Big BenD Bass Horn: Belts and Braces - Appendix

This appendix will show measurement of the unbraced wall and final performance of the braced wall with everything in place. It will contain one figure for each measurement point, with a few exceptions, divided into sections for each part. 

Rear Chamber

The bracing was applied at the end, after all other bracing, as the measurement at the back of the rear chamber was used as a level reference to keep all measurements comparable. 

Throat Bend

Not much was done here, so I suspect the reason for the difference in vibration comes from the way the horn parts were supported during the first measurements, compared to when the horn is upright. 

Spire/Middle Section 

The main objective here was to push the modes above the passband, and it does seem to have been fairly successful. 

Mouth Bend (Inner)

Mouth Bend (Outer)

Mouth Bend (Side)

Mouth Top

Mouth Bottom

The measurements do not show much improvement over the "unbraced" condition. That is most likely because the bottom panel was braced from the start; the braces were used as a jig for the curved panel. But a few additional braces were added (RA), although they don't seem to have improved things. This may be due to the ground not being completely flat when these measurements were made. The WH measurements were made inside the garage, with the horn firmly placed on a flat concrete floor. It also seems that some vibrations were transferred from other panels, possibly through the cross brace, as some additional modes appear in the WH case, compared to R (unbraced mouth).

Mouth Side

Here the lower bell mode(s) have been considerably reduced, especially by the addition of the extra side brace that turned the mouth side edges into 'C' beams. 

 Cross Brace

Positions 61 and 63 are the right and left sides of the horizontal brace, 62 is the top part of the vertical brace, and 64 is the bottom part. 

Big BenD Bass Horn: Belts and Braces part 1

[Previous: Rear chamber and Middle Section; Main; Next: Belts and Braces, part 2]

The horn, especially the spire and mouth sections, have large flat panels, and these must be braced. Panel vibrations will act like notch filters in parallel to the horn path, and will suck energy from the sound transmitted through the horn. And not just that, the panel resonances may have high Q values, re-radiating the absorbed vibrations at the wrong time, with ringing. We clearly don't want any of this, but it may be hard to elimiate. 

Bracing Basics

There are two papers that cover the basics of enclosure bracing: Loudspeaker Enclosure Wallsby Peter W. Tappan [1] and The Theory of Loudspeaker Cabinet Resonances by James K. Iverson [2]. These papers give both theoretical and experimental data on the effectiveness of wall construction and bracing, and should be studied by anyone making speaker enclosures. 

Both wall absorption and resonant frequencies affect how much the wall will vibrate. Absorption is more effective the higher the resonant frequency, so raising the resonant frequencies is effective in several ways. Below the first resonant frequency (mode), it is the stiffness of the wall that limits vibrations, higher up the mass dominates. 

If the first wall resonance could be moved out of the passband of the horn, this would massively reduce the contribution from the horn walls. Increasing the wall stiffnes can be done by using thicker material, adding tension, changing the shape, or bracing. The material is already 18mm birch ply and relatively stiff, and the whole structure could easily become difficult to handle if it was made thicker. The shape is given by the horn, and can't be changed (but it is possible to increase the tension in the panels by adding a slight curvature). Bracing is the most suitable approach, and tension is also automatically added in the curved section of the horn.

The most effective bracing method is braces along the long direction of a panel. Tappan recommends to place the braces so that the circles that can be inscribed in the unbraced parts of the panels are as small as possible. It is also important that the braces add enough stiffness to make a difference. If the brace isn't stiff enough, it will just add a bit of mass to the wall and may actually lower the resonant frequency. 

At high frequencies the wall radiation is very directional, and for most enclousures this means that the parasittic radiation is directed away from the listening area and can be more readily absorbed. But in this horn, the front of the spire, although partially covered by the midrange horn, is a large radiating surface pointing towards the listening area. It is therefore critical to reduce radiation from this wall.

Comparing Bracing Methods

Usually one would put braces internally and externally on the horn based on experience, gut feel and what "looks right". But this may result in a lot of unnecessary braces, adding weight, and unneccessary work. Below are data for a 12" by 18" (305 by 457mm) steel panel, 0.02"  (0.63mm) thick, clamped at the edges, and braced in different ways [1].

It is clear that the quite common perpendicular brace is not very effective in raising the resonance frequency, and that the perhaps less intuitive lengthwise brace is the most effective. 

