ON THE CHOICE OF THE OPTIMAL DEPTH AND NUMBER OF GROOVES IN THE STRIKER OF A SOLENOID HAMMER

N. P. RYASHENTSEV, A. V. FROLOV

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

At present, the stable maximum efficiency coefficient (efficiency) of solenoid hammers with a free run of the MC-15 type striker is 35–40%. Such a high efficiency, in comparison with other designs of impact-action machines [1, 2], is the result of careful design refinement of all the units of the hammer and of its power-supply circuit. The use of a specially shaped magnetic circuit [3, 4] made it possible to sharply reduce losses in the steel of the hammer, while work carried out to determine the rational shape of the coil [4] revealed the possibility of reducing losses in the copper of the coil while at the same time reducing its weight per unit power of the hammer.

Investigations carried out at the Department of Mining Machines and Mine Transport of the Tomsk Polytechnic Institute made it possible to outline the following principal ways of further increasing the efficiency of solenoid hammers with a free run of the striker.

1. Selection of rational parameters eliminating electromagnetic braking of the striker at the moment it leaves the position of magnetic equilibrium.

2. Selection of the stiffness and natural frequency of the damping spring corresponding to the operating mode of the hammer.

3. Reduction of losses due to friction of the striker against the walls of the guide tube.

4. Reduction of the radial forces acting on the striker as a result of its eccentric position in the guide tube.

5. Reduction of losses in the steel of the magnetic circuit and of the striker.

6. Reduction of ohmic losses in the coil of the solenoid hammer.

Analysis of the energy diagram of solenoid hammers with a free run of the striker shows that the main losses are the losses in the steel of the hammer and the ohmic losses of the coil, amounting in total to as much as 60% of the total power consumed, with losses in the steel predominating. The losses in the steel consist of magnetization-reversal (hysteresis) losses and eddy-current losses. Since the magnetic circuit of the solenoid hammer (the yoke and poles) is made of transformer steel, the magnitude of the hysteresis losses in it will be insignificant. Obviously, the hysteresis losses in the hammer will be determined mainly by the hysteresis losses in the steel of the striker, which performs—

It is made of high-quality structural steel with subsequent hardening to a specified hardness, which causes a further increase in hysteresis losses owing to an increase in residual induction and coercive force. If the striker were in an alternating magnetic field, the hysteresis losses in it would constitute a significant percentage in comparison with other energy losses. In practice, solenoid hammers with free travel of the striker are supplied by a single-phase rectifier circuit, and a unidirectional pulsating current flows through the hammer coil. In this case the magnetic-field intensity will also be unidirectional and pulsating, since the intensity is directly proportional to the first power of the magnetizing current in the winding, and remagnetization of the material will not be observed.

Thus, the losses in the steel of a solenoid hammer consist of eddy-current losses. The eddy-current losses in the hammer are made up of losses in the magnetic circuit and in the striker.

For the magnetic circuit of the hammer, made of sheets of weakly alloyed sheet steel E12 insulated from one another, the specific losses at an induction of \(14 \cdot 10^3\) gauss are about \(6\ \mathrm{W/kg}\).

With a magnetic-circuit weight of \(0.8\ \mathrm{kg}\), the total losses in the steel (including those due to remagnetization) will be equal to \(4.8\ \mathrm{W}\), or about \(2\%\) of the total power consumed by the hammer.

Thus, we have arrived at the conclusion that the principal losses in solenoid hammers with free travel of the striker are the ohmic losses in the copper of the coil, proportional to the square of the total current, and the eddy-current losses in the hammer striker. The magnitude of the ohmic losses, without changing the operating parameters, can be reduced only by reducing the magnitude of the current flowing in the coil, which, in turn, can be achieved only by reducing the active component of the current. It is inadvisable to reduce the magnitude of the magnetizing component of the current, since simultaneously with this the magnetizing force of the coil, which determines the useful work performed by the solenoid hammer, will also decrease.

It is known that the magnitude of the active component of the current of a coil with a core is directly proportional to the equivalent ohmic resistance of this core [5], or, in other words, to the magnitude of the eddy-current losses. Therefore the eddy-current losses in the striker are the element in the hammer design through which the efficiency can be substantially increased and, consequently, the heating of the solenoid hammer, which is one of its serious shortcomings, can be reduced.

The principal means of reducing eddy-current losses in the striker are:

1. The development of supply circuits for solenoid hammers that make it possible to obtain a flat top of the magnetic-induction curve.

2. The use of ferromagnetic materials with low specific electrical conductivity.

3. The selection of the mode and method of mechanical and heat treatment of the striker.

4. The selection of the shape and design of the striker having the greatest equivalent active resistance.

All these methods are covered more or less fully in the literature [6, 7, 8].

