ON LIMITING OPERATING MODES OF A BAR-TYPE WORKING MEMBER IN CUTTING FROZEN GROUND

I. G. BASOV

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

Cutting frozen ground with a bar-type working member is characterized by the fact that the cutting chain, simultaneously with separating the ground from the mass, transports (lifts) the loosened ground from the slot to the surface. The cutting chains used on earth-cutting machines are designed so that the conveying surface of an individual lug with a tooth by no means completely overlaps the cross section of the cutting slot through which the loosened frozen ground is lifted. Therefore, active transport of the ground from the slot begins only when the space in front of the working run of the chain is filled with the broken ground. In that case the lugs with cutting teeth move fully immersed in the loosened ground and impart to its particles a velocity equal to the velocity of motion of the chain. But as a result of the action of resistance forces (the resistance of the slot walls; the resistance of individual particles that have lost their velocity of motion; gravity), the average velocity of the flow of loosened material is always less than the velocity of motion of the cutting chain.

Consequently, the operating mode of the chain cutting member must be such that the productivity of the cutting chain in loosening frozen ground is less than or equal to its productivity in removing (lifting) the products of loosening from the cutting slot. If this relationship is not observed, then an excessive quantity of broken ground accumulates in the free cross section of the slot in front of the bar, becomes compacted, and hampers the process of separating the frozen ground from the mass. In this case the feed and pulling forces of the cutting chain increase, and ultimately the engine power consumption rises sharply.

Thus, the ratio of the velocities of motion of the cutting chain (cutting), \(v_p\), and of movement of the earth-cutting machine, \(v_p\), must be selected from the condition of timely removal of the products of ground destruction from the cutting slot.

To determine the conditions for normal operation of the bar member, let us consider the scheme of formation and removal of loosened ground from the cutting slot. In the general case, a bar-type earth-cutting machine (Fig. 1) cuts a slot of depth \(H_{\text{ш}}\) and width \(B\), with the bar set at an angle \(\beta\) to the vertical.

In the steady-state operating mode of the bar-type member (constant \(v_{\mathrm{p}}\) and \(v_{\mathrm{n}}\)), its productivities in loosening and transporting the soil must be equal, i.e.,

\[ Q_{\mathrm{gr}}+q_{\mathrm{c}}=Q_{\mathrm{pod}}+q_{\mathrm{p}}, \tag{1} \]

where \(Q_{\mathrm{gr}}\) is the productivity of the bar-type working member in separating the soil from the mass (taking into account the loosening coefficient), \(\mathrm{m^3/min}\);

\(q_{\mathrm{c}}\) is the volume of broken-up soil drawn by the slack run of the chain onto the working run per unit time, \(\mathrm{m^3/min}\);

\(Q_{\mathrm{pod}}\) is the productivity of the cutting chain in lifting the broken-up soil from the kerf, \(\mathrm{m^3/min}\);

\(q_{\mathrm{p}}\) is the quantity of loosened soil passing from the face space of the kerf into the gaps between its walls and the bar plates, \(\mathrm{m^3/min}\).

Fig. 1. Diagram of chip circulation in the kerf when cutting frozen ground with a bar machine

The productivity of the cutting chain in forming the loose mass of frozen soil can be found from the expression

\[ Q_{\mathrm{gr}}=H_{\mathrm{sh}} B v_{\mathrm{p}} k_{\mathrm{r}},\ \mathrm{m^3/min}, \tag{2} \]

where \(k_{\mathrm{r}}\) is the soil loosening coefficient. The quantity of loosened soil passing from the face space of the kerf into the gaps between its walls and the bar plates can be found from the expression

\[ q_{\mathrm{p}}=H_{\mathrm{sh}}(B-T)v_{\mathrm{p}},\ \mathrm{m^3/min}, \tag{3} \]

where \(T\) is the thickness of the guide frame of the bar, \(\mathrm{m}\).

The volume of soil drawn by the slack run of the chain onto the working run per unit time is

\[ q_{\mathrm{c}}=k_1 q_{\mathrm{p}},\ \mathrm{m^3/min}, \tag{4} \]

where \(k_1\) is the proportionality coefficient.

The volume of soil to be carried out of the kerf per unit time, on the basis of (1) and (4), will be equal to

\[ Q_{\mathrm{pod}}=Q_{\mathrm{gr}}+q_{\mathrm{p}}(k_1-1),\ \mathrm{m^3/min}. \]

Substituting in the last equation the values of \(Q_{\mathrm{gr}}\) and \(q_{\mathrm{p}}\) from (2) and (3), we find that

\[ Q_{\mathrm{pod}}=H_{\mathrm{sh}}v_{\mathrm{p}}\left[B(k_{\mathrm{r}}-k_1+1)+T(k_1+1)\right],\ \mathrm{m^3/min}. \tag{5} \]

Thus, for normal operation of the cutting chain it is necessary that its conveying capacity ensure timely removal of the destroyed soil, i.e., the condition must be satisfied

\[ Q_{\text{feed}} \geq Q_{\text{gr}} + q_{\text{p}}(k_1 - 1). \tag{6} \]

As was already noted above, the cutting chain, removing a chip of frozen soil of thickness \(h\), forms per unit time a volume of loose mass \(Q_{\text{gr}}\), of which one part is removed to the surface, \(Q_{\text{feed}}\), while the other part, \(q_{\text{res}}\), remains in the slot (Fig. 1).

