Help simulate a new loudspeaker box type

I don't understand why you want to convert a mechanical model to an electrical model for simulation when it is easy enough to model the mechanical parts in software. I simulate hydraulic servo systems in software all the time which is basically a non-linear version of a mass between two springs. See this http://www.engin.umich.edu/group/ctm/model/model.html http://www.engin.umich.edu/group/ctm/state/state.html If you have Matlab then you are close to being done. If you don't have Matlab the download free scilab from www.scilab.org. There are demo programs that should be close to what you want to do.

The simulation of a loudspeaker box is not as simple as it is the one of a hydraulic system. The reason is that you have several mechanical components which cannot be separated from each other and cannot be in an easy way reduced to a spring-mass system. On one side you deal with air which is compressible so that the problem cannot be considered as a system with concentrated parameters as in other mechanical simulations, on the other side the walls deform more at the center than on the edges so that it is difficult to define a plane equivalent deformation, in fact depending on the frequency the walls will deform differently leading to a non linear frequency depending model. The same is valid for the membranes. You could assume a mass-spring system only for the moving coil and its connection to the membrane but not for the rest of the moving equipment.

If you want to "linearize" and simplify the model it would be better to make a 3D FEA simulation first and look at the deformed walls as function of the frequency. Integrating the deformation all over the surface you could define an equivalent mass-spring system which would have same kinetic energy as the whole wall.

But you will be far from reality and results would be only a rough approximation. All depends on what you want as "precision" of your simulation.

But in all cases the previous comment is correct why go to electric models when you should stay mechanical?

Simple really, loudspeakers, enclosures, cross over networks etc. are designed by electrical engineers. They like to use the tools that they are familiar with. Just like gear heads like to use gears and springs to model everything, EEs like to use current and voltage.

Hydraulic systems are much more difficult than you think. I model them using a system of non-linear differential equations but I know this doesn't take into account the time it takes the pressure wave in oil, to move from one point to another. I agree a 3D FEA is the ultimate way to go if one want to take into account the speed of sound and how frequencies interact. It is probably more important with speakers because the frequencies are higher and the speed of sound is lower so there is much more interaction between the frequencies.

I don't know of anybody that does 3D FEA but I bet the better speaker companies do. I know I would like to at least take into account the speed of sound in oil.

Meanwhile, if the OP can convert his model to a system of non-linear differential equations it isn't too hard to optimize or tune the system to provide some desired response.

I do not know which kind of hydraulic systems you simulate so that I do not make any comment for the need of the pressure wave for them.

For usual industrial hydraulic systems the non linearity is only required for the simulation of flow through orifices or metering ports in proportional valves, servo-valves, pressure regulators or in pressure relief valves. The use of those non linear equations is a lot simplified by the presence on the market of programmes as SIMULINK or VISSIM or others which allow a "block" approach. The blocks are elements with concentrated parameters and do of course neglect the pressure difference arising in a -for instance- cylinder from one face of the volume to the other. There is however a domain of hydraulics (but not oil hydraulics) where the waves behaviour is important. It is the fuel injection system in engines. The combination of high pressure, long connections (ratios L/d >>1), stiff walls and short available times makes the "pressure wave speed" an important parameter. As I already mentioned in a previous post such parts of the system can be simulated with "lumped parameters" elements put in series and adapted to the frequency range of the system in order to reduce the number of blocks. In "normal" hydraulic systems the dimensions are so small with respect to the sound speed in oil (even if the wall elasticity is considered as a reduction effect on the bulk modulus) and the time constants so high that the delays due to the limited pressure wave speed are totally neglectable.

If you never the less want to quantify those effects you can develop your own numerical integration soft and take into consideration the partial differential equations which will control the wave amplitude and displacements.

It is much more different in the case of pneumatic systems since the high compliance of the medium leads to lower sound speeds and in some situations the wave delays and the time constants of the control can come to same order of magnitude.

"I might provide info how the conventional box types are translated to their electric analogs."

Then what don't you understand? Which part are you having problem with? Is it the electrical or the acoustic (Sound Pressure or the box acoustic characteristics...etc)?

Otherwise, you'd better make yourself more clear coz your Q isn't.

The conventional ported or "bassreflex" is the rear of the woofer placed in a chamber and the chamber is tuned via port to the outside world.The compliance of the volume of air in the chamber together with that of the woofer suspension act like a spring.The mass of the air moving in the port together with that of the cone act as a mass.

