On the Conditions for the Arrangement of Hoisting Machines Relative to the Mine Shaft

I. A. Balashev

Introduction

In the existing literature and in the practice of design and installation organizations, a firm procedure has become established regarding the arrangement of a normal two-drum hoisting machine relative to the mine shaft, consisting in the following requirements being satisfied: 1) the maximum length of the rope strand must not be greater than 55 m; 2) the angles of deviation of the ropes, both external and internal, must not be greater than \(1^\circ 30'\); 3) the horizontal distance from the shaft axis to the drum axis, from the condition of the possibility of placing the foundations of the headframe thrust struts and the foundation of the hoisting machine, must be not less than the value determined by Ya. V. Brovman’s empirical formula:

\[ L_{\min} \geq 0.6h_k + 3.5 + D_b\,[\text{m}] \tag{1} \]

and 4) the angle of inclination of the lower rope (usually the left one) to the horizontal must be not less than \(35^\circ\), in order to avoid contact of the rope with the machine frame.

Experience in the operation of hoisting installations in the mines of the Kuzbass shows that the indicated requirements are insufficient for reliable and accident-free operation of hoisting installations, and that a number of additional requirements arise, which it seems possible to satisfy only during the installation of the hoisting installation and very difficult to implement in an installation already in operation.

The purpose of the present article is to substantiate additional conditions, and also to clarify the basic geometrical relations and terminology in the question of the arrangement of a hoisting machine near a mine shaft.

Basic Geometrical Relations

In what follows we shall distinguish the following concepts, necessary in the question of arranging the machine. The installation axis is the trace of the plane passing through the middle of the axes of the rope run-off from the sheaves and perpendicular both to the line connecting the points of the axes of the hanging branches of the ropes and to the line of the drum axis (main shaft). When laying the machine foundation and installing it, the installation axis and the drum axis (main shaft) constitute the principal coordinates for carrying out installation work.

The machine axis (axis of symmetry of the machine) is a line perpendicular to the drum axis and dividing in half the distance between the inner flanges of the drums. In a particular case the machine axis may coincide with the installation axis. Sometimes the machine axis and the installation axis are called the hoist axis, which creates confusion in these terms and should be avoided.

The normal axis of the ropes is the line of the rope axes when, with the axis of the drums (head shaft), it forms a right angle. This is a special case of the position of the ropes on the drums, when the angle of deviation is equal to zero.

The axes enumerated are shown in Fig. 1 and fully characterize the operating conditions for the installation and operation of the entire hoisting installation.

Fig. 1. General layout diagram of a normal hoisting machine relative to the mine shaft.

over a long period of operation. The position of the named axes must be subjected to annual inspection by mine-survey verification, including also the position of the axes and planes of the guide sheaves.

Geometric layout diagram of the machine

When preparing the design of a hoisting installation, the question arises of the possible location of the hoisting machine, of the most advantageous location for a single machine, and of the arrangement within permissible limits when placing two machines operating in one shaft and situated on one side of the headframe. The latter case often occurs when one cage with a counterweight and a normal skip installation operate in the shaft.

The solution of such a problem is facilitated if, before constructing a structural layout of the arrangement of the type shown in Fig. 1, one first constructs the geometric diagram shown in Fig. 2.

The construction of the geometric diagram is carried out in the following sequence. Along the vertical, the known height of the headframe, \(h_k\), is laid off to a scale of 1:200. From the elevation of the shaft collar, at a distance \(h_m\), a horizontal line \(DE\) is drawn, on which the axis of the drums will be located.

The value \(h_m\) is obtained from the surface layout; in its absence, as a rough estimate it is normally, on the average, about \(1\ \text{m}\).

From point \(A\), corresponding to the center of the sheave, three lines are drawn: \(A_b\), equal on the drawing scale to the maximum length of the rope chord, and two lines, \(A_c\) and \(A_d\), determined by the limiting permissible values of the rope-deviation angles for the outer and inner angles and determined as follows.

