N. P. RYASHENTSEV, A. V. FROLOV

SELECTION OF THE OPTIMAL NUMBER OF COIL TURNS FOR A UE-1 ELECTROMAGNETIC IMPACT UNIT

(Submitted by the Department of Mining Machines and Mine Transport)

The influence of the number of coil turns on the operating mode of an electromagnetic impact unit can be analyzed using the equation of electrical equilibrium

\[ u = iR + \frac{d\psi}{dt}, \]

where \(u\) is the line voltage,

\(iR\) is the voltage drop across the ohmic resistance of the coil \(R\) when a current \(i\) flows through it,

\[ \frac{d\psi}{dt} \]

is the rate of change of the flux linkage \(\psi\) with time \(t\).

Replacing the flux linkage \(\Psi\) by the sum of the leakage flux linkage \(\Psi\) and the main flux linkage \(\Psi_0\), and assuming that the main flux \(\Phi_0\), passing directly through the working air gap, is linked with the full number of coil turns \(W\), we may write:

\[ u = iR + \frac{d}{dt}\left(W\Phi_0 + WK_p\Phi_p\right). \]

Here \(K_p\) is a coefficient taking into account the share of participation of all the coil turns in producing the leakage flux linkage, while the product \(WK_p\) is the equivalent number of coil turns linked with the leakage flux.

Replacing the magnetic flux by the magnetic permeance \(G\) and the magnetomotive force of the coil \(iW\), we have:

\[ u = iR + \frac{d}{dt}\left(W^2 iG_0 + W^2 \cdot K_p iG_p\right). \]

Differentiating expression (1), we find the number of coil turns

\[ W^2 = \frac{u - iR} {\left(G_0 + K_pG_p\right)\dfrac{di}{dt} + i\dfrac{d}{dt}\left(G_0 + K_pG_p\right)} . \tag{2} \]

Multiplying and dividing the right-hand side of the denominator by \(d\delta\), where \(\delta\) is the displacement of the striker, we obtain

\[ W= \sqrt{ \frac{u-iR} {(G_0+K_pG_p)\dfrac{di}{dt} +iV\dfrac{d}{dt}(G_0+K_pG_p)} }. \tag{3} \]

In expression (3), \(V\) is the velocity of displacement of the striker.

The magnetic permeances of the air gaps do not depend on the magnitude of the current flowing through the coil and, for a given design of an electromagnetic-type impact unit, are constant for the same air gaps. Consequently, at an unchanged mains voltage \(u\), when the number of turns is varied, first of all the magnitude of the current \(i\) flowing in the coil changes; moreover, the denominator changes faster than the numerator, since the voltage drop across the active resistance of the coil, \(iR\), is usually not more than 6%. It is known that the electromagnetic tractive force depends on the magnitude of the current, but not on the rate of its change [1]. Therefore, when the current in the coil changes, the magnitude of the electromagnetic force moving the striker will change and, as a consequence, so will the velocity of motion of the striker.

The denominator of expression (3) is the sum of the emf of transformation and the emf of motion [1, 2], or, if the numerator and denominator are multiplied by the current \(i\), the sum of the powers expended in producing mechanical work and the reserve of magnetic energy of the coil. Thus, analysis of expression (3) shows that, when the number of coil turns \(W\) is decreased or increased, there is a change in the relations between the powers expended in producing mechanical work and the reserve of magnetic energy of the coil, which characterize the efficiency and the power factor of the impact unit. In an electromagnetic-type impact unit, part of the active energy consumed from the mains is spent in performing useful work, and another part in overcoming harmful resistances (friction, deformation of the spring, hysteresis, eddy currents, energy losses in ohmic resistance). Analysis of expression (3) shows that, when \(W\) is increased, the current and the magnetic flux simultaneously decrease, i.e., copper losses and eddy-current losses decrease. The magnetic energy of an electromagnet is proportional to the product of the current and the flux linkage [1, 2]. When solving the equation of electrical equilibrium under the condition \(R=0\), it is seen that the flux linkage of the electromagnet is determined only by the magnitude and the character of the change in voltage \(u\). Consequently, when the number of turns is increased beyond the optimum value, the efficiency may increase (up to a certain limit), despite a decrease in the energy of a single blow. On the other hand, when the number of turns is decreased, losses in copper and steel increase as a result of the increase in current and magnetic flux. The magnetic flux reaches the saturation value; the demagnetizing action of eddy currents and radial electromagnetic forces increase (as a result of increased leakage fluxes and saturation of the poles). Therefore the impact energy, the efficiency, and \(\cos \varphi\) must decrease.

It is rather difficult to determine analytically from expression (3) the optimum value of the number of coil turns, since the law of variation of the current with time is unknown. Therefore, at present, the experimental determination of the optimum number of coil turns for each particular design of electromagnetic impact unit is of great practical interest. For this purpose, simultaneously

with studies of the working processes of the UE-1 electromagnetic impact unit [3], experimental investigations were carried out to select the optimal winding data for the coil of the impact unit. The results of the experiments (Fig. 1) show that, as the number of turns is increased from 380 and above, the efficiency increases, at first more rapidly and then more slowly.

Fig. 1. Dependence of the impact energy \((A_y)\), the power factor \((\cos\varphi)\), and the efficiency \((\eta)\) on the number of coil turns.

It should be emphasized that, at a number of turns \(W > 500\), unsatisfactory starting and an unstable operating mode of the impact unit are observed. Practically for any ratios of the initial air gap and the initial compression of the striker by the spring, the striker is observed to stop in the position of magnetic equilibrium both at start-up and during operation. Similar phenomena are also observed at \(W < 380\) turns. It should be noted that the obtained values of \(\eta\) and \(\cos\varphi\) are not limiting values for electromagnetic impact units with free striker run-out.

Thus, as a result of experimental investigations on selecting the optimal number of turns of the coil of the UE-1 electromagnetic impact unit, the following has been established:

1. The optimal number of turns at an impact energy of \(4.5\ \text{kgm}\) is 450.
2. When the number of coil turns deviates from the optimum, the energy of a single impact decreases.
3. If it is necessary to reduce the impact energy, the number of turns should be increased, since in this case the efficiency and the power factor of the UE-1 electromagnetic impact unit simultaneously increase.

REFERENCES

1. P. L. Kalantarov, L. R. Neiman. Theoretical Foundations of Electrical Engineering. GEI, 1951.
2. A. I. Moskvitin. Electrical Machines of Reciprocating Motion. Academy of Sciences of the USSR, 1950.
3. O. D. Alimov, N. P. Ryashentsev, A. V. Frolov. On the creation of electric drilling machines of rotary-impact action. Article in the present collection.