ON STRESSES INDUCED IN THE SELF-METERING LOADING DEVICE OF A SKIP HOISTING INSTALLATION

I. K. KHRUSTALEV

(Presented by the Scientific and Technical Conference of the Mining-Mechanical Faculty of TPI)

Types of Loading Devices

Metering device

In skip hoisting installations of coal mines, as a rule, self-metering loading devices with drum gates are used. The drum gate occurs in two varieties. In one case the counterweight, by means of which the gate of the metering device is closed, is fastened directly to the drum (Fig. 1). To limit the rotation of the drum gate of the metering device in this case there is a limiting device (usually a wooden beam fastened to the gate foundation).

In the other case (Fig. 2) the counterweight of the drum gate moves in separate guides and is connected to the drum by means of a rope.

As the operating experience of skip hoisting installations shows, in the second case the metering device operates more reliably, permitting a large load and therefore a high skip speed when landing on the carriage of the gate. Conversely, the first variety of drum gate does not permit high landing speeds of the skip. With sharp rotations of the gate during its opening and closing, dangerous mechanical stresses arise in the side plates of the unbalanced part of the drum (at the place where the weights are attached), which causes the weights to be torn off and the drum plates to rupture. This circumstance makes it necessary to land the skip on the carriage of the metering device at a very low speed, which greatly prolongs the period of skip landing. The same circumstance does not make it possible to operate with high acceleration at the beginning of the starting period, since in this case large forces arise when the drum of the gate strikes the limiting beam.

Types of carriages of metering devices for landing the skip

In skip hoisting installations of coal mines two types of carriages of metering devices are encountered: translational displacement (Fig. 2) and rotational displacement (Fig. 1). In the first case the carriage frame runs in guides; in the second, it is suspended by means of rods or ropes of the metering device and turns under the action of the descending skip or counterweight.

For landing the skip, carriages with translational displacement have a pedal, on which, to soften the impact of the skip, a wooden beam 150–220 mm thick is usually placed.

Fig. 1. Diagram of the self-metering loading device.

1. Gate drum.
2. Nose of the gate drum.
3. Bunker sleeve.
4. Counterweight.
5. Drum-rotation limiter.
6. Carriage of the metering device for rotational displacement.
7. Seating roller of the carriage.
8. Ropes or rods.

Fig. 2. Diagram of the self-metering loading device.

1. Drum \((G_b = 3149\ \text{kg};\ R_b = 1.18\ \text{m})\).
2. Nose \((G_n = 256\ \text{kg};\ \rho = 1.74\ \text{m})\).
3. Bunker sleeve.
4. Drum-rotation limiter.
5. Carriage of the metering device for translational displacement \((G_k = 547\ \text{kg})\).
6. Cushioning wooden beam.
   7, 8. Ropes.
7. Guide sheave \((G_{\text{sh}} = 50\ \text{kg})\).
8. Counterweight \((G_{\text{ctr}} = 4000\ \text{kg})\).

In carriages with rotational displacement, the skip is seated either on the landing roller or on a metal beam.

The travel of a carriage with translational displacement is usually \(1.4 \div 1.9\) m, and that of a carriage with rotational displacement is \(0.6 \div 1.6\) m. Carriages with translational displacement, owing to the presence of a wooden cushioning beam on the landing platform, operate under more favorable conditions; conversely, in carriages with rotational displacement there have often been cases of breakage of the landing roller or of its being torn out of the frame fastening.

Connection from the carriage to the measuring-device gate

The connection from the carriage to the gate of the measuring device is made either by means of steel rods or by ropes. Usually two rods or two ropes run from the carriage to the gate drum (one on each side).

It should be noted that a rope connection is more reliable, and the measuring device then operates under more favorable conditions, since ropes, possessing damping properties, reduce the mechanical stresses in the measuring device at the moment when the skip strikes the carriage of the measuring-device gate. The stresses in the parts caused by the instantaneous (impact) load that occurs when the skip is seated on the carriage of the measuring device are directly proportional to the modulus of elasticity \(E\) [1,2]. If for a solid steel rod \(E = 2 \cdot 10^6\) kg/cm\(^2\), then for a rope \(E = 0.7 \cdot 10^6\) kg/cm\(^2\) [3]. Hence, other conditions being equal, the mechanical stresses in the rope will be

\[ \frac{2}{0.7} = 2.85 \]

times smaller than those in solid steel rods.