From the geometrical constructions we have, for the right-hand drum,

\[ \tg \alpha_{\text{outer}}=\frac{B_1}{L_c} \tag{2} \]

and

\[ \tg \alpha_{\text{inner}}=\frac{B_2}{L_c}. \tag{3} \]

The meanings of the quantities are shown in Fig. 1. Expressing \(B_1\) and \(B_2\) in terms of the installation parameters: the distance between the axes of the hanging ropes \(S\) and the machine size \(a=a_1+a_2\), and assuming that the erection axis coincides with the axis of the machine, i.e.,

\[ a_1=a_2=\frac{a}{2}, \tag{4} \]

and also assigning to the outer and inner deviation angles their limiting values \(1^\circ 30'\), to which the value \(\tg \alpha=\frac{1}{38}\) corresponds, we obtain, respectively:

\[ \tg \alpha_{\text{outer}} = \frac{B+\frac{a}{2}-\frac{S}{2}}{L_c} \tag{5} \]

and

\[ L'_c=19(2B+a-S), \tag{6} \]

and also

\[ \tg \alpha_{\text{inner}} = \frac{\frac{S}{2}-\frac{a}{2}}{L_c}. \tag{7} \]

and

\[ L''_c=19(S-a). \tag{8} \]

Thus, we obtain expressions for the limiting value of the rope chord, \(L'_c\) and \(L''_c\), which, to scale, we lay off from point \(A\) (Fig. 2). It remains only to lay off from point \(C\)—the axis of the rope hang, or the axis of the mine shaft—the quantity

\[ L_m \geq 0.6h_k+3.5+D_b, \]

determined by the construction requirements of the foundation for the headframe supports and the machine foundation.

As a result of the constructions on line \(DE\) (Fig. 2), we obtain points \(d, c, a, b\); moreover, the distance between the last two points, \(a-b\), determines the zone of possible location of the drum axes.

In the present example the zone \(a-b\) is determined by the dimensions \(L_m\) and the maximum permissible rope length. It may turn out that the lower limit is determined by the position of \(L'_c\), i.e., by the maximum deviation angle; that is, point \(c\) will lie to the right of point \(a\).

With two machines arranged on one side of the headframe, there will be not two but four lines of the maximum angle of deviation, and the position of each machine is fully determined; it also becomes obvious which machine should be placed in front (closer to the shaft) and which behind, while maintaining between the axes of the machines the necessary distance of 10–12 m to allow installation of the machines and placement of the lower rope of the machine standing behind. In some cases this latter circumstance (the lower rope) receives a good structural solution by constructing the foundation of the rear machine one or two meters higher than that of the machine standing in front.

Fig. 2. Geometrical diagram for determining the possible location of a machine

The value of constructing a geometrical diagram for determining the possible and most advantageous location of machines lies in the simplicity of the construction and in clarifying the question of satisfying the installation conditions for the correct arrangement both of the machine being installed and of its subsequent replacement by a new machine after the expiration of its depreciation period, without a significant interruption in operation when changing from one machine to another, newly installed in the place provided in advance during the design and construction of the mine.

It should be noted that determining the limiting ropes according to formulas (5)—(8) is valid under condition (4). In cases where the installation axis does not coincide with the axis of the machine, in the indicated formulas one should substitute the values \(a_1\) in formulas 5, 6 and the value \(a_2\) in formulas 7 and 8, where \(a_1\) may have a negative sign, as will be shown below.

Place of fastening the ropes on the drum

Manufacturers of hoisting machines design machines in such a way that the ropes, both the right upper and the left lower, are fastened by their ends at the outer flanges of the drums; fastening them at the inner flanges of the drums is not provided for, and under production conditions it is resorted to rarely, in exceptional cases.

Fastening the ropes at the outer flanges gives a better distribution of bending moments on the main shaft, but it has practically no effect on the structural dimensions of the shaft.

However, from the point of view of operation, fastening the rope ends at the outer flanges has a very major drawback, sometimes bringing the machine into an emergency condition. The essence of this drawback is that, as can be seen from Fig. 3, during the entire cycle of the hoisting operation there occurs, in the first half of the cycle, a horizontal force component from each rope directed one-sidedly to the right, and in the second half of the cycle to the left, along the axis of the shaft, producing—

these forces add up and produce a displacement of the drums and of the main shaft to the right and to the left during each hoisting cycle.