The purpose of the present work is to clarify partially the question of the influence of grooves in the striker of a solenoid hammer on the losses in the steel.

The striker of a solenoid hammer with free travel is made of structural steel 5KhV2S in the form of a cylinder. In order to reduce eddy-current losses, grooves are cut along the generatrix of the striker.

(Fig. 1, b), and the number of grooves and their depth are chosen without substantiated considerations. This leads to an increase in the cost of manufacturing the striker because of the increased volume of milling work; the cross section of the striker is reduced, which leads to an increase in the magnetic reluctance of the striker without a substantial reduction in eddy-current losses as compared with the optimal number and depth of grooves.

Fig. 1. Connection diagram of the instruments—a—and external view of the hammer striker—b.

In order to determine the qualitative and quantitative influence of the depth and number of grooves on the magnitude of losses due to the action of eddy currents, studies were carried out to select a rational shape of the striker of a solenoid hammer with free run.

The research methodology was based on the following premises. All investigations were carried out in a mode in which the hammer striker was in a position of magnetic equilibrium and the magnetic energy of the coil was not converted into mechanical energy; this made it possible simply and with sufficient accuracy to determine the losses in the steel of the magnetic system of the hammer. During the investigation the armature and the poles were removed, in order to reduce the error in determining the losses in the steel of the striker. The measurements were made according to the circuit shown in Fig. 1, a.

The losses in the steel of the striker were determined by the ammeter-and-wattmeter method, the essence of which is that the power \(P\), indicated by the wattmeter connected into an electric circuit containing a coil with an iron core, is composed of the power of the losses in the steel of the core \(P_{\text{st}}\) and the power expended in the coil winding \(P_{\text{m}}\), taking into account the losses in the measuring instruments themselves.

The maximum value of the induction in the striker was determined by means of a measuring turn \(K\), placed on the guide tube of the solenoid hammer and measuring the induction in a strictly defined cross section of the striker. Measurement of the emf induced in the turn was performed by an instrument of the magnetoelectric system, connected in series with a germanium diode. The shape and magnitude of the emf of self-induction were monitored with an EO-6M electronic oscillograph.

It is known that an instrument of the magnetoelectric system indicates the average value of the measured current. With single-half-period rectification

\[ e_{\mathrm{av}}=\frac{1}{T}\int_{t_1}^{t_2} e\,dt =-\frac{W}{T}\int_{t_1}^{t_2} d\Phi = W f(\Phi_{t_1}-\Phi_{t_2}), \]

where \(f=\dfrac{1}{T}\) is the frequency of flux variation.

In the case of a germanium rectifier, the limits of integration must be taken from 0 to \(\dfrac{T}{2}\), which corresponds to the passage of the emf through 0. At these instants of time \(\dfrac{d\Phi}{dt}=0\), but the function itself has its maximum value. In the absence of even harmonics,

\[ \Phi_0=-\Phi_{T/2}=\Phi_{\max}. \]

Then

\[ e_{\mathrm{av}}=2Wf\Phi_{\max}. \]

Thus, by measuring the average value of the emf in the measuring turn, one can determine the maximum value of the magnetic flux passing through the section of the striker,

\[ \Phi_{\max}=\frac{e_{\mathrm{av}}}{2Wf}, \]

without additionally determining the shape factor of the self-induction emf curve in the measuring turn, and can carry out studies of losses in the striker steel both with sinusoidal and with pulsating currents in the hammer coil.

When studying with pulsating current, the rectifier in the circuit of the measuring turn must be connected in such a way as to measure the average value of the self-induction emf corresponding to the increase of current in the hammer coil.

The losses in the striker steel were determined as the difference between the wattmeter readings and the ohmic losses in the measured circuit,

\[ P_{\mathrm{st}}=P-I^2R. \]

The total active power consumed by the hammer coil and the magnitude of the current flowing in it were measured by instruments of the electrodynamic system with accuracy classes of 0.5 and 0.2, respectively. The relative errors of the instruments over the entire measurement range did not exceed 1.5% for current, 2.2% for power, 1.5% for resistance, and 4% for emf.

The relative error in determining the losses in the striker steel was calculated from the expression

\[ \gamma_{\mathrm{st}}= \frac{\Delta P+\Delta P_{\mathrm{m}}}{P-P_{\mathrm{m}}}\,100\%, \]

where

\[ \Delta P \]

is the absolute error in determining the power recorded by the wattmeter;

\[ \Delta P_{\mathrm{m}} \]

is the absolute error in determining the copper losses,

\[ \Delta P_{\mathrm{m}} =\left(\frac{2\Delta I}{I}+\frac{\Delta R}{R}\right)P, \]

where \(\Delta I\) and \(\Delta R\) are, respectively, the absolute errors in current and resistance. The relative error in measuring the losses in the steel did not exceed \(2.62\%\).

