Protection of hoisting installations against slack rope based on the position of conveyances in the shaft
Abstract Generated abstract
This paper addresses the problem of unreliable slack rope protection in mine hoisting installations and proposes monitoring slack by comparing the expected relative positions of the two conveyances in the shaft. It describes limit switch circuits that stop the hoist when this positional correspondence is violated, derives installation conditions and formulas for permissible emergency slack based on tensile impact calculations, and illustrates the method with a Kuzbass mine example. The authors conclude that, for many mines considered, switch adjustment based on preserving subsequent rope serviceability is impractical, so protection is often designed to prevent rope breakage, followed by inspection or testing. An improved circuit is proposed that also monitors operational slack, provides disturbance signaling, reduces contact wear, and can be assembled from standard industrial components.
Full Text
Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov
Volume 158 1968
Protection of Hoisting Installations Against Rope Slack Based on the Position of Conveyances in the Shaft
N. I. Klykov, V. S. Udut
(Presented by the scientific seminar of the Department of Mining Machines, Mine Transport, and Mining Mechanics)
The methods of monitoring rope slack that are currently used on mine hoisting installations are imperfect and unreliable in operation [1]. Protection of hoisting installations against rope slack based on the position of the conveyances in the shaft is applicable to mines of any depth, is simple to implement, and is reliable in service. The essence of this method is that, during normal operation of the hoisting installation, a definite position of one conveyance corresponds to the position of the other conveyance. In the event of emergency or operational rope slack, this correspondence is disrupted, which causes special devices to actuate, opens the protection circuit, and stops the hoisting machine.
At one of the mines of Kuzbass, the indicated principle was used to protect the hoisting installation against the conveyances becoming stuck in the unloading curves. For this scheme, ordinary limit switches were used, which are connected into the protection circuit (Fig. 1). The upper and lower emergency-slack switches \( \mathrm{VAN}_1 \) and \( \mathrm{VAN}_2 \) are connected in parallel into the protection circuit in such a way that, when the conveyances pass, one of them opens and the other closes. When the conveyances move in the opposite direction, the open contacts of the limit switches close, and the closed ones open. Thus, during normal operation of the installation the protection circuit is always shunted. If a conveyance becomes stuck in the upper part of the shaft, the limit switch \( \mathrm{VAN}_1 \) will remain open, and the lower conveyance that is moving upward will open the contacts of switch \( \mathrm{VAN}_2 \). This case corresponds to an opening of the protection circuit, which leads to stopping of the machine and application of the safety brake. Similarly, the limit switches \( \mathrm{VAN}_3 \) and \( \mathrm{VAN}_4 \) are connected into the protection circuit—for the other position of the conveyances. The group of switches \( \mathrm{VAN}_1 \) and \( \mathrm{VAN}_2 \) is connected in series with the group of switches \( \mathrm{VAN}_3 \) and \( \mathrm{VAN}_4 \). The protection circuit will be opened only in the case when both switches of one of the groups open their contacts.
The necessary operating conditions of the above scheme are as follows. When one conveyance is set at the unloading level and the other at the loading devices, the upper switch \( \mathrm{VAN}_1 \) must be open, and the lower switch \( \mathrm{VAN}_2 \) closed; this also applies to the switches of the other group—respectively \( \mathrm{VAN}_3 \) and \( \mathrm{VAN}_4 \).
To avoid breaking the protection circuit during normal operation of the installation, at the beginning of the hoisting operation the contacts of the upper switch \(BAN_1\) must close earlier than the contacts of the lower switch \(BAN_2\) open.
Fig. 1. Schematic diagram for monitoring emergency rope slack according to the position of the hoisting conveyances
the lower switch \(BAN_2\). In accordance with the above, the condition for installing switches to monitor emergency slack will take the form
\[ h_p + l_v + S_v - \Delta l_y - l_n - \Delta l_n \geq S_n + a_k, \tag{1} \]
where \(h_p\) is the amount by which the conveyance exceeds the normal unloading level, m;
\(l_v\) is the distance between the upper switch and the actuating cam of the conveyance installed at the unloading level, m;
\(l_n\) is the distance between the lower switch and the actuating cam of the conveyance installed on the landing devices, m;
\(S_v\) is the travel of the upper switch, m;
\(S_n\) is the travel of the lower switch, m;
\(\Delta l_y\) is the elastic shortening of the rope when the conveyance lands, m;
\(\Delta l_n\) is the permissible magnitude of operating rope slack, m;
\(a_k\) is the amplitude of oscillation of the conveyance on the rope, m.