The magnitude of the horizontal component depends on the end load of the rope and on the deviation angle. The numerical value of this force for a standard series of machines can easily be determined from the maximum permissible static load on the machine branches and the limiting deviation angle, as shown in Table 1.

Table 1

From the table given, compiled for the case in which the ropes are fastened at the outer flanges of the drums according to Fig. 3, it is seen that the maximum horizontal component reaches values from 516 to 1105 kg at the beginning of motion; then, after the ropes pass through the normal axis of the ropes,

Fig. 3. Distribution of the horizontal component over a hoisting cycle with the usual fastening of the ropes at the outer flanges of the drums (the horizontal components add up).

it changes direction and at the end of the motion also increases, approaching the same values. This phenomenon occurs during every hoisting cycle, provided that the machine is fully utilized in terms of end load and the winding part of the drums; moreover, the magnitude of the horizontal component will be considerably greater if the inertia forces during the machine acceleration period are taken into account. It is quite obvious that the presence of such a significant

forces will rock the shaft, wear away the babbitt lining of the main bearing shells by means of the shaft collars. As will be shown below, an increase in the shaft runout sometimes brings the machine into complete disorder and takes it out of service for lengthy major repairs, which is wholly inadmissible under mine operating conditions.

Proposed method of fastening the ropes

By changing the point at which the ropes are fastened on the drum—the right-hand rope at the inner groove, and the left-hand rope at the outer one, as shown in Fig. 4, or conversely—it is possible to attain a state in which the horizontal components along the shaft axis will be directed in opposite directions and will mutually compensate each other on the shaft, and only the difference of the horizontal forces will remain unbalanced. The difference of the forces, as is seen from

Fig. 4. Proposed fastening of the ropes—the right-hand rope at the inner groove, the left-hand rope at the outer one—and displacement of the machine axis to the left of the installation axis. The horizontal components mutually compensate each other.

the last column of Table 1, is small in magnitude and ranges from 104 to 315 kg under the same operating conditions of the machine. With this method of fastening the ropes, the internal dimensions \(a_1\) and \(a_2\) increase on account of the friction and reserve turns, since the machine axis and the installation axis cannot coincide; this must be taken into account in designing the machine and in constructing the installation diagram—Fig. 1—as well as the geometric diagram—Fig. 2—and during installation of the machine.

Fastening the ropes at opposite ends of the drums places the machine under more favorable operating conditions, and, in the case of incomplete use of the winding part of the drum, it is possible to achieve complete balancing of the horizontal components from the right-hand and left-hand ropes.

In the calculation formulas (5) and (7), when substituting the values \(B_1\) and \(B_2\) into the numerator of these formulas, a correction should be introduced, since instead of the magni-

... value \(a/2\) we shall have \((a+a_{\tau})/2\), where \(a_{\tau}\) is the winding part of the right-hand drum occupied by three friction turns and equal to

\[ a_{\tau}=3(d+e), \tag{9} \]

where \(d\) is the rope diameter and \(e\) is the clearance between turns. Then formulas (6) and (7) for this case will have the following form for the right-hand drum:

\[ L'_{c\,pr}=19(2B+a-a_{\tau}-S) \tag{10} \]

and

\[ L''_{c\,pr}=19(S-a+a_{\tau}). \tag{11} \]

For the left-hand drum, the expressions for determining the limiting length of the rope string will have the form

\[ L'_{c\,lev}=19(2B+a+a_{\tau}-S), \tag{12} \]

\[ L''_{c\,lev}=19(S-a+a_{\tau}). \tag{13} \]

The installation axis (the axis of symmetry of the hoist) must be displaced from the axis of the machine (the axis of symmetry of the machine) to the right by a distance \(a_{\tau}/2\), equal to half the winding part of the right-hand drum occupied by the friction turns. As is seen from a comparison of the calculated formulas 5–8 and 10–13, the magnitude of the angles of deviation changes only slightly as a result of shifting the installation axis.

