Experimental Study of the Working Process and Energy Characteristics of a Solenoid Hammer with Free Run-Out of the Striker

N. P. Ryashentsev, E. M. Timoshenko

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

The study of a solenoid hammer consists in investigating the processes occurring during its operation, determining the nature and magnitude of losses in order to select optimal parameters \[1\] and to find ways of increasing the efficiency and the energy of a single blow of the hammer.

The hammer MS-14 (Fig. 1, a) was studied; its yoke and poles are made as one piece of steel-3. In studying the hammer, the displacement \(S\) of the striker, the curves of variation of the voltage \(u\), and the current \(i\) flowing in the coil were recorded simultaneously by means of an MPO-2 magnetoelectric oscillograph. The circuit for connecting the loops is shown in Fig. 2, and the general view of the experimental setup is shown in Fig. 3. The oscillograms of the voltage, current, and striker travel were recorded at a mains voltage of 172 V. According to the instrument readings, the voltage on the coil was then \(U = 150\) V, the coil current was \(I = 5.3\) A, and the power consumed by the hammer was \(P_c = 360\) W.

The nature of the variation of the voltage on the coil and of the current flowing in it (Figs. 1, g, 4, a) is determined by the nature and magnitude of the applied voltage, the properties of the magnetic circuit, the electrical parameters of the circuit, and the rate of their variation over the hammer’s operating cycle.

The diagram of striker travel (Figs. 1, g, 4, a) was recorded by means of an induction sensor, the circuit and design of which were developed at TPI. On the diagram of striker travel, point \(a\) corresponds to the moment of impact on the tool; points \(b\) and \(v\) indicate the beginning and end of the right-hand pole of the coil; point \(g\) corresponds to the moment when the striker touches the spring (the beginning of spring compression); point \(d\) corresponds to the rear extreme position of the striker (maximum compression of the spring); point \(e\) corresponds to the moment when the elastic forces of the spring cease to act on the striker; and points \(k\) and \(m\) indicate the beginning and end of the left-hand pole of the coil (Fig. 1, v).

For analysis of the hammer operation, by the method of graphical differentiation curves were constructed for the variation of the striker velocity \(V\) over the cycle and of the acceleration, or, on another scale, of the resultant force \(F_b\) (Fig. 4, b) acting on the striker over its entire path of motion, which is determined by the expression

\[ F_{\mathrm{p}} = F \pm F_{\mathrm{п}} \pm F_{\mathrm{б}} \pm F_{\mathrm{э}} \pm F_{\mathrm{у}} \pm F_{\mathrm{т}}, \tag{1} \]

where

\(F\) — the tractive force of the coil;

\(F_{\mathrm{п}}\) — the force developed by the spring;

\(F_{\mathrm{б}}\) — the elastic forces of the air cushion formed between the striker and the tool or between the striker and the damper piston;

Fig. 1. Solenoid hammer MS-14:
a—general view; b—connection diagram; v—hammer diagram; g—oscillogram of the current \(i\), the displacement of the striker \(S\), and the voltage \(u\).

\(F_{\mathrm{э}}\) — forces due to residual induction and eddy currents, the magnitude of which depends on the properties of the magnetic-circuit material and on the structural design of the hammer;

\(F_{\mathrm{у}}\) — the mean value of the reaction force of the tool during the impact.

Fig. 2. Circuit for connecting the instruments and oscillograph loops for the displacement of the striker \(S\), the current \(i\), and the voltage \(u\).

\[ F_y = \frac{m V_y(1+e)}{\tau}, \tag{2} \]

\(e = \dfrac{V_{\text{re}}}{V_y}\) — coefficient of restitution upon impact;

\(V_y,\ V_{\text{re}}\) — striker velocities, respectively, at the moment of impact and rebound;

\(F_t\) — the force of friction of the striker against the guide tube, which depends on the coefficient of friction and the normal pressure force.

It should be noted that, in the case where the axis of the striker does not coincide with the magnetic axis of the solenoid, the electromagnetic forces increase the pressure of the striker on the guide tube. This leads to an increase in the opposing forces, whose magnitude is variable and depends on the position of the striker and on the current flowing in the coil.

Fig. 3. General view of the experimental setup.

