On the Question of Determining the Capacity of Scraper Conveyors

A. T. Martynenko
Docent, Candidate of Technical Sciences

Scraper conveyors, as conveying machines, are widely used not only in the mining industry, but also in other branches of the national economy; moreover, they are employed both independently and as working organs in various loading mechanisms. According to the conditions of use and the nature of their operation, scraper conveyors used in the coal industry are divided into stationary and portable. Whereas stationary scraper conveyors have become widely used as conveying machines in the equipment of coal-preparation plants, pithead buildings, railway loading bunkers, and mineral-storage facilities, portable conveyors are used chiefly as intermediate transport in stoping workings. In most cases stationary conveyors have a scraper height approximately equal to the height of the trough, while portable ones have a height several times smaller; consequently, by virtue of this, the character of the behavior of the material during movement in both types of conveyors will be different. According to the literature, many authors recommend determining the capacity of scraper conveyors whose scraper height is equal to the height of the trough by the general formula for transport devices for loose and lumpy materials, in which the volume of individual prisms of material moved by the scrapers is taken into account, i.e., by the generally known formula

\[ Q = 3{,}6 \frac{i}{a} v \cdot m \text{ t/hour}. \tag{1} \]

The accuracy of the results obtained by the above formula will depend on the correct determination of the volume of material moved before each scraper. On the basis of some experimental data it has been established that the change in the volume of material before the scrapers depends on the following factors: a) the kind and properties of the material being moved; b) the ratio of the scraper dimensions; c) the scraper pitch; d) the angle of inclination of the conveyor, and e) the speed of motion of the scrapers. All the above-listed factors, when establishing the volume of material moved by the scrapers, must in one way or another be taken into account with a sufficient degree of accuracy, since otherwise formula (1) may lose its practical meaning.

The experiments, unique of their kind, of the German professor Hanffstengel¹ with various materials provide some indications for establishing the law of variation of the volume of material moved before the scrapers, but these experiments, unfortunately, did not take into account all the factors indicated above. Therefore the results obtained by Prof. Hanffstengel remain

valid only for special cases. According to the experiments of Prof. Ganfshteṅgel, the coal in front of the scrapers accumulates in the form of a mass of trapezoidal cross-section (Fig. 1), the volume of which, with the designations adopted in the figure, may be calculated from the expression

\[ i=\frac{l+l_1}{2}\,b.h. \]

The upper base \(l_1\), as Prof. Spivakovsky indicates, must be taken, according to the experimental data of Prof. Ganfshteṅgel, for average values of \(h\), as equal to \(0.16\,h\). The lower base of the trapezoidal section for such materials as coal, coke, and coal dust is calculated from the expression

\[ l=l_1+h.\operatorname{ctg}\alpha. \]

for a constant value of the quantity \(\alpha\) for the given material.

Thus, as we see, the first question that arises is whether the quantity \(l_1\) really depends only on the height of the scraper, and whether it will not also change its value depending on the speed of the scrapers, the properties of the material being conveyed, and the angle of inclination of the conveyor. There are no direct indications on this question in Prof. Ganfshteṅgel’s work. As for the expression \(h.\operatorname{ctg}\alpha\), it will not be a constant quantity, since the angle \(\alpha\) is a function of many variables, such as: the properties of the material being conveyed, the condition of the grates, the dimensions of the scrapers, etc. Therefore the volume of material conveyed by a scraper, calculated by the formula indicated above, can be regarded only as a first approximation.

Fig. 1

Prof. P. S. Kozmin, in his book Machines of Continuous Transport (Part 2, 1935), analyzing the results of Prof. Ganfshteṅgel’s experiments, comes to the conclusion that, with an increase in the height of the layer of material, \(h\), both the angle \(\alpha\) and the ratio \(l_1/h\) will change, quite apart from the influence of the speed of motion of the scrapers, which we pointed out above. The Link-Belt Engineering Co. firm, for scraper conveyors with a trapezoidal section², on the basis of experiments carried out, gives results that do not agree with the experiments of Prof. Ganfshteṅgel, who, citing these materials in his book, recommends using them with great caution because it is unknown to what angles they refer. This remark of Prof. Ganfshteṅgel is undoubtedly justified, since the properties of the material cannot be neglected.

