ANALYSIS OF THE OPERATION OF CERTAIN LOADING MECHANISMS OF LOADING MACHINES

A. T. MARTYNENKO

Candidate of Technical Sciences, Docent

The creation of a new design of loading machine for both surface and underground operating conditions remains, to this day, a pressing question. The most labor-intensive processes—loading and shoveling in mines and pits—remain unmechanized, despite the purposeful efforts of individual inventors in this field, whose work has not yielded tangible results and has, in essence, amounted to copying, with minor design changes, Western European and American models.

How can it be explained that the enormous experience possessed by the machine-building industry has not become the property of the mining industry, which is experiencing an extremely acute need in this respect? As is known, world engineering has rich experience in the design of various loading mechanisms, but, unfortunately, even up to the present time there is no at all exhaustive analysis in the technical literature of the operation of loading mechanisms that would indicate the value of the principles underlying one mechanism or another, the rationality of selecting the trajectory of motion of the scooping blade with minimum expenditure of energy, etc. In other words, in the designs of loading and shoveling machines known to us, the loading mechanism has not received its final solution in the sense of taking coal from open piles. Undoubtedly, this gap has had a negative effect, since the designer and constructor have no point of departure from which they could create a new design of loading machine free from all the defects and design imperfections that burdened its predecessors. Indeed, the data available in our technical literature (not to mention foreign literature, where in most cases a mechanism is always promoted by the firm in a positive sense) are of an exclusively descriptive character.

Thus, there is no critical analysis of the operation of loading mechanisms in the technical literature. Meanwhile, the loading mechanism of any loading machine is the most responsible part, the perfection of whose design basically determines the productivity of the given loading apparatus. Structurally, the loading mechanism in the majority of loading machines consists of a scoop, bucket, blade, rakes, or a multi-bucket drum. The idea of the arrangement and the structural execution of one or another loading mechanism consisted in the capture of loosened (bulk) material lying in a free state. Most shoveling machines intended for underground conditions have loading mechanisms of a raking action; that is, the trajectory of motion of the collecting parts is, in most cases, located in a horizontal plane, which was undoubtedly dictated by considerations of the dimensional conditions of underground workings, since advance—

the movement of the scrapers in the mass of mineral cannot reduce the force required to overcome resistance during loading.

Thus, loading mechanisms of a raking action are widely represented by various loading machines: of the Jeffrey, Polyakov-Mamonov, Joy, Nepomnyashchii-Sinitskii type, as well as by those of Flottmann, Forster, and others. If in the first case the loading mechanisms, which are scrapers attached to a chain or to a rotating disk, may be assigned to the continuously acting type, then the idea of the design of loading mechanisms of the Flottmann and Forster machine type may be assigned to the group of scraper loading devices having a trajectory of scraper motion located in a vertical plane, which gives an undoubted advantage in the choice of the trajectory of scraper motion; since in this case (upper scraper raking) less expenditure of energy will be required to overcome resistance during loading. In addition, the impact action of the loading mechanism should be regarded as a desirable phenomenon in a loading machine intended for work on the surface of mines, since in winter coal delivered in a wet state freezes in mine storage yards.

In contrast to the above-mentioned loading mechanisms of raking action, there are also in practice loading machines with multi-bucket and bucket loading mechanisms of the ATG, Humboldt, Flottmann, Myers-Whaley, Arkhipov type; the Konuy shovel, Mac-Dermott, and others. Single-bucket loading machines of the Myers-Whaley, Konuy, and Arkhipov type, by the nature of operation of their loading mechanisms, are a structural modification of single-bucket excavators, the basic idea of which consisted in reducing the overall dimensions for the operation of machines in underground conditions.

Without dwelling on the classification of the loading mechanisms of loading machines, we shall consider questions of analyzing the operation of loading mechanisms of multi-bucket and single-bucket action. Any loading machine must include three basic elements: 1) discharge conveying organs; 2) a loading mechanism; and 3) dumping or unloading devices. As is known, a loading machine has one or two discharge transmission organs, in most cases consisting of belt, scraper, or plate conveyors. The second conveyor in a loading machine, if present, performs the role of a guiding boom, which is usually attached to the machine by a hinge, thereby permitting rotation both in the vertical and in the horizontal plane. Therefore the second conveyor of the machine must be of light construction with a flexible working member.

