Eng. S. BALAKSHIN.

STUDY

OF PRODUCT

PARTICLE SIZE

Tomsk
1929

Eng. S. Balakshin.

Study of Product Particle Size.

1. Introduction.

When, in 1923, the author set out to conduct a study of the operation of flour-milling millstones, which even at the present time are still very widely used for obtaining flour from grain (in the USSR more is ground on millstones than on roller mills), he was faced with the question of an objective determination of the particle size, first of flour, and then of bulk products in general.

It became clear that the concept of the particle size of bulk products, and especially of flour, strange as it may be, had until now remained rather individual, vague, and indefinite. The same flour, in different regions and at different times, is called now coarse, now medium, and now fine. In general, standardized scientific methods for determining the particle size of bulk products (especially flour) were lacking, and there were no instruments for its practical determination and recording.

Having worked for more than four years on the problem of developing methods and procedures for determining particle size, the author, after many experiments and a number of improvements, succeeded in designing for this purpose a special instrument (a granometer), which mechanically records particle size in the form of a curve, and in establishing certain standards.

The brief excerpt from the author’s works presented below is intended to acquaint the reader with the principal experiments carried out by the author and the results he achieved.

The author realizes that the question of determining the particle size of granular bodies is a very large one, and that his work is only a small part of what remains to be done in this respect; nevertheless, he believes that the methods he has developed and the instruments he has designed may serve as a basic foundation for further scientific work on this question.

The author cannot fail to note here that he was able to carry out the painstaking work of conducting numerous experiments to establish the basic principles and conclusions only thanks to the assistance of the student millers V. Bubnov and Nechaev, to whom the author here expresses his most sincere gratitude.

2. Particle size of products, its significance, definition, the uncertainty of its classification, etc.

The particle size of products manufactured in a whole series of industries, such as, for example, flour milling, cement, starch, etc., is of very great importance.

To determine coarseness, up to the present a method has usually been used in which the coarseness of a product is characterized depending on which sieve it passed through (was obtained as throughs) and from which sieve as oversize. In this case the numbers of fine metal sieves are usually determined by the number of threads per English inch, while for silk sieves used in flour milling a special numbering system is employed.

But such a determination of coarseness is undoubtedly very imprecise and gives no clear visual conception of it at all.

First of all, with one and the same number of threads per inch, owing to the different thickness of the wires, the size of the openings may be very different, varying*) sometimes by a factor of 5–6. Thus this determination of coarseness is very vague and imprecise. Moreover, even if these limiting largest openings of the sieves through which the product passed, and the smallest ones from which it was obtained as oversize, were once and for all standardized, the product itself, in its structure and in the dimensions of its particles, may be very heterogeneous; and by this method it is utterly impossible to compare bulk products more precisely and clearly with respect to coarseness.

Taking the above considerations into account, the author, after four years’ work on this question, constructed a special apparatus for determining coarseness, which he called a granometer, or, for flour, a farinogranometer.

But before passing to a description of the design and operation of this apparatus, it is necessary to dwell on the methods of determining coarseness with the aid of a set of sieves in general, on the use of coarseness curves, and on the concept of the coefficient of coarseness first introduced by the author.

Methods for determining coarseness with a set of sieves and the graphical representation of it by coarseness curves. Coefficient of coarseness, etc.

If we take a set of sieves arranged one above another and selected so that their openings decrease, beginning with the upper one and going to the lower one (according to a definite regularity), and sift some product on them, then in the general case on all the sieves there will remain some quantity of product which has passed through the preceding sieves but has not passed through the given sieve.

Drawing a series of ordinates corresponding to the number of sieves taken for the experiment and laying off on them segments corresponding to the quantity of product remaining unsifted on each sieve, we obtain one or another curve, which is called a coarseness curve.

In doing this, the “weight method” is usually used, i.e., the ordinate is laid off proportionally to the quantity of product remaining unsifted, by weight. But if these residues are reduced to the same density, then the “volume method” may also be used, laying off ordinates proportionally to the volumes of the product remaining unsifted on the sieves.

