Problème mécanique: Exemple

Remarque : Le contenu de cette page est en anglais et sera traduit ultérieurement en français.

Let's consider the Free-shape optimisation of the flux barriers in the rotor of the synchronous reluctance machine.

Figure 1. The synchronous reluctance machine subjected to free-shape optimization with mechanical constraints (a). A few constraints (symmetry and mechanical) of the mechanical problem are shown in (b).


The Mechanical problem created to constrain the Free-shape optimization uses two Mechanical regions, namely:

  • One Material region corresponding to the rotor, without the shaft, characterized by the following parameters:
    • Young modulus = 200,000 MPa;
    • Poisson ratio = 0.3;
    • Mass density = 7,650 kg/m3.
  • One Air region, corresponding to the flux barriers in the rotor.
Two Mechanical boundary conditions are also required to complete the Mechanical problem:
  • The mesh nodes lying at the interface between the shaft and the rotor are supposed static and constrained in the structural mechanics problem. This is achieved through a Constraint on degrees of freedom of nodes, with all three degrees of freedom set to Fixed, applied to the green dotted arc of circle in Figure 1b.
  • The mesh nodes lying on the periodical boundaries of the rotor are allowed to move radially only. This condition is also enforced with a Constraint on degrees of freedom of nodes (applied to the blue dotted lines in Figure 1b), with the Radial translation degree of freedom set to Free, and the others set to Fixed.

The Rotation speed for the Centrifugal load of the Mechanical problem was considered equal to 15,000 rpm, the maximum working speed of the machine. The other parameters characterizing the Optimization problem are given below:

Tableau 1. The design goal and the constraints for the free-shape optimization problem with mechanical constraints.
Objective or Constraint Response or Constraint type Definition
Objective Torque Ripple Minimize
Constraint Von Mises stress Lower than 260 MPa (i.e., 80% of the yield stress value of the electric steel M330_35A used in the rotor)
Constraint Volume Lower than 80% of the initial design volume
Constraint Average torque Larger than 11.9 N.m
Constraint Symmetry 45 degrees symmetry (i.e., with respect to the red dotted line shown in Figure 1b

The figure below shows a comparison between the initial design of the flux barriers (a) and the obtained results (b).

Figure 2. The initial geometry of the rotor (a) and the optimized geometry obtained through free-shape optimization with mechanical constraints (b).