The productivity of the machine’s discharge conveyors should be taken as equal to the productivity of the loading mechanisms. The latter, as we shall see below, may differ, since it is difficult theoretically to take into account all factors of the practical conditions of self-loading. It is not excluded that, at certain moments of favorable conditions for filling, the loading mechanism may give a productivity equal to or greater than the theoretical productivity, i.e., the filling of the buckets may be greater than their capacity (heaped filling). This circumstance undoubtedly may occur in storage yards with large cones of coal under the trestle and with good maneuverability of the loading machine. Proceeding from the foregoing, the productivity of the discharge conveyors of the loading machine should be taken as equal to the theoretical productivity of the corresponding design of loading mechanisms.

The selection of the transporting members of a loading machine must be made as a function of many factors, both economic and technical.

The loading mechanism of a loading machine is the most critical part, chiefly determining the productivity of the given loading apparatus. However, even with a completely perfected design of the loading mechanism, the effective productivity of the loading machine will depend on the distribution of the entire mass of coal over the storage-yard area, on its varying lump size, and on the degree of its compaction. In addition, the effective productivity will also depend on the amount of useful working time of the loading machine. All the factors enumerated above indicate that, generally speaking, the machine’s productivity will be a variable quantity; within a smaller unit of time, however, the operating conditions for the loading mechanism may be considered approximately constant.

The coefficient of useful operation of the loading mechanism is determined by the ratio:

\[ \beta = \frac{Q_n}{Q_m}, \]

where \(Q^n\) is the actual, practical productivity of the loading mechanism,

\(Q_m\) is the theoretical productivity, calculated by the corresponding formulas for the given type of loading mechanism.

In addition to the factors noted above, the maneuverability of the loading machine will also affect the value of the coefficient of useful operation of the loading mechanism.

Thus, even with a completely perfected design of the loading mechanism, the useful coefficient of its operation will decrease because of the general operating conditions of the loading machine; that is, the nonuniformity of the material in lump size, its varying caking, and, in wintertime, freezing cannot be taken into account theoretically with sufficient accuracy. Moreover, the uneven distribution of the entire mass of the mineral over the storage-yard area requires almost constant movement or turning of the loading end of the loading machine in order to create more favorable loading conditions.

Multi-bucket Loading Machines

The need to create the most powerful loading machine with the simplest loading mechanism in design led to the idea of using bucket elevators for loading loose materials into railway cars.

Elevators, or bucket conveyors, are used mainly for moving loads vertically or at a large angle to the horizontal, which is their advantage over belt and scraper conveyors, in which the inclination angle of the working member is limited. In addition, a positive feature of bucket elevators may be considered the absence of a special loading mechanism, since the elevator buckets, owing to their rigid attachment to the traction member, provide self-loading. All these qualities set forth above made it possible to use them for loading material both independently and in combination with various transporting machines.

The Jeffrey company’s mobile loader (Fig. 1) is a bucket elevator mounted on a wheeled running gear. The working part of the load—

... consists of two parallel articulated chains passing around the head and tail sprockets, with buckets attached to their links. The driving sprockets of the loader are set in motion by the motor by means of two chain drives through an intermediate shaft coinciding with the axis of rotation of the tractive element. Loading of the machine is carried out by the buckets themselves,

Fig. 1

for which purpose the buckets are made with toothed attachments along the scooping edge.