Since we agreed above to consider the cutting chain in a vertical slot as a continuous-action conveying device, its productivity will be equal to

\[ Q_{\text{feed}} = 60 \cdot S \cdot v_{\text{sh}} \cdot \kappa_{\text{p}},\ \text{m}^3/\text{min}, \tag{8} \]

where \(S\) is the cross-sectional area of the flow of loose soil, equal to the mean cross-sectional area of the free space in front of the cutting chain, \(\text{m}^2\);

\(v_{\text{sh}}\) is the velocity of the soil flow, \(\text{m/sec}\);

\(\kappa_{\text{p}}\) is the coefficient of density of the soil flow in section \(S\).

The mean cross-sectional area of the working space of the cutting slot in front of the working run of the cutting chain, which is filled with destroyed frozen soil, may be taken as equal to

\[ S = m \cdot B \cdot a,\ \text{m}^2, \tag{9} \]

where \(m\) is a coefficient of increase of the section \(S\) due to the space between the chain cams;

\(a\) is the projection of the cutting teeth, m.

The limiting productivity of the cutting chain in lifting the destroyed soil from the cutting slot, corresponding to the maximum possible feed speed of the machine, can be found from the expression

\[ Q_{\text{feed.max}} = 60 \frac{S \cdot v_{\text{r}} \cdot \kappa_{\text{p}}}{\kappa},\ \text{m}^3/\text{min}, \tag{10} \]

where

\[ \kappa = \frac{v_{\text{r}}}{v_{\text{sh}}} \]

is a coefficient indicating how many times the speed of motion of the cutting chain is greater than the velocity of the spoil flow.

In the period immediately preceding the state in which condition (6) will be violated, the density of the soil flow may be considered maximal, i.e., \(\kappa_{\text{p}} = 1\). Then, substituting the value of \(S\) from (9) into equation (10), we obtain

\[ Q_{\text{feed.max}} = 60 \frac{B \cdot v_{\text{r}} \cdot a \cdot m}{\kappa},\ \text{m}^3/\text{min}. \tag{11} \]

Equating the right-hand sides of equations (5) and (11), we find, with condition (6) satisfied, the value of the coefficient characterizing the velocity of the flow of loosened soil:

\[ \kappa = \frac{60 B v_{\text{r}} a m} {H_{\text{sh}} v_{\text{p}}\,[B(k_{\text{r}} - k_1 + 1) + T(k_1 + 1)]} \tag{12} \]

or the maximum possible feed speed at the given cutting speed,

\[ v_{\text{p.max}} = \frac{60 \cdot B \cdot v_{\text{r}} \cdot a \cdot m} {H_{\text{sh}} \cdot \kappa\,[B(k_{\text{r}} - k_1 + 1) + T(k_1 + 1)]}, \ \text{m/min}. \tag{13} \]

or the minimum possible speed of motion of the cutting chain at the given feed speed

\[ v_{p\min}= \frac{H_{\sh}\cdot \kappa \cdot v_{\п}\left[B(\kappa_{p}-\kappa_{1}+1)+T(\kappa_{1}+1)\right]} {60\cdot B\cdot a\cdot m}, \quad \text{m/sec.} \tag{14} \]

Figure 2 presents graphs of dependences (13) and (15), constructed in the form of a nomogram for a bar-type working member of the KMP type with \(\kappa=1.5\); \(\kappa_{p}=2\); \(\kappa_{1}=0.5\), \(\beta=0\); \(m=1.25\) [1]. From the nomogram, knowing the depth of the slot for a given cutting speed, one can find the maximum possible feed speed of the machine with respect to the conveying capacity of the cutting chain. For the same cutting speed, in the upper quadrant of the nomogram the limiting chip thickness for the given \(v_{p}\) and \(v_{\п}\) can be found. Thus, for example, at \(v_{p}=2.5\ \text{m/sec}\) and \(H_{\sh}=1.3\ \text{m}\), the limiting feed speed is \(v_{\п.\max}=128\ \text{m/hr}\) and \(h_{\text{cp}}=16\ \text{mm}\). With an increase in cutting speed for the given slot depth, the limiting chip thickness decreases. With an increase in \(H_{\sh}\), the maximum possible chip thickness must also decrease.

Fig. 2. Nomogram for determining the limiting operating modes of a bar-type working member of the KMP type

It is evident from equation (15) that when cutting slots in frozen ground of the same depth with a vertically positioned or inclined bar, in the latter case, all other conditions being equal, the limiting chip thickness will always be smaller. Consequently, the energy indices of these two cases of soil cutting will be different.

Thus, the parameters characterizing the operating mode of the chain working member when cutting frozen ground, selected according to optimal energy indices, must be checked from the condition of the conveying capacity of the cutting chain by the proposed method.

LITERATURE

1. V. P. Fomichev. Calculation of Loads on Slot-Cutting Machines. Moscow, Gosgortekhizdat, 1961.

2. A. I. Baron, A. S. Kazanskii, B. M. Leibov, E. Z. Pozin. Coal Cutting. Moscow, Gosgortekhizdat, 1962.