On the Parameters of a Solenoid Hammer with Free Coasting of the Striker
Abstract Generated abstract
This paper examines the design parameters governing a solenoid hammer in which the striker continues by free coasting after current in the coil ceases near the magnetic equilibrium position. Using an experimental single-coil hammer, oscillograms of striker travel, current, and voltage, and simplified electromagnetic and geometric relations, the authors analyze how spring stiffness, striker run-out, coil and striker dimensions, pole inclination, wire size, and number of turns affect stable reciprocating motion, braking, energy transfer, and useful impact power. The study argues that both insufficient and excessive striker travel reduce efficiency and power per unit weight, and that rational geometric proportions and spring parameters must be selected experimentally and theoretically to improve impact energy and efficiency.
Full Text
On the Parameters of a Solenoid Hammer with Free Coasting of the Striker
N. P. Ryashentsev, E. M. Timoshenko, A. V. Frolov, A. P. Tronov
(Submitted by the Department of Mining Machines and Mine Transport)
Work on the creation of electric impact-action machines of the solenoid type has been under way for more than one hundred years. However, up to the present time our industry has not produced electric solenoid hammers that could be used in many branches of the national economy. The main reason hindering the industrial application of previously proposed solenoid hammers is their technical imperfection, explained by the absence of a coherent theory of the solenoid drive.
Studies carried out at the Tomsk Polytechnic Institute (TPI) indicate the possibility of creating an operable design of an electric hammer of the solenoid type. At the institute an experimental model of a multi-coil solenoid hammer with a synchronous sparkless switch was developed and manufactured [2—7]. The problem of creating a hammer* without a switch was solved.
The design of such a hammer was developed at TPI and is presented in Fig. 1, a; the connection circuit is in Fig. 1, b; the hammer diagram is in Fig. 1, v; oscillograms of the stroke \(S\), current \(i\), and voltage \(U\) are shown in Fig. 1, g.
The hammer consists of a tool \(1\), fastened in the front flange \(3\), a striker \(4\), moving in a diamagnetic guide tube \(6\), a coil \(7\) with poles \(5\) and a yoke \(8\), a housing \(9\), a buffer \(11\) with spring \(10\), a textolite piston \(13\), and a switch \(12\). When the hammer coil is switched on according to a half-wave rectification circuit, the striker begins to perform reciprocating motion. We shall call the motion of the striker toward the tool (chuck) the working stroke, and the motion of the striker toward the spring the idle stroke. The magnitudes of the air gaps that occur at the beginning of the working and idle strokes will be called the initial air gap, respectively, for the working and idle strokes.
The position of the striker in the coil at which the magnitudes of the air gaps are equal will be called the middle position of the striker (relative to the coil), or the position of magnetic equilibrium. During operation of the hammer, the magnitude of the striker stroke from the middle position to the chuck
* In solving this question, considerable assistance was provided by work [1], carried out by Professor, Doctor of Technical Sciences A. I. Moskvitin.
determines the magnitude of the initial air gap during the idle stroke, and the magnitude of the striker travel to the spring and its deformation determine the initial air gap during the working stroke.
If the rebound of the striker from the chuck is not taken into account, then the idle stroke of the striker is effected only by electromagnetic forces. The working stroke of the striker is effected by electromagnetic forces and by the elastic forces of the spring, which accumulates the kinetic energy of the striker during the idle stroke of the striker.
The current pulses causing displacement of the striker in the working and idle directions will be called, respectively, the current pulses during the working and idle strokes.
During normal operation of the hammer, the flow of current in the coil ceases when the striker approaches the middle position. However, the striker does not stop, but, under the action of the accumulated kinetic energy, freely runs out to the spring during the idle stroke and to the chuck during the working stroke. Therefore hammers operating on this principle are called solenoid hammers with free coasting of the striker.
Fig. 1. Solenoid hammer with free coasting of the striker:
a—design; b—power-supply circuit; c—hammer diagram; d—oscillogram of striker displacement \(S\), voltage \(U\), and current \(I\).
In addition to the single-coil hammer described, two-, three-, and multi-coil hammers can operate according to the given scheme; in this case the striker must consist of links of ferromagnetic and diamagnetic material [4, 5, 8].
Stable reciprocating motion of the striker of a solenoid hammer is observed over a wide range of variation in the stiffness coefficient of the spring and in the magnitude of the free travel of the striker to the chuck and to the spring.
Figure 2 gives oscillograms of the displacement of the striker \(S\), the current \(i\), and the voltage \(U\) supplied to the coil. The oscillograms presented characterize the operation of the hammer under the following conditions:
a) in the absence of the spring and of impact of the striker against the chuck (Fig. 2, a);
b) in the absence of the spring and in the presence of impact of the striker against the chuck (Fig. 2, b);
c) in the presence of impact of the striker against the chuck and compression of the spring (Fig. 2, c, d).
Stable operation of the hammer is also observed when the striker strikes the chuck during the working stroke and a rigid stop during the idle stroke of the striker.