By creating better conditions for filling the buckets, the Barber-Green Co. proposed a bucket loader (Fig. 2) providing forced filling. The completeness of loading of the buckets of this loader, as is evident from the drawing, is achieved by two steel disks located on the sides in the lower part of the machine. The disks are installed at an inclination of 2.5° to the horizontal and rotate in different directions by means of bevel gears. This loading machine is mounted on a crawler track. Both the travel of the machine and the motion of its working member are effected by an internal-combustion engine or a single electric motor of 10 hp by means of chain drives. The machine has a differential and therefore obtains the possibility of maneuvering. The working member of the loader consists of two parallel chains, with a pitch of 150 mm, on which 24 buckets are fastened at equal distances, their width being 450 mm. For loading, the machine is advanced onto the pile; the disks enter the mass of coal and, by their rotation, bring it to the buckets of the loader. From the buckets the mineral is transferred to a universal chute, which can rotate 180° about the vertical axis and 90° about the horizontal axis, which almost ensures uniform loading of an open wagon over its entire area.

The bucket loading machine of the firm Haiss (Fig. 3) is also one with forced filling of the buckets and differs from the Barber-

Green C only with a different design of the loading device. To ensure better capture of the coal by the buckets in the Haiss machine, the lower working shaft is designed to be 60 cm longer than the upper one. Augers consisting of four helical blades arranged at right angles to one another are mounted on the projecting four-sided ends of the shaft. When the shaft rotates, all eight blades take coal from both sides and move it toward the axis of the bucket chain, from where it is picked up by the buckets and conveyed to the discharge point. This design of the loading device is more convenient than the one considered earlier.

Fig. 2

However, owing to the nonuniformity of the material being loaded, the lateral reactions at the augers may be different; as a result, during loading the machine may undergo oscillatory motions. The drive shaft of the Haiss machine receives rotation from the motor through a very complex transmission, consisting of a worm wheel on the intermediate shaft of the gearbox, a worm, a vertical shaft, a pair of bevel gears on the horizontal intermediate shaft, coinciding—

with the axis of rotation of the conveyor, and by chain transmission to the main drive shaft of the conveyor itself. When the machine is moved about the loading area, the elevator can be set in a horizontal position. The machine is turned by means of an automobile-type differential.

The machine described, in comparison with the Barber-Green C° machine, is more complex, bulky, and heavy, but provides greater productivity.

Fig. 3

In addition, it has an insufficient length of the working member and a small operating radius.

Besides the above-mentioned multi-bucket loading machines, there are a number of others of the same type, such as, for example, loaders by Nelson, Henzelmann, and the Institute of Industrial Transport, which implement the same idea of forced filling of the elevator buckets, only in a somewhat different structural design. Thus, the loading machine of the Institute of Industrial Transport has the same disks as the Barber-Green C° machine, but only with serrated teeth, and they are set at a large angle to the horizontal.

The German firms ATG, Humboldt, and Flottmann manufacture multi-bucket loading machines whose loading mechanism consists of a bucket wheel.

Let us consider an ATG-type loading machine with a six-bucket wheel (Fig. 4). When the wheel rotates in one direction, the buckets pick up the material encountered by them and carry it to the trough chute. From the chute the material passes to the receiving section of the front belt conveyor. By the latter the material is transferred to a second belt conveyor, from which, by means of a tray, it is directed directly into the wagon. The bucket wheel is rotated by means of an internally toothed ring gear mounted on the opposite side of the receiving section.

front conveyor. The first discharge conveyor is mounted on the lifting truss of the loading bucket wheel. This truss can rotate in a vertical plane, which makes it possible to change the height position of the bucket wheel at the moment of loading within limits of up to 4 m. The discharge part of the first conveyor is located above the receiving part of the second conveyor. The latter is installed on a metal frame, which can turn both in a vertical and in a horizontal plane. The center of rotation in the horizontal plane is a vertical shaft, which at the same time transmits motion to the driving drum of the conveyor.

