Peter Uzunov Associate professor , PhD Bulgaria, Gabrovo , 5300 , Stramnina str. 2 e-mails: pmuzunov@yahoo.com

Figure 11. Micromotor construction Permanent magnet executive DC micromotors Figure 11. Micromotor construction The cross-section of micromotor is shown in Fig.11.The micromotor is excited by a bipolar cylindrical permanent magnet 1(KONIALTI 32 А), magnetized radially. The magnetic flux is closed through the body 3 of soft magnetic material (E 10 steel grade). The armature winding 2 is hollow and rotates in the space between the permanent magnet and the body.

Table III. Major technical specifications of an executive low-inertia DC micromotor with position pick up of DPIMDP 42-20/3,5 type No Quantity Value 1 Rated voltage UN , V 15 2 Rated current IN , А 0,95 3 Rated rotation frequency nN , min-1 3000 4 Rated moment MN , Nm 0,025

OBJECTIVE AND FORMULATION OF THE RESEARCH TASK The theoretical research of the electromagnetic processes in the executive permanent magnet DC micromotor on the basis of the electromagnetic field requires developing of appropriate mathematical models, which take into account some specific features. In that case, the distribution of the magnetic field with actually accounting for the non-linearity of the environment in which it develops, may be obtained by means of a suitable numerical method, such as the FEM. It ensures the possibility to take into account the non-linearity of the magnetic materials forming the magnetic system of the micromotor. Applying this method, the equations of the magnetic field of the micromotor are solved and in result, its distribution is obtained. On that base a number of micromotor parameters can be calculated – torque, useful and consumed active power, efficiency ratio and rotational speed by proper postprocessing. On the basis of the results obtained also the micromotor operating characteristics can be plotted. In order to ascertain the correctness of the approach proposed, the operating characteristics obtained by calculation should be compared to the actual characteristics from the experimental study of the micromotor.

MODELLING OF A PERMANENT MAGNET DC MICROMOTOR MAGNETIC FIELD The micromotor magnetic field is stationary and it is described by the following equations: : magnetic flux density; : magnetic field intensity; : current density; : magnetic permeability The magnetic vector-potential is defined by magnetic flux density in the following manner: By appropriate transformations of these equations the basic equation describing the micromotor magnetic field is obtained:

MAJOR STAGES IN THE APPLICATION OF FEM Drawing the area wherein the problem is solved Fig. 12. Cross-section of the micromotor: 1 – permanent magnet; 2 – armature winding; 3 – motor frame; 4 –shaft;

Defining the properties of the materials TABLE IV The mictromotor materials, their properties and designations are given in Table II.

The program FEMM makes possible the solution to the non-linear problem accounting for the strong dependence of the magnetic properties of ferromagnetic materials upon magnetic flux density by introducing the key magnetization curves of these materials (Fig. 13). a) b) Figure 13. Main curves of magnetization: a) for steel E10(ВН curve №1); b) for Conialti 32A permanent magnet(BH curve №2)

Boundary conditions A necessary condition for the correct solving of the task for the analysis of the micromotor magnetic field is to formulate and input the boundary conditions, which guarantee a one and only solution. In relation with the specifics of this task, Dirihlet’s boundary conditions for the magnetic vector-potential are set to the outer circumference of the body (loop K1 in Fig. 2, а) i.e.

Discretization of the area The area, in which the task is solved (fig.2) is discretized into a mesh of 41924 nodes and 83486 triangular finite elements of first order. This is made automaticly with the help of program TRIANGLE.EXE . The discretized area is shown in figure 14. Fig. 14

Solving the system of linear equations For that purpose solver FKERN.EXE [5] is used. The solver takes a set of data files that describe problem and solves the relevant Maxwell’s equations to obtain values for the magnetic field through the solution domain. As a result of magnetic field analysis, the values of the magnetic vector-potential, magnetic flux density , and magnetic field intensity for each node and element of the discretized region are obtained. Magnetic field flux density distribution in the region concerned is shown in Fig. 15. Figure 15. Magnetic field flux density distribution for the micromotor.

INVESTIGATION OF THE DEMAGNETIZING ACTION OF ARMATURE REACTION Based on the results obtained for the magnetic flux density, the magnetic flux in the air gap and the torque of the micromotor are calculated.The magnetic flux in the air gap is calculated in accordance with the well-known equation: In order to calculate the micromotor torque the Maxwell’s stress tensor is used. In this way the force per unit area is determined, which acts on the surface of an object, placed in the magnetic field. The differential of the force is: The total force on the object is obtained by placing a contour in the air gap, which entirely encompasses the micromotor armature, and by integrating the magnetic force along this contour:

The calculation results are presented in TABLE V. On the grounds of the results the important conclusion can be made, that the demagnetizing action of the armature current is only slightly expressed and it does not influence considerably the operation of the micromotor.

CALCULATION OF THE MICROMOTOR OPERATIONAL CHARACTERISTICS Basing on the results from the calculation of the micromotor torque and from its experimental research, as shown in the last two columns of Table III, the following dependencies may be drawn in the same coordinate system: and for U=UH=const, which are actually a part of the operational characteristics of the micromotor (fig.16). The figure shows well that they coincide to a fine degree, which, on its turn, proves the correctness of the calculations.

Fig. 16. From this characteristic the torque constant kM and electromotive force constant kE are determined; Using these two constants, the rotational frequency, the useful power , the consumed power and the efficiency to the micromotor can be obtained:

The micromotor performance characteristics are plotted according to calculation results from these equations (Fig. 17). In order to ascertain the correctness of the approach proposed, the operating characteristics obtained by calculation should be compared to the actual characteristics from the experimental study of the micromotor. The comparison is shown in Fig. 7. Their remarkable coincidence is seen in the figure. Fig. 17.

8. CONCLUSION The finite elements model developed for analysis of the magnetic field of the executive permanent magnet DC micromotor being researched may be successfully applied in the scientific research when investigating the electromagnetic processes in this kind of electrical machines by means of the FEMM-analysis program based on the FEM. As in this type of electrical micromotors materials with strongly expressed non-linearity of their magnetic characteristics are used, one of the important features of the model developed is the possibility for accounting this non-linearity during the analysis of their magnetic field. The FEM models of the executive permanent magnet DC micromotors give me posibility for optimization procedure and finding the best size of this machine by the exelent electromagnetic parameters.

Furthermore, I have the opportunity, basing on the results obtained from the analysis of the filed by means of the post-processing developed by program means, to research the electromagnetic processes and to calculate a significant for the micromotor quantity such as magnetic flux density and magnetic flux in the air gap of the micromotor, the output torque, rotational frequency, useful power, consumed power and its efficiency. Basing on the result obtained, also the operational characteristics of the micromotor can be established, which have a great importance in the processes of micromotor design, research and operation.

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