To determine the value by which the conveyance exceeds the normal unloading level, formula (2) is proposed:
\[ h_p = 0.3 + 0.4 \cdot 10^{-3} H, \tag{2} \]
where \(H\) is the hoisting height, m.
The magnitude of the elastic shortening of the rope when the hoisting conveyance is set down is (3)
\[ \Delta l_y' = 0.84 \cdot 10^{-6} k_0 (L_{\text{pr}} - H_0), \tag{3} \]
where \(k_0\) is the terminal-load coefficient;
\(L_{\text{pr}}\) is the durable length of the rope, m;
\(H_0\) is the greatest length of the suspended portion of the rope, m.
It is proposed that the permissible amount of operational slack be taken as \(0.2\) m. The amplitude of oscillation of the conveyance on the rope depends on the hoisting height and on the nature of the motor starting. On average, this value is \(0.1\) m.
To determine the distances \(l_{\text{v}}\) and \(l_{\text{n}}\), it is necessary to substantiate the permissible magnitude of emergency rope slack. We solve this problem on the basis of two premises: 1) when a jammed conveyance breaks free, the rope is loaded by forces that do not exceed the maximum loads under normal operation, which ensures the suitability of the rope for further service; 2) in an analogous case, the rope is loaded by forces that considerably exceed the maximum working loads, but remains intact. The suitability of the rope for further service is
Fig. 2. Calculation scheme for determining the permissible magnitude of emergency rope slack
not guaranteed. Let us first establish the dependence between the magnitude of emergency slack and the forces arising in the rope when a jammed conveyance falls.
Investigating analogous phenomena, Prof. F. V. Florinskii, for determining stresses in the rope, gives an equation in the form of an infinite-
… series [4]. Proceeding from the analysis of this equation, the same source gives a formula for determining the maximum dynamic forces,
\[ F_{\mathrm{d}}=(a_{\mathrm{k}}+k_{\mathrm{d}})Q, \tag{4} \]
where \(a_{\mathrm{k}}\) is the ratio of the weight of the unwound part of the rope to the total end load;
\(Q\) is the weight of the load applied with velocity to the lower end of the rope, kg.
The coefficient \(k_{\mathrm{d}}\), in turn, depends on the cross section of the rope, the modulus of elasticity, the propagation velocity of deformation waves, and the velocity of the load suspended from the lower end of the rope. The value of this coefficient is given in the cited work. However, the solution by the method of Prof. F. V. Florinsky is rather complicated, and the determination of a number of initial quantities is practically difficult.
We present a solution of the problem based on the theory of tensile impact (5), neglecting the influence of the mass of the rope on the impact, the loss of energy of the falling load to dissipation, and the energy of waves. In accordance with the assumptions adopted, the work of the falling load is converted entirely into the potential energy of deformation of the rope (Fig. 2).
\[ Q\cdot(h_{\mathrm{a}}+\delta)=\frac{F_{\mathrm{d}}}{2}\,\delta, \tag{5} \]
where \(h_{\mathrm{a}}\) is the emergency slack, m;
\(\delta\) is the absolute deformation of the rope under dynamic loading, m.
The magnitude of the deformation is
\[ \delta=\frac{F_{\mathrm{d}}\cdot l_{\mathrm{k}}}{E_{\mathrm{k}}\sum S_{\mathrm{k}}}, \tag{6} \]
where \(l_{\mathrm{k}}\) is the length of rope involved in the tensile impact, m;
\(E_{\mathrm{k}}\) is the modulus of elasticity of the rope, kg/cm\(^2\);
\(\sum S_{\mathrm{k}}\) is the total cross-sectional area of the rope wires, cm\(^2\).