When loading from stockpiles located along railway tracks, the machine may be set with the bucket wheel against the face of the stockpile. The discharge end of the rear conveyor is placed in such a position that loaded cars can be rolled under it. During loading, the machine periodically moves toward the stockpile of bulk material. Thus, we have briefly considered certain multi-bucket loading machines, the operating principle of which, in scooping, may be likened to the theory of loading elevator buckets¹. When a bucket is loaded from open stockpiles (Fig. 5), the particles of material entering it are under the action of the force of gravity \(G = mg\) and the centrifugal force \(C = mr\omega^2\). The resultant of these forces is determined by the diagonal of the parallelogram constructed on these forces, which will intersect the vertical passing through the center of rotation \(O\) at the point \(P\), called the pole.

Fig. 5

To determine the pole distance \(S\), one may take the relation from the similarity of the triangles \(OMP\) and \(MGR\):

\[ \frac{S}{r} = \frac{G}{C}, \]

whence

\[ S = \frac{Gr}{C} = \frac{mgr}{mr\omega^2} = \frac{g}{\omega^2}. \]

Substituting \(\omega = \frac{\pi n}{30}\), we obtain

\[ S = \frac{g30^2}{\pi^2 n^2} = \frac{895}{n^2}, \]

where \(n\) is the number of revolutions of the loading drum per minute.

As can be seen from the formula given above, the magnitude of the pole distance \(S\) depends only on the number of revolutions of the loading drum.

In the case when there is liquid in the bucket, the outline of the latter will be, in form, a circular cylinder whose axis passes through the pole \(P\). Consequently, the surface of the liquid will be a level surface, since the former, in equilibrium, is situated normally to the forces acting upon it.

As a result of this, all particles of liquid lying above the cylindrical surface \(AK\) (Fig. 6) must pour out over the outer edge \(A\). If, however, there is loose material in the bucket, then its surface will be inclined to the level surface of the liquid at the angle of the natural slope of the material, \(\varphi\); therefore the surface of the loose material will be outlined by the curve \(AN\). The angle between the tangents to these curves \(AK\) and \(AN\) must be equal to the angle of the natural slope of the material \(\varphi\), and the angle between the tangent to the curve \(AK\) and the radius vector \(AP\) will be equal to \((90-\varphi)\). Therefore the curve of the natural slope must satisfy the condition under which the angle between its tangent and the radius vector \(AP\), in any position, must be equal to \((90-\varphi)\).

Thus, the curve of the natural slope will be a logarithmic spiral with pole \(P\), whose equation in polar coordinates is expressed as

\[ R = a e^{f\Theta}, \]

where
\(a\) is the radius vector at
\[ \Theta = 0; \]

\(\Theta\) is the angle of rotation of the radius vector;

\(e\) is the base of natural logarithms;

\[ f = \operatorname{tg}\varphi = \operatorname{ctg}(90-\varphi). \]

As a result of the fact that, for a given angle \(\varphi\), it is possible to construct only one logarithmic spiral, independent of the scale of the drawing, then for any point and for any position of the buckets it is possible, by means of a template made according to a logarithmic spiral, to construct the curve of the natural slope of the material passing through the outer edge of the bucket \(A\). Those particles of material which lie above this curve will spill out of the bucket, and thus, during scooping by the bucket, this curve can determine the outer outlines of the material contained in the bucket. On the basis of the foregoing, it can be seen that the outer outline of the material in the bucket will depend on the magnitude of the pole distance, and, consequently, on the number of revolutions of the loading drum. With a large number of revolutions the pole distance will decrease, and a condition may arise in which the material will not be retained in the bucket.

Fig. 6

When the loading wheel operates on open stockpiles, this reasoning will hold only after the bucket has left the stockpile,

since, with its position in the mass of the material being loaded, the pressure of the portions lying above it will prevent discharge from the bucket over edge \(A\). If, however, by the time the bucket leaves the pile it passes from curvilinear to rectilinear motion, then the above-mentioned possible ejection of material from the bucket will not occur at all. If the latter condition is not fulfilled, then, in order to ensure more efficient operation of the loading mechanism, low speeds must be assigned to the motion of the buckets. The filling coefficient of the buckets, in addition to the foregoing, will also depend on special raking devices that assist in filling the buckets, which are observed on some bucket loading machines (Figs. 2, 3).

