Determination of Criteria for a Rational Approach to Reducing the Time of Operations Performed by the Drive of Drilling Machines
Abstract Generated abstract
The paper examines how auxiliary operations performed by or related to the drive of drilling machines affect overall drilling productivity. It formulates productivity as a function of drilling time and auxiliary time, classifies auxiliary operations by their dependence on the drive, and proposes the average duration of one drive-performed operation as a criterion for evaluating improvements. The authors derive criteria for choosing whether to reduce operation times, eliminate operations, or combine both approaches, including cases where operations are interrelated. They conclude that these criteria and the proposed calculation procedure can identify a rational sequence for reducing drive-operation time in the region where such operations substantially influence productivity.
Full Text
DETERMINATION OF CRITERIA FOR A RATIONAL METHOD OF REDUCING THE TIME OF OPERATIONS PERFORMED BY THE DRIVE OF DRILLING MACHINES
V. F. GORBUNOV, V. I. BAZHENOV, N. A. DUBROVSKII, L. A. SARUEV
(Presented by the scientific seminar of the Department of Economics)
The productivity of a drilling machine is determined not only by the time of pure drilling of the borehole, but also by the time spent on various auxiliary operations associated with the operation of its drive and its servicing.
Numerous studies in the area of drilling-machine productivity have dealt mainly with the effect of drilling speed on productivity, while auxiliary operations were taken into account only in a general form and were not linked with the operation of the drilling-machine drive [1–4]. This makes it impossible to assess the effect of the drive on drilling productivity. However, studies and time-and-motion observations show that the driller spends only one third of the working shift on productive work—drilling—while the remaining part of the shift is spent on all kinds of manual operations associated with the operation and servicing of the machine drive [4].
For this purpose, studies were carried out on the influence of the operation of the drilling-machine drive on its productivity. As initial data, calculated values for certain auxiliary operations and time-and-motion data were used.
The productivity of a drilling machine \(Q\) is determined by the borehole drilling speed \(V_{\text{б}}\) and by the time of auxiliary work not overlapped by drilling.
\[ Q = V_{\text{б}} \cdot K_{\text{п.в}}, \tag{1} \]
where \(K_{\text{п.в}}\) is a coefficient that accounts for time losses on auxiliary operations. This coefficient can be determined from the formula
\[ K_{\text{п.в}} = \frac{T_{\text{б}}}{T_{\text{б}} + T_{\text{в.о}}}, \tag{2} \]
where \(T_{\text{б}}\) is the drilling time;
\(T_{\text{в.о}}\) is the time of all auxiliary operations.
All auxiliary operations may be represented as operations not connected with the operation of the drive, as operations not directly connected with it but whose duration depends on its operation, and as operations dependent on switching on the drive.
The first group may include operations for waiting for flushing fluid, installing and removing the bit; the second—operations associ-
associated with lubricating the machine, connecting it to the pneumatic network, securing the machine with spreader struts; the third includes operations associated with turning the machine frame toward the next borehole, moving the drill head away and toward it, turning the machine, collaring, etc.
Thus, the quantity \(T_{\mathrm{v.o}}\) can be written in the form
\[ T_{\mathrm{v.o}} = T_{\mathrm{n.p}} + T_{\mathrm{n.s.p}} + T_{\mathrm{z.s.p}}, \tag{3} \]
where \(T_{\mathrm{n.p}}\) is the time of operations not associated with operation of the drilling-machine drive;
\(T_{\mathrm{n.s.p}}\) is the time of operations not directly associated with, but dependent on, operation of the drive;
\(T_{\mathrm{z.s.p}}\) is the time of operations dependent on operation of the drive.
Substituting the value \(K_{\mathrm{p.v}}\) into formula (1) and carrying out transformations, we obtain
\[ Q = \frac{1}{ T_{\mathrm{b}} + \frac{1}{H} \left(T_{\mathrm{n.p}} + T_{\mathrm{n.s.p}} + T_{\mathrm{z.s.p}}\right) }. \tag{4} \]
Figure 1 presents the dependence of productivity on various factors; analysis of these factors shows that the time of operations associated with operation of the drive has a substantial effect on drilling productivity, which may be increased significantly by reducing it.
Since \(T_{\mathrm{z.s.p}}\) includes the time expenditures for a large number of operations performed by the drive, finding a rational way to reduce it is difficult.
This can be simplified by calculating a criterion that would make it possible to assess, as a whole, the operation of the drive.