For fastening rods or ropes to the carriage of the measuring device, spring shock absorbers are sometimes used. A diagram of such a shock absorber is shown in Fig. 3.

Fig. 3. Spring shock absorber. 1. Body. 2. Spring. 3. Washer. 4. Rod. 5. Lugs for fastening to the carriage and rods.

Such shock absorbers, while not improving the operating conditions of the measuring-device carriage itself, undoubtedly improve to a greater extent the operation of the connection and of the gate of the measuring device, since they soften the impact jolts on the measuring-device gate.

Among the shortcomings of these shock absorbers it should be noted that, because of the unfavorable conditions of their operation (usually under conditions of a large dripping of water and a polluted mine atmosphere), springs with a wire diameter of \(18 \div 20\) mm have to be installed, and this reduces the damping properties of the shock absorber. In addition, a spring shock absorber causes oscillatory motions of the measuring-device gate, and consequently oscillatory stresses in it.

On the stresses induced in the elements of the loading device

Forces experienced by the elements of the loading device

During operation, the elements of the loading device experience two kinds of loads: 1) static and 2) dynamic.

The static loads include: 1) the pressure of the coal located in the bunker sleeve on the gate of the measuring device; 2) the pressure of the skip on the carriage of the measuring device; 3) the force produced in the frame of the measuring-device gate by the weight of the latter; 4) the tearing force produced by the counterweight in the side plates of the drum of the measuring-device gate; 5) the pressure of the skip on the fixing landing beams.

The dynamic loads include: 1) the instantaneous (impact) load on the carriage, on the connection from the carriage to the gate, and on the measuring-device gate during seating.

the skip onto the metering carriage; 2) impact load on the fixing beams when the skip is seated on them at the end of its motion; 3) impact load caused by the impact of the metering drum against the limiting device when the gate is closed; 4) inertia forces arising in the moving elements of the metering gate when their velocities of motion change; 5) vibrational loads caused by oscillations of the moving system during opening and closing of the metering gate.

The static loads in the elements of the loading device are insignificant in comparison with the dynamic ones. They cannot cause dangerous mechanical stresses.

Among the dynamic loads, the greatest significance is attached to the impact loads arising in the loading device at the moment when the skip strikes the metering carriage. The numerous failures in the elements of the loading device that have occurred in the operation of skip hoisting installations have, in most cases, arisen during this period.

Until now, no attention has been paid to the problem of determining the forces and mechanical stresses in the elements of the loading device due to impact and other dynamic loads. Not a single investigation has been carried out on this subject. The calculation of the indicated elements is performed for a static load; dynamic loads are accounted for by a certain safety margin which, in the absence of data on the nature of the action and the magnitude of these loads, is adopted conventionally. Often individual parts of the loading device (for example, rods or ropes connecting the metering carriage with the gate) are installed without any calculation at all, structurally, on the basis of operating experience.

Determination of the forces and actual stresses in the loading device under impact loads is further complicated by the fact that the problems of impact of machine and structural parts have been studied very little, while problems of impact in such devices as loading devices have not been studied at all.

Possibility of using the developed propositions of impact theory for determining stresses in the loading device

It was indicated above that the elements of the loading device experience the following types of impact loads: 1) impact loads in the metering carriage. Here a bending impact occurs when the skip is seated on the landing roller or pedal of the metering carriage; 2) tensile impact loads in the ropes and rods (in the connections from the carriage to the metering gate and from the gate to the counterweight), caused during seating of the skip on the carriage; 3) forces arising in the drum of the metering gate during its opening and closing—torsional impacts.

