ON THE CALCULATION OF THE ROTATION MECHANISM OF THE CUTTER BAR OF AN EARTH-CUTTING MACHINE

I. G. Basov

The rotation mechanism of the cutter bar of an earth-cutting machine is intended to create the necessary force when deepening the bar or to hold it at the required angle of inclination to the soil during the cutting of a slot in frozen ground and in the transport position.

In earth-cutting machines that cut slots in frozen ground with the combined motions of the cutting chain and of the entire installation, the most widespread are cutter-bar rotation mechanisms whose basic diagrams are shown in Fig. 1, a, b, c.

Fig. 1. Diagrams for calculating the cutter-bar rotation mechanism

Before proceeding to consider the operation of the mechanisms presented in Fig. 1, let us adopt the following conventional notation:

\(O_1O_2 = a\) — distance from the center of rotation of the bar to the suspension point of the hydraulic cylinder;

\(O_2O_3 = b\) — hydraulic cylinder;

\(O_2O_3 = c\) — rocker arm, rigidly connected with the bar and hinged to the hydraulic cylinder;

\(L_b\) — length of the bar;

\(H\) — distance from the ground to the center of rotation of the bar;

\(H_{\mathrm{sh}}\) — depth of the cutting slot;

\(l_{\mathrm{c}}\) — distance from the center of rotation to the center of gravity of the bar;

\(G_b\) — weight of the bar;

\(F_{\mathrm{p}}\) — active area of the piston;

\(p\) — oil pressure;

\(P_{\mathrm{p}}\) — feed force;

\(\gamma\) — angle, constant for each design, between the axes of the bar and the rocker arm;

\(\alpha\) — angle between the axis of the rocker arm and the line connecting the suspension points of the hydraulic cylinder and the bar. This angle is constant for the given design of the bar-rotation mechanism if the latter is in the vertical lowered position and with the hydraulic cylinder shortened to the greatest possible extent. \(\alpha\) changes with a change in the inclination angle of the bar;

\(\beta\) — angle of inclination of the bar to the vertical;

\(h\) — arm of the force of the hydraulic cylinder;

\(L_{\mathrm{tr}}\) — length of the track;

\(a_{\mathrm{t}}\) — longitudinal coordinate of the center of gravity of the earth-cutting machine relative to the middle of the track;

\(G_{\mathrm{m}}\) — weight of the earth-cutting machine.

Let us consider the three most characteristic cases in the operation of the bar rotation mechanism (Fig. 1, a): I — raising the bar into the transport position; II — beginning of penetration of the bar; III — operation of the bar set at an angle \(\beta\).

Position I. The hydraulic cylinder must develop on the rod a force

\[ P_{\mathrm{rod}} = F_{\mathrm{p}}p = \frac{G_b l_{\mathrm{c}}\sin\beta + M_{\mathrm{fr}}}{h}, \tag{1} \]

where \(M_{\mathrm{fr}}\) is the moment of friction in the pivot pins of the suspension of the bar working member.

The moment of resistance due to friction in the pivot pins may be found from the expression

\[ M_{\mathrm{fr}} = (\overline{P}_{\mathrm{rod}} + \overline{G}_b)\, f \cdot r_{\mathrm{c}}, \]

where \(f\) is the coefficient of friction in the pivot pins;

\(r_{\mathrm{c}}\) is the radius of resistance of the rubbing surfaces;

\(\overline{P}_{\mathrm{rod}}, \overline{G}_b\) are components of forces representing the tangential circumferential force in the sphere of the rubbing surfaces.

Let us express \(h\) through the constants \(a, b, c\).

\[ h = \frac{c \cdot a}{b}\sin(\alpha \pm \beta). \]

By the cosine theorem,

\[ b = \sqrt{a^2 + c^2 - 2a \cdot c \cdot \cos(\alpha \pm \beta)}, \]

then

\[ h=\frac{c \cdot a \sin(\alpha \pm \beta)} {\sqrt{a^2+c^2-2ac\cos(\alpha \pm \beta)}} . \tag{2} \]

The signs \(+\) and \(-\) in expression (2) are used when calculating the schemes of the cutter-bar rotation mechanisms shown, respectively, in Fig. 1, \(a\) and Fig. 1, \(b\).

