijacking a spare empty unused pin slot on the switch center plug receptacle so that the pdc harness could be wired into the main switch center plug for a plug and Play solution?

This is the kind of stuff I used to do before I had kids lol now three kids later I'll hardly have time to even diagnose my own problems.

I love the solution of using the f10 sensors so I'll save those part numbers. Since I'm using the M3 front bumper that doesn't have the bumper strip, I like the idea of using the f10 sensors with the brackets for a more flush solution. It sucks that I can't hide them in a bumper strip like on the non-M bumpers.

[YoitsTmac]

You can certainly add another resonating part to the exhaust, like welding a tuning fork on which would add new resonant frequencies but not necessarily remove or materially affect any existing ones. This mechanical resonance is a bit different than acoustic resonance but they're very related in concept (wave propagation vs mechanical stiffness). You can tune out acoustic resonances by adding pipes of certain length (quarter wave length) to effectively cancel out certain frequencies, like the damper is doing for mechanical resonance. To kill an acoustic resonance you'd need to understand the frequency of the sound that's loud, rather than just the speed of the motor, even though they're related.

You'll also note that the modern M cars have exhausts without dampers but they do not resonate (in these frequency ranges). This is because the pipes are far apart from each other, so they are stiff like an I beam. Our exhausts are flimsy because the pipes are so close together for the whole length. The stiffer the 'beam', the higher the natural frequency. Ideally it's so high that the first mode is higher than the engine's operating rpm.

Think of how much easier a 2x4 or 2x6 bends along its thin edge than its thick edge

I was basically saying that if there was a 1ft long tube, you could weld like a 0.25” thick metal sheet perpendicular to the pipe to increase the rigidity of the pipe at the 6” mark. Could I not just use a microphone to record the frequency to understand what length pipes I'd want to add?

And with modern M cars, the exhaust is hanging and not having any rigidity outside of the pipe thickness, right? You're referring more to a coupling effect, right? If the exhaust was hard mounted to the chassis, I could understand what you're saying in terms of rigidity, but it's hanging.

[Bry5on]

How come welding a very rigid piece of metal in the middle of large, uninterrupted pieces of the exhaust can't achieve the same effect? I'm not a physics or mechanical major, but i thought doing so would change the length of the vibrating piece and therefore the resonant frequency. IE. A 1ft piece resonates at 1hz but two 0.5ft pieces will resonate at 2hz.


This was my original idea to kill my headache inducing drone at 2500-2800rpm on my M3, but I ended up buying a stock section 2 (still to be installed)

You can certainly add another resonating part to the exhaust, like welding a tuning fork on which would add new resonant frequencies but not necessarily remove or materially affect any existing ones. This mechanical resonance is a bit different than acoustic resonance but they’re very related in concept (wave propagation vs mechanical stiffness). You can tune out acoustic resonances by adding pipes of certain length (quarter wave length) to effectively cancel out certain frequencies, like the damper is doing for mechanical resonance. To kill an acoustic resonance you’d need to understand the frequency of the sound that’s loud, rather than just the speed of the motor, even though they’re related.

You’ll also note that the modern M cars have exhausts without dampers but they do not resonate (in these frequency ranges). This is because the pipes are far apart from each other, so they are stiff like an I beam. Our exhausts are flimsy because the pipes are so close together for the whole length. The stiffer the ‘beam’, the higher the natural frequency. Ideally it’s so high that the first mode is higher than the engine’s operating rpm.

Think of how much easier a 2x4 or 2x6 bends along its thin edge than its thick edge

[YoitsTmac]

Oh wow you're right! I'd mistakenly thought that both auto and manual tied to the transmission. Yes, this would definitely make a difference! The natural frequencies would be slightly shifted higher for the manual in this case, something like ~2100 and ~5800 rpm instead of 1900 and 5400, if I had to guess. This is due to having a shorter suspended length (to the factor of 1/L^2).

How come welding a very rigid piece of metal in the middle of large, uninterrupted pieces of the exhaust can't achieve the same effect? I'm not a physics or mechanical major, but i thought doing so would change the length of the vibrating piece and therefore the resonant frequency. IE. A 1ft piece resonates at 1hz but two 0.5ft pieces will resonate at 2hz.


This was my original idea to kill my headache inducing drone at 2500-2800rpm on my M3, but I ended up buying a stock section 2 (still to be installed)

[Bry5on]

Could it be because the MT connects to the transmission where the auto just connects to itself up in that area?

Oh wow you're right! I'd mistakenly thought that both auto and manual tied to the transmission. Yes, this would definitely make a difference! The natural frequencies would be slightly shifted higher for the manual in this case, something like ~2100 and ~5800 rpm instead of 1900 and 5400, if I had to guess. This is due to having a shorter suspended length (to the factor of 1/L^2).

[George Hill]

Could it be because the MT connects to the transmission where the auto just connects to itself up in that area?

[Bry5on]

While we're talking about exhaust resonance, for the fellow nerds out there:

A non-m e46 actually has two dampers if it's an automatic and one damper if it's a manual. So an auto e46 should feel smoother throughout the rev band than a manual because the exhaust system is otherwise identical (weight, size, shape, supports). The automatic has both #4 (at muffler) and #12 (at resonator) dampers in this image, where the manual only has #12.



Here's the nerd part: The muffler damper is tuned to 32Hz and the resonator damper is tuned to 60Hz. In an earlier thread we discussed first, second, third, etc frequency resonant modes/natural frequencies. A rough approximation for the second and third modes is 2* and 3* the first natural frequency due to the mass being concentrated at the end of the exhaust. Recall this image (it's technically slightly incorrect, but you get the idea) and note that the largest oscillations for the first and third mode are at the END of the vibrating member, while the second mode oscillates at the MIDDLE of the vibrating member:



So here we can see the the non-m e46 has a first resonant mode around 32Hz, a second mode around 60Hz and a third mode around 90Hz. This corresponds to 1920rpm, 3600rpm and 5400rpm respectively.

So why the difference between manual and automatic? Likely that the vibrations higher in the rev range around 5400rpm make the engine feel more sporty, and the manual car is the sporty version, so they left the damper out that would have otherwise arrested the first and third mode. The automatic has dampers that should be arresting all primary natural frequencies of the exhaust that are excited by the rotation and firing of the engine. This is one of the major things that makes the automatic cars so buttery smooth.

Thanks for reading, hope this was as interesting for you as it was for me.

[0-60motorsports]

I think they've been out of production for 15+yrs

Oh wow. They really look like art.

[George Hill]

Nice! are they still making those headers?

I think they've been out of production for 15+yrs

[0-60motorsports]

The only reason I initially S54 swapped my wagon was because I had a set of Kromer Kraft headers. They were old and tired but sounded amazing. They needed some repair and were pulled in favor of a "temporary" euro setup. I think that was 4yrs? ago, lol. My spring goal is to get them back on and I'm probably going to make a muffler to quiet everything down as I can't really buy anything I like at least that I can find.

Going from E36 to ZHP, I think there's room on the table to make more power and be similar sound level even if you are guessing at some parts of the design. IIRC we saw a ZHP left 15whp on the table vs a Stromung conversion muffler, Dinan or BMW Performance mufflers (E36 was even more than that).

Nice! are they still making those headers?

[Bry5on]

What is a shear plate?

That aluminum plate that ties the subframe to the frame rails. Which reminds me, I also want to design a flat sheet to close that M3 plate out and stiffen it up like the non-m plate