Method for the Experimental Determination of the Optimal Parameters of a Solenoid Hammer with Free Running of the Striker

N. P. Ryashentsev, E. M. Timoshenko

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

In a solenoid hammer [1], as in any electrical machine, the power is limited by heating. Therefore, before proceeding to the experimental determination of the optimal parameters of the hammer, it is necessary, having specified the overall dimensions of the solenoid, to determine the permissible magnitude of the losses in it.

The task of the experimental investigations, therefore, is to determine such parameters of the hammer at which, from a given solenoid size, the greatest useful power can be obtained at the permissible value of overheating of the winding.

For given solenoid dimensions, without changing the body part of the hammer and thereby without changing the cooling surface, it is possible to vary the following hammer parameters: a) the diameter of the winding wire and the number of turns, seeking the best use of the coil window; b) the mass of the striker by changing its length and diameter; c) the pole taper angle; d) the stiffness of the spring; e) the magnitudes of the travel of the striker to the chuck and to the spring.

It is convenient to compare different design variants of the solenoid according to two main indicators characterizing the operation of the hammer: the consumed and useful power, which make it possible to determine the efficiency and the specific power per unit weight of the hammer. Therefore, if one does not set as the objective the study of electromechanical transient processes, oscillographic recording of the working process need not be carried out. It is advisable to determine only the velocity of the striker immediately before impact by the simplest and most reliable method. Such a method is the determination of the striker velocity before impact by means of a contact sensor, since it is simple in design, convenient and reliable in operation, has less influence on the operating mode of the hammer in comparison with other sensors (potentiometric, inductive), and permits tests to be carried out under conditions close to real ones (when the hammer is working on concrete, brick masonry, and similar materials).

The contact sensor (Fig. 1, a) consists of sensor rod 6, moving in textolite bushing 5; spring 3, which presses sensor rod 6 against chuck 2 through textolite piston 4; tex—

of the ebonite bushing 1, which insulates the adapter from the hammer body, and constitutes a switch that makes it possible, by means of the hammer striker 7, to control the measuring circuit, consisting of battery Б and the ENO-1 electronic oscilloscope.

Fig. 1. For determining the velocity of the striker before impact using a contact sensor and an electronic oscilloscope:
a—design of the sensor and the measuring circuit; b—for determining the time scale; c—for determining the time between current pulses.

The measuring circuit is closed at the moment the striker 7 touches the sensor rod 6, and is opened when the sensor rod is recessed and the electrical contact between the sensor rod and the cartridge is broken. The circuit is closed again when the striker strikes the cartridge, and is opened when the striker rebounds. Two pulses appear on the oscilloscope screen. The distance \(l_2\) (Fig. 1, c) between the beginnings of these pulses corresponds to the time during which the striker travels the path \(S\) (Fig. 1, a) before impact. The velocity of the striker before impact is

\[ V = \frac{S}{l_2 m_t}. \]

The time scale \(m_t\) is determined from the oscilloscope screen (Fig. 1, b)

\[ m_t = \frac{n \cdot t_0}{l_1}, \]

where

\(n\) — number of calibration marks;
\(t_0\) — time between the preceding and following marks;
\(l_1\) — distance between \(n\) marks.

The relative error in calculating the striker velocity before impact is

\[ \frac{\Delta V}{V} = \frac{\Delta S}{S} + \frac{\Delta l_1}{l_1} + \frac{\Delta l_2}{l_2} + \frac{\Delta t_0}{t_0} = 0.05, \]

where

\[ \frac{\Delta S}{S}=\frac{0.04}{4}=0.01 \]

is the relative error of measuring, with a micrometer, the length of the projecting part of the sensor rod \(S=4\) mm (Fig. 1, a);

\[ \Delta l_1=\Delta l_2=1\ \text{mm} \]

is the absolute error in determining with a ruler with millimeter divisions, respectively, the distance between the \(n\) marks \(l_1=100\) mm (Fig. 1, b) and the distance between the current pulses \(l_2=50\) mm (Fig. 1, c);

\[ \frac{\Delta t_0}{t_0}=00.1 \]

is the time error of the ENO-1 oscillograph.