From the oscillograms presented, it is seen that, when the striker moves toward the spring after leaving the position of magnetic equilibrium, the current in the coil continues to flow, and on the section of the path \(b, g\) there is appreciably sharp braking. The tractive force of the coil on this section changes its sign to the opposite one and reaches its maximum braking value at point \(g\). By the time equal to 17 milliseconds, the magnetic field of the solenoid collapses, and the action of the braking forces on the striker is considerably reduced. The braking forces acting over the section of the path from 12 to 17 milliseconds cannot be regarded as caused solely by electromagnetic braking, since, in addition to the latter, at the same time—as along the entire path of motion of the striker—mechanical braking forces act, due to friction of the striker against the walls of the guide tube, as well as the elastic forces of the air cushion formed between the striker and the piston (Fig. 1, \(a\)). On the section of the path \(g\)—\(e\), the striker is acted upon by

elastic forces of the damping spring, whose magnitude is determined by the formula

\[ F_{\mathrm{p}} = C_{\mathrm{p}} l_{\mathrm{p}}, \]

where

\[ \begin{aligned} C_{\mathrm{p}} &\text{ is the stiffness of the spring, kg/mm;}\\ l_{\mathrm{p}} &\text{ is the amount of compression of the spring, determined from the oscillogram}\\ &\text{of the striker travel } S \text{ (Fig. 4, a), mm.} \end{aligned} \]

To determine the magnitude of the braking forces during the portion of the cycle from 16 to 20 milliseconds, it is necessary to subtract the spring forces from the forces acting on the striker, i.e. \(F_{\mathrm{t}} + F_{\mathrm{b}} + F_{\mathrm{e}} = F_{\mathrm{r}} - F_{\mathrm{p}}\). After the instant of time equal to 20 milliseconds, current begins to flow in the coil, but the striker still continues to move in the direction of compressing the spring. In this case electromagnetic braking is observed. However, in magnitude the braking electromagnetic forces are small, since at this time the current flowing in the coil is comparatively small, while the working air gap reaches its maximum value. After the striker reaches the extreme point \(d\) and begins moving toward the tool, the action of the electromagnetic forces of the coil and of the elastic forces of the spring coincides with the direction of motion of the striker.

Curve \(A\) (Fig. 4, c) shows the change in the kinetic energy of the striker

\[ \left(A = \frac{mV^2}{2}\right) \]

during the cycle. At point \(b\) the kinetic energy of the striker in the first half of the cycle reaches a maximum value equal to \(0.32\ \mathrm{kgm}\), but by the time it approaches the damping spring (point \(c\)) it decreases by 40%, which indicates a large magnitude of the braking forces in this segment. Further, the kinetic energy of the striker is expended on mechanical losses and on accumulation of energy in the damping spring. At point \(d\) the kinetic energy of the striker is zero. Then the kinetic energy of the striker, as a result of the action of the elastic forces of the spring and the electromagnetic forces of the coil, increases and, at the instant of impact of the striker (point \(a\)) on the shank of the working tool, reaches \(A = 0.43\ \mathrm{kgm}\), whence the useful power of the hammer at an impact frequency \(n = 1500\ \mathrm{blows/min}\) will be

\[ P_2 = \frac{A \cdot n}{0.102 \cdot 60} = \frac{0.43 \cdot 1500}{0.102 \cdot 60} = 105\ \mathrm{W} \tag{3} \]

and the efficiency of the hammer (without allowance for the efficiency of transfer of kinetic energy during impact)

\[ \eta = \frac{P_2}{P_1} = \frac{105}{360} = 0.292 \text{ or } 29.2\%. \]

To determine ways of increasing the efficiency of the hammer, it is necessary to know not only the resultant efficiency, but also the nature of the distribution of the power consumed during the cycle. For this purpose we shall consider the power-balance equation.

Multiplying the equation of electrical equilibrium [2] by the instantaneous value of the current, we obtain

\[ u \cdot i = i^2 R + Li \frac{di}{dt} + i^2 \frac{dL}{dt}. \tag{4} \]

It is known that the energy of the magnetic field is

\[ W_{\mathrm{m}} = \frac{Li^2}{2}. \]

and the rate of its change

\[ \frac{dW_{\mathrm{m}}}{dt} = \frac{d\frac{Li^2}{2}}{dt} = Li\frac{di}{dt} + \frac{1}{2}i^2\frac{dL}{dt}. \tag{5} \]