Substituting the value (6) into formula (5) and making the corresponding transformations, we obtain
\[ h_{\mathrm{a}}=\frac{F_{\mathrm{d}}^{2}\cdot l_{\mathrm{k}}}{2QE_{\mathrm{k}}\sum S_{\mathrm{k}}} -\frac{F_{\mathrm{d}}\cdot l_{\mathrm{k}}}{E_{\mathrm{k}}\sum S_{\mathrm{k}}}. \tag{7} \]
The length of rope involved in dynamic stretching is
\[ l_{\mathrm{k}}=L_{\mathrm{c}}+\frac{\pi D_{\mathrm{sh}}(\varphi^\circ+90^\circ)}{360^\circ}+h_{0}, \tag{8} \]
where \(L_{\mathrm{c}}\) is the length of the rope strand, m;
\(D_{\mathrm{sh}}\) is the diameter of the guide sheave, m;
\(\varphi^\circ\) is the angle of inclination of the rope strand to the horizontal, degrees;
\(h_{0}\) is the smallest length of rope overhang, m.
Substituting into formula (7) the value of the length of rope subjected to tensile impact (8), we obtain
\[ h_{\mathrm{a}}= \frac{ \dfrac{F_{\mathrm{d}}}{E_{\mathrm{k}}\sum S_{\mathrm{k}}} \left(\dfrac{F_{\mathrm{d}}}{2Q}-1\right) \left[ L_{\mathrm{c}}+\dfrac{\pi D_{\mathrm{sh}}(\varphi^\circ+90^\circ)}{360^\circ}+h_{0} \right] }{ 1-\dfrac{F_{\mathrm{d}}}{E_{\mathrm{k}}\sum S_{\mathrm{k}}} \left(\dfrac{F_{\mathrm{d}}}{2Q}-1\right) }. \tag{9} \]
To satisfy the condition for preserving the rope for further operation, the maximum dynamic force under a tensile impact must not exceed twice the maximum static force (6),
\[ F_{\mathrm{d}} \leq 2(Q_0+pH_0), \tag{10} \]
where \(Q_0\) is the design end load, kg;
\(p\) is the weight of 1 m of rope length, kg/m.
To satisfy the condition for preventing rope breakage, the dynamic force under a tensile impact must not exceed the breaking load on the rope, i.e.,
\[ F_{\mathrm{d}} \leq \frac{F_{\mathrm{r}}}{k_{\mathrm{br}}} = \frac{m_{\phi}(Q_0+pH_0)}{k_{\mathrm{br}}}, \tag{11} \]
where \(F_{\mathrm{r}}\) is the breaking force for the rope, kg;
\(k_{\mathrm{br}}\) is the safety factor against rope breakage;
\(m_{\phi}\) is the actual strength reserve of the rope.
Substituting into formula (9) the value of the dynamic force (10), we obtain the permissible magnitude of emergency lowering, proceeding from the conditions for preserving the serviceability of the rope,
\[ h'_{\mathrm{em}} = \frac{ \dfrac{2(Q_0+pH_0)}{E_{\mathrm{k}}\sum S_{\mathrm{k}}} \left(\dfrac{Q_0+pH_0}{Q}-1\right) \left[ L_{\mathrm{c}}+ \dfrac{\pi D_{\mathrm{sh}}(\varphi^\circ+90^\circ)}{360^\circ} +h_0 \right] }{ 1- \dfrac{2(Q_0+pH_0)}{E_{\mathrm{k}}\sum S_{\mathrm{k}}} \left(\dfrac{Q_0+pH_0}{Q}-1\right) }. \tag{12} \]
Making an analogous substitution of the values of the dynamic force (11) into formula (9), we obtain the permissible magnitude of emergency lowering, proceeding from the conditions for preventing rope breakage:
\[ h'_{\mathrm{em}} = \frac{ \dfrac{m_{\phi}(Q_0+pH_0)}{k_{\mathrm{br}}E_{\mathrm{k}}\sum S_{\mathrm{k}}} \left[ \dfrac{m_{\phi}(Q_0+pH_0)}{2k_{\mathrm{br}}Q}-1 \right] \left[ L_{\mathrm{c}}+ \dfrac{\pi D_{\mathrm{sh}}(\varphi^\circ+90^\circ)}{360^\circ} +h_0 \right] }{ 1- \dfrac{m_{\phi}(Q_0+pH_0)}{k_{\mathrm{br}}E_{\mathrm{k}}\sum S_{\mathrm{k}}} \left[ \dfrac{m_{\phi}(Q_0+pH_0)}{2k_{\mathrm{br}}Q}-1 \right] }. \tag{13} \]
The derived formulas (12) and (13) are applicable both to the case of jamming of the empty conveyance and to the case of jamming of the conveyance with a load.