Such a criterion may be the average duration of one operation performed by the drive, whose value is determined from the relation
\[ \bar{t}_{\mathrm{o.p}} = \frac{T_{\mathrm{z.s.p}}}{n}, \quad (\text{min}), \tag{5} \]
where \(n\) is the number of operations performed by the drive.
For productivity to increase, it is necessary that the average time for performing one operation decrease, i.e., \(t_{\mathrm{o.p}} \to 0\).
Fig. 1. Effect of auxiliary-operation time on drilling productivity
From formula (5) it is clear that this can be achieved in the following way:
1) by reducing the total duration of operations,
\[ T_{\mathrm{z.s.p}} \to 0 \quad \text{with} \quad n = \mathrm{const}; \]
2) by reducing the number of operations performed by the drive,
\[ n \to 1; \]
3) by reducing the duration of individual operations while simultaneously reducing their number,
\[ t_i \to 0 \quad \text{and} \quad n \to 1. \]
In implementing all methods for reducing \(\bar t_{\mathrm{op}}\), it is necessary to determine the sequence in which the number of operations and their magnitudes are to be changed in such a way that, each time, the maximum possible reduction in the average duration of one operation is obtained. This can be done most simply by means of criteria adopted for each method.
In determining the criteria, it is necessary to resolve the question of the relationship between the operations performed by the drive. From this point of view, one should distinguish between interrelated operations, when a connection exists between them, and non-interrelated operations, when any value of one operation may correspond to one value of another operation.
Thus, if \(t_i, t_j, \ldots, t_n\) are not interrelated and can be reduced respectively by \(\Delta t_i, \Delta t_j, \ldots, \Delta t_n\), and \(\Delta t_i > \Delta t_j > \ldots > \Delta t_n\), then first of all it is necessary to reduce operation \(t_i\), secondly \(t_j\), and so on.
Consequently, for the first method, the criterion for reducing \(\bar t_{\mathrm{op}}\) may be the greatest magnitude of change of the operation, \(\Delta t_i = \max\).
If the second method of reducing \(t_{\mathrm{op}}\) is used, then the criterion of the rational path will be the maximum absolute value of the operation, that is, \(t_j = \max\).
With the third method of reducing \(\bar t_{\mathrm{op}}\), and also in the case of non-interrelated operations, the rational path will be determined with the aid of the following criterion:
\[ \Delta t_i + t_j = \max . \]
In the presence of interrelated operations, irrespective of the method of reducing \(\bar t_{\mathrm{op}}\), the criterion for choosing the rational path is
\[ \left(\sum_{i=1}^{i=a} \Delta t_i + \sum_{i=1}^{i=b} t_j\right) - \left(\sum_{i=1}^{i=c} \Delta t_k + \sum_{i=1}^{i=d} t_f\right) = \max, \]
where \(a\) is the number of operations being reduced;
\(b\) is the number of operations being eliminated;
\(c\) is the number of operations whose time increases when the magnitudes of the \(i\)-th operations are reduced;
\(d\) is the number of operations that appear when the \(j\)-th operations are eliminated;
\(t_f\) is the magnitude of the operation that appears.
All the criteria obtained are particular ones and, under certain conditions, make it possible to find the rational path for changing \(\bar t_{\mathrm{op}}\) without performing large and complex calculations. However, the stated problem can be solved independently of the methods for reducing \(\bar t_{\mathrm{op}}\) by a single procedure, which consists of the following:
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The average duration of performance of one operation is determined for the initial drive parameters.
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The value of \(\bar t_{\mathrm{op}}\) is calculated when each parameter is changed.
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The difference \(\Delta \bar t_{\mathrm{op}}\) is found between the value of \(\bar t_{\mathrm{op}}\) obtained for the initial drive parameters and the values of \(\bar t_{\mathrm{op}}\) obtained when each parameter is changed.
- The operation is selected for which \(\Delta \bar t_{\mathrm{op}}\) has the maximum value and the sum of the operations after the change becomes minimal
\[ \left(\sum_{i=1}^{i=n} t_i=\min\right), \]
and, by reducing its time, a decrease in \(\bar t_{\mathrm{op}}\) is achieved.
A successive reduction of \(\bar t_{\mathrm{op}}\) is rational in that region where the time of operations associated with the drive affects productivity more substantially than the time of operations not dependent on the drive [5].
Thus, the criteria obtained and the method presented make it possible to determine a rational way to reduce the time of operations performed by the drive.
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