It is obvious that the coarser the product, the more of it will remain on the coarse sieves, and the curve will have the character of falling (if ordinates corresponding to the coarse

) See the author’s special work: S. Balakshin.—Investigation of Mill Sieves*.

sieves); in Fig. No. 1, curve \(ab\). If, however, the product is fine, then the curve will rise (\(cd\)).

However, although the size-distribution curve does already give an idea of the structure of the product and, from it, one can to some extent judge its coarseness as well, nevertheless, because these curves are usually quite tortuous, it is still rather difficult to compare from them the coarseness of different products.

Fig. 1. Size-distribution curves of different products.

Fig. 2. Cumulative size-distribution curves for different products.

In view of this, one usually also constructs the so-called integral or cumulative (summary-collective) size-distribution curve.

The cumulative size-distribution curve is obtained if one plots ordinates obtained by successive summation of the ordinates of the ordinary size-distribution curve. Thus, each ordinate of the cumulative size-distribution curve shows how much of the product would have remained unsifted on a given sieve if there had been no coarser sieves before it.

Thus, in Fig. 2 two cumulative size-distribution curves are shown, corresponding to the coarse and fine product respectively to the size-distribution curves shown in Fig. No. 1. Ordinate 2 of the cumulative curve of the product in Fig. No. 2 corresponds to ordinate \(ef\) of the size-distribution curve in Fig. No. 1; ordinate 3—to the sum of ordinates 1 and 2 of the size-distribution curve (Fig. 1), i.e.

\[ op \;(\text{in Fig. No. 2}) = cf + gh \;(\text{in Fig. No. 1}) \quad \text{and so on.} \]

The cumulative size-distribution curve gives a quite definite representation both of the coarseness of the product and of its structure, and cumulative size-distribution curves constructed for products of different coarseness make it possible easily to compare their coarseness with one another.

It is clear that the ordinates of the size-distribution curve and of the cumulative curve may be plotted proportionally to the weight or volume of the product remaining unsifted on the sieves.

It should be noted that, when the volumetric method is used, although for the experiment the same quantity of product by weight is taken and the product remaining unsifted on the separate sieves may be reduced to an almost uniform density, nevertheless the total height of the cumulative curves usually turns out to be different, and in order that,

in order to make them comparable, one has to reduce them to a definite height (see below the instructions for processing experiments with the farinogrameter).

By reducing, in one way or another, the cumulative size curves of different products to one height, the fineness of the product will then be characterized by the areas bounded by these curves.

It was already indicated above that the coarser the product, the larger will be the initial ordinates of the cumulative curve reduced to a definite height; that is, the larger will be the relative area occupied.

The author proposes to call the ratio of the area occupied by the cumulative curve \(aocb\) (Fig. 2) to the entire area of the rectangle \(abcd\) the coefficient of fineness of the product, or simply the fineness of the product.

Since the cumulative curves for homogeneous products have the same character, this makes it possible to compare them with one another very conveniently.

It is clear that this coefficient will always be less than unity, and for one and the same product will be constant only for a definite constant set of sieves. For the set of sieves adopted by the author (see below), the coefficient of fineness, for example, was obtained as:

For granulated sugar . . . . . \(\eta = 0.925\)
For wheat flour . . . . . \(\eta = 0.460\)
For potato starch . . . \(\eta = 0.110\)
For cement . . . . . . . \(\eta = 0.070\)

The determination of fineness used up to the present time—by sifting a definite quantity of product through one or another standard set of sieves, weighing the residues remaining on each sieve, and then constructing size curves—required a great deal of time and was very inconvenient. This is what prompted the author to undertake the development of an apparatus of his own design, the so-called granometer.

3. A new apparatus for determining fineness.

S. Balakshin’s granometer.

Construction of the granometer.

The granometer constructed by the author consists of a sifter (Fig. 4—sieves A, A) with a set of sieves (Fig. 3, Fig. B) arranged one above another, the openings of the sieves decreasing from top to bottom according to a known regularity.

