OPTIMUM SKIP CAPACITY

I. K. Khrustalev

The question of selecting the optimum lifted load has been the subject of many works by Soviet scholars. The first in-depth investigation of this question was carried out by the outstanding scholar in the field of mining mechanics, Academician M. M. Fedorov, in 1926. Taking as the basis the smallest sum of costs for operation and depreciation of equipment, M. M. Fedorov obtained a complex expression for determining the optimum capacity of the vessel. A less complex dependence was later obtained by Prof. V. I. Belov, and then by Prof. G. M. Elanchik and Docent V. N. Kiselev.

Corresponding Member of the Academy of Sciences of the USSR Prof. A. S. Il’ichev developed a method for the techno-economic calculation of a hoisting installation by parameters. Using this method facilitates comparison of individual variants. To compare variants at a given hoisting height and mine productivity, different vessel capacities are adopted, and the optimum capacity is taken to be that at which the greatest efficiency of the installation and the smallest energy consumption occur [5].

The work of Docent Z. M. Fedorova [1] is devoted to the question of designing a rational series of skips for deep mines. At present, in designing skip hoisting installations, the dependencies obtained by Prof. G. M. Elanchik [2] and Docent V. N. Kiselev [3; 4] are most widely used.

Prof. G. M. Elanchik gives the following formula for determining the optimum lifted load (the optimum skip capacity):

\[ A_{\text{hour}} \frac{2.05\sqrt{H}+17}{3600} \leq Q_n \leq A_{\text{hour}} \frac{4\sqrt{H}+9}{3600}, \tag{1} \]

where
\[ \begin{aligned} A_{\text{hour}}&\text{— hourly hoisting capacity in } t,\\ H&\text{— hoisting height in } m,\\ Q_n&\text{— optimum skip capacity in } t,\\ \Theta&=9_{\text{sec}}\text{— pause between hoists.} \end{aligned} \]

The right-hand side of this inequality was obtained by Prof. Elanchik from the condition of minimum annual expenditures for energy and minimum power of the hoisting motor. This optimum useful load corresponds to the optimum time of motion of the hoisting vessels \(T_n = 4\sqrt{H}\), at which the operating costs and the cost of the drive will be minimal. In the opinion of Prof. G. M. Elanchik, this optimum time corresponds to the point of inflection \(\rho=f(t)\), the characteristic of the dynamic regime as a function of the duration of hoisting.

The left-hand side of the inequality, which determines the smallest permissible load, was obtained on the basis of the maximum vessel speeds permitted by safety regulations. The validity of Prof. G. M. Elanchik’s formula is beyond doubt, since the profitability of the operation of the hoisting insta-

...of the installation are influenced chiefly by operating costs, of which the decisive factor is the cost of energy. But here it is necessary to make two observations: 1) Prof. G. M. Elanchik does not investigate the dependence \(\eta=f(t)\), the efficiency of the installation, as a function of skip capacity; 2) the skip capacity obtained from formula (1) is not coordinated with the rated speeds of domestic hoisting machines. As a result of these omissions, when selecting the capacity of vessels by formula (1), the efficiency of the hoisting installation often falls below 50%, and the speed of the vessels goes beyond the rated speeds developed by our hoisting machines.

Assoc. Prof. V. N. Kiselev, proceeding only from the least drive power, obtained the following relation for determining the most advantageous skip capacity

\[ Q=5.7 A_{\text{hour}} \sqrt[4]{H}. \tag{2} \]

The values obtained from formula (2) are close to those obtained from formula (1). Here, too, the efficiency of the installation and the speeds developed by domestic machines are not taken into account.

Associate Professor of the Kharkov Mining Institute Z. M. Fedorova solves the question of selecting the most advantageous capacity of skips for deep mines [1], taking into account the hoisting speed, the type of winding member and its parameters, motor power, operating and depreciation costs, and rope diameter. On the basis of an analysis of these factors she establishes a series of skips for deep mines (down to 1300 m) with an output of 1 million tons and 800 thousand tons per year. Among the shortcomings of the method for determining the most advantageous skip capacity proposed by Assoc. Prof. Z. M. Fedorova should be included, first, the fact that she considers a narrow range of mine outputs and, consequently, the series of skips proposed by her can be used only under certain specific conditions; second, she does not give a generalized relationship between the most advantageous useful weight of the skip, the output, and the depth of the mine, which makes it difficult to select a skip for different conditions; and, third, here too the rated speeds of the winding members of domestic hoisting machines are not taken into account.

