Influence of Various Factors on the Performance of an Earth-Cutting Machine

I. G. Basov, N. A. Dubrovskii

(Presented by the Department of Mining Machines, Mine Transport, and Mining Mechanics)

It is expedient to calculate the productivity of a bar-type earth-cutting machine either in \(m^2\) of slots cut, or in \(m^3\) of frozen soil prepared for excavation per unit time. Moreover, if the first indicator depends only on the technical capabilities of the machine and on the physicomechanical properties of the frozen soil, then the magnitude of the volume of the frozen layer prepared for excavation per unit time will also be determined by the technology of cutting the grid of slots.

Obviously, the smaller the dimensions of the cells in the grid of slots, the more slots must be cut in order to prepare \(1\ m^3\) of frozen soil for excavation, and the greater will be the unproductive time expenditures associated with the maneuvering operations of the machine. Consequently, in order to increase the productivity of the bar-type machine, the cell dimensions in the grid of slots being cut must be increased to the maximum possible values, proceeding from the lifting capabilities of the excavating machine.

The magnitude of the slot area that must be cut in order to prepare one \(m^3\) of frozen soil for excavation can be found from the expression

\[ s=\frac{(L_{\text{pr}} n_1+L_{\text{pop}} n_2)H_{\text{sh}}}{V},\quad \text{m}^2;\text{m}^3 \tag{1} \]

where

\[ \begin{aligned} L_{\text{pr}} \text{ and } L_{\text{pop}} &\text{ are the lengths of the longitudinal and transverse slots, respectively, } m;\\ n_1 \text{ and } n_2 &\text{ are the numbers of longitudinal and transverse slots, respectively;}\\ H_{\text{sh}} &\text{ is the depth of the slots, } m;\\ V=L_{\text{pr}}\cdot L_{\text{pop}}H_{\text{sh}} &\text{ is the volume of frozen soil prepared for excavation, } m^3. \end{aligned} \]

Replacing in expression (1) \(n_1\) and \(n_2\) by \(L_{\text{pr}}\) and \(L_{\text{pop}}\) and by the distances between the longitudinal \(l_1\) and transverse \(l_2\) slots, and carrying out a number of transformations, we obtain

\[ s=\frac{1}{l_1}+\frac{1}{l_2}+\frac{1}{L_{\text{pr}}}+\frac{1}{L_{\text{pop}}},\quad \text{m}^2/\text{m}^3. \tag{2} \]

Then the dependence of the technical productivity of the earth-cutting machine on the technological scheme for preparing frozen soil for excavation can be determined by the formula

\[ Q_{\mathrm{t}}=\frac{v_{\mathrm{p}} H_{\mathrm{sh}} \kappa_{\mathrm{t}}}{s}, \tag{3} \]

where

\(v_{\mathrm{p}}\) is the travel speed of the machine when cutting a slot, m/h;
\(\kappa_{\mathrm{t}}\) is the coefficient of technically possible productivity.

The coefficient \(\kappa_{\mathrm{t}}\) can be expressed as the ratio of the net time \(T\) of the machine’s work in cutting slots to the total time, which also takes into account the duration of auxiliary operations \(T_{\mathrm{ao}}\), i.e.,

\[ \kappa_{\mathrm{t}}=\frac{T}{T+T_{\mathrm{ao}}}. \tag{4} \]

The net time of the machine’s work in cutting slots can be determined from the expression

\[ T=\frac{\sum L_{\mathrm{pr}}+\sum L_{\mathrm{pop}}}{v_{\mathrm{p}}}. \]

The duration of auxiliary operations in preparing a given area for excavation is

\[ T_{\mathrm{ao}}=T_{\mathrm{z}}+T_{\mathrm{p}}+T_{\mathrm{i}}+T_{\mathrm{m}}, \tag{5} \]

where

\(T_{\mathrm{z}}\) and \(T_{\mathrm{p}}\) are the time spent, respectively, on the operations of lowering and raising the bar when preparing a given area for excavation;
\(T_{\mathrm{i}}\) is the duration of tool replacement;
\(T_{\mathrm{m}}\) is the time spent carrying out maneuvering operations associated with moving from one slot to another.

Fig. 1. Diagram of the mechanism for lowering the bar.