The impact energy and the useful power of the hammer are determined from the formulas

\[ A=\frac{mV^2}{2}; \qquad P_p=\frac{A\cdot n_1}{0.102\cdot 60}=246\cdot A, \]

where \(m\) is the mass of the striker;

\(n_1=1500\) is the number of hammer blows per minute at a current frequency of 50 Hz.

The error in calculating the impact energy and the useful power of the hammer consists of the errors in determining the striker velocity before impact and the striker mass. Thus, with a striker weight of 200 g and an absolute error in its determination of 1 g, the relative error in calculating the useful power is

\[ \frac{\Delta P_p}{P_p} = \frac{\Delta m}{m} + 2\frac{\Delta V}{V} = \frac{1}{200}+2\cdot 0.05 = 0.105\ \text{or}\ 10.5\%. \]

Since, for constant solenoid parameters, the magnitude of the consumed \(P_c\) and useful \(P_p\) power of the hammer depends to a large extent on the striker overtravel toward the chuck \(Y\) and toward the spring \(X\), in carrying out the investigations it is necessary, for each version of the solenoid design, to determine such striker travel parameters \(X\) and \(Y\) as ensure the greatest value of useful power at an admissible value of winding overheating. For this purpose, using a contact sensor and a wattmeter, the variation of the useful hammer power \(P_p\) and consumed power \(P_c\) is determined as the magnitude of the striker overtravel toward the chuck \(Y\) is varied, for various fixed values of overtravel toward the spring \(X_i\).

A family of curves is plotted (Fig. 2): consumed power \(P_c=f_1(Y)_{x_i}\), useful power \(P_p=f_2(Y)_{x_i}\), and losses \(P_{pp}=f_3(Y)_{x_i}\), as the difference \(P_c-P_p\), for all fixed values \(x_i\).

In the investigation it is desirable to take a large range of values of \(X\) and \(Y\), since in this case it becomes possible to determine the region of striker-travel parameters for which the hammer operates stably. In Fig. 3 the region of striker-travel parameters for which the hammer operates stably is represented by the hatched area. Then, by the resistance method or with thermocouples, the magnitude of the losses in the hammer is determined at which the heating of the coil does not exceed the permissible values. A straight line \(A-A\) (Fig. 2), corresponding to the magnitude of the permissible losses, is drawn parallel to the abscissa axis, intersecting the curves \(P_{pp}=f(Y)_{x_i}\) at points \(a\), \(b\), \(c\).

In Fig. 2, the subscript of the quantity \(X\) corresponds to the magnitude of the striker travel up to the spring, expressed in mm. Thus, the points \(a, b, c\) that have been found make it possible to construct the curve \(a, b, c\) (Fig. 3) of the dependence of the striker travel up to the

Run-up of the striker to the spring \((X)\), mm. Run-up of the striker to the cartridge \((Y)\), mm.

Fig. 2. Curves of dependence of the consumed \(P_c\), useful \(P_n\) power and losses \(P_{nm}=P_c-P_n\) on the magnitude of the run-up to the cartridge and to the spring.

cartridge \((Y)\) on the striker travel along the spring \((X)\), for which the losses in the hammer will be constant. This curve divides the region of stable operation of the hammer (Fig. 3) into two zones: the first of them lies below the curve and corresponds to the parameters of striker travel that provide losses in the hammer below the permissible value; the second—above the curve of equal losses—corresponds to the parameters of striker travel for which the losses in the hammer exceed the permissible value.

It remains further to determine for which parameters of striker travel, lying on the curve of equal losses (Fig. 3), the hammer has the greatest useful power and, correspondingly, efficiency. For this purpose, from the points \(a, b, c\), lying on the curves \(P_{nm}=f_3(Y)_{x_i}\) (Fig. 2), vertical lines are drawn to their intersections with the corresponding curves \(P_c=f_1(Y)_{x_i}\) and \(P_n=f_2(Y)_{x_i}\). For example, through the point \(a\), lying on the curve \(P_{nm}=f_3(Y)_{x_{15}}\) (Fig. 2), a vertical straight line is drawn to its intersections with the curves \(P_c=f_1(Y)_{x_{15}}\) and \(P_n=f_2(Y)_{x_{15}}\).

The obtained intersection points \(a'\), \(b'\), \(c'\) and \(a''\), \(b''\), \(c''\) lie on the curves of useful and consumed power, respectively, for such parameters of the striker travel at which the losses in the hammer are identical and equal to an admissible value.

