CONTROL OF ROPE SLACK IN HOISTING INSTALLATIONS

N. I. Klykov

(Presented by the scientific seminar of the Department of Mining Mechanics, Mining Faculty)

Rope slack occurs when the hoisting vessel is set down on a rigid support. In the process of slack formation, elastic shortening of the rope takes place. As shown by our observations and the investigations of Eng. V. F. Kutsenalenko [1], free slack is especially dangerous, since it causes bending of the wires at the point where the lower end of the rope is socketed. When the vessel starts upward, dynamic stresses arise in the rope as a result of the slack.

Thus, in order to limit dynamic forces and to reduce wear of the wires at the point of socketing, the rope slack must not exceed the maximum permissible value.

In practice there occur: a) emergency slack, caused by the wedging of a descending vessel in the mine shaft; b) operating slack, arising when the vessel is set down for loading. Control of emergency and operating slack pursues quite different aims. Emergency rope slack is monitored in order, at the moment it forms, to bring the hoisting machine to a timely stop and avoid the vessel falling from a great height, which may lead to rupture of the rope. Operating slack is monitored for the purpose of making timely adjustments to the rope length and thereby reducing the destruction of wires in the socketing and the magnitude of dynamic forces in the rope.

Continuous monitoring consists in the fact that, when emergency or maximum operating slack forms, an appropriate signal is given to the hoist operator. Provision may also be made for automatic stopping of the machine by timely application of the safety brake. Periodic monitoring of slack is carried out for the purpose of determining the actual elongation of the rope and adjusting its length.

Analyzing the various methods of continuous slack control, they may be combined into two groups: 1) by the upper part and 2) by the lower part of the working branch of the rope.

In the first case, sensors or special devices are installed on the surface at a definite location and are actuated when rope slack forms above the vessel. Special contact devices installed at the rope opening have, for example, become widely used for this purpose (Fig. 1). At the moment slack forms, the rope strand sags and actuates

contact device, which sends a signal to the hoist operator or actuates the safety brake. Sometimes sensors are used that are installed directly on the rope and respond to changes in the force in the rope.

In the second case, sensors are installed at the hoisting conveyance, and wires are laid to the signaling devices and safety apparatus to connect the conveyance with the hoist operator. A test section of the rope (Fig. 2), distinguished by color or having radioactive isotopes, may serve as the sensor. When this section descends below a certain level, a relay is actuated, sending an impulse to the hoist operator’s compartment. Contact sensors in combination with radio or telephone apparatus have also found some application.

The indicated methods of slack control have their own advantages and disadvantages. For example, monitoring slack by the sagging of the rope strand is very simple and reliable in operation, but the disadvantage of this method is the interference caused by oscillations of the rope strand, which makes adjustment of the sensor difficult. The method of installing sensors on the upper part of the rope with the use of special amplifiers and constant power sources is complex and unreliable.

Fig. 1. Diagram of control of rope slack by sagging of the strand.

Methods of controlling slack by the lower section of the rope are applicable at any mine depth and may be used for other purposes, for example, for communication between the mechanic inspecting the shaft and the hoist operator. In addition, the devices used in this case can be set to operate at a specified amount of slack. The disadvantages of these methods are the complexity and unreliability of sensor operation under conditions of high humidity and dustiness, the presence of a current-conducting line of great length, constant power sources, etc. In foreign practice, attempts have been made to use radio transmitters installed on the conveyances to transmit signals to the hoist operator’s compartment. However, because of the technical complexity, unreliability in operation, and high cost of the apparatus, this method has not become widespread on freight hoists. A somewhat simpler method is slack control using spring contact devices at the conveyance and an insulated conductor inside the rope. The power sources and signaling devices may be located on the moving part of the machine or in the machine room—

in the presence of current-collecting devices. The introduction of this method is possible only if ropes are manufactured with an insulated current-conducting strand.

The field of application of slack control by the weakening of the upper part of the rope is established as follows. When the cage is set down, or when it becomes jammed in the mine shaft, sagging of the rope strand occurs under the condition

Fig. 2. Diagram of slack control by the lower section of the rope when using relays responding to a change in the position of the monitored section of the rope

1 — hoisting cage; 2 — monitored section of the rope; 3 — sensing element of the relay; 4 — actuating contacts; 5 — signaling circuit.

\[ pH_0 + F_{ik} + F_{ish} < F_c + F_{tsh} + F_{tk} + F_{zhk}, \tag{1} \]

where \(p\) is the weight of 1 m of rope length, kg/m;
\(H_0\) is the length of the suspended rope, m;
\(F_{ik}\) is the inertia force of the sagging part of the rope, kg;
\(F_{ish}\) is the inertia force of the sheave, kg;
\(F_c\) is the component of the weight of the rope strand, kg;
\(F_{tsh}\) is the friction force of the sheave axle in the bearings, reduced to the circumference of the sheave, kg;
\(F_{tk}\) is the resistance due to flexible friction of the rope, kg;
\(F_{zhk}\) is the resistance force caused by the stiffness of the rope, kg.