To determine the modulus of elasticity of the rope, one may use the formula proposed by Prof. F. V. Florinsky (4),
\[ E_{\mathrm{k}} = 0.86\cdot 10^6 \left(\frac{\sum S_{\mathrm{k}}}{p}\right)^4. \tag{14} \]
The strength length of the rope (7) is
\[ L_{\mathrm{pr}}=\frac{10^6\sigma_{\mathrm{pc}}}{\gamma m_{\phi}}, \tag{15} \]
where \(\sigma_{\mathrm{pc}}\) is the design tensile strength of the rope, kg/cm²;
\(\gamma\) is the fictitious weight of 1 m³ of rope, kg/m³.
To ensure the operability of the above-described lowering-control scheme (Fig. 1), the adopted value of the permissible emergency lowering must in any case satisfy the condition
\[ h_{\mathrm{em}} \geq \Delta l_y + \Delta l_{\mathrm{n}} + l_{\mathrm{n}} + S_{\mathrm{n}} + S_{\mathrm{t}}, \tag{16} \]
where \(S_{\mathrm{t}}\) is the additional length of rope paid off from the drum after the braking impulse is issued until the machine stops, m.
From formula (16), the distance from the actuating cam of the lower conveyance to the position of the emergency-slack switch is
\[ l_{\mathrm{n}}=h_{\mathrm{na}}-\Delta l_y-\Delta l_{\mathrm{n}}-S_{\mathrm{n}}-S_{\mathrm{t}} . \tag{17} \]
In view of the fact that, when emergency slack is formed in the upper part of the shaft, the speed of the conveyance is insignificant, and the deceleration during safety braking in this case is about \(5\ \mathrm{m/sec^2}\), the braking distance entering formulas (16) and (17) is no more than \(0.1\ \mathrm{m}\). In the case of jamming of the conveyance in the middle part of the shaft, the braking distance is many times greater than the indicated value and can most simply be determined experimentally.
For the upper switch, the distance from its installation point to the actuating cam of the conveyance located at the unloading level is determined from condition (1):
\[ l_{\mathrm{v}}=l_{\mathrm{n}}+\Delta l_y+\Delta l_{\mathrm{n}}+S_{\mathrm{n}}+a_k-h_{\mathrm{p}}-S_{\mathrm{v}} . \tag{18} \]
Example. Install limit switches to protect the hoisting installation of the S. M. Kirov mine (Kuzbass) against emergency rope slack in the upper part of the shaft, according to the position of the hoisting conveyances. The normal weight of the hoisted load is \(7000\ \mathrm{kg}\); the dead weight of the skip is \(6000\ \mathrm{kg}\); the greatest and smallest lengths of the rope suspension are, respectively, \(245\) and \(10\ \mathrm{m}\); the actual factor of safety of the rope is 8; the weight of \(1\ \mathrm{m}\) of rope length is \(6.1\ \mathrm{kg/m}\); the cross-sectional area of the rope wires is \(7\ \mathrm{cm^2}\); the length of the strand, including the portion of the rope located on the sheave, is \(45\ \mathrm{m}\).
