Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Volume 113, 1960

Protection of a Mine Hoisting Installation Against Rope Breakage Under Emergency Loads

V. F. Kutepalenko

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

Mine hoisting ropes during operation quite often experience emergency loads. These loads cause damage to and breakage of ropes, disruption in the operation of the hoisting installation, and accidents involving people.

Long-term observation of the operation of hoisting ropes in the Kuzbass shows that emergency loads may be both safe and dangerous for the rope. Safe loads arise when falling bodies strike the hoisting vessel. In these cases the impact force is applied at some distance from the axis of the rope. The moment of the force causes rotation and jamming of the vessel in the guides. Consequently, the impact is absorbed mainly by the vessel and the guides, while the rope does not receive a dangerous load.

Dangerous loads arise: 1) when a descending vessel becomes stuck in the unloading curves or in the mine shaft, with its subsequent fall onto the rope; 2) in the case of jamming of an ascending vessel in the guides or impacts against fastening elements and the shaft lining.

In both cases, an impact (emergency) load acts on the rope, tending to tear it apart. For rupture to occur, it is necessary that the work of the tensile forces be greater than the internal potential energy of the rope.

Let us find the condition for rope rupture using as an example the operation of a vertical hoisting installation driven by an asynchronous motor. In Fig. 1, the positions of vessels I and II correspond to the appearance of an emergency load in the descending and ascending branches of the rope.

An emergency load in the descending branch of the rope occurs when a stuck vessel falls from a height equal to the length of the slack that has formed. The impact on the rope in this case will be most dangerous when the vessel becomes stuck at the beginning of its travel, when the rope length is minimal. The condition for rope rupture is

\[ \frac{m_c\left(v_{nk}^{2}-v_{vk}^{2}\right)}{2} > A, \tag{1} \]

where \(m_c\) is the mass of the stuck vessel;

\(v_{nk}, v_{vk}\) are the velocities at the lower and upper ends of the rope at the moment of impact application of the load;

\(A\) is the potential energy equal to the work of rope rupture.

Fig. 1. Schematic mechanical diagram of a hoisting installation:
1 — winding organs;
2 — guide sheaves;
\(l_{eo}, l_{ep}\) — length of rope subjected to the emergency load from the descending and ascending conveyances.

After substituting in formula (1) the mass of the conveyance by its weight, and the velocities by accelerations and distances traveled, we obtain

\[ h_n > \frac{A}{Q_c} + h, \tag{2} \]

where \(h_n\) is the length of the rope slack;

\(Q_c\) is the weight of the jammed conveyance;

\(h\) is the path over which the falling conveyance reaches the velocity of motion of the hoisting system.

The emergency load in the ascending branch of the rope will be maximal when the conveyance is stopped abruptly at the end of the period of uniform motion, since at this moment the velocity of motion is maximal and the length of rope is small. Until the conveyance stops, the hoisting motor operates on its natural characteristic at point 1 (Fig. 2), developing a force corresponding to the static load of the rope. When the conveyance jams, the rope is additionally loaded at the expense of the energy of the moving mass of the hoisting system and of the motor force, increasing to a critical value (point 2 in Fig. 2). The condition for rope rupture is

\[ A_1 + A_2 + \frac{v^2 \sum m_e}{2} = A, \tag{3} \]

where \(A_1\) is the work of static stretching of the rope by the end load;

\(A_2\) is the work of stretching the rope by the motor force;

\(v\) is the velocity at the circumference of the winding organ at the considered instant of action of the emergency load;

\(\sum m_e\) is the moving mass participating in the creation of the emergency load, equal to the total reduced mass of the system minus the mass of the jammed end load.

Fig. 2. Natural mechanical characteristic of an asynchronous hoisting motor.

The most dangerous state of the rope will occur when the motor operates at point 1 or 2 (Fig. 2).

For practical use of expressions (2) and (3), it is necessary to know the dependence of the tensile deformation of the rope on the load. We studied this dependence in the laboratory of the Eastern Scientific-Research Institute for the Safety of Mining Operations (VostNII) on TK-type ropes of the \(6 \times 19 + 1\) o.c. construction with diameters of 31 and 34 mm. The average test results for 20 specimens are given in Table 1.