The total time spent on operations for lowering the bar when preparing a given area for excavation is

\[ T_{\mathrm{z}}=(n_1+n_2)t_{\mathrm{z}}, \]

where \(t_{\mathrm{z}}\) is the duration of one lowering of the bar. The duration of a single lowering of the bar, based on the operating diagram of the mechanism for rotating the working member (Fig. 1), can be found from the formula

\[ t_{\mathrm{z}}=\frac{\beta_0-\beta}{\omega} = \frac{ \left[ \arccos \frac{H_{\mathrm{p}}}{L_{\mathrm{b}}} - \arccos \frac{H_{\mathrm{sh}}+H_{\mathrm{p}}}{L_{\mathrm{b}}} \right] L_{\mathrm{b}} }{v_{\mathrm{pb}}}, \]

where

\(\omega\) is the average angular velocity of rotation of the bar, rad/min;
\(L_{\mathrm{b}}\) is the length of the bar;
\(H_{\mathrm{p}}\) is the height of the location of the bar’s axis of rotation above ground level;
\(v_{\mathrm{pb}}\) is the average linear velocity of rotation of the end of the bar.

Then

\[ T_{\mathrm{z}}=(n_1+n_2) \frac{ \left( \arccos \frac{H_{\mathrm{p}}}{L_{\mathrm{b}}} - \arccos \frac{H_{\mathrm{sh}}+H_{\mathrm{p}}}{L_{\mathrm{b}}} \right)L_{\mathrm{b}} }{v_{\mathrm{pb}}}. \tag{6} \]

The time spent on operations of raising the bar when preparing the area for excavation is

\[ T_{\mathrm{p}}=(n_1+n_2)t_{\mathrm{p}} \]

where \(t_{\mathrm{p}}\) is the duration of one raising of the bar.

The duration of one raising of the bar, in accordance with Fig. 1, can be found from the expression

\[ t_{\mathrm{p}}= \frac{\dfrac{\pi}{2}-\beta}{\omega'} = \frac{ \arcsin\left(\dfrac{H_{\mathrm{p}}+H_{\mathrm{sh}}}{L_{\mathrm{b}}}\right) l_{\mathrm{k}} F_{\mathrm{d}} }{ Q_{\mathrm{n}}\cos\beta }, \]

where

\[ \begin{aligned} \omega'&\text{— average angular velocity of raising the bar;}\\ l_{\mathrm{k}}&\text{— length of the crank of the lever mechanism for turning the bar;}\\ F_{\mathrm{d}}&\text{— working area of the piston of the hydraulic cylinder of the bar-turning mechanism, } \mathrm{cm}^2;\\ Q_{\mathrm{n}}&\text{— capacity of the hydraulic pump, } \mathrm{cm}^3/\mathrm{min}. \end{aligned} \]

Then

\[ T_{\mathrm{p}}=(n_1+n_2) \frac{ \arcsin\left(\dfrac{H_{\mathrm{p}}+H_{\mathrm{sh}}}{L_{\mathrm{b}}}\right) l_{\mathrm{k}} F_{\mathrm{d}} }{ Q_{\mathrm{n}}\cos\beta }. \tag{7} \]

The time spent on replacing a worn tool is

\[ T_{\mathrm{i}}=(L_{\mathrm{pr}}n_1+L_{\mathrm{pop}}n_2)H_{\mathrm{sh}}z_{\mathrm{i}}t_{\mathrm{i}} = L_{\mathrm{pr}}L_{\mathrm{pop}}H_{\mathrm{sh}}sz_{\mathrm{i}}t_{\mathrm{i}}, \tag{8} \]

where \(z_{\mathrm{i}}\) is the number of cutters consumed per \(1\,\mathrm{m}^2\) of cut slot;
\(t_{\mathrm{i}}\) is the average duration of replacing one tooth.

The time spent on maneuvering operations is

\[ T_{\mathrm{m}}=(n_1+n_2-2)t_{\mathrm{m}} = \left(\frac{L_{\mathrm{pop}}}{l_1}+\frac{L_{\mathrm{pr}}}{l_2}\right)t_{\mathrm{m}}, \tag{9} \]

where \(t_{\mathrm{m}}\) is the time for the bar machine to move from one slot to another.

Substituting into expression (5) the values of \(T_{\mathrm{z}}, T_{\mathrm{p}}, T_{\mathrm{i}}, T_{\mathrm{m}}\) from formulas (6), (7), (8), (9), and carrying out the corresponding transformations and simplifications on the basis of operating data for actual machines, we obtain a simplified formula for determining the time spent on auxiliary operations:

\[ T_{\mathrm{vo}}=(1.7+3.2H_{\mathrm{sh}})(n_1+n_2-2). \tag{10} \]

Calculations show that, depending on the technical scheme used to prepare frozen soil for excavation, the coefficient of technically possible productivity of the machine may vary within wide limits, \(0.3\leq \kappa_{\mathrm{t}}\leq 0.98\). Moreover, \(\kappa_{\mathrm{t}}\) is smaller the smaller the cell sizes in the grid of slots and the volume of frozen soil being prepared for excavation.