Solution. We determine the modulus of elasticity of the rope (14):
\[ E_k=0.86\cdot 10^6\left(\frac{7}{6.1}\right)^4 =1.5\cdot 10^6\ \mathrm{kg/cm^2}. \]
The permissible magnitude of emergency slack, from the conditions for preserving the serviceability of the rope after a tensile impact (12), is
\[ h'_{\mathrm{na}}= \frac{ 55\cdot \dfrac{2(6000+7000+6.1\cdot245)}{1.5\cdot10^6\cdot7} \left( \dfrac{6000+7000+6.1\cdot245}{6000}-1 \right) }{ 1- \dfrac{2(6000+7000+6.1\cdot245)}{1.5\cdot10^6\cdot7} \left( \dfrac{6000+7000+6.1\cdot245}{6000}-1 \right) } = \]
\[ =0.19\ \mathrm{m}. \]
We adopt a safety factor of \(1.2\). The permissible magnitude of emergency slack, from the conditions for preventing rope breakage (13), is
\[ h''_{\mathrm{na}}= \frac{ 55\cdot \dfrac{8(6000+7000+6.1\cdot245)}{1.2\cdot1.5\cdot10^6\cdot7} \left[ \dfrac{8(6000+7000+6.1\cdot245)}{1.2\cdot2\cdot6000}-1 \right] }{ 1- \dfrac{8(6000+7000+6.1\cdot245)}{1.2\cdot1.5\cdot10^6\cdot7} \left[ \dfrac{8(6000+7000+6.1\cdot245)}{1.2\cdot2\cdot6000}-1 \right] } = \]
\[ =3.25\ \mathrm{m}. \]
The solution by the method of Prof. F. V. Florinskii gives, respectively for the first and second cases, \(h'_{\mathrm{na}}=0.18\ \mathrm{m}\) and \(h''_{\mathrm{na}}=3.32\ \mathrm{m}\), i.e., the difference obtained in the results is of no essential significance. In view of the fact that the permissible magnitude of emergency slack, proceeding from the conditions for preserving the serviceability of the rope, is considerably lower than the amount by which the normal unloading level is exceeded, we take the second case as our guide. We adopt the end-load coefficient as \(0.55\); the design tensile strength of the rope as \(180\ \mathrm{kg/mm^2}\); the fictitious weight of \(1\ \mathrm{m^3}\) of rope as \(9200\ \mathrm{kg/m^3}\). The strong length of the rope (15) is
\[ L_{\mathrm{pr}}=\frac{180\cdot10^6}{9000\cdot8}=2440\ \mathrm{m}. \]
Elastic deformation of the rope when the conveyance is being landed (3)
\[ \Delta l_{y}=0.84 \cdot 10^{-6}\cdot 0.55(2440-245)\cdot 245=0.25\ \text{m}. \]
Magnitude of the unloading-level overshoot (2)
\[ h_{\text{p}}=0.3+0.0004\cdot 235=0.435\ \text{m}. \]
We take: \(\Delta l_{\text{n}}=0.2\ \text{m};\ a_{\text{k}}=0.1\ \text{m};\ S_{\text{t}}=0.1\ \text{m};\ S_{\text{n}}=S_{\text{v}}=0.1\ \text{m}\). Determine the distance from the actuating cam of the conveyance installed on the landing devices to the lower emergency-slack switch (17)
\[ l_{\text{n}}=3.35-0.25-0.2-0.1-0.1=2.7\ \text{m}. \]
The distance from the actuating cam of the conveyance installed at the unloading level to the upper emergency-slack switch (18)
\[ l_{\text{v}}=2.7+0.25+0.2+0.1+0.1-0.435-0.1=2.815\ \text{m}. \]
Calculations by the formulas given for specific mines of the Kuzbass showed that, for the most part, it is not possible to satisfy the condition for preserving the serviceability of the rope after impact loading, since the results obtained in this case do not make it possible to adjust the limit switches according to the scheme considered. For this reason it is recommended to be guided by the second variant, which guarantees only the integrity of the rope. The possibility of further use of the rope is decided on the basis of the effect of the impact loading or by testing the rope.