Substituting (2) into equation (1), we obtain

\[ P_{\mathrm{rod}}= \frac{(G_b l_c \sin\beta + M_{\mathrm{fr}}) \sqrt{a^2+c^2-2a \cdot c \cdot \cos(\alpha \pm \beta)}} {c \cdot a \cdot \sin(\alpha \pm \beta)} . \tag{3} \]

It follows from equation (3) that the force on the hydraulic-jack rod when lifting the cutter bar from the slot depends on the weight and length of the cutter bar and on the design parameters of the rotation mechanism. The calculation must be made for the case in which the moment of resistance to rotation of the cutter bar is maximum, i.e., at \(\beta=90^\circ\).

Position II corresponds to the beginning of the destruction of frozen soil by the cutting chain (Fig. 1, \(a\)), when the earth-cutting machine is not moving. At the end of the cutter bar there arises a force resisting its rotation

\[ P_{\mathrm{res}}= \frac{P_{\mathrm{rod}} \cdot h + G_b l_c \sin\beta - M_{\mathrm{fr}}} {L_b}. \tag{4} \]

An excess of the cutter-bar rotation speed over the possible speed of its penetration into the soil may lead to the component \(P_{\mathrm{res}}\sin\beta\) tending to overturn the machine about point \(A\) (Fig. 1, \(a\)). To prevent such a case, the following condition must be observed:

\[ P_{\mathrm{res}}\sin\beta\,(L_b\sin\beta \pm l_1 + L_{\mathrm{gus}}) \ll G_m(0.5L_{\mathrm{gus}}\pm a_m)\ldots\ldots \tag{5} \]

Solving (4) and (5) simultaneously, we find that, in order to prevent overturning of the earth-cutting machine when the cutter bar is being sunk, the force on the hydraulic-jack rod must not exceed the value that can be found from the expression

\[ P_{\mathrm{rod}}\ll \frac{L_b G_m(0.5L_{\mathrm{gus}}\pm a_m)} {\sin\beta\,(L_b\sin\beta \pm b + L_{\mathrm{gus}})} +M_{\mathrm{fr}}-G_b l_c \sin\beta . \tag{6} \]

With the dimensions of the hydraulic cylinder known, for the given design of the cutter-bar rotation mechanism one can find from (6) the maximum permissible oil pressure \(p\) during sinking.

Position IIIa corresponds to the case in which the cutter bar is being sunk. The earth-cutting machine is stationary. The amount of sinking is close to the maximum. The resistance to rotation of the cutter bar in this case will consist of the resistance due to friction in the pivot pin and the resistance to penetration of the cutting teeth into the frozen soil. If it is assumed that the resultant of the forces resisting penetration of the cutting teeth, \(P'_i\), passes through the middle of the sunk part of the cutter bar, then from the equation of the sum of moments about point \(O_1\) one can find the force on the hydraulic-jack rod

\[ P_{\mathrm{rod}}= \frac{P'_i(L_b\cos\beta+H)+2M_{\mathrm{fr}}+2G_b l_b \sin\beta} {2h}, \tag{7} \]

necessary to overcome the forces resisting rotation of the cutter bar.

Position IIIb corresponds to the case in which the cutter bar is set at an angle \(\beta\) and cuts a slot in the frozen soil of depth \(H_{\mathrm{sl}}\) during continuous movement of the earth-cutting machine.

In this case the force on the rod of the hydraulic cylinder required to hold the cutter bar in the required position is

\[ P_{\text{rod}} = \frac{ P_{\text{p}}(L_{\text{b}}\cos\beta + H) - 2M_{\text{tr}}\cos\beta - 2G_{\text{b}}l_{\text{c}}\sin\beta\cos\beta }{ 2h\cos\beta }. \tag{8} \]

From equation (8) one can find the maximum \(p\) to which the safety valve of the hydraulic system must be adjusted. At the same time, however, all units of the cutter-bar rotation mechanism and their attachments must be checked for strength, taking into account the action of the forces, the calculation procedure for which was given above.

The calculation of the forces arising during operation in the cutter-bar rotation mechanism, whose schematic is shown in Fig. 1, c, is carried out analogously, except only that in this case \(h = \dfrac{D_i}{2} = \text{const}\). The maximum stroke of the piston of the hydraulic cylinder is determined by the value of the adopted angle \(\delta\) between the extreme possible positions of the cutter bar (working and transport) and can be found from the equation

\[ l_{\text{p}} = \frac{\pi D_i \delta}{360} \simeq 0.00872\,D_i\delta. \]

The advantage of this scheme in comparison with those considered above is that, with comparatively small dimensions of the cutter-bar rotation mechanism, it is possible to obtain an angle \(\delta\) equal even to \(180^\circ\). The latter is desirable in order to reduce the longitudinal overall dimensions of the machine and to reduce the dynamic loads on the attachment parts of the reducer of the working member during idle runs of the earth-cutting machine.