Substituting the expressions for the time derivative of the inductance and of the coil current, given in paper [3], and (5) into equation (4), we obtain

\[ u\cdot i = i^2R + \frac{d\frac{Li^2}{2}}{dt} + F\cdot V \tag{6} \]

or, what is the same,

\[ P_{\mathrm{c}} = P_{\mathrm{m}} + P_{\mathrm{e}} + P_{\mathrm{b}}, \tag{7} \]

where

\[ \begin{aligned} P_{\mathrm{c}} &= u\cdot i &&\text{— instantaneous value of the power consumed from the network;}\\ P_{\mathrm{m}} &= i^2R &&\text{— instantaneous value of the power expended on copper losses;}\\ P_{\mathrm{e}} &= \frac{d\frac{Li^2}{2}}{dt} + (F-F_{\mathrm{p}})V &&\text{— the sum, respectively, of the rate of change of the magnetic-field energy of the solenoid and the instantaneous value of the power expended by the striker on mechanical losses when }(F-F_{\mathrm{p}})V>0\\ &&&\text{or consumed by it when }(F-F_{\mathrm{p}})V<0\text{ from an internal source of energy, for example, a damping spring;}\\ P_{\mathrm{p}} &= F_{\mathrm{p}}V &&\text{— the power consumed (when }F_{\mathrm{p}}V>0\text{) or delivered (when }F_{\mathrm{p}}V<0\text{) by the striker.} \end{aligned} \]

In the case when the tractive force of the coil is directed opposite to the motion of the striker (electromagnetic braking), the energy accumulated by the striker is spent on increasing the energy of the magnetic field, which is partly returned to the network, dissipated in the form of heat, and, under certain conditions, performs useful work.

The curves of variation of \(P_{\mathrm{c}}\), \(P_{\mathrm{m}}\), \(P_{\mathrm{e}}\), and \(P_{\mathrm{b}}\) (Fig. 4,c) give a clear picture of the conversion of electrical energy into mechanical energy. In plotting the power curves \(P_{\mathrm{c}}\), \(P_{\mathrm{m}}\), and \(P_{\mathrm{b}}\), the values of the current \(i\) and voltage \(u\) were taken from oscillograms (Fig. 4,a), the active resistance of the winding \(R\) was measured with a universal dc bridge of the UMV type, and the instantaneous value of the velocity of the striker \(V\) and of the force \(F_{\mathrm{p}}\) acting on it were determined from the corresponding diagrams (Fig. 4,b). The instantaneous value of \(P_{\mathrm{e}}\) was determined by algebraic summation of the powers \(P_{\mathrm{c}}\), \(P_{\mathrm{m}}\), and \(P_{\mathrm{b}}\).

From Fig. 4,c it is seen that, from the moment the striker begins to move toward the spring, the power \(P_{\mathrm{c}}\) consumed from the network is expended on copper, steel, and mechanical losses, on increasing the magnetic energy of the solenoid, and on producing useful work. In the time interval from 8 to 10 milliseconds, the magnetic energy of the solenoid is also expended on covering losses and producing useful work, and from the time instant of 10 milliseconds onward the magnetic energy of the solenoid, in addition, is partly returned to the network.

In the second half of the cycle the character of the power distribution is analogous to that in the first half of the cycle. With known values of the current, the inductance of the solenoid, and the rates of their change during operation of the hammer

one can determine the magnitude of the braking forces at any point of the striker’s path. This will make it possible to carry out a complete analysis of the distribution of the energy consumed by the hammer and to determine ways of reducing losses.

Fig. 4. Diagram of the working process of the MS-14 solenoid hammer:
a—oscillograms of the displacement of the striker \(S\), the current \(i\), and the voltage \(u\); b—diagrams of the velocity of motion of the striker \(U\), and of the resultant force taking into account the elastic forces of the spring; c—power diagrams: \(P_c\)—power consumed from the mains; \(P_m\)—power expended on copper losses; \(P_b\)—power consumed or delivered by the striker; \(P_e\)—the sum of the rate of change of the magnetic-field energy and the power expended by the striker on mechanical losses, or consumed by the striker from an internal energy source; \(A\)—diagram of the kinetic energy of the striker.

The curves of the variation of powers shown in Fig. 4, c make it possible, in quantitative terms, to establish the distribution of energy, con-

consumed by the hammer, since the areas bounded by each curve and the time axis determine the magnitude of the corresponding energy.