Taking the above into consideration, we have attempted to determine the most advantageous load raised at one time by a skip hoisting installation. For various mines of Siberia and the Far East, by the method of variants, we carried out numerous calculations to determine the most advantageous skip capacity. In each case the operation of the hoist was designed with the execution of a theoretically possible speed diagram and with the maximum efficiency of the hoisting installation, i.e., a complete calculation of the kinematics and dynamics of the hoist was performed. The results of these calculations are summarized in Tables 1 and 2.

In view of the fact that we determined the most advantageous useful weight of the skip for specific conditions, i.e., for definite mine outputs and depths and definite types of hoisting machines, it may be assumed that both economic factors (the efficiency of the hoisting installation) and technical factors (the types of hoisting machines produced in the USSR and their rated speeds) have been taken into account.

On the basis of Table 2 we derived a generalizing formula for determining the most advantageous skip capacity.

Let us assume that this most advantageous skip capacity \(Q_n\), in tons, is related to the output and the hoisting height by the following dependence:

\[ Q_n=a A_{\text{hour}} H^n, \tag{3} \]

where
\[ \begin{aligned} a &\text{— an unknown coefficient,}\\ A_{\text{hour}} &\text{— hourly output in tons,}\\ H &\text{— hoisting height in meters.} \end{aligned} \]

Table 1

Most advantageous skip capacity, in tons

Table 2

Most advantageous skip capacity by average values

$n$ — unknown exponent,

$Q_k$ — most advantageous capacity in $t$.

To determine $a$ and $n$, we shall use the data of Table 2.

For the skip $Q=3\ t$ we have:

\[ 3=a\cdot 157.5\cdot 297^n, \tag{c} \]

for $Q=8\ t$:

\[ 8=a\cdot 398\cdot 366^n. \tag{e} \]

Dividing equation $(e)$ by $(c)$, we obtain:

\[ \frac{8}{3}=\frac{398}{157.5}\left(\frac{366}{297}\right)^n, \]

whence

\[ n=0.237. \]

Substituting this value into equation $(c)$, we obtain

\[ 3=a\cdot 157.5\cdot 297^{0.237}, \]

whence $a=0.005$.

Thus:

\[ Q_k=0.005\,A_{g.hour}H^{0.237}[t]. \tag{4} \]

To check the correctness of the dependence obtained, let us carry out several examples, taking data on capacity and hoisting height from the tables given above.

1) $A_{hour}=216\ t;$ $H=262\ m,$

\[ Q_k=0.005\cdot 216\cdot 262^{0.237}=4.03\ t. \]

From the table we see that for this case $Q=4\ t$,

2) $A_{hour}=304\ t;$ $H=270\ m,$

\[ Q_k=0.005\cdot 304\cdot 270^{0.237}=5.79\ t. \]

For this case we had $Q=6\ t$,

3) $A_{hour}=380\ t;$ $H=446.2\ m,$

\[ Q_k=0.005\cdot 380\cdot (446.2)^{0.237}=8.05\ t. \]

For this case we had $Q=8\ t$.

From these and other analogous calculations it may be concluded that the most advantageous skip capacity in tons obtained from formula (4) must be rounded to the nearest standard value.

Literature

1. Fedorova Z. M. Fundamentals of designing a rational series of skips for deep mines. Scientific Transactions of the Kharkov Mining Institute, vol. I, 1952.

2. Elanchik G. M. Mine hoisting installations. Gostoptekhizdat, 1941.

3. Kiselev V. I. Mining mechanics. Metallurgizdat, 1952.

4. Kiselev V. I. “Determination of the most advantageous useful load of a dumping skip,” Non-Ferrous Metals, No. 7, 1939.

5. Ilyichev A. S. Mine hoisting machines. ONTI—NKTP—USSR, 1933.