Modelling strategy for cross section area driven design: horn loudspeaker

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TomPinnegar
0
Hi guys!
 
I'm designing a horn for a new loudspeaker on Solidworks 2020. Horn geometry is governed by its cross sectional area expanding from its throat to its mouth which in my case is also going from a circular section where the speaker driver is mounted to a rectangular opening at the front.
 



 
Currently the only way I have found to maintain the exponentially expanding area (for the most part - there are some tweaks to the exact shape, and version 2 will get split into a few sections with different equations governing the cross sectional area expansion) is to create sketches every 10mm initially and later every 20mm and lofting through these profiles. The transition from circular to rectangular is achieved with elliptical corners on the profiles whose dimensions are defined by eyeballing a proportion of the height and width and feeding those proportions back into the equation for width. Using dimensions directly gave me circular reference problems. The height of the profiles is controlled by an equation driven curve and the width is allowed to be whatever is required to give the section its required cross sectional area.
 
Examples of my current set of equations (height of sections is defined by some guide curves in the sketch already):
 

 
Example of my sketch with elliptical corners:

And this approach leads to both a wiggly edge on the edge that is not controlled by the equation driven guide curve, and also means that I have to input the values for the elliptical corners by manual guesswork and adjustment (above, the 2.9 in the equation shown).

The wiggly edge of the horn, with the wiggly line of elliptical corners (highlighted with red corresponding to that "cornerwidth" dimension in the sketch above):

 
You can imagine that when we want to tweak this design a little here or there, to adjust the expansion rate, length of the horn and so on, the whole model falls apart and is very time consuming to reconnect all these cross sections where guide curves no longer connect with profiles and go through each equation to alter the ellipse dimensions and to feed those new denominators back into the equation for the width of the profiles. Generally making any change to this inner surface also causes all of the subsequent modelling operations to fail because they connect to this first surface.
 
In the ideal world, I would like to find a way in which I can make this process a little less messy, make it so that I can make adjustments without having to rebuild most of the model, maintain control over the cross sectional area expansion of the horn, and generally make my modelling method a bit more elegant, preferably avoiding so many cross sectional almost-copies-but-not-quite sketches if it were possible.
 
Any tips for other strategies to try? How would you go about this?
 
Many thanks!
Mecanikad
0
Hi
Here is a much easier solution. Other are possible too. 
You can replace the sketches 1,2,3,4,6,7 by equation driven curve. 
Horn example

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