**4. Computer modeling of dynamic electromagnetic processes in HMB**

The developed mathematical apparatus can be used to study the general physical processes in HMB, as well as for engineering calculation of basic geometric dimensions of HMB and AMB considering nonlinear electromagnetic and thermal processes. At the same time, developed mathematical apparatus does not allow making selection of the most rational radial HMB design with magnetic inserts. To solve these problems, the computer simulation methods of the magnetic field of various HMB and AMB designs are more appropriate to use.

Software complex Ansoft Maxwell was used to solve this problem, where two main radial HMB designs with magnetic inserts considered, **Figure 1**, and AMB design present for comparing.

Overall dimensions and constructive parameters of the researched designs are presented in **Table 5**.

Comparison of the considered HMB designs was made under the same weight and overall dimensions, output power and materials properties on the following criteria: the magnitude of the force in the air gap of the HMB (main energy characteristic), stiffness when the rotor is displaced by 60% of the air gap. The forces in the air gap were also compared in the absence of current in the windings. Comparison results are presented in **Figure 9**.

Comparison of HMB and AMB characteristics produced in relative units, the characteristics ascribed to the AMB. The AMB strength and stiffness were taken as 1, and the HMB characteristics are already determined from this base value.


**Table 5.** HMB and AMB researched designs.

**Figure 9.** Comparison of the AMB parameters and various HMB designs.

## **5. Results and conclusions**

From the obtained data analysis, it is seen that the maximum stiffness and force value in the air gap has HMB with tangentially magnetized inserts (50 and 40%, respectively, more than AMB indicators for the same weight and overall dimensions). Achieving these characteristics due to the PM inserts will reduce the AMB power consumption at almost two times. The use of a radially magnetized inserts gives little effect: increasing the strength of AMB characteristics by 5–8% and stiffness by 10–12%. In this case, the AMB consumption can be reduced by 8–10%.

HMB with tangential insert provides strength about 130 N in the absence of current in the windings, while the impact strength falls uniformly on the whole rotor. The presence of this force value (25% of the AMB power at maximum current) allows more "gently put" rotor on the bearing harnesses and minimizes the consequences of super heavy transients at AMB failure. HMB with radial inserts provides power of 125–130 N in the absence of power supply, but this force is applied to a small rotor section, and this may lead to a complication of the transition process in case of AMB failure, as it will cause additional "build up" of the rotor.

This chapter also shows that at high temperatures and magnetic core saturation HMB loses control. Thus, generalized approach to the design of AMB and HMB considering nonlinear electromagnetic and thermal dependencies has been developed in this paper.