The scheme shown in Fig. 1 has the following shortcomings: 1) absence of monitoring of operational slack; 2) closing and opening of the contacts of the emergency switches occurs under current, which causes burning of the contacts and reduces the reliability of operation of the scheme; 3) there is no signaling of the nature of the disturbance in the operating mode of the installation. The proposed scheme (Fig. 3) is free of the listed shortcomings. The emergency-slack switches are included not in the common protective circuit, but in a separate supply circuit of the contactor coils. Thus, the group of emergency-slack switches \(VAN_{1}\) and \(VAN_{2}\) is included in the circuit of the emergency-slack contactor \(KAN_{1}\), which provides protection against jamming of one of the conveyances. The switches of the second group, \(VAN_{3}\) and \(VAN_{4}\), are included in the circuit of the emergency-slack contactor \(KAN_{2}\) and protect the installation against jamming of the other conveyance. The switches of one group are installed in series with one another and with the supplied contactor, with the calculation that during normal operation one of the switches is closed and the other is open. When emergency slack is formed, both switches of one group close their contacts, supplying power to the coil of the corresponding contactor. The contactor that has received power opens the normally closed contacts in the common protective circuit and closes the normally open contacts in the circuit of a separate signaling device. The machine is stopped with simultaneous delivery of a signal to the hoist operator: the emergency-slack lamps \(LAN_{1}\) and \(LAN_{2}\) light up.
To monitor the operational slack of the rope, one more group of switches has been introduced into the scheme: \(VEN_{1}\) and \(VEN_{2}\). These switches have normally open contacts, which are connected in series with one another and into the circuit of the operational-slack contactor coil \(KEN\). Consequently, the coil of the \(KEN\) contactor will receive power only in the event of simultaneous closing of the contacts of the \(VEN_{1}\) and \(VEN_{2}\) switches. This occurs when the operational elongation of the ropes exceeds the permissible value, i.e., when the possible actual
the rope slack will exceed the permissible value. When power is supplied, the coil of contactor KEN opens contacts in the common protection circuit and closes the contacts feeding the operating-slack lamp LEN. In contrast to the emergency-slack switches, switches VEN\(_1\) and VEN\(_2\) register the “closed” position only during the passage, near them, of the actuating cams on the conveyances. The operating-slack switches are installed after careful adjustment of the rope lengths, when all plastic deformation of the ropes has been taken up. The upper switch VEN\(_1\) is installed arbitrarily, 5–10 m below the actuating cam of the conveyance set at the unloading level. The upper conveyance is then lowered until switch VEN\(_1\) operates. At this time the second conveyance is raised to almost the same height, and switch VEN\(_2\) is installed below the actuating cam of this conveyance by the amount of the permissible slack or the adopted rope-adjustment increment. The reverse procedure for installing the operating-slack switches is also acceptable: first the lower switch VEN\(_2\) is installed arbitrarily, the lower conveyance is raised until VEN\(_2\) operates, and then, with the adopted lowering, the upper switch VEN\(_2\) is installed. In either case the switches must not fall within the loading and unloading zone. To focus the operator’s attention, it is possible to recommend a slack siren SN, switched on when any emergency- or operating-slack contactor operates. Bypass switches PO\(_1\), PO\(_2\), and PO\(_3\) are provided to restore the protection circuit. The procedure for setting the emergency-slack switches does not differ from that described above.
Fig. 3. Proposed circuit for protecting a hoisting installation against rope slack
In addition to the advantages listed, the proposed circuit does not require energy consumption, since the making and breaking of contacts during normal operation of the installation occur in open circuits. All the necessary apparatus is assembled in blocks from elements manu-
manufactured by industry. It is preferable to use contactless-type switches for operational and emergency slack protection.
REFERENCES
-
N. I. Klykov. Control of rope slack in hoisting installations. Kolyma, No. 1, 1960.
-
N. I. Klykov. Adjustment of limit switches and speed limiters on skip hoisting installations. Kolyma, No. 5, 1959.
-
N. I. Klykov. Comparison of the operating qualities of mechanisms for repositioning the drums of mine hoisting machines. In: Wear and Strength of Mining Equipment, Ugletekhizdat, 1959.
-
F. V. Florinskii. Dynamics of the Mine Hoisting Rope. Ugletekhizdat, 1955.
-
N. M. Belyaev. Strength of Materials. Gostekhizdat, 1945.
-
N. I. Klykov. On the maximum dynamic forces in ropes at the rim of drums of mine hoisting machines. Proceedings of the Tomsk Polytechnic Institute, vol. 104, 1959.
-
N. K. Pravitskii. Mine Hoisting Installations. Metallurgizdat, 1956.