The areas bounded by the curve \(P_c\) and the time axis determine the energies \(W_1, W_3\) and \(W_2, W_4\) (Fig. 4, c), consumed from the network and returned to the network during the first and second halves of the cycle. The energy losses in copper \(W_{11}\) and \(W_{12}\) (Fig. 4, a), respectively for the first and second halves of the cycle, are determined by the areas bounded by the power curve \(P_m\) and the horizontal axis. The energy expended on all losses (except losses in copper) is determined by the algebraic sum of the areas bounded by the curve \(P_e\) and the horizontal axis (Fig. 4, c).

\[ W_t = W_{13} - W_{14} + W_{15} - W_{16} + W_{17}. \]

The kinetic energy accumulated by the striker during its motion toward the spring, \(W_5\), is expended on electromagnetic braking, mechanical losses, and compression of the damper spring \(W_8\) (together constituting \(W_6\)).

The reserve of kinetic energy of the striker at the instant of impact,

\[ W_p = W_7 - W_{10}, \]

(Fig. 4, c) is determined by the algebraic sum of the areas bounded by the curve \(P_b\) in the second half of the cycle and the time axis.

The numerical value of the energy was determined by multiplying the corresponding area, expressed in \(\text{mm}^2\), by the scale factor

\[ k = m_p m_t, \]

where \(m_p\) is the power scale, \(\text{W}/\text{mm}\), and \(m_t\) is the time scale, \(\text{s}/\text{mm}\). On the basis of the results of the calculations performed, an energy diagram (Fig. 5) was constructed for the MS-14 hammer. From the diagram presented it is evident that the efficiency of the hammer (without taking into account the efficiency of the transfer of kinetic energy at impact) is 29.2%, and the largest amount of the energy consumed from the network (48.7%) is expended on thermal losses in copper.

Fig. 5. Energy diagram of the MS-14 hammer.

In the study of a solenoid hammer, it is also of interest to determine the efficiency of the solenoid separately for the first and second halves of the hammer operating cycle. The efficiency can be determined approximately as follows. The useful work of the solenoid during the first half of the cycle is equal to the potential energy accumulated by the damper spring. In Fig. 4, c, the latter is denoted by \(W_8\) and is determined by the area enclosed between the curves \(P_b\) and \(P_b - P_p\). The energy consumed from the network to perform this useful work is equal to \(W_1 - W_2\) (Fig. 4, c), and the efficiency of the solenoid during the first half of the cycle is

\[ \eta_1 = \frac{W_8}{W_1 - W_2}\,100 = 12.3\%. \]

The efficiency of the solenoid during the second half of the cycle is determined by the expression

\[ \eta_2 = \frac{W_7 - W_{10}}{W_3 - W_4 + W_8}\,100 = 42.9\%, \]

where

$W_c - W_{10}$ is the reserve of kinetic energy of the striker at the moment of impact;

$W'_e$ and $W'_t$ are, respectively, the energy consumed from the mains and returned to the mains in the second half of the cycle.

The high efficiency of the solenoid in the second half of the cycle shows that, even with such an imperfect magnetic-circuit design in the laboratory prototype of the MS-14 hammer (the yoke and poles are made from solid pieces, the striker has no grooves), there are considerable possibilities for increasing the efficiency by selecting rational parameters that eliminate electromagnetic braking of the striker. In addition, in order to increase the efficiency of the hammer, the friction forces of the striker against the walls of the guide tube should be reduced by decreasing the coefficient of friction (machining, lubrication) and by reducing the forces acting normally on the friction surface (reducing to a minimum the differences in the air-gap values around the perimeter of the “collar”).

To reduce losses in the steel it is necessary to make the magnetic circuit (the yoke and poles) of powdered material, or laminated from electrical steel. For reasons of mechanical strength the striker cannot be made laminated. It should be made of 5KhVS steel [4] with grooves. The presence of grooves on the striker reduces eddy-current losses, decreases the forces opposing the displacement of the striker that arise as a result of the formation of an air cushion, and increases heat removal.

Elimination of electromagnetic braking and reduction of losses in the steel and of mechanical losses will entail a decrease in the energy consumed from the mains and, consequently, a reduction in copper losses. In addition, in order to reduce copper losses, the magnitude of parasitic air gaps at the joints of the yoke, poles, and striker should be reduced to a minimum, and rational geometrical dimensions of the solenoid should be selected. Taking into account the investigations carried out, the MS-15 solenoid hammer was developed (Fig. 6). The hammer consists of tool 1, fastened in chuck 3, shaped washers 4, front flange 7, body 8, striker 9, which moves in guide tube 11 made of stainless steel 1Kh18N9T, coil 10, pole 12 and yoke 13, made laminated from electrical steel, stop spring 14, textolite piston 15, damping spring 16 with nut 17, and switch 18. The MS-15 hammer operates in a similar manner to the MS-14 hammer [1].