A Case from Practice

In the Kuzbass, at mine A, in June 1949, an NKMZ hoisting machine of type \(2\times5\times2.3\) was put into operation for hoisting a maximum load of \(5.25\) t (rock), equipped with two three-ton single-deck cages. The maximum terminal load of the strands was 16 and 10 t, the hoisting height from the first level was 105 m, and the working part of the turns on the drum amounted to 7 turns and occupied a total of 450 mm across the width of the drum.

The ropes were secured by their ends normally at the outer flanges. For accidental reasons, the working parts of the ropes were wound on both drums to the right of the normal axis of the rope, as shown in Fig. 5.

As is seen from Fig. 5b, the horizontal components proved to be unidirectionally directed to the left, without a change of sign during the entire hoisting cycle, amounting in magnitude to a force varying from 180 to 410 kg during hoisting of the right-hand cage and somewhat less during hoisting of the left-hand cage.

After \(2\frac{1}{2}\) years of operation, the machine fell into complete disorder, manifested in the following: the main shaft with the drums moved to the left and, together with the key, considerably wore away the liners of the left bearing, as a result of which the gear for the depth indicator on the right-hand drum disengaged and the depth indicator ceased to operate; finally, the toothed clutch located to the left of the left-hand drum ceased to disengage, and it became impossible to adjust the rope. Temporary operation was ensured by bracing the shaft on the left side with a hydraulic prop.

The radical solution was achieved by transferring the working turns of the ropes of both the right-hand and the left-hand drums to the left of the normal rope axis so that a small horizontal component directed to the right was ensured.

After several runs, the main shaft and the drums assumed their normal position, the depth indicator began to operate reliably, and became

possible to disengage the left drum by means of a toothed coupling, i.e., the machine was brought to an operable condition.

The example presented shows how great an influence the horizontal component from the ropes has on the operation of the installation and, moreover, provides a prescription that, in certain operating cases, when the winding part of the drum is not fully used, it is possible to regulate the magnitude and direction of the horizontal component by selecting the working part of the turns at a definite place on the winding part of the drum, in order to improve the operating conditions of the hoisting machine.

Fig. 5. Diagram of the hoisting installation of Mine A.

a) Machine \(2 \times 5 \times 2.3\). b) Force diagram when hoisting rock with the right cage. The horizontal component varies from 410 to 180 kg and has one direction—to the left. \(\times\) Place where the rope ends are fastened on the drum.

Additional conditions

From the foregoing it appears possible to propose additional conditions for the arrangement of the machine relative to the mine shaft. These conditions relate both to the arrangement of the machine and to minor structural additions in the machine.

1. The place where the ropes are fastened on the right drum must be at the inner flange, and on the left drum—at the outer flange.

2. For fastening the right rope on the inner flange from the inner side of the drum, the design of the machine must provide devices (clamps) for fastening the rope. From the outer side of the inner flange it is inconvenient to fasten the rope because of the proximity of the left drum.

3. When arranging the machine relative to the mine shaft, the installation axis and the axis of symmetry of the drums must not coincide. The position of the installation axis must be selected with allowance for equality of the rope deviation angles on the right and left drums according to formulas 9–13, and from this point of view the installation axis is the axis of symmetry of the hoisting installation, while the axis of the drums may be called the axis of symmetry of the machine (and not of the installation).

4. The axis of the machine must be shifted to the left from the installation axis by the amount

\[ \frac{a_T}{2}. \]

Conclusions

1. The conditions for arranging the machine relative to the mine shaft must be supplemented by the condition of compensating the horizontal components along the drum shaft.

2. The ropes must be fastened on the drums in such a way that the end of the right rope is fastened at the inner flange of the right drum, and the left rope at the outer flange of the left drum.

1. The installation axis of the unit must pass through the middle of the sum of two distances: between the flanges of the drums and the magnitude of the friction turns on the right-hand drum—

\[ \frac{a+a'_{\mathrm{т}}}{2}. \]

Compliance with the proposed additional conditions will place the hoisting machine in a better operating regime and increase its productivity, since the number of major repairs caused by machining of the liners and the associated labor-intensive work of recasting the bulky bearing liners will be reduced.

Noted Misprints