The developed theory of bending impact considers the interaction of the simplest colliding bodies. As the body being struck, a homogeneous beam with supported ends (a simply supported beam) or a beam with an embedded end—a cantilever—is considered. With the aid of the known propositions of impact theory, it is possible to determine the stress in a beam with elastic supports, or when the impact is applied to a shock absorber fastened to the beam, if steel springs are used as these elastic supports or shock absorbers [6]. With the aid of these known propositions, it is almost impossible to determine the stress in beams if rubber is used as the elastic supports and shock absorbers. While steel springs have a constant stiffness, that is, they obey Hooke’s law, the stiffness of a rubber shock absorber is not constant, but varies depending on the load and the duration of its action; that is, rubber (especially in compression) does not obey Hooke’s law [7]. For rubber products, relaxation phenomena play an essential role. To clarify these features, we carried out tests of shock absorbers—

…rubber in compression. The test results are given in Table 1 and shown in Figs. 4 and 5.

As is known, Hooke’s law is obeyed by those materials for which the stress–strain relationship is represented by a straight line. We do not have this for rubber (Fig. 5).

In calculating rubber products, the basis should evidently be not the stress, but the capacity for absorbing energy [8].

Table 1

Compression test of cushioning rubber of group 5-a, mixture No. 3311
Plate dimensions 200 × 200

Note. The load is static. No residual deformations were observed.

We have set forth one of the circumstances that limits the use of the known calculation formulas under impact loading. This circumstance consists, briefly, in the fact that the indicated formulas are applicable in the case of determining stress in bodies obeying Hooke’s law. In addition, the existing theory does not consider the case of the impact of a body on an interrelated movable system of bodies, such as, for example, we have (Figs. 1, 2) when considering the question of the landing (impact) of the skip on the metering-device carriage. Here the impact of the skip occurs on the roller or pedal of the metering-device carriage, which has the possibility of movement. The carriage, in turn, is connected by links to the gate drum, and the latter to the counterweight.

The behavior of the material of the parts of such interrelated movable systems, as indicated above, has not been studied at all, and their strength dimensions are at present, in most cases, adopted constructively, on the basis of operating experience.

This is the second circumstance limiting the use of the known calculation formulas for calculation under impact loading.

For the same reasons, the existing provisions also cannot be used in determining the impact forces and stresses in the feeder gate and the connections of the gate drum with the carriage and counterweight.

Fig. 4. Compression curves of cushioning rubber. (Base size \(200 \times 200\) mm, \(a\)—rubber-layer thickness 107 mm, \(b\)—rubber-layer thickness 34 mm)

Fig. 5. Compression curve of cushioning rubber (base size \(200 \times 200\) mm, \(a\)—layer thickness 107 mm, \(b\)—layer thickness 34 mm)

Stresses Induced in the Metering Device When the Skip Is Set Down on the Metering Carriage, and the Permissible Speeds in This Operation

Character of the Motion of the Metering Carriage When a Skip Is Set Down on It

Having obtained no answer to the question posed by means of the known propositions of impact theory, we attempted to determine the forces induced in the elements of the metering device when the skip is set down on the metering carriage from other assumptions.

Observations of the operation of skip hoisting installations show that when a skip is set down on the metering carriage, the latter, together with its translational motion, acquires oscillatory motions; moreover, the character of these oscillatory motions depends on the magnitude of the landing speed of the skip and on the type of cushioning device on the metering carriage. To clarify these points, we carried out laboratory tests on a model of the landing device. The impact of the load (skip) was produced from various heights, and its landing was effected on various cushioning materials. During these tests, with the aid of an indicator, we recorded the displacement diagrams of the carriage. Differentiation of the displacement diagrams gives the velocity diagrams of the carriage motion. The velocity diagrams of the carriage motion show clearly that the greater the landing speed of the load and the worse the cushioning properties of the cushioning material, the more pronounced are the oscillatory motions of the carriage, and the more rapidly the change in velocity occurs. In each of the tests performed we found the maximum accelerations of the carriage, which are given in Table 2. On the basis of the data of Table 2,

Table 2

Accelerations of the carriage during free fall of the load onto it

curves of the carriage accelerations were plotted as a function of the magnitude of the speed at which the load comes into contact with it (Fig. 6).

These curves show that the smallest accelerations of the carriage are caused when the load is set down on a damper landing device, and consequently in this case the smallest inertial forces occur. Rubber cushioning gives very good results, and wooden cushioning pads give considerably worse results.