Thus, as we see, there are far from enough experimental data making it possible to reveal a definite regularity in the change of the volume of the prism of material conveyed in front of each scraper, with allowance for all the factors affecting this. Therefore Prof. P. S. Kozmin’s remark is quite fair: until the necessary experimental data have been obtained, it is best to calculate the capacity of scraper conveyors by the formula for conveying devices

with a continuous stream, introducing the corresponding trough filling coefficient.

Next the question arises: how should the value of the trough filling coefficient be chosen correctly?

If one proceeds from the experimental data of Prof. Ganfstengel, then, when comparing productivity formulas expressed in terms of the displacement of material by individual flights and by a distributed layer along the trough, the filling coefficient is obtained as approximately about 0.5. Meanwhile, as is known from our practice in operating flight conveyors, and also from data of American firms, the value of the trough filling coefficient when transporting coal is recommended to be taken greater than was indicated above. In view of the fact that the trough filling coefficient \(\psi = 0.5\) is a special case of the ratio of the height of the flights to the pitch, i.e. \(a_o = 3h\), Prof. Spivakovsky\(^{3}\), in the productivity formula for flight conveyors expressed through the uniformly distributed flow of coal along the trough, proposes introducing, to the coefficient indicated above, a correction that takes into account the change in the flight pitch, representing the ratio

\[ \frac{a_o}{a}. \]

Then the general productivity formula takes the following form:

\[ Q = 36 \cdot b h v \gamma \frac{a_o}{a}\ \text{t/hour}. \tag{2} \]

In establishing the correction coefficient, Prof. A. O. Spivakovsky proceeds from the fact that in practice the distance between flights is not much less than three times the height of the flights, and therefore the volume of material in front of the flights decreases only slightly owing to the cutting off of the acute angle of the trapezoid (Fig. 1). Unfortunately, this is not quite so; it is enough to look at the ratios of the height of the flights to the adopted pitch in standard flight conveyors of Shakhtstroy to be convinced of the opposite. In fact, for standard conveyors this ratio ranges from \(+460\) mm to \(-360\) mm, i.e. the distance between flights may be 460 mm greater than three times the height of the flights and 360 mm less. The firm Link Belt Engineering Co for flight conveyors with a trapezoidal section likewise gives the distance between flights with a considerable deviation from three times the height, i.e. from \(-159\) mm to \(+304\) mm.

Thus, as can be seen from the examples given, in practice the distance between flights in relation to three times the height of the flights varies within considerable limits, and therefore the change in the volume of material in front of the flights will not be so insignificant as Prof. Spivakovsky imagines. Moreover, one cannot agree that a simple dependence of the correction coefficient on the general trough filling coefficient, taking into account only the change in the flight pitch, can compensate for inaccuracies in the formula for determining the productivity of flight conveyors expressed in terms of the displacement of material by individual prisms. It seems to us that the change in the volume of material in front of the flights will by no means follow a simple dependence, since the cross-sectional area of the material moved by the flights, as already indicated above, depends on many factors that were not taken into account in the experiments carried out by Prof. Ganfstengel.

If one compares the results obtained by Prof. Spivakovsky’s formula (formula 2) with the experimental data of the firm Link-Belt Engineering Co

\(^{3}\) A. O. Spivakovsky. Conveyor Installations, Part 1, 1935.

for scraper conveyors with a trapezoidal section, with scraper height from 102 mm to 254 mm and width 254–610 mm, for a pitch of 406, 457, and 610 mm, large discrepancies are obtained, reaching in individual cases up to 50% and more. Thus, for example, at \(h=102\) mm, \(b=305\) mm, \(a=610\) mm and a scraper travel speed of \(0.51\) m/sec, the firm gives an hourly capacity of 26 t/hr, whereas by Prof. Spivakovsky’s formula only 11.5 t/hr is obtained.