Prof. Hanfshtengel, on the basis of his experiments, gives the following coefficients for filling buckets from closed shoes: for small coal \(\psi = 0.6—0.7\), and for large coal \(\psi = 0.4—0.5\).

In the standards of Shakhtstroi, the bucket filling coefficients for inclined elevators operating on coal with closed shoes are taken within the range \(0.75—0.90\). As for the bucket filling coefficient of elevator loaders and loading machines with bucket wheels from open piles of coal delivered in ordinary fashion, it will undoubtedly be smaller; and, in the presence of special devices that help to fill the buckets forcibly, this coefficient will approach the filling coefficient from closed shoes. To establish these coefficients more precisely, it is necessary to carry out experimental investigation and observations.

Single-bucket loading machines

In contrast to the multi-bucket loading machines considered above, which are used chiefly on the surface, we shall next consider some single-bucket machines intended exclusively for work in underground mine conditions. Figs. 7 and 8 show the general appearance, design, and principal phases of operation of the loading mechanism of the Myers-Whaley single-bucket loading machine. As can be seen, the loading mechanism is made in the form of a composite bucket, provided along its cutting edge with strong teeth. The bucket is set in motion from a common electric motor by means of a crankshaft. When the control clutch is disengaged, the edge of the bucket cuts into the pile of material being loaded in the horizontal direction by almost 350 mm. At the next moment the entire bucket begins to rise, while its cutting edge moves along the trajectory indicated in the figure by a dashed line. At the moment when the cutting edge reaches the upper position, all the material gathered by the bucket falls onto its rear tilting part. With further rotation of the crankshaft, the rollers of the rear part of the bucket enter their guides. Moving along the guides, the rear part of the bucket first rises upward and then tips over. In this way, the material being loaded that has been gathered into the bucket is delivered to the first elevating-and-conveying conveyor. The front part of the bucket, even before the moment when the rear part tips over, as it descends, begins to separate from the rear part—moving forward on the hinge. After tipping, the rear part of the bucket returns to its place, first under the action of the guide rollers and then under the action of its own weight. Without dwelling on a more detailed description of the operation of the gathering mechanism of the Myers-Whaley loading machine, we consider it necessary to point out the circumstance that, owing to the presence of a complex system of drives, clutches, and the dynamic action of the loading-

of the loading mechanism, as practice in their operation shows, has frequent breakdowns of various parts.

A loading machine of another type, designed by Eng. Arkhipov, while carrying out the same idea of gripping material from open stockpiles (Fig. 9), is equipped with a one-piece bucket that constitutes the loading mechanism. The trajectory of motion of the front part (the scooping edge) of the bucket,

as can be seen from the drawing, is a closed curve \(abcd\). The reciprocating motion of the bucket is imparted by disk \(A\) by means of the articulated joints \(K\), \(L\), and \(M\). Hinge \(M\) is mounted eccentrically on disk \(A\), which is rotated by the motor through a whole series of transmissions. When, during rotation of disk \(A\), the bucket reaches the position indicated in the drawing by the dashed line, coal is discharged from it onto the conveyor. At the moment of unloading the bucket, its motion ceases for a certain time. The necessary stopping of the bucket, so that the material can be completely spilled onto the belt during its working cycle, is accomplished by means of—

power of a special device. Omitting all the other shortcomings inherent in it as a gathering machine, we consider it necessary to point out only the design feature of the loading mechanism. A substantial defect of the loading mechanism of the gathering machine designed by Engineer Arkhipov consists in the frequent cessation of motion of the bucket. Frequent and instantaneous stoppages of the bucket (60 rev/min) must undoubtedly be—

—come the cause of various breakages and malfunctions, which does not give full assurance of the operability of this mechanism.

The basic purpose of any loading mechanism of any loading or gathering machine should consist only in taking in, in grasping the material and, in the extreme case, if this is necessary, in carrying out a lift to the position of self-rolling onto the conveying members of the machine. From this point of view it may be considered that the loading mechanisms of the loading machines considered will be better, since in their

in the working cycle spend a minimum of time on transportation and work a maximum amount on scooping.