The data of Table 2 and the curves in Fig. 6 also show that when the load strikes directly against the metal of the carriage, the greatest maximum accelerations are produced, and their magnitude increases sharply with an increase in the landing speed of the load.

Forces Induced in the Elements of the Loading Device during Landing of the Skip, and the Permissible Instantaneous Accelerations of the Carriage Motion

Having the maximum instantaneous accelerations during landing of the skip on the measuring carriage, we can, on the basis of Newton’s second law, also determine the maximum forces thereby induced. In fact, the inertia force is

\[ P = mj, \tag{1} \]

where \(m\) is the mass of the body and \(j\) is its acceleration.

Fig. 6. Curves of instantaneous accelerations of the carriage.

In view of the fact that the landing (impact) of the skip in our case occurs not on the simplest body, but on the measuring carriage, which is one of the elements of the connected moving system of the loading device, in order to determine the inertia force the mass of all connected moving parts must be reduced to the place of landing (impact) of the skip. In this case equation (1) will have the form: \(P = \mathfrak{M}j\), where \(\mathfrak{M}\) is the reduced mass.

Let us consider a specific example. Take a standard self-metering loading device (Fig. 2). This loading device has moving parts with both translational and rotational displacements; consequently, the reduced mass will be

\[ \mathfrak{M} = \mathfrak{M}_{\text{trans}} + \mathfrak{M}_{\text{rot}} . \tag{2} \]

In turn,

\[ \mathfrak{M}_{\text{trans}} = m_{\text{car}} + m_{\text{rope}} + m_{\text{cr}} \quad \text{and} \]

\[ \mathfrak{M}_{\text{rot}} = m^i_{\text{bar}} + m^i_{\text{nose}} + m^i_{\text{sh}} . \]

Reduced mass of the translationally moving parts

Since the translationally moving masses are directly connected with the point at which the skip is seated on the carriage, their mass is reduced to the point of impact. It is equal to:

\[ m_{\text{trans}}=m_{\text{car}}+m_{\text{cr}}+m_{\text{rope}} =\frac{547+4000+25}{9.81} =\frac{4572}{9.81} \]

\[ =466\ \text{kg}\,\text{m}^{-1}\,\text{sec}^{2}. \]

Reduced mass of the rotationally moving parts

We shall find the reduced mass of the drum from its moment of inertia. The moment of inertia of a rotating body, as is known, is \(\Theta=M\rho^{2}\), where \(M\) is the mass of the body and \(\rho\) is the radius of inertia.

For a cylinder \(\rho=\dfrac{R^{2}}{2}\) [9]. The mass of a cylinder reduced to the circumference will be:

\[ m_i=\frac{\Theta}{R^{2}}=\frac{MR^{2}}{2R^{2}}=\frac{M}{2}. \tag{3} \]

Using this proposition, for the drum of the feeder gate we have:

\[ m_{i b}=\frac{m_b}{2}=\frac{G_b}{2g}=\frac{3149}{2\cdot 9.81} =160\ \text{kg}\,\text{m}^{-1}\text{sec}^{2}. \]

In the same way we determine the reduced mass of the guide pulley (Fig. 2):

\[ m_{i\text{sh}}=\frac{G_{\text{sh}}}{2g} =\frac{50}{2\cdot 9.81} =2.6\ \text{kg}\,\text{m}^{-1}\text{sec}^{2}. \]

The radius of inertia of the gate nose is \(\rho=1.74\ \text{m}\) (the distance from the center of rotation to the center of gravity); consequently, its moment of inertia will be:

\[ \Theta_n=m_n\rho^{2} =\frac{256}{9.81}\cdot 1.74^{2} =79\ \text{kg}\,\text{m}^{-1}\text{sec}^{2} \]

and the mass reduced to the circumference of the gate drum is

\[ m_{i n}=\frac{\Theta}{R_b^{2}} =\frac{79}{1.18^{2}} =56.7\ \text{kg}\,\text{m}^{-1}\text{sec}^{2}. \]

Total reduced mass of the moving parts

\[ \mathfrak{M}=466+2.6+160+56.7 =685.3\ \text{kg}\,\text{m}^{-1}\text{sec}^{2}. \]

Substituting in formula (1) the accelerations given in Table 2, we obtain the maximum forces in the elements of the loading device when the skip is seated on the feeder carriage. These forces are given in Table 3.