The determination of the quantities entering expression (1) is carried out by the generally accepted method. Substituting these quantities into expression (1) and performing certain transformations, we obtain the maximum length of the suspended rope for which it is possible to apply rope-slack control by sagging of the strand:

\[ H_0 < \frac{ L_c \sin \beta + \frac{f_0 d_0}{D_{sh}} \left( L_c \sin \beta - \frac{P_{sh}}{p} \right) - \frac{(GJ)^2}{D_{sh}^{\,2}}\frac{j}{g} }{ 2 + \frac{j}{g} - \frac{f_0 d_0}{D_{sh}} - e^f - \xi_{zhk} }. \tag{2} \]

where \(l_c\) is the length of the rope strand, m;
\(\beta\) is the angle of inclination of the rope strand to the horizontal, degrees;
\(f_0\) is the coefficient of friction between the bushing and the sheave axle;
\(d_0\) is the diameter of the sheave axle, m;
\(D_{\mathrm{sh}}\) is the sheave diameter, m;
\(P_{\mathrm{sh}}\) is the absolute weight of the sheave, kg;
\(GD^2\) is the flywheel moment of the sheave, kg/m\(^2\);
\(j\) is the deceleration of the rope motion, m/sec\(^2\);
\(g\) is the acceleration due to gravity (\(g = 9.8\) m/sec\(^2\));
\(e\) is the base of natural logarithms (\(e = 2.718\));
\(f\) is the coefficient of friction between the rope and the sheave rim;
\(\varphi\) is the angle of wrap of the sheave by the rope, rad.;
\(\xi_{\mathrm{zh}}\) is the stiffness coefficient of the rope.

The stiffness coefficient of the rope during slack may be determined from the expression

\[ \xi_{\mathrm{zh}} \approx 125 \cdot 10^{-6} d_k \left(\frac{1+p}{p}\right), \tag{3} \]

where \(d_k\) is the rope diameter, mm.

Numerous calculations for specific production conditions show that this method of slack control is applicable when the length of the suspended rope does not exceed 120–150 m. Experimental verification of this method on hoists in the Kuzbass confirms the above. Thus, when slack was artificially produced on skip hoists with shaft depths of 80–120 m (the “Fizkulturnik,” “Andreevskaya-2,” and other mines), the corresponding signal was given to the hoist operator. On other hoists, where the shaft depth was 200–400 m, the devices for giving a signal to the operator did not operate. However, the method described is suitable for monitoring emergency slack, since the conveyance usually becomes jammed in the upper part of the shaft.

Before a simple and reliable method is developed for controlling slack along the lower part of the rope in deep mines, it is recommended that periodic control of slack be carried out by measuring it. For this purpose, at a distance of 5–8 m from the hoisting conveyance, special blocks with clamps are attached to the rope (Fig. 3), over which a flexible cord is passed. One end of the cord is attached to the conveyance, and a weight is suspended from the other. With the rope taut, the movable marks \(A\) and \(B\) on the branches of the cord are brought into coincidence, and the conveyance, together with the observer, is lowered into the mine until it is set on the landing devices and free slack is formed:

\[ \Delta l_{\mathrm{sn}} = \frac{\Delta S}{2}, \tag{4} \]

where \(\Delta S\) is the vertical distance between the marks, m.

Fig. 3. Diagram for measuring rope slack with the aid of a suspended block.

The magnitude of the operational slack, with precise stopping of the conveyances, will be

\[ \Delta l_{en} = \Delta l_{sn} - h_{pr}, \tag{5} \]

where \(h_{pr}\) is the amount by which the conveyance exceeds the unloading level at the moment of measurement, m.

The magnitude of the possible slack in this case will be

\[ \Delta l_{vn} = \Delta l_{en} + h_{vk}, \tag{6} \]

where \(h_{vk}\) is the overwind height for which the limit switches are set, m.

The operation of the hoisting installation may be considered normal if, when the conveyances are stopped precisely, there is no free slack, and the magnitude of the possible slack does not exceed \(0.2\) m. Otherwise, it is necessary to adjust the length of the ropes.

References

1. V. F. Kushpalenko. Investigation of slack in a mine hoisting rope. Occupational Safety in Industry, No. 2, 1959.