Considering the operation of the loading mechanisms of Myers-Whaley, Arkhipov, and other loading machines of the same type, we observe that the scooping blade or bucket, as it penetrates into the material, describes some complex trajectory of motion. On detailed examination, separate phases of motion can be established for it, each accompanied by its own resistances to scooping.

In Fig. 10 a diagram is presented of the different positions of the blade or bucket of the loading mechanism. As can be seen from the diagram shown, at the initial moment of penetration the blade has a segment \(CC_1\) close to rectilinear motion. The magnitude of this segment will be different for each design of loading mechanism. In some loading mechanisms this motion occurs with the penetrating plane inclined, which is always accompanied by significant resistance forces due to shearing of the prism in the position of the plane \(c_1d_1\).

In some other loading mechanisms (Thieu blades)\(^1\) the blade enters the coal pile in a horizontal position. In this case the forces of resistance to shearing will occur to a lesser degree, but significant forces of frontal resistance to penetration will appear. At the next moment of penetration, the blade moves along the curve \(C_1C_2\). In traversing this path, resistance forces arise from the shearing of the prism of material located on the blade, and friction forces of its entering edge along the line of separation \(C_1C_2\). And, finally, the segment \(C_2C_3\) corresponds to the withdrawal of the loading blade from the coal pile. This segment of motion is characterized by the fact that the resistance forces occurring on the segment \(C_1C_2\) will diminish as a result of the continuous sliding of the material from the loading blade at the angle of natural repose.

Fig. 10

Thus, the force required for penetration, according to the above diagram, undergoes considerable fluctuations during the loading (scooping) process. Therefore, in order to obtain an analytical dependence when determining the loading forces, it is necessary to introduce correction coefficients that take into account: 1) the constant change in the properties of the material being loaded; 2) the state of the penetrating plane (bucket), and 3) the dynamic action of the loading mechanism.

These coefficients will have different values for each of the above-mentioned phases of motion of the loading blade. Their quantitative expression analytically, without setting up special experiments, is, generally speaking, extremely difficult to determine.

Below a possible analytical solution is given for determining the required force during penetration. Suppose that we need to determine what force \(P\) must be applied to the blade \(ab\), representing the bucket of a loading mechanism without side boards, when it penetrates into a coal pile by the amount \(x\) (Fig. 11). Let us assume that, during penetration, the blade moves from point \(a\) to point \(a_1\), remaining parallel to its initial position. To determine the force \(P\), let us establish what forces will act—

\(^1\) Charles E. Van Barneveld.—Mechanical Underground Loading in Metal Mines, 1932.

act on the blade in position \(a_1b\). From direct penetration, an amount of material expressed by the volume of the triangular prism \(aa_1b\), which will occupy some position on the plane \(a_1b\), will act on the blade. If the weight of the material of the prism \(aa_1b\) is denoted by \(G\), then its magnitude can be expressed as

\[ G=\omega_{\Delta} b\gamma. \]

Let us express the weight of the material of the prism \(aa_1b\) as a function of the depth of penetration, the width, and the angle of inclination of the blade entering the coal pile. Then the expression for the force \(G\), after the corresponding transformations, takes the final form

\[ G=\frac{\gamma b x^2}{2(\operatorname{ctg}\varphi+\operatorname{ctg}\alpha)}, \]

where
\(\alpha\)—the angle of inclination of the blade (bucket);
\(\varphi\)—the angle of natural repose of the material;
\(b\)—the width of the penetrating blade;
\(\gamma\)—the unit weight of the material.

