In this study, the direction of a magnet that can be oriented along the 3 axes of X, Y, and Z is expressed by 3 bit variables, and the

magnetic flux density generated is formulated using the variable and Bio-Savart's law, one of the laws of electromagnetism, and an objective function (function whose value should be maximized) as a combinatorial optimization problem in which the

magnetic flux density is maximized for a specific part.

To find the relations between the dimensional initial and mass-dimensional parameters, we represent the maximum value of the

magnetic flux density at a certain point of the winding as

In the study, both 2D and 3D methods have been used to calculate electromagnetic parameters and the outcomes of 3D simulations,

magnetic flux density results are illustrated as shown in Fig.

While to evaluate

magnetic flux density B the "Magnetic Fields (mf)" physics was chosen.

Once the

magnetic flux density B is obtained, the entropy span and corresponding temperature increase of the Gd material inside the aperture can be calculated.

where E is the signal voltage in a conductor, [bar.v] is the average flow velocity, B is the

magnetic flux density, and D is the pipe diameter.

[DELTA]B is the change of

magnetic flux density, [DELTA][sigma] is the change of stress, and [DELTA]V is the change of voltage.

Formula (10) shows that, in the areas of stress concentration, the significantly greater force will reduce the local

magnetic flux density, and this leads to magnetic distortion in the local region, that is, the formation of magnetic memory signal.

The excitation frequency was adjusted from 1 Hz to 30 Hz, excitation amplitude was changed from 0.4 mm to 1.4 mm, and applied current was driven from 0 A to 6 A (

magnetic flux density was adjusted from 0 mT to 326 mT).

Figure (11) shows the

magnetic flux density distribution for two broken rotor bars as a sample for show the effect of broken bars on the flux distribution.

So this part concentrates on current density distribution and

magnetic flux density distribution graphs at different gap distances and the voltage frequency is fixed at 400 Hz.

In all the 2D FE models, the radial component of the

magnetic flux density is neglected.

The types of matrix material, concentration of magnetizable particles, and

magnetic flux density can influence the modulus change of MRE [4, 5],

the relative reluctivity of the material [[upsilon].sub.r] = 1/[[mu].sub.r] is a function of the

magnetic flux density, which is a function of the unknown vector [{a}.sup.n+1], the residual {r} in Eq.