The influence of the depth of soil freezing on the productivity of a bar machine can be taken into account by the coefficient \(\kappa_{\mathrm{p}}\). The dependence of \(\kappa_{\mathrm{p}}\) on the depth of soil freezing, constructed in accordance with the discrete series of values of \(\kappa_{\mathrm{p}}\) recommended by ENiR [1], is well approximated by the equation

\[ \kappa_{\mathrm{p}}=\frac{0.83}{H_{\mathrm{pr}}}-0.1, \]

where

\[ H_{\mathrm{pr}}\text{— depth of soil freezing, m.} \]

The influence of soil properties on the productivity of a bar machine can be taken into account by the coefficient \(\kappa_{\mathrm{g}}\). Depending on the soil group, the val—

\[ S=\frac{1}{L_{\mathrm{pr}}}+\frac{1}{L_{\mathrm{nom}}}+\frac{1}{l_1}+\frac{1}{l_2} \]

Key:

\[ L_{\mathrm{pr}}-\gamma_1-L_{\mathrm{nom}} \]

\[ l_1-\gamma_2-l_2 \]

\[ \gamma_1-S-\gamma_2 \]

Fig. 2. Nomogram for determining the quantity

Visible labels in the nomogram:

\[ Q_1=\frac{V_n}{S} \]

\[ Q_2=Q_1 k_1 \]

\[ Q_3=Q_2 k_2 \]

\[ Q=Q_3 k_3 \]

\[ V_n,\ \mathrm{m/h} \]

\[ Q,\ \mathrm{m^3/h} \]

\[ S=1.0 \]

\[ l=0.5\,\mathrm{m},\quad 1.0\,\mathrm{m},\quad 1.5\,\mathrm{m},\quad 2.0\,\mathrm{m} \]

\[ k_{\mathrm{r.u}},\quad k_{\mathrm{r.o}},\quad k_{\mathrm{r.v}},\quad k_u \]

\[ k_2=0.3,\ 0.4,\ 0.5,\ 0.6,\ 0.7,\ 0.8,\ 0.9 \]

Fig. 3. Nomogram for determining the productivity of a cutter-bar machine

1. Order 3135.

…the value \(k_{\mathrm{g}}\), in accordance with the recommendations of ENiR [1], has the following values:

Thus, the dependence of the productivity of a bar machine on the principal factors affecting it will have the form

\[ Q=\frac{v_{\mathrm{p}} H_{\mathrm{sh}}}{s}\left(\frac{0.83}{H_{\mathrm{p}}}-0.1\right) k_{\mathrm{g}} k_{\mathrm{t}}. \tag{11} \]

It follows from the nomogram (Fig. 2) that the value \(s\) will be the smaller, the larger the area of frozen ground being prepared for excavation \((L_{\mathrm{pr}}\cdot L_{\mathrm{pop}})\) and the distances between the longitudinal \((l_1)\) and transverse \((l_2)\) slots.

To increase the volume of frozen ground prepared for excavation per unit time by cutting a system of slots, it is necessary (Fig. 3), above all, to increase the speed \((V_{\mathrm{p}})\) of slot cutting by increasing the power of the earth-cutting machines and establishing optimal operating modes of the working members. In addition, the productivity of an earth-cutting machine (in \(m^3/\text{h}\)) can be substantially increased (by a factor of 2.0–2.5) by reducing the number of slots cut (the value \(s\)). The slot-cutting scheme should be selected from the condition of obtaining the minimum possible value of \(s\). This can be achieved when only longitudinal slots are cut. The latter is possible either with insignificant freezing (up to 1 m) of the ground, when the excavating machine can break out the inter-slot blocks from the side of thawed ground, or with considerable freezing (up to 2 m and more), but in the case of using hydraulic rock breakers for the destruction of the inter-slot block simultaneously with the cutting of the next slot [2]. Reducing the number of slots cut in preparing a cubic meter of frozen ground for excavation reduces the time spent on auxiliary operations (increases \(k_{\mathrm{t}}\)) and, consequently, leads to an increase in the productivity of the earth-cutting machine.

REFERENCES

1. Unified Norms and Rates for Construction, Installation, and Repair-and-Construction Work. Collection 2. Earthworks. Issue 1. Mechanized and Manual Earthworks. Stroiizdat, Moscow, 1964.

2. O. D. Alimov, I. G. Basov, A. A. Sdobnikov, F. F. Zelinger. Cutting Frozen Ground with Simultaneous Breaking. Mekhanizatsiya stroitel’stva, No. 1, 1966.