According to Shakhtstroi data, for standard conveyors the deviations are still more striking and reach up to 70%. As is known, for standard conveyors Shakhtstroi gives different capacities only as a function of the dimensions of the scrapers, while the change in pitch is not taken into account. It is very characteristic that with a scraper pitch equal to \(3h\) (according to Shakhtstroi data), the capacity is obtained as 40–45% greater than by Prof. Spivakovsky’s formula.

Analyzing Prof. Spivakovsky’s formula according to the data for Shakhtstroi standard scraper conveyors, we observe the following regularity.

1. With an increase in scraper dimensions at the minimum distances between scrapers, the discrepancy in the results decreases, and in some cases Spivakovsky’s formula gives a capacity 10% even greater than Shakhtstroi’s tabular data.

2. With a decrease in scraper dimensions and an increase in pitch to the limits adopted by Shakhtstroi, Spivakovsky’s formula gives a capacity, relative to the tabular data, underestimated by 43–70%.

3. With a decrease in the distance between scrapers within the limits adopted by Shakhtstroi for standard conveyors, according to Spivakovsky’s formula the capacity increases by 166–242%.

In the capacity formula for a scraper conveyor, composed on the assumption of a uniform distribution of coal along the trough, the expression

\[ \psi=\frac{a_0}{a} \]

is, in essence, a general filling coefficient.

It is therefore of some interest to check it against catalog data of certain foreign firms. Below we give a table in which, for comparison—

Table 1

comparison, values are given for the total coefficient of trough filling, both as calculated by the above-mentioned formula of Prof. Spivakovsky and as recommended by foreign firms.

As can be seen from the data presented in this table, the value of the total coefficient of trough filling, calculated by Prof. Spivakovsky’s formula, in almost all cases turns out to be smaller than those recommended by the firms.

Thus, on the basis of the analysis carried out, and guided by the considerations of Prof. Spivakovsky that he used as the basis in compiling his formula, we arrive at the following preliminary conclusion.

a) We consider erroneous the assertion that the adopted distance between scrapers is practically never much less than or greater than three times the height of the scrapers.

b) Proceeding only from the conditions of conveyor capacity, we see that there is no need to establish different values of the scraper pitch for the same scraper sizes, which is not confirmed by practice.

c) According to the formula proposed by Prof. Spivakovsky, the capacity of typical scraper conveyors falls very sharply at the lower limits of the scraper pitch; therefore there is no point in retaining the above-mentioned dimensions, which requires experimental verification.

d) The trough filling coefficient \(\psi = 0.5\), calculated by Prof. Spivakovsky from a comparison of capacity formulas for a scraper pitch equal to three times their height, contains serious errors, or, at best, its value is valid only for the particular ratios under which Prof. Hanfshtengel experimented.

e) Proceeding from the conditions of capacity and, at the same time, of reasonable expenditure of power in overcoming the resistances of idle motion, it appears to us that the optimal distances between scrapers will be within limits up to \(3h\).

A. A. Lukashev, in his book Transport on the Surface of Mines, 1933, proposes introducing into the capacity formula for scraper conveyors, expressed through the movement of material by individual prisms (formula 3), a correction coefficient \(\psi\), taking into account the filling of the trough with material in front of the scrapers,

\[ Q = 3{,}6 \psi \frac{i}{a} \cdot v \gamma \, m^{3}/\text{hour}. \tag{3} \]

Lukashev determines the value of the correction coefficient \(\psi\) from the empirical dependence \(\psi = \rho(1.25 - \eta n)\), where \(\rho\) is a practical coefficient, taken within the limits from 1.75 to 2.25; \(\eta\) is the ratio of the scraper height to its width, and \(n\) is the number of scrapers per 1 linear meter of conveyor. Consequently, as we see, the very fact of introducing a correction coefficient into the above-mentioned formula casts doubt on the value of the true volume \((i)\) of material moved by the scrapers, determined by the method of Prof. Hanfshtengel. If Prof. A. O. Spivakovsky introduces a correction to the filling coefficient, partly consistent with the experimental data of Prof. Hanfshtengel, then Lukashev follows the path of selecting coefficients that make it possible, in a definite arithmetical dependence on certain parameters, to establish the correction coefficient directly. According to the instructions contained in A. A. Lukashev’s book, the value of the correction coefficient, for

on the basis of experimental data, should be taken within the limits from 0.6 to 0.95, i.e., less than unity. It would seem that the empirical formula proposed by Lukashev should also give results consistent with the experimental data to which he refers; meanwhile, when checked against data from foreign firms and standard Shakhtstroi conveyors, in almost all cases the value of the correction coefficient proves to be greater than unity.