The data of Table 3 indicate the obvious advantages of rubber shock absorbers.

Proceeding from the strength limit of the rope connections of the loading device, shown in Fig. 2, the permissible maximum acceleration is equal to:

\[ j=\frac{P}{\mathfrak{M}} =\frac{Q_p}{\mathfrak{M}} =\frac{334000}{685.3} =487\ \text{m}/\text{sec}^{2}, \]

where \(Q_p=334000\ \text{kg}\) is the total breaking force of all the wires of the two connecting ropes.

Using the acceleration curves (Fig. 6), we find the maximum landing speeds at which the ropes break at \(j = 487\ \text{m/sec}^2\). This speed, when the skip strikes the metal of the carriage, is \(0.5\ \text{m/sec}\); when it strikes a wooden cushion, \(0.81\ \text{m/sec}\); and there is no dangerous landing speed, within the limits of the graph (Fig. 6), when the skip lands on the carriage with rubber shock absorbers.

Table 3

For reliable operation of the loading device, these speeds must be considerably reduced. Taking a strength safety factor \(n = 1.2\), we obtain \(j_{\max} = 406\ \text{m/sec}^2\); then the permissible landing speeds for our case will be: for a carriage without the use of cushioning, \(0.24\ \text{m/sec}\); with the use of a wooden cushion 100 mm high, \(0.4\ \text{m/sec}\); and with the use of a rubber shock absorber, it is above \(1.0\ \text{m/sec}\).

In view of the difficulty of verifying the stated propositions under production conditions, we carried out a laboratory experimental check. For this purpose three tests were performed. In the first test the carriage model was suspended on 3 wires taken from a steel rope. The diameter of each wire was \(\delta = 1.8\ \text{mm}\), and the breaking force for 3 wires was \(Q_p = 1221\ \text{kg}\). In our case \(Q_k = 6\ \text{kg}\), \(Q_{kgo} = 21\ \text{kg}\), and the weight of the two blocks was \(3\ \text{kg}\); consequently, the reduced mass was

\[ \mathfrak{M} = \frac{6 + 21 + \frac{3}{2}}{9.81} = 2.9\ \text{kg}\,\text{m}^{-1}\,\text{sec}^2 . \]

The acceleration at which 2 connecting ropes, each consisting of 3 wires, will break is:

\[ j = \frac{2 \cdot 1221}{2.9} = 840\ \text{m/sec}^2 . \]

These ropes did not break when the load fell onto the carriage at speeds of \(0.415\ \text{m/sec}\), \(0.66\ \text{m/sec}\), and \(1.02\ \text{m/sec}\) when wooden pads and rubber shock absorbers were used on the carriage. Breakage occurred when the load struck the carriage without cushioning at a speed of \(1.02\ \text{m/sec}\).

With two wires in the rope, one of the wires broke when the load struck the carriage without cushioning at a speed of \(0.66\ \text{m/sec}\), and the rope broke when struck at a speed of \(1.02\ \text{m/sec}\), both with the wooden cushioning pad and without cushioning.

When, as the connection from the carriage to the counterweight, one wire on each side was used (2 wires in all), their breakage occurred at a falling speed of the load onto the carriage with rubber shock absorbers of \(1.02\ \text{m/sec}\).

The reduced mass of the moving parts in the latter case was \(\mathfrak{M} = 3.3\ \text{kg}\cdot\text{m}\,\text{sec}^2\). Consequently, the permissible acceleration was

\[ j = \frac{2 \cdot 407}{33} = 247\ \text{m/sec}^2 . \]

According to Fig. 6, such an acceleration is obtained when the speed of setting the load down onto the carriage with rubber shock absorption is 0.92 m/sec. At speeds exceeding 0.92 m/sec, the wires must break, which is what occurs in our case.

From what has been said above it follows that the values obtained by us in processing these experiments are close to the true ones. The stated propositions are also confirmed by the operating practice of skip hoisting installations.