Measurements

 My first thoughts about reducing panel vibrations was to drive the horn with a signal generator and feel around for areas of excessive vibrations. My second thought was that maybe a knuckle test using the spectrum analyzer in Arta together with a measuring microphone could provide some more useful data, and allow me to move resonances out of the passband. Then I remembered I had an ACH-01 accelerometer. I built a phantom powered preamp for it, allowing me to use a normal sound card with microphone input. Then I could make repeatable, quantifiable measurements of bracing performance. 

Initial Measurements

The first measurements were done on a rear chamber, throat bend and middle section (spire). 

Rear Chamber

The rear chamber is a square box of about 65 liters. There is no bracing apart from a frame with T-nuts to bolt on the rear cover. 

The panels will be left unbraced until the end. The back wall provides a reference measurement to check that the system is run at the same levels throughout the tests. 

Throat Bend

The throat bend has a lot of built-in stiffness from the bending. The main vibrations seem to be above about 800Hz, so there doesn't appear to be a great need for extra bracing here. 

The next article will cover the bracing of the spire. 

[Previous: Rear chamber and Middle Section; Main; Next: Belts and Braces, part 2]

References

[1] Tappan, Peter W.: "Loudspeaker Enclosure Walls"; JAES Volume 10 Issue 3 pp. 224-231; July 1962

[2] Iverson, James K.: "The Theory of Loudspeaker Cabinet Resonances"; JAES Volume 21 Issue 3 pp. 177-180; April 1973

Big BenD Bass Horn: Belts and Braces part 2

[Previous: Belts and Braces, part 1; Main; Next: The Mouth Bend]

 As shown in the previous part, the wall vibrations in the throat bend are essentially out of band, thanks to the dimensions of the bend being rather small. Not so in the middle section (spire), though. Here the main culprit will of course be the front and back, but let's start looking at the sides first. 

In the figures below, the curve legends correspond to the file names. The numbers refer to the measurement position, and the letter after the number refer to the bracing that has been applied. A list is given at the end of this article. 

Side Walls

I measured the vibrations at the straight side wall in three places along the centre line: 200mm and 500mm from the top, and 200mm from the bottom. 

Similar with the curved side wall, here I also measured along the centre line, but at the centre of the three straight panels that make up the curve.

There are some strong resonances in these panels, and both have strong peaks at around 125Hz. There are also troublesome peaks at about 200Hz and 300Hz too, these are in, or too close to the working range (up to about 300Hz) to leave them alone. 

The first thing I did was to add a flange to the mouth end of the spire. This is quite effective in moving the lowest (125Hz) mode, which is a bell mode. For the sides, I added braces along the length of the horn, this also reduced the vibration significantly. Most of the vibration is now moved above 200hz, and the leve is reduced by about 10dB. 

Here is a compraison between braced and unbraced panels for the straight sidewall:

And here are the curves for the three measurement positions along the curved side wall, after bracing:

Front Panel

This part is quite important, as it will face the listener. Unbraced, the responses at 7 different positions at the front wall look like this:

There are some very strong modes inside the working range, and we need to kill those. For the following curves, I will only use measurement position 22, which is 800mm from the top (about 200mm from the mouth), and about 290mm from the straight side wall. 

Adding a brace close to point 22, running all the way along the front from top to bottom, in addition to the flange (unfortunately I don't have measurements of the effect of the flange alone at point 22), reduces the level below 300Hz a bit. There seems to be several modes located around 180Hz. 

It is clear that for bracing to be really effective, the brace needs to be significantly stiffer than the panel it braces. For the braces applied so far, I used 18mm birch ply on end, about 50mm wide strips (apart from the brace for the curved side wall). While it helps, plywood has limited stiffness. I therefore tried adding a 40x40mm L angle iron, 4mm thick, to the D brace. This cleaned up the range above 200Hz significantly, but didn't suppress the 180Hz modes much. 

Adding a second brace from top to bottom improved the vibration above 200Hz further.

Finally I added corresponding braces on the back, a small brace on the front near the mouth on the curved side, and a small brace near the throat of the spire. This introduced some modes aroudn 700 and 1000Hz, which may come from the coupling between back and front. 

In any case, the bracing has improved the wall vibrations a lot, what is left is the big bump around 180Hz, which is probably the bell mode shifted higher due to the mouth flange. 