Fig. 3. Region of stable operation of the hammer and the curve of equal losses.

If the gap between the obtained points is large, as, for example, between points \(a\) and \(b\) in Fig. 2, and it is difficult to draw a smooth curve connecting the points \(a'\), \(b'\), \(c'\) and \(a''\), \(b''\), \(c''\), then additional points are found by the following constructions. The distance between points \(a\) and \(b\) is divided in half and a vertical straight line \(B—B\) is drawn. In Fig. 2 it corresponds to a value of the striker run to the cartridge of 19 mm. From the points obtained at the intersection of the curves \(P_c = f_1(Y)_{x_i}\), \(P_{\mathrm{con}} = f_3(Y)_{x_i}\), and \(P_u = f_2(Y)_{x_i}\) with the straight line \(B—B\), the curves (Fig. 2) of the dependence of \(P_c\), \(P_{\mathrm{con}}\), and \(P_u\) on the value of the run to the spring at a constant run to the cartridge are constructed. Through the point of intersection \((d)\) of the straight line of equal losses \(A—A\) (Fig. 2) with the constructed curve \(P_{\mathrm{con}} = f_3(X)_{y_{19}}\), a vertical line is drawn up to its intersection with the curves \(P_c = f_4(X)_{y_{19}}\) and \(P_u = f_6(X)_{y_{19}}\), and the additional points \(d''\) and \(d'\) are determined; these are then projected onto the straight line \(B—B\). From the points thus found, \(a''\), \(d''\), \(b''\), \(c''\) and \(a'\), \(d'\), \(b'\), \(c'\), the curves \(P_c\), \(P_u\), and the efficiency, etc., are constructed (Fig. 4). The points of the efficiency curve are determined by dividing the useful power by the consumed power, taken from the curves \(P_c\) and \(P_u\) (Fig. 4) for identical values of the striker run to the cartridge.

The maximum value of the efficiency corresponds to the optimum value of the striker run to the cartridge. Thus, for the case shown in Fig. 4, the greatest value of the hammer efficiency is reached when the striker run to the cartridge is within 19–22 mm. It should be remembered that each value of the striker-travel magnitude to the cartridge corresponds to a quite definite value of the striker travel to spring compression, which is determined by the curve of equal losses \(a\), \(d\), \(b\), \(c\) (Fig. 3). If the limiting values...

of the magnitude of the striker travel up to the chuck at which the efficiency of the hammer has the greatest value (19 and 22 mm for Fig. 4), plot them on the abscissa axis (Fig. 3) and restore from these points perpendiculars to their intersection with the curve \(a,d,b,c\) at the points \(N\) and \(M\), then the coordinates of the points of the segment \(N—M\) of the curve of equal losses will correspond to the best parameters of the striker travel for the specified duration of switching on the hammer, at which the permissible magnitude of losses was determined, and for the given design of the solenoid. When comparing different variants of solenoid design, the best is selected according to the greatest value of the efficiency at the permissible magnitude of winding overheating.

Fig. 4. Curves of consumed \(P_c\), useful \(P_p\) power and efficiency \(\eta\) at permissible losses in the hammer.

Conclusion

The method described makes it possible, with a comparatively small expenditure of time on investigation and with sufficient accuracy, to determine the following optimal parameters for given heating temperature and dimensions of the solenoid:

a) the diameter of the winding wire and the number of turns of the coil;
b) the geometric parameters of the striker;
c) the angle of inclination of the poles;
d) the stiffness of the spring;
e) the magnitudes of the run of the striker up to the chuck and of the spring.

Experimental determination of the optimal parameters of the soleno-

of other overall dimensions will not be required when applying the method of similarity and dimensions to the calculation of solenoid hammers [2].

REFERENCES

1. Ryashentsev N. P., Timoshenko E. M., Frolov A. V., Tronov A. N., “On the parameters of solenoid hammers with free running of the striker.” The article is included in the present collection.

2. Alabuzhev P. M., Ryashentsev N. P., “Application of the method of similarity and dimensions to the calculation of solenoid hammers.” Proceedings of the Tomsk Polytechnic Institute, vol. 108, 1959.