The oscillograms presented were recorded by means of an N-102 loop oscillograph for different values of the free travel of the striker and with all other conditions unchanged.
Lines 1, 2, and 3 (Fig. 2) respectively mark the positions of the cartridge, magnetic equilibrium, and the spring. Point \(a\) on the curve of the striker travel \(S\) corresponds to the instant at which the striker strikes the cartridge; points \(b\) and \(c\) correspond to the position of magnetic equilibrium of the striker, respectively during the idle and working strokes. Point \(d\) corresponds to the instant at which the striker touches the spring during the idle stroke, and point \(f\) to the instant of guaranteed separation of the striker from the spring during the working stroke. The current pulses during the working and idle strokes of the striker are denoted respectively by \(i_2\) and \(i_1\).
Fig. 2. Oscillograms of the working process of a solenoid hammer:
\(a\)—with no impact on the cartridge and the spring; \(b\)—with impact of the striker on the cartridge and no impact on the spring;
\(v, g, d\)—with impact of the striker on the cartridge and with compression of the spring.
The hammer operating modes shown in Fig. 2, \(a\), and Fig. 2, \(b\), are of no practical significance for impact-action machines, since in the first case (Fig. 2, \(a\)) there is no impact on the cartridge, while in the second case (Fig. 2, \(b\)) the striker during the idle stroke is braked by electromagnetic forces caused by the current \(i_3\) flowing in the coil. The kinetic energy accumulated by the striker during the idle stroke is in this case not used to accelerate the motion of the striker during the working stroke.
Of greatest practical interest is such an operating mode of the hammer (Fig. 2, \(v, g, d\)) in which the striker delivers a blow to the cartridge and the kinetic energy accumulated by the striker during the idle stroke is stored by the spring, and during the working stroke of the striker is again converted into kinetic energy.
It should be noted that not all the potential energy accumulated by the spring is transmitted to the striker during the working stroke. This is explained by the fact that, in addition to the elastic forces of the spring, electromagnetic forces act on the striker.
the force of the coil, which under certain conditions reduce to zero the contact force between the striker and the spring. With a lower spring stiffness, a smaller fraction of the potential energy is converted into kinetic energy of the striker; with a higher stiffness, a larger fraction is converted, but the forces arising as a result of the natural oscillations of a spring of high stiffness may bring the striker out of synchronism. It is obvious that the spring parameters must be quite definite for each type of hammer.
With a normal value of the travel to the tool and to the spring, the striker approaches the position of magnetic equilibrium simultaneously with the instant at which the current in the coil disappears. A mode close to such an ideal mode is the operating mode of the hammer shown in Fig. 2, б. Here the current in the coil during the working and idle strokes ceases almost simultaneously with the instant at which the striker approaches the middle position. If the free travel to the spring is insufficient (Fig. 2, г), the striker approaches the position of magnetic equilibrium a time \(t_2\) before the current in the coil disappears; the current pulse during the working stroke of the striker is stretched out and, as a result of electromagnetic braking, the velocity of motion of the striker is sharply reduced. If the free travel to the spring is excessively large (Fig. 2, д), the current in the coil during the working stroke of the striker ceases long before (\(t_3\)) the instant at which the striker approaches the middle position, which entails an increase in the power consumed by the coil. The useful power of the hammer in this case does not increase, but decreases. This is evident in Fig. 2, в, д from the angle of inclination of the curve of striker travel \(S\) at point \(a\) to the horizontal axis. From the foregoing it follows that both insufficient and excessive values of the free travel of the striker to the chuck and to the spring lead to a decrease in the efficiency and useful power per unit weight of the hammer.
The weight of a solenoid hammer is determined first of all by the electromagnetic loading of its active materials (current density in the winding and magnetic induction in the striker). The ratio of the dimensions of the coil window and of the striker cross-section also affects the weight. The existence of an optimum ratio between the outside and inside diameters of the solenoid can be established by assuming that the energy delivered by the solenoid \(Q\) is proportional to the product of the flux and the number of ampere-turns,
\[ Q = k\Phi_m I_m w . \tag{1} \]
The maximum value of the magnetic flux \(\Phi_m\) is determined by the cross-section of the striker,
\[ \Phi_m = B_m \frac{\pi d_{\sigma}^{2}}{4}, \tag{2} \]
where
\[ \begin{aligned} B_m &\text{— maximum induction in the striker;}\\ d_{\sigma} &\text{— diameter of the striker.} \end{aligned} \]
The value \(B_m\) must not exceed the saturation induction for the material adopted for the striker, since at large values of induction, as a result of the sharp increase in the reluctance of the magnetic circuit, the tractive forces increase very little while the supplied power and heat losses increase considerably.
The maximum value of the magnetizing force \(I_m w\) is limited by the area of the coil window and is determined by the expression
\[ I_m w = \frac{f_k q}{k_a} S_k , \tag{3} \]
where
\(f_k\) — coefficient of filling of the coil window with copper;
\(q\) — permissible current density in the coil;
\(k_a\) — coefficient of the amplitude of the current curve;
\(S_k\) — area of the coil window.