The size of the openings of the sieves is chosen depending on the products being investigated.

Each sieve has, on the side, an outlet opening M, closed by a special cover H.

Having weighed on the scales (Fig. 3, Fig. A) a definite quantity of the product to be tested (usually 9–20 grams), which has previously been thoroughly mixed, and having closed the side outlets M from the sieves, the weighed quantity is poured onto the upper sieve, and this entire set of sieves is placed in a special device for sifting, set in motion mechanically (or sifted by hand), in which the sifting is carried on until the transfer of the product from one sieve to another ceases (usually 15 minutes).

When the sifting is finished, then, by opening the slide M closing the side outlets from the individual sieves, they attach to the sifter a part,

For the article by Eng. S. Balakshin, “Study of Product Particle Size.”

Fig. 3. S. Balakshin’s granometer for determining product particle size.

of the apparatus, the so-called curvimeter (see Fig. 5), consisting of a plate P, into which a series of partitions C) is cut, covered in front by glass, C, the compartments of these partitions P corresponding exactly to the side spans of the sieves*).

Fig. 4. Set of sieves (section) of the Granometer.

Having then turned the set of sieves with the curvimeter attached to it through 90°, that is, bringing them into a vertical position, by tapping on the curvimeter one causes the product that has remained unscreened on each sieve to pour into the corresponding compartment of the curvimeter.

It is clear that, according to the coarseness of the product under investigation, different amounts of it remain unscreened on the individual sieves; and these residues, poured into the compartments of the curvimeter (visible through its front glass), will visually characterize the coarseness of the product, at once giving a rough curve of its coarseness.

To bring this curve to a normal form and to fix it mechanically, the instrument has the following device. After the product left unscreened on the individual sieves has been poured, as described above, into the corresponding compartments of the curvimeter, a special column B, provided in its upper part with a small sharp pin G, is inserted into each of these compartments P (Fig. 5). It is clear that these columns, resting on the product poured into the compartments of the curvimeter, will likewise be arranged according to the coarseness curve (Fig. 5).

Since the screened product pours into the compartments of the curvimeter with uneven density, in order to obtain the reduced constant curve, as experiments have shown, it must be brought to the same density—compacted.

Fig. 5. Curvimeter for the Granograph.

*) To avoid misunderstanding, we should note that in the drawing the number of partitions of the curvimeter has, for simplicity, been reduced to 6, whereas in the figure there are 15.

**) Instead of this, a series of glass tubes corresponding to the compartments of the sieves may be used.

For this purpose the following part of the instrument is used, the so-called “compactor.”

The compactor (see Fig. 6) consists of a board with a row of partitions, between which pins can move, each resting on a spring D (the pins are arranged at the same distances as the posts in the curvimeter).

Fig. 6. Granograph compactor.

To compact the products in the curvimeter, it is applied to the compactor so that each of its posts comes opposite the corresponding pin with a spring. Having then fixed the compactor immovably, the curvimeter is pressed against it several times (3–5), so that each post of it, resting on the corresponding pin, compresses the spring and thereby compacts the product lying beneath it.

After such compaction, the posts of the curvimeter (and the pins on them) are arranged along the size curve. This curve can then be recorded by pressing paper against the sharp pins of the curvimeter posts, on which they prick out its points; for this purpose the following part of the apparatus is used—the granograph (described below).

The size curve, at the first glance at it, gives a clear idea of the size of the product, showing not only its relative coarseness, but also quite clearly characterizing the structure of the product: it indicates of what elements, by size, it consists (see Fig. 5). Here the arrangement of the lower and upper ends of the pins along the size curve is visible.

For recording the size curve, the author has constructed a special apparatus, the so-called “granograph” (see Fig. 7).

The granograph consists of two parts connected to one another by hinges; i.e., one part can turn relative to the other like the covers of a book, one of them having a device for clamping the paper on which the size curves are imprinted, while the other has a row of partitions for placing the posts of the curvimeter.