Below is a photo of the applied bracing. The braces are labelled according to the legend.

Next up will be the construction and bracing of the mouth bend.

[Previous: Belts and Braces, part 1; Main; Next: The Mouth Bend] 

Legends

Big BenD Bass Horn: Belts and Braces part 3

[Previous: Belts and Braces, part 2; Main; Next: The Mouth Section]

The mouth bend has larger surfaces that most of the other parts so far. They are curved, which does add some stiffness, but they are still large.

Outer Bend

The outer bend is the largest surface, and still resonates quite a bit despite the tension from curving. 

With all measurements in a single plot, it's quite difficult to make out the individual curves. But it is clear that there is quite a bit of vibration from 200Hz and up, and also a few resonances around 80Hz which are probably the bell mode. 

If we take a look at point 33, which is in the middle, 600mm along the curve from the throat end,  we find clear peaks at 240Hz and 340Hz, with smaller peaks nearby. By adding a brace across the width of the horn 250mm from the mouth end, brace n, the lowest of these are reduced substantially, while those around 300-400Hz remain. Adding braces along the horn reduces the 240Hz modes by 5dB more, but does not help much above 300Hz. 

At point 35, which is at the center, 900mm from the throat, we find other modes. The cross brace now reduce the modes up to 400Hz at this point. 

Two bends along the horn, near the middle, also reduce the vibration quite a bit. 

The two braces along the horn near the edges actually increase the vibration a bit, but they are required for the stand, so they have to stay.

I also experimented with a sash clamp across the mouth. Across the width of the mouth it cleaned up the 90-180Hz range a bit, across the height it cleans up the 180-300Hz range. 

Side Panels

the side panels mainly have modes in the 200-500Hz range. 

I added two braces to the side. The first was vertical (with the horn in the upright position), and reduced the vibration at position 36 by about 5dB.

Adding a horizontl brace added another 5-10dB. Since I actually braced the side before the outer bend, I also include a measurement with the mouth bracing added, this also helped reduce the side vibration somewhat. Below 250Hz the level is now about 20dB from where it started. 

Inner Bend

The inner bend already has some braces, and the siginficant resonances are above 200Hz. 

Some additional braces were added in between the original braces, but this was done rather late in the process. Here is a measurement of the inner bend with the mouth section added. This reduced the vibration enough to be insignificant compared to the vibration from other panels.

Final Bracing

The final bracing of the mouth bend is shown below, as is the two measurement positions 33 and 35 used for checking the mouth bend. 

[Previous: Belts and Braces, part 2; Main; Next: The Mouth Section]

Legends

Big BenD Bass Horn: Belts and Braces Part 4

[Previous: Mouth Section; Main; Next: Performance Measurements] 

In this final article on bracing, we will look at the mouth section braces, and also compare the measurements of the final horn with some of the original, unbraced measurements. This article will be quite long, as there is a lot of ground to cover, and many experiments. As before, I can't show all the measurements, as there is just too much data too look at. But I will include measurements at strategic positions, which I used to evaluate the performance during application. 

At the bottom of the article is a photo of the braces with letters to identify them (the letter R indicates the mouth without bracing). These letters correspond with the letters in the curve legends. 

The bottom wall was fairly well braced from the start, as the braces were used as a jig. But additional braces were added later. We will take a look at the bottom wall when looking at the final results. 

Mouth Side Wall

 The first set of measurements show the vibration at the unbraced side wall at all the measurement positions. While quite messy, we see some strong modes at 112, 185 and 350Hz, the lowest is the bell mode of the mouth and is very hard to get completely rid of. 

 Adding the centre horizontal brace on the side wall, S, shifts the bell mode down somewhat, and cleans up another weaker mode around 58Hz. The range above the bell mode is also cleaner, but the upper modes are not much affected. Adding the T braces (upper and lower horizontal braces) helps in the range above 300Hz. 

 A vertical side brace, U, does not do much with the bell mode by itself, but it cleans up the upper modes. 

 At this stage I was starting to think I may have to apply some more drastic measures to the mouth to kill the bell mode. So I got some more angle iron, and applied around the mouth. Below are the measurements of these reinforcements by themselves, V indicates side angle iron only, W indicates side and top angle iron. It's actually not much of an improvement by itself, apart from at the 58Hz mode. Well, at least that indicates that something is right...