Or, taking the inner diameter of the coil \(d_k = d_b\) for a coil with a rectangular window shape, we obtain
\[ I_m w = \frac{f_k q}{k_a}\cdot \frac{D_k-d_b}{2}\,l_k, \tag{4} \]
where
\(l_k\) — length of the coil;
\(D_k\) — outer diameter of the coil.
Substituting into expressions (1) the values of \(\Phi_n\) and \(I_m w\), we obtain
\[ Q = k' d_b^2(D_k-d_b), \tag{5} \]
where
\[ k'=\frac{k B_m f_k q l_k}{8k_a}. \]
From the formula given it is evident that, when the diameter of the striker is increased to the outer diameter of the coil, the power delivered by the coil will tend to zero. When the striker diameter is decreased to zero, the power \(Q\) also tends to zero.
Taking the derivative of expression (5) with respect to \(d_b\) and equating it to zero, one can, under the assumption adopted above, determine the optimal ratio between the outer diameter of the coil and the diameter of the striker (the inner diameter of the coil)
\[ \frac{dQ}{d(d_b)}=k'(2D_k d_b-3d_b^2)=0 \]
or
\[ 3d_b^2-2d_bD_k=0, \]
whence
\[ d_b=\frac{2}{3}D_k. \tag{6} \]
In determining the optimal ratio between the outer diameter of the coil and the diameter of the striker, the mass and motion of the striker were not taken into account; therefore the obtained ratio (6) cannot be considered optimal. However, the reasoning presented shows the existence of optimal ratios of the geometric parameters of the coil and the striker.
The length of the striker also has a substantial influence on the operating regime of the hammer. Thus, by increasing the length of the striker, it is possible to eliminate its electromagnetic braking as it leaves the coil. However, this increases the mass of the striker, which, for the same impulse of force, reduces the kinetic energy of the striker by as many times as the mass of the striker is increased. Therefore, in order to increase the kinetic energy for the same impulse of force, the mass of the striker should be reduced at the expense of its length, using poles 5 (Fig. 1, a, b) made in the form of truncated cones.
In this case, by changing the angle of inclination of the pole, it is possible within wide limits to vary the mass of the striker. The weight of the machined copper at equal masses
coil and magnetizing forces for a coil with a tapered window shape (Fig. 3) will be
\[ G_{k}=\gamma k_{z}\,\frac{b+h}{2}\,a l_{\mathrm{av}} . \tag{7} \]
where
\(\gamma\) is the specific weight of the winding wire;
\(k_{z}\) is the coil filling factor;
\(b\) is the height of the coil window at the outside diameter;
\(h\) is the height of the coil window at the inside diameter;
\(a\) is the width of the coil window;
\(l_{\mathrm{av}}\) is the mean turn length.
For simplicity of calculation, we neglect the transition of the window into a rectangular shape at the outside diameter of the coil. Then the mean length of a coil turn [2] is
\[ l_{\mathrm{av}} = 2\pi\left\{ \frac{D}{2} - \frac{a(b+2h)}{3(b+h)} \right\}, \tag{8} \]
where \(D\) is the outside diameter of the coil.
After transforming equation (7), we obtain
\[ G_{k} = \pi\gamma k_{z}(b+h)a \left\{ \frac{a}{d}\left[ 1-\frac{b+2h}{3(b+h)} \right] + \frac{1}{2} \right\}, \]
where \(d\) is the inside diameter of the coil.
Fig. 3. For determining the rational geometry of the solenoid.
The weight of a coil with a rectangular window shape (Fig. 3) is
\[ G_{p} = \gamma k_{z} S_{k} l_{\mathrm{av}} = \pi\gamma k_{z}ah(a+d). \]
In a coil with a rectangular window shape,
\[ h=b . \]
Then the reduction in the weight of a coil with a conical window, as compared with a coil with a rectangular window, will be
\[ \frac{G_k}{G_n} = \frac{(b+h)\left\{\frac{a}{d}\left[1-\frac{b+2h}{3(b+h)}\right]+\frac{1}{2}\right\}} {h(a+d)}. \]
Thus, by changing the angle of inclination of the pole, it is possible to vary the mass of the striker over wide limits and to reduce the consumption of winding copper or aluminum.
Conclusions
Since limitations are imposed on the magnitude of the effective value of the current, determined by the permissible losses for heating the hammer, and on the time of motion of the striker until the moment it leaves the position of magnetic equilibrium, it follows from the foregoing that the following optimal parameters of a solenoid hammer exist:
a) the diameter of the winding wire and the number of turns of the coil;
b) the geometric parameters of the coil window and of the striker;
c) the angle of inclination of the poles;
d) the stiffness of the spring;
e) the magnitude of the striker’s run-out to the chuck and to the spring.
In order to increase the efficiency and the impact energy per unit weight of the hammer, experimental-theoretical investigations of solenoid hammers should be directed toward determining the parameters listed above.
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