Here is a follow-up question that I and another poster asked Dan regarding point 5 on the Split Coil Design:
5. Motor size. Because the overall voice coil effective length is much longer, you simply need to have a deeper/taller magnet stack. And that brings the issues with rocking, etc. with it.
we asked:
What are the Pros and Cons with using multiple spiders in Split Coil designs to help reduce Rocking? Of course using them will alter some of the T/S parameters but it should definitely help with rocking issues and the designers could always use softer spiders to counteract the use if multiple units, right?
Interesting response from Dan Wiggins:
====================================
First off, linearity. For an ideal spring, your have a force F(x)=kx, where k is the spring stiffness, and x is displacement from rest. A very linear force function! Stretch the spring a certain amount, and we can directly calculate the force, and it's nice and linear. Here's a cool page that shows how consistent this really can be:
http://www.myphysicslab.com/spring1.html
Note that the spiral is nice and consistent, proportional as it "damps down". Spacing between the cycles are proportional, etc. It all looks good, and it should, because of the math involved - F=kx, it doesn't get much simpler than that! For the math, and those interested in it, read the rest of that page. Quite instructive!
Now, let's look at the twin-spring situation - two springs controlling the mass. The best page with graphics to show this is:
http://dept.physics.upenn.edu/course..._TwoWalls.html
Stop the graph, and enter the following different values:
Initial pos. = 0 (we start at the rest point)
d = 0.1 (initial tension in the springs)
Initial vel. = 1 (we start off with a velocity of 1, to the right).
Look at the upper graph you get now - it's not nice and round, but figure-8 shaped. That graph is the velocity versus displacement, and we see that it is NOT nice and smooth. The lower graph shows this in another view - energy versus displacement is not continuous, meaning that the force is not continuous.
Scroll down that page a bit, and you'll see why - look at the equation of motion! It's nice and high-order. That's the reason for the nonlinear motion and forces.
Now, keep in mind that these examples assumed the springs are perfectly linear, and obey the F=kx equation. However, real spiders are NOT linear, and the stiffness function is typically of the form:
F(x) = kx + bx² + cx³
Add that into the above mix, and we see things get REALLY ugly. Using more than one spring in a system will create greater nonlinear behavior - it's a bad thing.
Now about rocking. Dual spiders again don't help. Why? Consider the following diagram:
So, we have a stiff rod (blue line) that rests on a fulcrum (the green checked triangle), connected to the ground via a spring (the red circles on the right), and pulled down by a weight (the black trapazoid on the left).
This is analogous to a driver. Let's assume that the cone/former (the blue rod) is infinitely stiff. And let's assume the spiders (the green checked fulcrum) won't give left or right - they will always keep things centered left and right.
The red spring represents the surround - the front of the cone.
The weight represents the mass of the voice coil, trying to pull the system to the side. It will scrape if it touches down on the rectangle below it. So we see that we want to keep the red springs (surround) strong enough that the mass won't touch down, right? The only way the voice coil can scrape is if the springs aren't stiff enough, the fulcrum collapses, or the rod bends. If none of those happen, the voice coil won't scrape.
Now, let's add a second spider into the mix...
We now have two of the fulcrums on which the rod rocks. So let's try to rock once again... We pull down with the weight, and if the fulcrum doesn't collapse, the rod doesn't bend, and the springs are strong enough, we don't touch down.
What did the second fulcrum do? NOTHING. In fact, it's widened the pivot point, but that's it. It has done nothing to stiffen the rod, or to strengthen the springs, or lighten the weight. All it has done is created a wider fulcrum on which your rod can rock.
Think about a lever - to lift your car, do you want a wider fulcrum under your lever, or more force down on your end of the lever? Simple choice, isn't it?
In fact, rocking is controlled by the spider-to-surround distance! That is what allows the spider to keep the voice coil from rocking - the lateral stiffness of the surround, and the distance over which the surround can work. Make the cone taller, and the surround stiffer laterally, and you end up with greater resistance to rocking.
Now, all this goes away if your spider isn't stiff enough to hold up laterally - if it squishes to one side or another. However, spiders tend to be quite stiff in a side-to-side motion, so that really isn't a real-world concern. If it can squish, then you need a stiffer spider in the first place (you tend to have a LOT more stiffness in the radial - side to side - dimension than the axial - in and out - dimension).
===========================================
I guess it is somewhat obvious then, that dual spiders do two things:
1. Reduce suspension linearity (make it worse)
2. Do not reduce rocking