After inserting the paper and applying the curvimeter to the second half of the granograph so that its posts are located in the corresponding compartment of the partitions, by turning the cover of the granograph the paper is pressed down, and then the pins Г of the curvimeter posts prick out on it the points of the size curve (see Fig. 7—left).

Fig. 8. Sliders on the posts of the curvimeter.

To obtain the cumulative size curve, special sliders B are arranged on the posts of the curvimeter (see Fig. 8), furnished with springs that hold them on the posts in any position. The sliders have plates Ц (folding back on a hinge) of such a length that they can rest on the pin of the neighboring post when the posts are inserted in the curvimeter.

Fig. 7. Granograph with a reducer for S. Balakshin’s granometer.

When, as indicated above, the products have been compacted in the curvimeter and its rods have been arranged according to the size curve, the aforementioned sliders are moved on them so that the slider of the far-left rod of the curvimeter is pressed by the upper part of the plate against the pin of this rod, while the remaining sliders are thereby positioned opposite it, perpendicular to the rods, along a straight line. In this case, the distance from the slider to the pin of each rod will correspond to the height of the ordinate of the size curve.

When the rods of the curvimeter have been inserted into the granograph and the size curve has been pierced, its left half together with the paper is folded back, and all the rods are moved out of the curvimeter into the granometer (removing the curvimeter) so that the previously set sliders (see above) successively touch the pin of the adjacent rod (the first rod is at this point always held in a definite position by partition п (see Fig. 7)); then the rods will be arranged according to the cumulative size curve of the product being tested (see Fig. 7 on the right and Fig. 3—D).

The height of the cumulative curve obtained in this way, owing to the fact that even with the same charge it is difficult to obtain the same density of the screened fractions of the product in the compartments of the curvimeter, turns out to be different, and this, as we explained above, does not make it possible to compare visually the size of the products being tested.

Taking this into account, it was necessary also to equip the granograph with a special “reducer.”

The reducer (see Fig. 7 and Fig. 3, fig. D) consists of a row of rods similar to those present in the curvimeter, only with pins E at the bottom.

These rods can move between the partitions along the granograph.

Each of the rods is provided at its end with a crosspiece З fastened perpendicular to it (see Fig. 7), with a pin projection И, which can slide in the slot of the corresponding lever Ж. All these levers are mounted on a common axis К (to the right of the apparatus), which in turn can move in a direction perpendicular to the rods of the granograph.

After the rods of the curvimeter have been arranged in the granograph according to the cumulative curve, they are fixed in this position by a special latch, and the movable rods of the reducer are brought up tightly to them (the axis К of its levers being at this time in the extreme right-hand position).

When the rods of the reducer have assumed this position, the levers are fixed on the axis by tightening the wing nut (Fig. 8) of the clamping screw (on the right).

After this the rods of the curvimeter are removed; the granograph is placed in a vertical position and, by gradually shifting to the left the axis of the levers К of the reducer, with the aid of the pins of the reducer rods sliding in their slots, the latter are moved downward until the rightmost rod of it (Fig. 7), with its lower sharp pin, reaches the fixed, once-and-for-all determined, overall height of the reduced cumulative size curve. The lower pins of the rods of the granometer will then be arranged along this curve, and all that remains is to make an imprint of it by piercing the paper placed in the left half of the granograph, which is pressed against the right half for the time being; in Fig. 7 and in Fig. 3, fig. D, the cumulative curves are shown as they are obtained imprinted on the paper.

4. Sieve Set of the Granometer

It is clear that, depending on the size of the particles of the products whose coarseness is to be determined, the sets of sieves must be selected accordingly; moreover, it is evident that one and the same set may be used for investigating various products that are more or less homogeneous in particle size (for example: sand, flour, gunpowder, etc.).

We shall not dwell here in detail on the selection of sieves; we shall indicate only the general principles for their selection.

Experience has shown that 15 sieves are usually quite sufficient. Of these, the coarsest should be chosen on the basis that the largest particles of the product under investigation pass through its openings of size \(b_1\); the finest, with openings \(b_n\), should, as far as possible, separate out the smallest particles.