Below we give a table of the results of calculating the value of the correction coefficient \(\psi\) by the formula of A. A. Lukashev, for \(\rho = 2\) (Table 2).

Table 2

Analyzing the formula of A. A. Lukashev, we consider it necessary to point out first of all the circumstance that the correction coefficient \(\psi\), in the sense in which it is presented by Lukashev, must always have a value less than unity, and, consequently, the capacity of the conveyor calculated by formula 3 will be less than by formula 1. If, according to Prof. Spivakovskii’s formula (formula 2), the capacity of the conveyor falls only in the case when the distance between the scrapers is greater than three times the height of the scrapers \((a > 3h)\), then according to Lukashev, regardless of this, in both cases the capacity decreases. Thus, the capacity of scraper conveyors calculated by formula 1, as is known, already gives understated results; but when a correction coefficient less than unity is introduced into it, as proposed by A. A. Lukashev, it becomes simply unsuitable for practical use.

The results of the calculations we have carried out show that the equation for calculating the correction coefficient proposed by A. A. Luka-

... by the sheave, contrary to his indications, in most cases gives a value greater than unity. Without going into an assessment of the correctness of the absolute values of the coefficient (Table 2), it is necessary only to point out that this correction coefficient in the formula for the productivity of scraper conveyors, expressed through the displacement of the material by individual prisms in front of the scrapers, as practice shows, must indeed be greater than unity.

In the equation for the correction coefficient $\psi$, as indicated above, there appears the empirical coefficient $\rho$, whose value varies within certain limits. Although its numerical value is given by A. A. Lukashev, unfortunately the book contains no indications or references as to what its nature is and on the basis of what experiments it was obtained. As for the other parameters—the ratio of scraper dimensions, the number of scrapers per 1 running meter, and the constant coefficient 1.25—we believe that these are still far from sufficient for establishing the law governing the change in the volume of the prisms of material in front of the scrapers.

Take, for example, the velocity of motion of the material, which undoubtedly exerts a substantial influence on the change in the volume and shape of the material moved in front of the scrapers. This requires no special proof, since it is quite clear that the frictional forces inside the bulk material, under the action of external forces of different magnitudes, will change their value. The same must also be said with respect to the properties of the material being moved and other parameters, as Prof. P. S. Kozmin quite rightly points out.

Thus, summarizing what has been said above, we believe that the values of the coefficient can be determined only by practical means, and that only on the basis of detailed experimental investigations can the regularity in the change of the volume of material moved by scrapers be established.

The productivity of scraper conveyors installed at some angle to the horizontal is theoretically calculated on the assumption that the volume of material moved by the scrapers changes owing to a change in the overall slope angle of the material on the conveyor relative to the horizontal line (Fig. 2). It is assumed in this connection that the upper base of the trapezoidal cross-section of the material remains the same as in horizontally installed conveyors, while the lower base changes its value in proportion to the installation angle of the conveyor—$\beta$. In accordance with these considerations, the volume of material moved in front of the scrapers is recommended to be calculated by the expression given below:

\[ i=\left[l_1+\frac{h \operatorname{ctg}(\alpha \pm \beta)}{2}\right]bh . \tag{4} \]

The values of $i$ calculated from this expression, as Prof. Spivakovsky points out, turn out to be somewhat smaller than the experimental data of foreign firms. However, if it is taken into account that the plane of the material slope, together with the bottom of the inclined trough, creates support for a certain additional quantity of material (Fig. 2), then owing to this the slope angle may be reduced by the amount $\delta$. With $\delta=7—8^\circ$, the volume of material calculated by the above expression agrees with the experimental data (A. O. Spivakovsky, Conveyor Installations, Part 1, p. 439).