In addition to the force \(G\), when the blade penetrates there will also arise forces of resistance to the displacement of some part of the mass of material, which may be allowed for, according to the theory of granular bodies, from the triangle \(a_1cd\) (pressure triangle). Then this resistance force will be expressed as

\[ Q=F_{\Delta} b\gamma. \]

Fig. 11

The force \(Q\) will be directed at an angle \(\varphi_0\) (the angle of friction of the material on the bucket) to the normal to the plane \(a_1b\). We determine the segment \(a_1d\) from \(a_1b\) and the angles \((\varphi+\varphi_0)\) and \((\alpha+\varphi)\)

\[ a_1d=a_1c=\frac{x\sin\varphi}{\sin(\alpha+\varphi_0+2\varphi)}. \]

The area of the triangle \(a_1cd\) is determined as follows:

\[ F_{\Delta}=\frac{x^2\sin^2\varphi}{2\sin(\alpha+\varphi_0+2\varphi)}; \]

then, denoting the weight of the triangular prism \(a_1cd\) by \(Q\), we obtain the second component of the resistance force to penetration in its final form

\[ Q=\frac{\gamma b x^2\sin^2\varphi}{2\sin(\alpha+\varphi_0+2\varphi)}. \]

Determine \(N\)—the reaction force on the area \(aa_1\), neglecting the displacement of the forces \(G\) and \(Q\) to the right. From Fig. 11 it is seen that

\[ N=G+Q\sin(\alpha-\varphi_0). \]

Project all acting forces (the force \(P\) and the friction forces) onto the direction of the plane \(a_1b\):

\[ P-Nf_1\cos\alpha-f_2G\cos\alpha-f_2Q\cos\varphi_0=0, \]

where
\(f_1\)—the coefficient of friction of the entering edge of the blade on the area \(a_1a\);
\(f_2\)—the coefficient of friction of the same blade on coal.

From the equation given above, using the relations of the expressions for \(G\), \(Q\), and \(N\), and also carrying out the corresponding transformations, we obtain:

\[ P=\frac{\gamma b x^2}{2}\left[ \frac{(f_1+f_2)\cos\alpha}{\operatorname{ctg}\alpha+\operatorname{ctg}\varphi} + \sin^2\varphi \left\{ \frac{f_1\cos\alpha\sin(\alpha-\varphi_0)+f_2\cos\varphi_0} {\sin(\alpha+\varphi_0+2\varphi)} \right\} \right]. \]

Express the quantity \(x\) in terms of \(a\)—the length of penetration into the stack of coal by the blade \(ab\):

\[ \frac{x}{\sin [180-(\alpha+\varphi)]}=\frac{a}{\sin \varphi}, \]

whence

\[ x=\frac{a\sin(\alpha+\varphi)}{\sin\varphi}. \]

The final form of the formula obtained will be

\[ P=\frac{\gamma a^{2}b\sin^{2}(\alpha+\varphi)}{2\sin\varphi} \left[ \frac{(f_{1}+f_{2})\cos\alpha}{\operatorname{ctg}\alpha+\operatorname{ctg}\varphi} + \sin^{2}\varphi \left\{ \frac{f_{1}\cos\alpha\sin(\alpha-\varphi_{0})+f_{2}\cos\varphi_{0}} {\sin(\alpha+\varphi_{0}+2\varphi)} \right\} \right]. \]

This analytical expression for the force \(P\) of penetration according to the scheme (Fig. 11) takes into account only the resistance from pushing the material onto the plane and the frictional resistance, determined through the normal pressure. Using this relation, one can proceed to determine the force for direct penetration of the loading blade. In this case, obviously, \(f_{1}=f_{2}\) and \(\alpha=0\). In addition, in direct penetration it is necessary to take into account the frontal resistance of the material, acting along the perimeter of the entering edge of the loading bucket.

It must be said that, in loading mechanisms with direct loading, close to the type of loading machines “duckbill,” mechanical loaders “Main,” the frontal resistance to penetration will be significant. It is impossible to take the magnitude of this resistance into account without carrying out special experiments, since the different lump size of the material being loaded, the condition of the penetrating implement, and also the dynamics of penetration will obviously be functions of the frontal resistance to penetration of the bucket.

Fig. 12.