The ratio of the opening size \(b_n\) of the rarer sieve to the opening size of the neighboring, more frequent sieve \(b_{n+1}\)—(i.e. \(b_n > b_{n+1}\))—is usually called the modulus—\(M\)—of the sieve set.

This ratio \(M\) may remain either constant or vary.

Our experiments in the study of flour and certain other bulk solids have shown that it is very rational to take \(M = \mathrm{Const}\), constant.

In this case, as is easily derived, the following relations are obtained:

\[ M=\frac{b_1}{b_2}=\frac{b_2}{b_3}=\frac{b_3}{b_4}\ \text{etc.}\ =\frac{b_{n-1}}{b_n}=\mathrm{Const} \]

whence

\[ b_1=b_2\cdot M;\quad b_2=b_3\cdot M, \]

or, substituting from the preceding equation, we have

\[ b_1=b_3 M^2 \]

and also

\[ b_1=b_4 M^3. \]

Or, for a set of 15 sieves, if the opening of the finest is \(b_{15}\), we obtain:

\[ b_n=b_{15}M^{(15-n)} \tag{1} \]

whence

\[ \lg b_n=\lg b_{15}+(15-n)\lg M \tag{2}, \]

i.e., for example, the opening of sieve No. 5 (counting as No. 1 the sieve with the largest openings) will be:

\[ b_5=b_{15}M^{(15-5)} \tag{3} \]

For the study of flour*) we adopted the following set of sieves (this set may also be successfully used for the study of other bulk products similar to flour, such as, for example, starch, salt, tooth powder, sand, gunpowder, etc.).

The set is based on the finest flour silk sieve No. 25 with opening \(b_{15}=29\) thousandths of a mm, and the coarsest metal sieve (12 threads per 1″) with an opening of 1620 thousandths of a mm.

From this, the value of the constant modulus \(M\) is determined from

\[ \lg b_1=\lg 1620=3{,}20952 \]

\[ \lg b_{15}=\lg 29=1{,}46240 \]

\[ \text{Difference } 1{,}74712 \]

whence

\[ \lg M=1{,}74712:14=0{,}124794 \]

and

\[ M=1{,}3627. \]

) See S. Balakshin. Study of the Coarseness of Flour by the Farinogranometer,*

The magnitude of the openings and the appropriate sieves are selected according to formula (1). Thus, for example, the opening of sieve No. 10 is determined from equation (2).

\[ \lg b_{10}=\lg b_{15}+(15-10)\lg M=1,46240+5\cdot 0,124794 \]
\[ \text{or } \lg b_{10}=2,08635 \text{ and } b_{10}=122 \text{ thousand mm,} \]

and the nearest suitable sieve will be sieve No. 12 with an opening
\(b=116\) thousand mm.

Table No. 1.

Sieve set of S. Balakshin’s pharyngranometer.

In the mining industry of North America, a set of sieves of the Tyler system is usually used, and in England a series of sieves of the Institute of Mining and Metallurgy.

1) The Tyler Standard Screen Scale series of sieves, manufactured by W. S. Tyler Co., Cleveland, Ohio, U.S.A., has a constant modulus

\[ m=\sqrt{2}=1,414 \]

or, since the sieves have square openings, the area of the opening of each subsequent sieve is \((\sqrt{2}\times\sqrt{2}=2)\) twice the area of the opening of the preceding sieve.

In all, the set has 18 sieves. As the basic opening, the opening of a sieve with 200 threads per \(1''\) is taken, \(b=0,029\) inch (0,074 mm).

From the table one can see the dimensions of the openings and the thickness of the wire of the other sieves.

Table No. 2.

Series of Tyler standard sieves.

2) Series of sieves of the Institute of Mining and Metallurgy in London
(Institute of Mining and Metallurgy), or, in abbreviated form, I. M. M.