 Some slight changes by adding the vertical side brace:

 We'll revisit the side when more bracing is in place. 

Mouth Top

 Without bracing, two things are clear: The absolute level of the peaks is lower (for the most part) than for the side, and the actual bell mode is the mode at 58Hz. 

Adding the angle iron (W) reduces the bell mode by 5dB, and adding the front lateral brace (WB) reduces it by another 5dB. But these braces do not do much for the rest of the modes. 

Adding a rear lateral brace (WC) and two longitudinal braces (WD) helps somewhat, adding another four longitudinal braces helps even more. 

Mouth Cross Brace

There was no way around it: The mouth needed a cross brace. A cross brace is of course very efficient in killing the bell mode, but it's not as good for killing the other higher modes of the panels. So both are needed. Adding the cross brace certainly reduces the panel vibration over a wide range, the bell mode is now down by 25dB, and the rest of the range up to 300Hz is much cleaner. Adding Mutestrip between the two braces, where they intersect, doesn't do much, but I left it there since very little of the material is used anyway. 

But of course the mouth braces themselves will vibrate too! The horizontal brace has two distinct peaks at 67 and 70 Hz and a strong one around 300Hz, while the vertical brace has several peaks above 300Hz. 

 In order to combat the resonances of the horizontal brace, which were the most troublesome since they were quite strong in-band, I tried various things like stiffening with steel L-profiles. But the most efficient turned out to be mass loading the arms of the horizontal brace with pieces of flat steel. The result of this is shown below, it took the level of the peaks down by over 10dB. 

The braces added to the outside so far are shown in the photo below:

Order of Application

When braces are glued onto the side walls, it's not easy to experiment with the order of application. But since I'm building two horns, I decided to test out the order of application at the mouth section. 

Side Walls

For the first horn, here are a couple of measurements with no bracing (R), all outer braces (WF) and finally outer braces pluss cross brace (WH).

If the cross brace is added first (includes also the rim braces, I haven't measured without those), there isn't actually too much of a difference when the outer braces are added. 

But what really killed the vibration, especially the lower modes (at this position) was the addition of a second layer of bracing at the mouth, that can be seen at the photo below. This was an idea suggested by my friend Torbjørn at the very end of the experiment, so it is not included in the previous mouth bracing experiments. It basically turns the rim braces and horn walls into 'C' beams.

Mouth Top

For the top wall, similar tests were done. Again, R is with no bracing, WF is with all outer braces, and WH is all braces including cross brace. 

RA indicates the rim braces and cross brace, but now the outer braces (RD) makes some difference, especially around 100-200Hz. 

Conclusion

The measurement of the efficiency of the bracing has been quite extensive. Over 300 measurements have been saved, but probably the same number have been taken in the process of testing things, finding good measurement points, and so on. The articles have presented only a select few of these. For those interested in a summary of "before" and "after" measurements for all measurement points, curves wiht a few comments are presented here.

For the most part, the bracing has been successful. Vibration has been reduced by at least 10dB most places, and in many cases a lot more. Several places the modes have been pushed out of band, other places they have been usefully attenuated. In a few cases, coupling has introduced vibrations in surfaces that weren't there to begin with. 

Bracing and vibration are definitely complex topics, and this study has taught me a lot about practical bracing. The main points:

• The braces must be stiffer than the panel it is meant to brace, and considerably so. Otherwise they will just add mass and lower the resonance frequency. 
• Raising the resonance frequency by partitioning the panel works, if the braces are stiff enough. 
• The bell mode is hard to kill by external bracing, and typically need cross bracing, although turning the rim braces into 'C' beams helps considerably. 
• Cross bracing can transmit vibration from one panel to another, and excite vibrations in the panels that were quiet. They are not perfect solutions and should be used with care. 
• The larger the panels, the more difficult it seemed to raise the mode frequencies by bracing. My initial goal of moving all modes out of band were not met for the larger parts of the horn, probably for a large part because the braces weren't stiff enough. 

But all in all, the horn is a lot deader than in its unbraced state, and although it's hard to quantify the amount of vibration contributed by the horn walls, I think it's probably not much compared to the direct radiation from the horn mouth, as there are no definite dips or peaks in the response that could come from spurious resonances or vibration.

Appendix

[Previous: Mouth Section; Main; Next: Performance Measurements]