Fig. 6. Solenoid hammer MS-15:
a—section of the hammer; b—connection diagram;

Technical characteristics of the MS-15 hammer

1. Motor — solenoid type.
2. Number of coils — 1.
3. Current frequency — 50 cps.
4. Mains voltage — 220 V.
5. Type of current — alternating, single-phase.

1. Power consumption — 320 W.
2. Impact energy — 0.45 kg·m.
3. Number of blows — 1500 blows per minute.
4. Overall dimensions — 110×250 mm.
5. Weight (without cable and tool) — 5.5 kg.

The hammer is connected to the mains through a converter substation with germanium rectifiers of type VG-10-80.

Fig. 6b. General view of the MS-15 solenoid hammer.

To investigate the working process of the hammer, simultaneous recording was carried out of the displacement of the striker \(S\), the curves of variation of voltage \(u\), power \(P\), and current \(i\) flowing in the coil (Fig. 7, a). The circuit for connecting the instruments is shown in Fig. 2, and the general view of the experimental setup in Fig. 3.

By graphical differentiation of the striker-displacement curve \(S\), curves were constructed for the variation of the striker velocity \(V\) over the cycle and of the acceleration, or, on another scale, of the resultant force \(F_p\) (Fig. 7, b), acting along the entire path of motion of the striker, and of the elastic forces of the spring \(F_p\). Then, by the method described above, curves were constructed (Fig. 7, c) of the power consumed from the mains \(P_c = u \cdot i\), expended on copper losses \(P_m = i^2 R\); of the power consumed or delivered by the striker \(P_b = F_p \cdot V\); and of the sum of the rate of change of the energy of the magnetic field of the solenoid and the instantaneous value of the power consumed or delivered by the striker,

\[ P_e = \frac{d \dfrac{Li^2}{2}}{dt} + (F - F_p)V . \]

From the oscillograms presented, the curves of variation of the striker velocity and of the resultant force, as well as the power curves, it is evident that the MS-15 hammer operates without clearly expressed electromagnetic braking of the striker. The notation for the energies over the working cycle of the MS-15 hammer corresponds to the notation for the energies of the MS-14 hammer, the distribution of which was described above. The energy diagram of the hammer

Fig. 7. Diagram of the working process of the solenoid hammer MS-15:
a—oscillograms of the displacement of the striker \(S\), current \(i\), voltage \(u\), and power \(P_c\); b—diagrams of the striker velocity \(U\), the resultant force \(F_p\) taking into account the elastic forces of the spring, and \(F_p - F_\text{p}\)—the same without the elastic forces of the spring; c—diagrams of power: \(P_c\)—consumed from the network, \(P_m\)—expended on copper losses, \(P_b\)—consumed or delivered by the striker, \(P_e\)—the sum of the rates of change of the energy of the magnetic field and the power delivered or consumed by the striker, \(A\)—diagram of the kinetic energy of the striker.

MS-15, shown in Fig. 8, indicates that the efficiency of the hammer (without accounting for the transfer of kinetic energy during impact) is 33.3%; a significant portion of the energy (36%) is spent on ohmic losses, while the remaining losses amount to 30.7%. In the hammer design presented, by selecting rational hammer parameters and using laminated poles and a yoke made of electrical steel, it was possible to reduce copper losses.

Fig. 8. Energy diagram of the MS-15 hammer.

LITERATURE

1. Ryashentsev N. P., Timoshenko E. M., Frolov A. V., Gronov A. P., On the parameters of a solenoid hammer with free runout of the striker. The article is included in the present collection.

2. Buildin A. D., Fundamentals of Electrical Apparatus Engineering. Gosenergoizdat, 1946.

3. Ryashentsev N. P., Timoshenko E. M., On the theory of a solenoid hammer with free runout of the striker. The article is included in the present collection.

4. Ryashentsev N. P., Frolov A. V., On the question of reducing losses in the steel of a solenoid hammer. Proceedings of the Tomsk Polytechnic Institute, vol. 108, Metallurgizdat, Sverdlovsk, 1959.