Influence of Various Factors on the Performance of Slot Machines

I. G. Basov, N. A. Dubrovsky

(Presented by the Department of Mining Machines)

The productivity of slotting (bar, disk-cutter) machines depends both on the design features of the machines and on the technological scheme for preparing frozen ground for excavation over a given area. The technical productivity of the machines can be found from the formula

\[ P_{\mathrm{sh}} = \frac{v_{\mathrm{p}} H_{\mathrm{sh}} k_{\mathrm{gr}} k_{\mathrm{pr}} k_{\mathrm{tsh}}} {s_{\mathrm{sh}}} ,\ \text{m}^3/\text{h} \tag{1} \]

where
\(v_{\mathrm{p}}\) is the speed of movement of the machine, m/h;
\(H_{\mathrm{sh}}\) is the depth of the slot-trench being cut, m;
\(k_{\mathrm{gr}}, k_{\mathrm{pr}}\) are coefficients taking into account, respectively, the influence of the properties and the depth of freezing of the soil;
\(k_{\mathrm{tsh}}\) is the coefficient of time losses for auxiliary operations;
\(s_{\mathrm{sh}}\) is the area of the slots cut per cubic meter of frozen ground prepared for excavation, m\(^2\)/m\(^3\).

The value \(s_{\mathrm{sh}}\) can be determined by the formula

\[ s_{\mathrm{sh}} = \frac{(L_{\mathrm{pr}} n_1 + L_{\mathrm{pop}} n_2) H_{\mathrm{sh}}}{V} ,\ \text{m}^2/\text{m}^3, \tag{2} \]

where \(L_{\mathrm{pr}}\) and \(L_{\mathrm{pop}}\) are the lengths of the slots, respectively longitudinal and transverse, m;
\(n_1\) and \(n_2\) are the numbers of slots cut in parallel over the area, respectively longitudinal and transverse;
\(V = L_{\mathrm{pr}} L_{\mathrm{pop}} H_{\mathrm{pr}}\) is the volume of frozen ground prepared for excavation, m\(^3\);
\(H_{\mathrm{pr}}\) is the depth of freezing of the ground, m.

Substituting into expression (2) the value of \(V\) and replacing \(n_1\) and \(n_2\) by \(L_{\mathrm{pr}}, L_{\mathrm{pop}}\) and the distances between the longitudinal \(l_1\) and transverse \(l_2\) slots, and also carrying out the corresponding transformations, we obtain

\[ s_{\mathrm{sh}}=\left(\frac{1}{l_1}+\frac{1}{l_2}+\frac{1}{L_{\mathrm{pr}}}+\frac{1}{L_{\mathrm{pop}}}\right)\frac{H_{\mathrm{sh}}}{H_{\mathrm{pr}}},\ \mathrm{m^2/m^3}. \tag{3} \]

Usually, when preparing frozen ground for excavation by slotting machines, it is assumed that \(H_{\mathrm{sh}}=H_{\mathrm{pr}}\). In this case expression (3) is simplified.

In addition, the technological parameters of the scheme for preparing frozen ground for excavation, along with the technical characteristics of the loosening machine, affect productivity through the coefficient of time losses for performing auxiliary operations. The latter can be found from the expression

\[ \kappa_{\mathrm{tsh}}=\frac{T}{T+T_{\mathrm{v}}}, \tag{4} \]

where \(T\) and \(T_{\mathrm{v}}\) are, respectively, the duration of the machine’s pure operating time and the time spent on auxiliary operations.

The duration of the auxiliary operations is

\[ T_{\mathrm{v}}=T_{\mathrm{z}}+T_{\mathrm{p}}+T_{\mathrm{per}}, \tag{5} \]

where

\[ T_{\mathrm{z}}=\frac{\beta_0-\beta}{\omega_{\mathrm{z}}} \]

is the time spent on deepening the working member at speed \(\omega_{\mathrm{z}}\);

\[ T_{\mathrm{p}}=\frac{\beta_0-\beta}{\omega_{\mathrm{p}}} \]

is the duration of raising the working member at speed \(\omega_{\mathrm{p}}\);

\[ T_{\mathrm{per}}=\frac{L_{\mathrm{per}}}{v_{\mathrm{per}}} \]

is the duration of a relocation over a length \(L_{\mathrm{per}}\) at speed \(v_{\mathrm{per}}\);

\(\beta_0-\beta\) is the angle of rotation of the boom or of the center of the disk-type member when deepened by the amount \(H_{\mathrm{sh}}\).

Substituting into formula (4) the value \(T_{\mathrm{r}}=\dfrac{L}{v_{\mathrm{p}}}\), \(T_{\mathrm{v}}\) from (5), and carrying out certain transformations, we obtain

\[ \kappa_{\mathrm{tsh}}= \frac{1}{ v_{\mathrm{p}}\left\{\frac{1}{v_{\mathrm{p}}} +\frac{1}{L}\left[(\beta_0-\beta)\left(\frac{1}{\omega_{\mathrm{z}}}+\frac{1}{\omega_{\mathrm{p}}}\right) +\frac{L_{\mathrm{per}}}{v_{\mathrm{per}}}\right]\right\} }. \]

Then the productivity of the slotting loosening machine is expressed by the dependence

\[ P_{\mathrm{sh}}= \frac{H_{\mathrm{sh}}k_{\mathrm{gr}}k_{\mathrm{pr}}}{ s_{\mathrm{sh}}\left\{\frac{1}{v_{\mathrm{p}}} +\frac{1}{L}\left[(\beta_0-\beta)\left(\frac{1}{\omega_{\mathrm{z}}}+\frac{1}{\omega_{\mathrm{p}}}\right) +\frac{L_{\mathrm{per}}}{v_{\mathrm{per}}}\right]\right\} },\ \mathrm{m^3/hour} \tag{6} \]

Figure 1 presents the dependences of the productivity \(P_{\mathrm{sh}}\) on various factors, constructed in relative coordinates according to formula (6), from which it follows that, along with increasing the working travel speed, in order to increase productivity it is necessary to choose a rational scheme for cutting slots that provides the minimum possible value of \(s\).

The latter can be substantially reduced by using a hydraulic device for static shearing of the inter-slot blocks.

... factors [1]. Other parameters have an insignificant effect on the productivity of slot machines.

Fig. 1. Dependence of the productivity \(P_{\mathrm{sh}}\) of slot machines, expressed in relative units, on various factors \(x\): 1 — unit forces \(s\); 2 — speed \(v_{\mathrm{p}}\); 3 — slot length; 4 — \((\beta_0-\beta)\); 5 — \(\omega_{\mathrm{z}}\); 6 — \(\omega_{\mathrm{p}}\); 7 — travel distance; 8 — travel speed.

References

1. O. D. Alimov, I. G. Basov, A. A. Sdobnikov, F. F. Zelinger. Cutting frozen ground with simultaneous chipping. Journal Mechanization of Construction, No. 1, Moscow, Stroiizdat, 1966.