In the operation of skip hoisting installations, the limiting speeds for setting skips down onto the metering carriage have been established at 0.5 m/sec. We see that for carriages with rotational displacement, in which the impact of the skip is made against a metal roller or a metal bar, even this speed is dangerous. On the other hand, when rubber shock absorbers are used on the metering carriage, the landing speed of the skip can quite well be brought up to 1 m/sec.

As was indicated above, in the operation of skip hoisting installations at mines, in order to avoid accidents in the loading device, with the adopted rigid landing system the landing speed of the skip onto the metering carriage must not exceed 0.5 m/sec. Sometimes this speed (especially when carriages with rotational displacement are used) is reduced to 0.1 m/sec, and the time of motion of the skip together with the metering carriage sometimes reaches 15 sec.

The latter circumstance greatly prolongs the time of the entire hoisting operation, which leads to a decrease in the productivity of the installations, as well as to an increase in energy consumption by the drive, both because the hoisting operation is lengthened and because the operating time of the installation for delivering the mine’s daily output is increased.

From what has been said it follows that improving the skip-loading regime is important and necessary. For this purpose, the use of damping landing devices (Fig. 7) or rubber shock absorbers (first of all on the metering carriage) may be recommended; this will make it possible to set the skip down onto the metering carriage at a speed close to 1 m/sec, and therefore will to a considerable extent shorten the time of motion of the skip together with the carriage and the time of the hoisting operation.

The indicated criteria for the landing speed of the skip are justified both by the operating practice of Kuzbass skip hoisting installations and by the experimental material presented.

Fig. 7. Damping landing device. 1. Cylinder. 2. Hollow piston. 3. Needle. 4. Opening for the outflow of oil into the inner cavity of the piston. 5. Seals. 6. Metering carriage. 7. Shock absorbers. 8. Ropes connecting the carriage with the drum gate. 9. Skip landing cushion. 10. Rollers. 11. Guides. 12. Beams fixing the skip landing.

Conclusions

Summarizing the material considered in the present work, the following conclusions may be drawn:

1. The dynamics of skip loading currently employed cause an increase in the time of the hoisting operation and create a danger of accidents in the elements of the loading device, and consequently lead to a reduction in the service life of the latter.

2. As gates for metering devices, the drum gate operates more reliably; its counterweight moves along its guides and is connected to the gate drum by means of a rope. However, by using an elastic seating of the skip on the metering-carriage and by using rubber shock absorbers (made of rubber washers) as limiters for the rotation of the drum when the gate is closing, a drum gate with a counterweight fastened directly to the gate drum can be used successfully.

As carriages of metering devices, both carriages with translational motion and carriages with rotational motion may be used equally well. To improve the seating conditions of the skip and the operation of the metering and seating devices, in either case it is necessary to use cushioning devices that would make it possible to bring the skip up to the metering carriage at maximum speed without causing accidents in the metering and seating devices.

Fig. 8. Rubber packet shock absorber. 1. Packet of rubber plates. 2. Bracket attached to the metering carriage. 3. Box cover. 4. Guide rod. 5. Guide pins. 6. Guide slots.

As connections from the carriage to the metering-device gate, it is necessary to recommend steel ropes, which, possessing sufficient strength and elasticity in operation (which is especially important under impact loads), contribute to improving the operation of the metering devices.

For final fixation of the skip during its loading, rubber cushioning pads must be placed on the landing timbers or beams used in practice. This will reduce the dynamic stresses in the skip and in the landing timbers when the skip comes to its final stop.

1. To improve the loading regime of skips and the operation of the metering devices, it is therefore necessary to use damping landing and limiting devices in the loading device. The latter circumstance will make it possible to shorten the time of the actual operating cycle and to increase the output of skip hoisting installations; it will make possible their more reliable and accident-free operation and will reduce the energy consumption by the drive of the hoisting installation, both by shortening the time of the hoisting operation and by shortening the operating time of installations for delivering the daily output of mines. In addition, improving the dynamics of skip loading makes it possible to reduce the power of hoisting motors in the case of unchanged or only slightly increasing output and mine depth.

2. As damping landing devices, it is necessary to recommend damper (air-oil and oil) devices and rubber packet shock absorbers, which are shown in Figs. 7 and 8.

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