Table 1

Figure 3 shows, in load--relative-deformation axes, the tensile diagram for ropes 31 mm in diameter. The area of the entire diagram expresses the potential energy of rope failure. Marking on the diagram points 1 and 2, corresponding to the rope loads when the motor operates at the like-numbered points of its characteristic, and drawing ordinates through these points, we obtain (Fig. 3) the areas \(0--1--3\) and \(0--2--4\) for a new rope, and \(0--1'--3'\) and \(0--2'--4'\) for a rope removed from service. The magnitude of these areas gives the work \(A_1\) and \(A_2\).

The tensile work of the rope due to the energy of the moving mass of the system is determined by calculation. The speed of motion of the mass, referred to the circumference of rope winding, at point 1 of the motor characteristic is equal to the nominal value, and at point 2 to the critical value.

Fig. 3. Diagram of rope rupture test: 1--new rope (before suspension); 2--rope removed from service on the basis of breakage of 5% of the wires over one lay pitch (operated for 16.5 months).

Expressing the critical speed through the synchronous speed, and the latter through the nominal speed, we obtain

\[ v_{\mathrm{cr}} = \frac{v_n(1 - s_{\mathrm{cr}})}{1 - s_n}, \tag{4} \]

where \(v_{\mathrm{cr}}\) is the critical speed of motion;
\(v_n\) is the nominal speed of motion;

\(s_{kr}\) — the critical slip of the motor on the natural characteristic, equal to \(10\text{–}15\%\);

\(s_n\) — the nominal slip of the motor.

The total breaking strength of all the wires of the tested rope with a diameter of 31 mm is 57,086 kg. According to calculations, this rope can operate on a cargo hoist equipped with a 2BM-2×3×1.5 machine and with skips having a useful capacity of 4,000 kg and a dead weight of 4,100 kg. At a hoisting height of 200 m the safety factor of the rope is 6.5.

Having determined, with the aid of a planimeter, the required areas on the rope-extension diagram and having calculated the other quantities entering into formulas (2), (3), and (4), we obtain: 1) for a new rope \(A = 88100\ \text{kg·m}\), \(h_n = 22.9\ \text{m}\), the work of the breaking forces at point 1 of the motor characteristic is \(56680\ \text{kg·m}\), and at point 2—\(50160\ \text{kg·m}\); 2) for a rope removed from service, \(A = 50070\ \text{kg·m}\), \(h_n = 13.6\ \text{m}\). In the ascending branch, the energy of the breaking forces proves to be greater than the potential energy of the rope¹.

In deep mines, for the same conditions of occurrence of an emergency load, the energy that breaks the rope increases because of the greater mass and speed of motion of the hoisting system; at the same time, however, the potential energy also increases owing to the higher safety factor and the greater length of the rope.

It follows from the above:

1. The rope is broken by a freely falling conveyance if the path of fall from the upper receiving platform, caused by slack rope, exceeds, depending on the service life of the rope, 12–22 m.

2. With an increase in rope length and hoisting speed, the safe path of fall of the conveyance increases.

3. In a deep mine, emergency loads associated with jamming of the ascending conveyance may cause rope breakage; in a shallow mine, breakage may occur only in the last period of rope service.

To increase the reliability of operation of hoisting ropes, it is necessary systematically to eliminate the causes of emergency loads and to create technical means that make it possible to prevent conditions under which ropes break.

For the purpose of warning of emergency loads, signaling of rope slack is used. However, this signaling reacts to the appearance of slack only within the descending branch of the rope; it does not warn of possible breakage of the ascending branch of the rope and is unsuitable for hoisting installations with automatic control.

In the present work, a more advanced and reliable protection against rope breakage is proposed (Fig. 4). In designing the protection it was taken into account that the action of a dangerous load is preceded by stopping of the descending conveyance or by a decrease in the speed of the ascending conveyance. As a result, excessive or unexpected deceleration occurs, negative acceleration appears, the hoisting motor is overloaded, and the current drawn by it from the network increases.

The protection monitors the operation of the hoist with respect to motor overload and sends an impulse for safety braking of the hoisting machine. For general protection of both branches of the rope, an op—

specified controlled overload. Taking into account the dynamics of hoisting, the magnitude of this overload will not be the same for different periods of motion of the hoisting system. The protection provides for monitoring the motion when the conveyances start from rest, during periods of acceleration, steady running, and deceleration, and is carried out by high-speed current relays.

Fig. 4. Schematic circuit diagram of protection against breakage of the hoisting rope under emergency loads: PD—hoisting motor; TG—tachogenerator; VBD1, VBD2, VBD3—contacts of the inductive switch; TP—safety-brake contactor; KS—signal-reset button.

