Design Processing Technologies

An approximate model is known as analytical when it is entirely described using mathematical equations.

These equations represent the physical characteristics (Mechanics, Thermal, Electrical Electrotechnics, Electromagnetism, Matérials, Pneumatics, Hydraulics, Thermodynamics, etc…) and economic of the device.

The quality of the model is the result of the expertise and the know-how on the company, source of its competitiveness.

An analytical model can arise in various forms, more or less hidden:

·        A sheet of paper – Simple but difficult to make more than the rule

·        of three!

·        A file of mathematical language: Maple, ASCII, Doc…. – Simple but similar limitation.

·        A worksheet Excel – more complex especially if the model grows bigger. Problem also with the implicit loops.

·        A Matlab program – Problem of maintenance, management of complexity and the implicit one.

·        A Fortran home made program, C or VB – Powerful, but problem of maintenance, loss of consciousness of the model drowned in the lines of codes as of the model becomes important.

Pro@DESIGN combines the simplicity of a model in the form of equations, and the power of a home made program, by removing the problems related to the programming: time and budget of development, cost of maintenance, complex coding of model, management of the implicit loops, loss of consciousness drowned in the lines of data-processing code.

An example of analytical model of an actuator:

A.D. KONE, B. NOGAREDE, M. LAJOIE MAZENC, “Le dimensionnement des actionneurs électriques: un problème de programmation non linéaire”, dans “Journal de Physique III, Février 1993, pp. 285-301

Dimensioning parameters:

·        sigmaem = Math.PI/(2*landa)*(1 – kf)*sqrt(kr*beta*ech*ge)*pow(d,2)*(d + ge)*be;

·        ech = a*jcu;

·        a = kr*ge*jcu;

·        kf = 1.5*p*beta*(pe + ge)/d;

·        be = (2*la*m)/(d*log((d + 2*ge)/(d – 2*(la + pe))));

·        c = Math.PI*beta*be*d/(4*p*bfer);

·        p = (Math.PI*d)/deltap;

Cost parameters:

·        vu = Math.PI*d/landa*(d + ge – pe – la)*(2*c + ge + pe + la); volume du cuivre

·        va = Math.PI*beta*la*d/landa*(d – 2*pe – la); volume du fer

·        pj = Math.PI*rhocu*d/landa*(d + ge)*ech; perte joule

·        fonction de coût = cvu*vu + cva*va + cpj*pj;