Here the following is taken as the basis of the series:

1) the opening is square; 2) in each sieve the wire diameter is equal to the diameter of the opening; 3) the effective screening area of the sieve is 25% of its total area; 4) the product of the number of openings in each sieve by the diameter of the opening is a constant quantity, equal to 0,5.

If \(x\) is the number of openings per linear inch,

\(y\) is the diameter of the opening, then

\[ xy = 0,5,\quad \text{whence } y = \frac{0,5}{x} \]

For example, 100 threads in \(1''\), then \(y = 0,005'' = 0,127\), and 5) the modulus is not constant and varies from 1,258 to 1,33.

Table No. 3.

Series of standard sieves according to I.M.M.

A drawback of this system of sieves is that the wire is too thick and the clear opening of the sieves is too small.

In addition to the above-mentioned series, series with moduli \(3\sqrt[4]{3}\) or \(\sqrt{2}\) and others are also used, but already comparatively rarely.

Undoubtedly, depending on the type of product under investigation and on the requirements imposed on the investigation, one or another set of sieves may be used.

5. Study of the fineness of a product with a granometer.

When studying the fineness of various products with a granometer, certain features of its operation were revealed, which we present below.

Obtaining uniform fineness curves.

Obtaining uniform curves for one and the same product always required many months of intensive work by the author and the elimination of all factors affecting the shape of these curves.

In addition to the above-described device for compacting the sifted products in the compartments of the curvimeter, it was necessary to identify and eliminate the influence of: 1) clogging of the sieves, 2) the duration and method (with shaking, etc.) of sieving, 3) the moisture content of the product.

1) Clogging of the sieves.

In the experiments, the necessity of mechanical cleaning of the sieves soon became clear.

After testing the cleaning of sieves by placing on them a certain quantity of wheat grains (as is used in mill sieves), the method of cleaning sieves with small lead weights covered with rubber and fastened on chains was finally adopted as giving the best results.

2) Duration and method of sifting.

Analyzing the change in the curves depending on the method of sifting (by hand or mechanically, with shaking or without it) and on its duration, the experiments showed that, when the above-mentioned mechanical sieve cleaners are used, shaking of the apparatus during sifting is not required; the curves are always homogeneous if the duration of sifting, as the experiments showed, is not less than 15 minutes.

In Fig. No. 9 it is clearly seen how the cumulative size curves change depending on the duration of sifting.

In Fig. No. 9 the limiting curve obtained with 15-minute sifting is visible.

Experiments with sifting for a longer time, for example 20–25 minutes, showed that curves are obtained analogous to the 15-minute curve, that is, abrasion of the product in the apparatus is not observed.

3) Influence of the moisture content of the product on the size curve.

In this respect the author carried out experiments with flour. Experiments with the determination of somewhat moist and strongly dried flour gave curves differing very little from one another (see Fig. 10), but, of course, for more accurate experiments it is desirable to test products, as far as possible, dried in air to the moisture content normal for most bulk products, 10–14%.

Comparison of the volume curve obtained on the granometer with the weight curve.

As has already been indicated above, the most widespread method of size analysis up to the present consists in constructing size curves by the weight of the product remaining on each of the sieves of the sieve set used.

The granometer gives size curves corresponding to the volumes of these residues (volume curves).

It was, of course, very interesting to compare how far the volume curves given by the granometer differ from the accepted weight curves. For this purpose we carried out a series of experiments, which showed that, thanks to the use of the “compactor,” the difference obtained is so insignificant that for practical purposes it may be neglected and the volume curves obtained by the granometer may be regarded as “weight” curves.

In order to reveal the difference of the granometer’s volume curves, we carried out a series of experiments with a product of comparatively low specific gravity (flour) and with a product of high specific gravity (cement). The very carefully mixed product was first analyzed with the aid of ...

by plotting the curve with a granograph, and the second time—a sample of the same product—by sieving it in a granometer sieve set and weighing the residues on analytical balances.

The results obtained (see Fig. 11 and Fig. 12) show how insignificant the difference between the cumulative curves turned out to be.