In order to eliminate false operation of the protection and to prevent dangerous emergency loads, the monitored overload of the motor must be greater than the usual overloads caused by a decrease in voltage at the motor terminals, by exceeding the normal weight of the load, etc., but less than the motor overload that occurs when the descending conveyance becomes jammed.

The permissible voltage drop at the motor terminals is found from the expression

\[ \gamma_n \left( \frac{U_n - u}{U_n} \right)^2 \geq \gamma_0 . \]

When the left- and right-hand sides in expression (5) are equal, we have

\[ u = 100\left(1-\sqrt{\frac{\gamma_{0}}{\gamma_{n}}}\right), \tag{6} \]

where \(\gamma_{n}\) is the nominal overload capacity of the motor;

\(U_{n}\) is the value of the normal motor voltage, equal to \(100\%\);

\(u\) is the value of the permissible voltage reduction, \(\%\);

\(\gamma_{0}\) is the permissible motor overload.

In designing the asynchronous drive of a mine hoist, the maximum overload capacity of the motor is taken as up to 2.4, and the minimum permissible overload as 1.6. In this case the maximum permissible voltage drop is \(18\%\), and the current of a motor loaded with the normal torque increases by no more than \(18\%\).

Overload due to a disturbance in the weight metering of vessels, as shown by check weighings, does not exceed \(25\%\) of the weight of the normal load.

The motor overload caused by jamming of the descending vessel corresponds to the weight of the latter. Therefore, when standard vessels are used, the increase in static load, compared with normal, in coal mines occurs within the following limits: for skips, by a factor of 1.4–1.8; for ordinary cages, by a factor of 2–3; and for tilting cages, by a factor of 3.7–5.3.

Using data on overloads of the hoist motor and the equation of hoisting dynamics, it is possible to establish the specific value of the controlled overload for each period of the hoisting cycle. The relay setting current is selected in accordance with this overload. According to our calculations, the setting current during the period of uniform motion and motor deceleration should be taken above the normal operating current of the motor in these periods by \(40\)–\(80\%\) for skip hoists and by \(80\)–\(100\%\) for cage hoists. During the deceleration period, performed normally in the free-running or dynamic-braking mode, the setting current is selected according to the motor current corresponding to a load equal to 1.4 times the weight of the normal vessel load on skip hoists, and 1.8 times on cage hoists.

Protection against rope breakage has been developed for a hoisting installation equipped with an asynchronous drive with contactor control. The contactors have main contacts \(1U \ldots 6U\) in the motor rotor circuit, of which the first, fifth, and sixth (last) contacts are, in addition, equipped with auxiliary contacts \(1U_{1}\), \(5U_{1}\), \(6U_{1}\), \(6U_{2}\), connected into the circuit of the control devices. The auxiliary contacts (Fig. 4) are shown in the position when the contactors are disconnected.

The motion of the vessels during the period of uniform travel and deceleration is monitored by relays \(RKR\), \(RKZ\). Both relays are connected into the motor stator circuit through a common current transformer.

During the acceleration period, motor overload will cause not an increase in current, but a decrease in acceleration, as a result of which the travel speed will be less than normal. Motion control during this period is carried out by a minimum-current relay \(RKU\), which is connected into the tachogenerator circuit. If a danger of rope breakage arises, the tachogenerator current will decrease in proportion to the magnitude

motor overload. The selection of the relay setting current is made on the basis of experimental data: during the acceleration period, the tachogenerator current is measured under normal motor load and under an overload produced by artificially delaying the descending conveyance in its upper position. The setting current is equal to

\[ I_y = I_{2n} - (I_{2n} - I_{2e}) \frac{k_0}{k_f}, \tag{7} \]

where \(I_{2n}\) is the tachogenerator current during starting under normal motor load;

\(I_{2e}\) is the tachogenerator current under extreme load;

\(k_0\) is the coefficient of permissible static motor overload;

\(k_f\) is the coefficient of the actual static overload when the descending conveyance is jammed.

By means of the adjustable resistance \(r\), the current \(I_{2n}\) is kept constant in magnitude. Relay \(RKU\) sends an impulse for protective braking when the current has a value from zero to the setting current. In the absence of current (after the end of motor starting and during the pause period), protective braking must not occur. This is achieved by means of relay \(P\), which, in the de-energized state, opens its contact and does not allow the \(RZEH\) protection relay to operate. The contact of relay \(P\) closes at the lowest possible tachogenerator current.