To determine the productivity of bucket loading mechanisms operating according to the scheme considered (Fig. 11), let us assume that the bucket has penetrated into the mass of coal and, before leaving the stack, occupies the position shown in Fig. 12, where point \(d\) is the hinge of rotation of the bucket about a horizontal axis. During its rotation relative to point \(d\), the bucket can take material from the section \(dce\), which in Fig. 12 has the form of a triangle, taking the arc \(ce\) as a straight line.

Such filling of the bucket will occur only under the condition that the coal lying above the plane \(ce\) will not roll down, and that after capture the coal will not spill from the bucket. In reality there will be no such situation, since the coal lying above will tend, under the action of the force \(T\), to occupy its natural position. The particles of material lying above the plane \(ce\), as the bucket leaves the stack, will exert pressure on the coal located in the bucket along the line \(ce\) with a force equal to

\[ T=fG\cos\varphi. \]

If it is assumed that the prism of coal \(dce\), located on the scoop, is in a solidified state, then the overlying particles will offer only resistance to the scoop’s exit from the pile and will have no effect on the filling of the scoop. Therefore, if we consider that material bounded by a triangular pyramid of width \(b\) will remain in the scoop, then the filling of the scoop is expressed by the formula

\[ q=\frac{b a^{2}\sin\varphi}{2}. \]

Now let us suppose that, when the scoop is withdrawn from the coal pile, the overlying particles will pour onto the scoop; then, provided it has side walls and a rear wall, we may obtain better filling. In this case it may be assumed that there will be no smaller filling, as occurred in the first case with fine coal, because the overlying layer of coal will impede pouring off. But when we are dealing with coal of varying lump size and compactness, the uneven and incomplete filling of the scoop due to the falling in of large lumps, which carry fines with them, must be taken into account. Therefore a correction coefficient must be introduced into the formula for scoop filling (the scoop filling coefficient); then the expression will take the form

\[ q=\psi \frac{b a^{2}}{2}\sin\varphi . \]

Under these conditions, the hourly capacity, in tons, of scoop loading mechanisms, taking into account the coefficient of utilization of working time, may be expressed by the formula

\[ Q=k\psi n\gamma b \cdot \frac{a^{2}}{2}\sin\varphi\ \text{t/hour}, \]

where
\(k\)—coefficient of utilization of working time,
\(\psi\)—coefficient of scoop filling,
\(n\)—number of scoop cycles per hour,
\(\varphi\)—angle of natural slope of coal in a pile,
\(\gamma\)—volumetric (bulk) weight of coal,
\(a\)—depth of penetration of the scoop into the coal pile,
\(b\)—width of the scoop.

The analytical solution given above for determining the force of penetration of the scoop of a single-scoop loading mechanism, as well as the magnitude of scoop filling and the capacity of the loading machine as functions of scoop filling and the number of scooping operations, does not claim to establish definitively the force required for scooping and, consequently, the machine’s power consumption for self-loading, since without carrying out special experiments it is difficult to determine analytically the values of the coefficients entering into the mathematical relationship. Therefore the proposed solution for establishing the expenditure of force for scooping in single-scoop loading mechanisms is given as a first approximation and, undoubtedly, may be taken as a basis in designing single-scoop loading mechanisms for loading machines.

In addressing the question of mechanizing the loading of coal into railway cars from mine storage yards, the author of the present article naturally seeks to choose rational forms and methods for organizing the work in the most labor-intensive process taking place on the surface of mines. If many means had been proposed under underground conditions for mechanizing shoveling, then in ...

of various designs of loading machines: Ivannikov’s, Polyakov-Mamonov’s, Nepomnyashchy-Sinitsky’s, Arkhipov’s, Bratslavsky’s, the PM-2 type, PE-1, etc., some of which even reached the stage of experimental industrial prototypes, extremely few loading machines of new designs have been proposed over the last ten years for servicing emergency stockpiles at mines. Therefore, the attention of designers and inventors must be directed to this matter, since the existing machine of T. Fluss’s design by no means solves the problem of mechanizing loading operations on the surface of mines.

1. Prof. P. S. Kozmin, Continuous-Transport Machines, Part 2, 1935. ↩