The amount of product required for determining its particle size by granometer.

Experiments showed that, in order to obtain particle-size curves of various products on the granometer, it is necessary to take the corresponding quantity of them by weight. At the same time it became clear that such products as flour, potato starch, etc., require, for the dimensions of the apparatus used by the author, 10 grams; granulated sugar, 14 g; and cement—20 g.

Cumulative particle-size curves of various products obtained by granometer.

After hundreds of experiments carried out by the author, mainly with different grades of flour and, in part, with various bulk products, it proved possible to establish for them typical curves and particle-size coefficients.

In Fig. 13 these typical cumulative particle-size curves are presented, and in Table No. 4 the values of the particle-size coefficients obtained for various products are given. These curves not only give a visual representation of particle size, but also indicate of what individual particles, and of what size, the product consists, and how much of it, in %, passes up to a given sieve.

Thus, for example, from the cumulative curve for granulated sugar it is seen (from its intersection with the vertical lines corresponding to the sieve numbers and the corresponding horizontal lines in %) that:

and that beyond the 4th sieve the granulated sugar is not sifted.

From the curve for cement it is seen that up to the 10th sieve it all passes through and remains:

Table No. 4

Particle-size coefficient of various products, obtained by granometer.

5) Wheat flour of medium grinding . . . $\gamma_{15}=0.410$
6) Wheat flour of fine grinding . . . $\gamma_{16}=0.350$
7) Rye flour of fine grinding . . . $\gamma_{17}=0.352$
8) Potato starch . . . $\gamma_{18}=0.110$
9) Cement . . . $\gamma_{19}=0.070$
10) Tooth powder . . . $\gamma_{10}=0.066$
11) Rice powder . . . $\gamma_{11}=0.0526$

Experiments in determining the coarseness of molding sand.

The author carried out experiments in determining the coarseness of molding sand before casting and after casting. In this connection, its disintegration and the increase in the amount of fine particles became clearly evident. This undoubtedly creates a lower gas permeability of the sand and cavities during casting. The addition of fresh sand again makes the molding sand more gas-permeable. In any case, the granometer could render a great service here, indicating in a purely mechanical way the properties of the molding sand (Fig. 14).

6. Conclusion.

The author believes that, insofar as the scope of the present work has permitted, he has elucidated the question of investigating the coarseness of products, presented the methods used for recording it, and given a description of the construction and operation of the apparatus invented by him.

The author believes that from all the foregoing it has been quite definitely established:

The advantages of the granometer for determining coarseness, as compared with the methods that have existed up to now, consist in the fact that the granometer makes it possible not only to obtain mechanically a visual coarseness curve, but also to record it graphically. The granometer also makes it possible to obtain recorded coarseness curves reduced to a definite constant height, which in turn makes it possible, by simply superimposing them, quickly and clearly to compare with one another the coarseness of different products.

The use, for granograms, of paper with a special grid printed on it makes it possible quickly to determine the amount of product, in percent, remaining on each sieve.

The author’s experiments with the granograph have shown that the volumetric curves obtained with its aid differ only very slightly (tenths of a percent) from the coarseness curves obtained by the weighing method, and that the apparatus possesses an accuracy entirely sufficient for practice; meanwhile, obtaining these curves here requires considerably less time.

Provided that a definite standard set of sieves is adopted for a definite kind of product, using the granometer it is possible to express the coarseness of the product in the form of a fraction.

The granograph is especially useful in the manufacture of products, for example: flour milling (farinogranometer), cement, gunpowder, tooth powder, face powder, starch, etc., making possible continuous mechanical analysis and control of coarseness. Continuous analysis and control of coarseness will undoubtedly make it possible to introduce corrections into production in timely fashion.

and to produce products of better quality, since fineness, in addition to its direct significance, also strongly influences the quality of products in general.

In conclusion, it may be noted that, after many years of work, the author has succeeded in developing an apparatus which, so far as he is aware, for the first time makes it possible mechanically to determine and record the fineness curve.