In the protection circuit an inductive switch of type \(VBD\) is used (not shown in the figure), which is installed at the upper receiving platform. The place of installation must be within the zone of influence of the unloading conveyance and must make it possible to monitor the movement of this conveyance downward over the initial section of the path. In the circuit, the \(VBD\) contacts are shown in the position when the conveyances are at the receiving platforms.

When the hoisting motor is switched on, block contact \(1U_1\) closes the circuit of relay \(RKT\). If the upper conveyance descends normally, the circuit of this relay is opened by contact \(VBD_1\); if the movement of the conveyance is delayed, the relay operates after a certain time. The time delay of relay \(RKT\) is selected on the basis of the calculated normal passage by the conveyance of the path over which it exerts its influence on switch \(VBD\).

During the period when the conveyance starts moving, relays \(RKU\) and \(P\) are shunted by contact \(VBD_2\). Subsequently this contact opens and contact \(VBD_3\) closes; relay \(RKU\) is included in the tachogenerator circuit and monitors the movement of the conveyances during the starting period, while relay \(P\) closes its contact.

After contactor \(5U\) is energized, its block contact in the \(RKZ\) circuit opens. Then the last contactor \(6U\) is energized and the period of uniform travel begins. Block contacts \(6U_1\) and \(6U_2\) close: the first switches on relay \(RKR\), which monitors the movement of the conveyances; the second switches on the intermediate relay \(RP\), which by contact \(RP_1\) opens the tachogenerator circuit and closes contact \(RP_2\) in the \(RKZ\) circuit.

At the end of the period of uniform travel, the acceleration contactors are disconnected, block contacts \(6U_1\) and \(6U_2\) open, and contact \(5U_1\) closes. The latter switches on relay \(RKZ\), which monitors the movement of the conveyances during the retardation period. Block contact \(6U_2\) in the \(RP\) circuit is shunted by the relay’s own contact.

At the end of the hoisting cycle, switch \(BBD\) returns to its initial position. Contact \(BBD_3\) switches off relay \(RP\), as a result of which relay \(RKZ\) drops out of the control system before the start of the deceleration period in the next cycle.

If the tachogenerator, in addition to the indicated purpose, is also used for other purposes (electrical monitoring of maximum speed, etc.), then the windings of the corresponding devices are connected into its circuit, and contact \(RP_1\) is transferred to the circuit shown by the dashed line in Fig. 4 and serves to shunt relay \(RKU\) during periods of uniform and decelerated motion.

As is known, the stopping of the conveyances at the end of hoisting does not occur simultaneously: the lower conveyance lands on the support while the upper one is still continuing to move. As a result, conditions are created analogous to the jamming of the descending conveyance, and safety braking of the hoisting machine may occur. In addition, the resulting slack above the lower conveyance causes destruction of the rope.

To monitor rope slack and to prevent false operation of the protection, contact \(UG\) is introduced into the circuit; it is installed on the depth indicator and is switched by the nut of the lead screw. Contact \(UG\) opens when the rising nut is at a distance from the upper division of the depth-indicator scale corresponding to 2--5 m of conveyance travel. Moving downward, the nut closes contact \(UG\).

Thus, by introducing contact \(UG\), the effect of rope slack on safety braking is eliminated, but relay \(RKZ\) will still operate and close the contact in the signaling circuit. The presence of slack is monitored by applying a signal when button \(KN\) is pressed manually. The amount of slack will be equal to the length of rope wound onto the machine drum during the time from the moment the signal is applied until the conveyance stops at the upper receiving platform. If the slack exceeds 150--200 mm, it must be eliminated by means of the hoisting-machine drum-repositioning mechanism.

In the protection circuit, all relays that monitor the motion of the conveyances, when operated, close their contacts in the circuit of protection relay \(RZEN\), and the latter opens the common protection circuit of the hoisting installation. The contact of \(RZEN\) in the protection circuit, when hoisting especially heavy loads, may be shunted by button \(KSh\). In the event of an emergency shutdown of the hoisting installation due to operation of the rope-break protection, a special signal must be given.

The protection circuit considered is quite simple, is assembled from standard devices, and is applicable to hoisting installations with any drive system. This circuit provides continuous automatic monitoring of the motion of the hoisting conveyances and makes it possible to eliminate the occurrence of dangerous emergency loads.

Corrections Noted

Bulletin of TPI, vol. 113

1. The potential energy of the rope was determined for a length of 100 m, close to its actual value during the fall of the descending conveyance from the unloading curves or during stopping of the conveyance ascending at a speed of 5–6 m/sec at the beginning of the deceleration path. ↩