Figure 2 presents the results of investigations of the losses in the steel of the striker of a solenoid hammer as a function of magnetic induction for different numbers of grooves and their constant depth.

Fig. 2. Dependences of losses in steel on magnetic induction.

Owing to the nonuniformity of the strikers in terms of weight characteristics due to the grooves, the losses in the steel are referred to unit weight of the striker.

In Fig. 2 the following are denoted, respectively: 1—a solid striker, without grooves; 2—one groove; 3—two grooves; 4—four grooves; 5—six grooves; 6—five grooves of the same depth as for the case of curves 2–5 and one to the center.

The losses in the steel of the striker represent a typical quadratic dependence on induction, i.e., a parabolic curve symmetric with respect to the ordinate axis. It is evident from Fig. 2 that the magnitude of the losses in the steel of the striker at the same value of induction is smaller the greater the number of grooves in the striker; moreover, this decrease does not obey the law of inverse proportionality, but has a more complex dependence. Up to certain limits, increasing the number of grooves leads to a sharp decrease in losses; with a further increase in the number of grooves, the losses in the steel decrease only insignificantly. Increasing the depth of one of the grooves does not lead to any appreciable decrease in the losses in the steel of the striker (curves 5 and 6). This is evidently explained by the influence of the surface effect.

Thus, increasing the number of grooves in the striker leads to a decrease in the losses in the steel, which, in turn, reduces the active component of the current passing through the hammer coil. As a result, the ohmic losses in the coil also decrease, determined by both the reactive and the active components of the current, as shown in Fig. 3, which presents the dependence of the losses in the copper of the coil on induction for

in the same notation as in Fig. 2. It is seen from Fig. 3 that increasing the number of grooves leads to a decrease in the copper losses of the hammer, despite the fact that the equivalent inductance of the hammer decreases as the number of grooves increases, owing to the decrease in the magnetic conductivity of the air gap. Obviously, the decrease in the active component of the current occurs by a more significant amount than the increase in the reactive component.

Fig. 3. Dependences of copper losses on magnetic induction.

In order to clarify more precisely the nature of the influence of the number of grooves on the losses in the steel of the striker, Fig. 4 presents the dependences of the losses in steel on the number of grooves in the striker for different values of magnetic induction. It is seen from Fig. 4 that the number of grooves has a substantial influence on the losses in the steel of the striker, and in quantitative terms this influence does not depend on the magnitude of the magnetic induction.

Indeed, at an induction of \(5.5\) kGs, increasing the grooves from one to two causes a reduction of losses by a factor of \(1.48\); at an induction of \(8\) kGs, by a factor of \(1.4\); and at an induction of \(13\) kGs, by a factor of \(1.48\). Increasing the number of grooves from 4 to 5 gives a reduction of losses, for the same induction values, by factors of \(1.24\), \(1.28\), and \(1.24\). Thus, the character of the influence of the number of grooves on the losses in the steel of the striker is the same for different values of magnetic induction (within the limits of measurement error).

This makes it possible to construct a percentage characteristic that most fully reflects the relationship between the losses in steel and the number of longitudinal grooves in the striker of a solenoid hammer. In constructing this characteristic, along one axis we shall plot the number of grooves, and along the other—the specific losses in the striker steel, expressed in percent, i.e.

\[ \delta = \frac{P_0 - P_n}{P_0} 100\%. \]

where \(P_0\) is the loss in the steel of a solid striker (without grooves);
\(P_{\text{п}}\) is the loss in the steel of a striker with longitudinal grooves.

The calculation results are presented in Fig. 4 in the form of the curve \(\delta\), emerging from the origin; from it one can see that the greatest reduction in losses is achieved in the case of two grooves. With a further increase in the number of grooves from 2 to 5, the losses decrease more smoothly. When the number of grooves is greater than 5, the losses in the steel decrease by an insignificantly small amount, remaining practically the same. This can be explained by the fact that, as the number of grooves in the striker increases, the cross section of the striker simultaneously decreases. Consequently, for the same value of the magnetic flux, the induction in the striker will increase, and the eddy-current losses will increase in proportion to its square. Indeed, when the number of grooves is increased from 6 to \(\infty\), the losses in the steel decrease by only 20% (Fig. 4).

In Fig. 4: vertical axes—“Eddy-current losses, \(\delta\), %” and “Steel losses, W”; horizontal axis—“Number of grooves.”

Fig. 4. Dependence of the losses in the steel on the number of grooves.

