The influence of the geometric profile of the air gap on the power and energy characteristics of an electromagnetic engine

The influence of the geometric profile of the air gap of the magnetic circuit on the power and energy characteristics of an electromagnetic engine is considered. The research is relevant because of the need to improve the methods for the optimal construction of electromagnetic engines to solve the complex problem of increasing the efficiency of vibration systems with linear displacements of executive parts. The object of research is the construction of an electromagnetic motor created on the basis of an electromagnet with a flat attracting armature. The research was performed using finite element magnetic field simulation using the program Finite Element Method Magnetics (FEMM). Options for building models are considered. The differences in the efficiency of using the compared structures of electromagnetic motors of the same size and weight from the conditions of their economy are shown. The magnitude of the electromagnetic force and mechanical work are used as evaluation criteria. The research results are interesting for specialists in the field of electromechanical engineering devices with linear displacements of executive parts.


Introduction
Due to the relative simplicity of design, controllability and reliability, linear electromagnetic motors are widely used in various industries [1][2][3][4][5]. These are, for example, vibration and vibration-shock machines and installations, compressors, construction power tools, electric pumps [6][7][8][9]. The main requirements for modern electric drives based on electromagnetic engines are high reliability and performance, low power consumption, low manufacturing cost, the high value of force on the interval of armature movement, restrictions on overall dimensions and weight [10][11][12][13]. Analysis of existing types of electromagnetic engines shows that these requirements for a certain category of devices can be partially satisfied, for example, due to the special construction of the magnetic system. In that case, if the rational type and, accordingly, the shape of the magnetic system of the electromagnetic motor are known, the task of multivariate analysis with the choice of the best of several options does not cause difficulties. An analysis of the existing types of electromagnetic engines leads to the main conclusion that during certain construction conditions must exist that correspond to some optimal function in the formation of the traction characteristic due to the spatial geometry of the interacting elements of the internal structure of the magnetic circuit [14,15]. One of these provisions is the change in the geometric profile of the air gap, which allows getting different forces on the interval of movement of the armature, increase the magnetic induction in the working air gap due to the highest concentration of the magnetic field, decrease in magnetic resistances [16][17][18][19]. The main goal of the research is to solve the problem of improving the methodology for the optimal construction of an electromagnetic engine created on the basis of an electromagnet with a flat

Methods and Tools
In this work, we performed a comparative analysis of electromagnetic engines of the same size and weight of active materials and showed the influence of the geometric profile of the air gap of the magnetic circuit through output indicators widely used in practice, obtained using finite element modelling of the magnetic field. When obtaining static traction characteristics, only the shape of the air gap profile of the magnetic circuit was changed. The remaining parameters of electromagnetic engines, including the number of turns of coils, external dimensions and volumes occupied by active materials, were maintained unchanged throughout the experiment. To obtain comparable data, all the studied profiles of electromagnets had the same steel grade and the cross-sections of the magnetic circuit in the main flow path. The number of turns of the coil w = 1200, current I = 4 А. The value of the working air gap varied within the same range of 0...10 mm. Traction characteristics were taken at the same values of magnetizing forces. The measures taken ensure that the cooling and heating conditions are identical when comparing different options. The design of the electromagnetic motor is shown in Figure 1. An example of calculating the magnetic field in the FEMM program is presented in Figure 2.  In the final position of the armature, all electromagnetic engines have the same magnetic circuit profile.
As an example, Figure 2 shows the final results of constructing the field of model variants in the form of magnetic flux lines. The results are obtained by numerically calculating the active volume of the created models using finite element modelling in the FEMM program [23][24][25][26].
As follows from Figure 4, in the range of the armature stroke 0.05 ... 2 mm, the electromagnetic motor with the geometric profile of the magnetic circuit prevails with the classical (flat) configuration of the air gap in terms of maximum traction forces (Figure 3, e).    (Figure 3, b); 6with an inclination of 30 degrees (Figure 3, b); 7with an inclination of 45 degrees to the other side (Figure 3, b); 8with cone profile (Figure 3, a); 9with an inclination of 45 degrees (Figure 3, b); 10with 3 teeth (Figure 3, c); 11with an inclination of 60 degrees to the other side (Figure 3, b); 12with an inclination of 60 degrees (Figure 3, b) With an increase in the size of the working air gap in the range of 6 ... 12 mm, the maximum values of traction forces are dominated by electromagnets with the constructive shape of the magnetic circuit, made according to Figure 3 The full mechanical work was defined as the area bounded by the corresponding traction curve and the abscissa axis within the armature displacement x = 0 ... 12 mm. The maximum conditional useful work was understood as the maximum value of the product of electromagnetic force and the value of the armature stroke corresponding to a given force. The maximum conditional useful work determined the optimal value of the working air gap. The same value of the working air gap corresponds to the optimum force for maximum work.

Conclusion
The research results prove the feasibility of determining the optimal use of different geometric profiles of air gaps from the analysis of the estimated traction characteristics obtained using finite element modelling of the magnetic field, which simplifies the solution of the optimal search problem.
For the same operating conditions for given dimensions and parameters of the magnetic system, the magnitude of the electromagnetic force and mechanical work substantially depend on the geometric profile of the air gap of the magnetic circuit.
For different geometric profiles of the air gap, the conditional useful work of the investigated variants of magnetic systems can differ significantly.