Thus, as we see, this theory is also based on the results of experimental data of Prof. Ganfstengel. Therefore the absolute value of the results obtained in the change of the volume of material being moved ...

by scrapers, in inclined conveyor installations, may be of interest only for relative comparison, since detailed experimental studies on the basis of which it would be possible to

Fig. 2

confirm the correctness of the results obtained are far from sufficient.

Shakhtstroi, for standard conveyors, gives no difference in their capacity for installations up to \(22^\circ\), whereas some foreign firms (Bartlett and Snow, Chain-Belt) recommend, at an angle of \(10^\circ\), reducing the capacity by 15–20%. Below we give Table 3, in which the capacity of inclined conveyors is given as a percentage relative to horizontal installations, as obtained by certain foreign firms on the basis of their own experiments, and also as calculated theoretically by the formula of Prof. A. O. Spivakovsky.

Thus, as we see, the most detailed data are given by the firm Link-Belt Engineering Co. The discrepancy in their results is within 10%. This circumstance may evidently be attributed to the inaccuracy of the measurements, since it is difficult to imagine that the dimensions of the scrapers would have any influence in this case on changes in the volume of material moved by the scrapers.

When calculated theoretically, the results obtained are approximately consistent with the data of the foreign firms only upon introducing an additional angle \(\delta = 7^\circ\), without which the capacity is greatly underestimated relative to the experimental data. We consider it necessary to note that some doubt is raised by the value of the additional angle \(\delta\) as a constant quantity for all conveyor installation angles \(\beta\). It seems to us that the additional angle \(\delta\) should be a function of the angle \(\beta\); otherwise, at small conveyor installation angles, up to \(7\text{–}8^\circ\), the capacity would come out greater than in horizontal installations, which ...

Table 3

should not be. In addition, it must be noted that the formula for the change in the volume of material for inclined conveyor installations is theoretically correct only up to certain limits of the angle \(\beta\). Indeed, when the conveyor is installed on an incline with \(\beta = \alpha\), the capacity increases to infinity, which cannot be the case, since in this case the coal at an angle \(\beta = 21—22^\circ\) must move by gravity, and this can occur only if the magnitude of this angle is greater than the angle of friction of the bulk material on the troughs. At a value \(\beta > \alpha\), the formula loses its physical meaning.

Prof. Spivakovskii, analyzing his formula, comes to the conclusion that when the angle of inclination of the conveyor troughs is equal to the angle of repose, the material will move by gravity. We believe that the material may spill down the trough even when the conveyor setting angle is less than the angle of repose, but here it will not be spilling, but rather the sliding of an as-if solidified prism of bulk material along the trough, since in individual cases the angle of friction of the material on the trough may be less than the angle of internal friction of the bulk material.

Thus, the theoretical basis considered for calculating the capacity of scraper conveyors installed at some angle to the horizontal requires appropriate correction. For

* Calculated with allowance for the angle \(\delta\), as the ratio of the volumes of material in front of the scrapers—of the inclined installation to the horizontal one—for \(\alpha = 21^\circ\) and \(\delta = 7^\circ\).

for this, it is first of all necessary to establish experimentally the dependence of the angle $\delta$ as a function of $\beta$, as well as the relation between the angle of friction of the loose material on the grates and the angle of natural slope (taking into account the kind and properties of the material being conveyed and the condition of the conveyor grates).

Turning to the consideration of scraper conveyors with scrapers submerged in the mass of the mineral, it is first of all necessary to note the complete absence in our literature of any materials of a research character. The available instructional literature relating to this question is devoted mainly to descriptions of designs, all possible advantages and disadvantages, and, to a lesser extent, to the theory of calculation. Meanwhile, the theory for calculating these types of conveyors, even if only in the part concerning the determination of capacity, cannot be likened to belt conveyors, since in this case the average velocity of motion of the material will not be equal to the velocity of motion of the chain.