Thus, an investigation of the dependence of the losses in the steel of the striker on the number of grooves shows that, from the standpoint of reducing the losses in the striker steel and the amount of milling work, it is advisable to choose the number of grooves within the range \((5—8)\), depending on the diameter of the striker (increasing them as the striker diameter increases).

To determine the optimal groove depth, Fig. 5 presents the dependence of the losses in the striker steel on the groove depth for several values of the magnetic induction. Along the abscissa axis is plotted the relative groove depth in percent, i.e.

\[ h_0 = \frac{h}{R}\cdot 100\% . \]

where

\(h\) — groove depth,
\(R\) — striker radius.

From Fig. 5 it is seen that, with an increase in the groove depth, the losses in the striker steel decrease to certain limits, which are different for different values of magnetic induction. For example, at an induction of 13 kGs, increasing the groove depth from 70% to 100%, i.e., by 30%, reduces the losses in the steel by 3.5%, whereas at an induction of 8 kGs it reduces them by only 0.5–0.8%.

Fig. 5. Dependence of losses in steel on groove depth.

Constructing a percentage characteristic, as was done for the case considered in Fig. 4, is impossible here, since the rate of change of losses in the steel, as shown, depends not only on the groove depth but also on the magnitude of the magnetic induction; this is explained by the manifestation of the skin effect [5, 9]. The penetration depth of the magnetic flux is determined by

\[ \Delta = k \sqrt{\frac{\rho}{\mu f}}, \]

where

\(k\) — a constant quantity;
\(\rho\) — the electrical resistivity of the striker material;
\(\mu\) — magnetic permeability;
\(f\) — mains frequency.

High-quality structural steel grade 20-45 is characterized by the fact that, with an increase in magnetic induction from 0 to 4–6 kGs, the relative magnetic permeability increases to a maximum value. With a further increase in induction, the magnitude of the magnetic permeability decreases, and the faster, the greater the magnetic induction [7, 10]. For example, when the magnetic induction is increased from 5 to 14 kGs (for steel 20), the magnetic permeability decreases by a factor of 2.2, and consequently the penetration depth \(\Delta\) increases by a factor of 1.48; therefore, to reduce eddy-current losses, the groove depth must be increased by no less than a factor of 1.48. Obviously, for any

for the values of magnetic induction in the striker of a solenoid hammer, there exist quite definite optimal values of the groove depth, i.e., such values of the groove depth at which the losses in the steel and the volume of milling work will be minimal. On the basis of the research results given in Fig. 5, the dependence of the groove depth in the striker of a solenoid hammer on the magnitude of the magnetic induction is shown, which is presented in Fig. 2 as the curve \(h_0\); from this curve, knowing the value of the induction in the striker, one can choose the optimal value of the groove depth.

All values of the groove depth lying above the curve lead to an increase in the volume of milling work, a reduction in the cross section of the striker and in its mechanical strength, without any substantial reduction in losses in the steel of the striker.

Conclusions

The research method employed makes it possible, with sufficient accuracy, to select the number and depth of grooves in the striker of a solenoid hammer for the purpose of reducing eddy-current losses.

A study of the dependence of losses in the striker steel on the number of grooves showed that, from the standpoint of reducing losses and the volume of milling work, it is advisable to choose the number of grooves within the range \((5\text{--}8)\), depending on the diameter of the striker. It has been established that for any value of magnetic induction there exists a quite definite groove depth corresponding to the minimum volume of milling work and the maximum reduction of losses in the striker steel.

In Fig. 2 a dependence is constructed for determining the optimal groove depth.

References

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2. Alabuzhev P. M., Ryashentsev N. P., “Solenoid Hammers.” Proceedings of TPI, vol. 108, 1959.

3. Ryashentsev N. P., Alimov O. D., Timoshenko E. M., Frolov A. V., Author’s Certificate No. 132578.

4. Ryashentsev N. P., Frolov A. V., Timoshenko E. M., Author’s Certificate No. 139622.

5. Kalantarov V. I., Neiman L. R., Theoretical Foundations of Electrical Engineering. GEI, 1951.

6. Ryashentsev N. P., Investigation of the Working Process of Solenoid Hammers with a Sparkless Switch. Candidate dissertation, TPI, 1959.

7. Vonsovskii S. V., Modern Theory of Magnetism. GTTI, 1953.

8. Ryashentsev N. P., Frolov A. V., “On the Question of Reducing Losses in the Steel of Solenoid Hammers.” Proceedings of TPI, vol. 108, 1959.

9. Vainberg A. M., Induction Melting Furnaces. GEI, 1960.

10. Vitenberg V. I., Calculations of Electromagnetic Relays. GEI, 1961.