The port has ration surface/length which tunes the system.The larger the surface the longer the port has to be to preserve the tunning and sometimes it wouldn't fit in the box so smaller is selected but sometimes the air velocities pass the Reynolds number, the air becomes turbulent and smaller is not an option.A great problem is small Vas drivers demanding small boxes because the port length is a function of the box volume.In this situation the only way for low tunning is the passive woofer (suspended motorless membrane, tuned with anything heavy+glue).

What I want is a ported whose port opens in another ported chamber and then to the outside world.A series ported.Mind that if both the ported and woofer are placed in a second ported chamber it is not what I want but a series tuned 6th order bandpass.

I will find someone in the university to do it on LabView.Just if I had the transition from mechanical to electrical network

If you want, although results will not be good, to make a concentrated parameters simulation then a volume acts as a capacity since it integrates the flow (current) to build up pressure (voltage) and a "tube" acts as an inductance + resistor whose impedance is ρ*L/A with L= length/A=section/ρ=specific mass, the resistor equivalent value is usually based on a laminar air flow friction with the wall and in the fluid itself. The combination between a volume and a tube builds up a low-pass filter and is often used to filter out ground noise by mechanical means.

This way the coupling between the input and the air is not correct but at least you can work with Simulink or equivalents as Vissim or others.

Have a look also at the "Helmholtz Resonators" and their theory, it could help you to better understand some aspects.

I would be interested in the results.

A more complex but less imprecise approach is a multi-mass-spring model which is a simplification of the differential equations for a continuum.

It's a Helmholtz resonator.It does act as a lowpass filter, filtering the highs from the back of the speaker.And below tunning frequency it gets out of phase with the wave from the speaker and thus a steeper 24dB/octave curve [24 if I'm not wrong :)].

As I see you already have the solution. In fact you do not need any help.

Only a short remark : the loudspeaker diaphragm has variable active area depending on the excitation frequency. How do you take it into consideration with your fixed values model?

I have nothing hey!This is normal ported(1 chamber 1 port).I am for the series ported 2 chambers 2 ports (back of the woofer,first chamber,first port,second chamber,second port,outside).

This is all done by Small and Thiele,scientists.

Your remark arises from the fact I use speaker in order to be more comprehensible but I mean bass woofers.I am talking about subwoofer boxes.The speakers incorporate other solutions like transmission lines and horns and other exotic sruff.For speakers this is incredibly low-fi

Some speakers don't have dustcaps but bullet like polepiece,because they interfere and some treat the backwave from the dustcap with a transmission line.It is said in the subwoofer simulating programs that things are real up to 150-200Hz.After that ports start behaving like organ pipes.

However this does not suit me,this is regular ported!

The, you write your equations for two in series, if you have one you have 2.

If you can transform your transfer equation into a differential equation, system of differential equations or transfer function in the s domain I can find values that will smooth out the response. I need to have a desired response and then the program adjusts your tuning values that yields a response as close to the desired response by minimizing the sum of squared errors.

As I mentioned the equations are non linear so that the "s-domain" approach via the laplace transform cannot be used.

I am barely comprehending your thoughts but, what I gather the length of the tuning duct is your problem, is it? In that case you can also vary the cross section of the duct in order to reduce the length of it.

I do not know enough about multi-cavity (labyrinth style) speaker-box!!! And with the passive membrane arrangements the problem is however, you have to have a hermetically sealed box, so much so, that any movement by the driven speaker membrane must be perfectly reflected by the passive membrane. It's not easy to maintain a box well sealed over long time due to deterioration.

Analogs are useful for understanding the relationships between engineering disciplines. Examples can be found in many texts. I use "Sonics" by Hueter and Bolt.

It was not my purpose to deviate the discussion so much.The labyrinth enclosure is like this because you have to fit something the length of your car or twice (check the organ pipes) into a box and that's why you fold it.This is the labyrinth.

The problems with ports are great for some woofers but I don't use that kind of type.

I can make a box perfectly sealed, so can any boat builder.There is bracing on the internal walls so they don't vibrate...I was looking for some program that incorporates "Resistance of Materials" discipline...I believe it is "Finite Element Analysis" or something, so I can make the bracing more sophisticated.Similar program "FEMM" can help you design the motor of the driver and optimize it...I had idea for commutating voicecoils but I saw another guy (in a forum archive) complaining long time ago that a third guy had patented it as well long time ago...this is a hobby of mine so I've spent many days and nights searching and discovering things, but I can't let it deepen because I've many other hobbies and I'm positive my hearing is unable to grasp the difference of such a sophisticated audio-system.Mostly I enjoy the wide spectrum of activities and the way they enrich me.I don't want to become a slave,nor have I the finance for that.

Anyways with what I have so far it should be a piece of cake,like nick name says.