TEAM Workshop Problem No. 20
3-D Static Force Problem



1. General description

The model is shown in Fig. 1. The center pole and yoke are made of steel. The coil is excited by a dc current. The ampere-turns are 1000, 3000, 4500 and 5000 which is sufficient to saturate the steel.
The problem is to calculate the magnetic field and electrmagnetic force.


2. Analysed Region and Boundary Conditions

If the symmetrical boundary conditions can be used, the ¼ region shown in Fig. 2 is a sufficient for analysis.


Mesh Description

The mesh is no specified.


4. Nonlinearity

The B-H curve of the steel shown in Fig. 3 is to be used. The typical values of B(T) and H(A/m) are also shown in Table 1. The curve at high flux densities (B>2.3 T) cannot be measured and is approximated by the following equation:

B = µoH + Ms,


where µo is the magnetic constant and Ms is the saturation magnetization (2.16 T).


5. Quantities to be Calculated

To compare results, please complete Tables 2, 3, 4 and 5. Fig. 4 shows the positions at which the flux density should be calculated.


6. Description of Computer Program

To compare formulations, variables, etc., please complete Table 6. The used memory in item No. 16 in Table 6 is defined as the sum of dimensions declared in the program.




Fig. 1 3-D model for verification of force calculation.





Fig. 2 Analysed region.





Fig. 3 B-H curve of steel.





Fig. 4 Positions at which the flux density should be calculated
(see Tables 2, 3 and 4).





Table 1 - Typical data of B-H curve

Table 2 - z - directional components Bz of flux densities at points P1 and P2 (see Fig.4)

Table 3 - z - directional component Bz of average flux densities in center pole (alpha-beta) and yoke (gamma-delta) (see Fig. 4)

Table 4 - x - directional components Bx of flux densities along lines a-b and c-d (see Fig. 4)

Table 5 - z - directional components Fx of force

Table 6 - Description of computer program


References

  1. O. C. Zienkiewicz: "The Finite Element Method (Third Edition)", McGraw-Hill (1977).
  2. P. P. Silvester, H. S. Cabayan & B. T. Browne: "Efficient Techniques for Finite Element Analysis of Electrical Machines", IEEE Trans. PA & S, PAS-92, 6, 1274 (1973).
  3. J. H. Hwang & W. Load: "Finite Element Analysis of the Magnetic Field Distribution inside a Rotating Ferromagnetic Bar", IEEE Trans. Magnetics, MAG-10, 4, 1113 (1974).
  4. H. Akima: "A New Method of Interpolation and Smooth Curve Fitting Based on local Procedures", Journal of ACM, 17, 4, 589 (1970).
  5. C. R. I. Emson: "Methods for the Solution of Open-Boundary Electromagnetic-Field Problems", IEE Proc., 135, Pt. A, 3, 151 (1988).
  6. P. Tong & J. N. Rossetos: "Finite-Element Methood (Basic Technique and Implementation)", MIT Press (1977).
  7. P. Sonneveld: "CGS, a Fast Lanczos-Type Solver for Nonsymmetric Linear Systems", Report 84-16, Department of Mathematics and Informatics, Delft University of Technology, The Netherlands (1984).
  8. A. Bossavit & J. C. Verite: "The 'TRIFOU' Code: Solving the 3-D Eddy-Currents Problem by Using H as State Variable", IEEE Trans. Magnetics, MAG-19, 6, 2465 (1983).