As was already indicated above, in scraper conveyors used in underground conditions the height of the scrapers is many times smaller than the height of the trough walls. Thus, for example, the Jeffrey sectional scraper conveyor, type 47-A, has a scraper height of 42 mm, and a trough-wall height of 220 mm, i.e., 5 times greater; for the ST.5 conveyor, approximately 3 times greater. Therefore there is reason to suppose that the velocity of motion of the upper layers of material will lag behind the velocity of motion of the chain. In addition, when material of various sizes, such as run-of-mine coal, is transported by the conveyor scrapers, the large lumps, together with translational motion, will also be given rotary motion. Thus, into the formula for the capacity of scraper conveyors of the indicated type it is necessary to introduce a correction coefficient that takes into account the lag of the material behind the velocity of motion of the chain. In an investigation of the operation of swing and scraper conveyors under the production conditions of the Leninugol Trust of the Kuzbass Combine, carried out by engineer Kropachev, the fact of coal lagging behind the velocity of motion of the chain was established by means of simple observations. Although these experiments were not of a special character, the fact itself deserves attention and requires serious, specially designed experimental studies.

In the cross section of the grates of the type of conveyors under consideration, the motion of the material occurs with mutual displacement of particles; this is especially pronounced when material of different sizes is being conveyed. This occurs because particles of the material experience different frictional forces at different moments. The particles of the loose material, while moving on the conveyor, may be under the action of normal frictional forces, rolling-friction forces, the so-called abrasive frictional forces, and undoubtedly the masses of the individual particles of the material being conveyed will also exert their influence here. All these frictional forces, in mutual combination, will create within the mass of loose material a certain frictional force causing the material in the upper layers to lag behind the velocity of motion of the chain with the scrapers.

The change in the magnitude of the frictional forces within the loose material will be determined not only by the properties of the material being transported; external factors will also have an effect here, such as the velocity of motion of the scrapers, the installation angle, and the type of conveyor. In view of the fact that the velocities of motion of the chain in these types of conveyors are taken to be small, this factor by itself (apart from combination with others) will not have any particular influence, since it is difficult to suppose that a change of velocity within small limits, for one and the same material and with all other conditions equal, would affect the coefficient of internal friction of the material being moved.

Changing the installation angle of the conveyor, as well as the pitch and dimensions of the flights, will in this case cause a considerable lag of the coal, which must be taken into account by means of some correction coefficient applied to the velocity of motion of the flights.

Portable flight conveyors, unlike stationary ones, operate with a continuous flow of material, and if the feed is constant, the material is arranged in an evenly distributed layer along the trough. Therefore, the capacity must be calculated according to the general formula for transport devices with a continuous stream of material, with the introduction into it of two correction coefficients, taking into account, on the one hand, the filling of the trough and, on the other, the lag of the material behind the velocity of motion of the flights under the various operating conditions of the conveyor.

For this type of conveyor, the trough-filling coefficient is not a matter of principle that would require theoretical and experimental investigation, since in this case its value is a function of the method by which the material is fed onto the conveyor. For purposes of establishing the capacity it should be taken equal to unity, while for determining the power it is necessary to bear in mind the possible filling of the grates up to the top. However, the trough-filling coefficient is such a factor that cannot be neglected when conducting experiments intended to establish the average velocity of motion of the material on the conveyor. As for the coefficient taking into account the lag of the material behind the velocity of motion of the flights, detailed experimental investigations are necessary here; only on their basis can a definite regularity be established in the change of the velocity of motion of the material in the section of the grate as a function of all the factors affecting the magnitude of the lag.

Thus, summarizing all that has been set forth above, we establish that flight conveyors, as transport machines, do not have a sufficiently substantiated theory of calculation in the matter of determining capacity, confirmed by experiments from detailed experimental investigations. Therefore, the task of our further work is the theoretical and experimental investigation of the operation of these types of conveyors.

1. Forschungsarbeiten, herausgegeben von VDI, No. 115, 44. ↩

2. Prof. Ganfshteṅgel. Conveying of bulk loads, 1927. ↩