It is clear that practice will introduce further improvements and modifications to the granometer; nevertheless, even in its present form it is quite suitable for the practical determination of fineness and will undoubtedly find wide application in the laboratories of the flour-milling and powder industries, in the manufacture of tooth powder, face powder, potato starch, and other industries producing finely divided bulk products.

INSTRUCTIONS

for determining the particle size of products with the granulometer of
Eng. S. Balakshin.

A. Preparation for the experiment.

1) Before taking a sample, mix the product well and thoroughly (otherwise the particle-size curves obtained will not correspond to the average particle size of the product).

2) Weigh out the quantity of product given in the table.

Table of weighed portions for determining the particle size of a product.

3) Carefully inspect the sieves and shake them so that there is no residue on them.

4) Make sure that the slide closes tightly (not allowing passage of the product past the sieves).

5) To avoid possible errors in the exact determination of the particle size, at least two experiments are carried out for each product, and only if the curves have the same character (coincide) is the experiment considered correct. Otherwise the experiment is repeated until uniform curves are obtained.

6) To save time, while sieving is taking place, the curves of the preceding experiment are imprinted.

B. Carrying out the experiment.

7) After pouring in the weighed quantity of product, carry out the sieving on the mechanical sieve or by hand until they no longer ...

uniform granularity curves are obtained (which usually requires 15 minutes).

8) Having opened the slide of the sifter, take it in the right hand, with the openings upward in an inclined position; with the left hand press the curvimeter against it, making sure that the inlet openings of the sieves coincide with the corresponding compartments of the curvimeter. They are turned, bringing the curvimeter into the normal position, and by tapping on the sifter the products contained on the sieves are poured into the corresponding compartments of the curvimeter.

9) Having inserted the rods into the curvimeter, the sliders on them are carefully set approximately in one line (without in any way pressing on the product under the rod), after which the curvimeter is inserted, by the ends of the rods, into the compacting (spring) apparatus and, by 3–4 movements (to the indicated limit) back and forth, the product is compacted.

10) When the curvimeter rods have settled, without removing them from the compactor, a special clamp is put on them and, by tightening its screw, they are fixed in this position; after that, using a ruler, the sliders located on them are finally aligned along a straight line (in such a way that the top of the sliders coincides with the pin of the rod of that compartment in which there is absolutely no product).

11) Take paper for printing the curves and, having made on it the notations: experiment number, date, grade of flour, quantity of flour taken for the experiment by weight, sieving time, etc., insert it into the left part of the granograph with the reverse side (the inscription toward the cover of the granograph) and fasten it with the special side clamps. The pin of the reducer must at this point be in the uppermost position, and the axis of the levers in the extreme right-hand position.

12) The curvimeter is placed so that its rods fall into the corresponding places of the granograph, and the pin of the rod where there is no product must correspond to the zero line of the granularity curve.

13) Then, bending back the cover of the granograph, the rods with the clamp are pulled out of the curvimeter and, having released the clamp, they are moved carefully along the granograph (placed horizontally) so that, touching with their sliders successively each protruding pin of the next one, they are arranged along the cumulative curve, after which they are fastened in the granograph in this position with a special clamp.

14) Having released the clamp of the reducer, its rods are carefully advanced toward the clamped, dead-position rods of the curvimeter (at this point the movable axis around which the reducer levers rotate must be, as already stated above, moved to the extreme right-hand position).

Then, having tightened the screw on the axis of the reducer levers, the curvimeter rods are removed by pushing them into the curvimeter of the next apparatus.

15) Bringing the granograph into an inclined position (holding it with the left hand), while lightly shaking it with the right hand, the axis of the reducer levers is then moved to the left until the total height of the integral curve has been brought to a certain constant value (which is indicated by a mark on the apparatus)—after which the cumulative (integral) curve is printed by pressing the cover of the granograph with the inserted paper; this completes the experiment (the screw of the levers is released and all the rods of the reducer are brought to the upper position).

Since after compaction the product is pressed rather firmly in the compartments of the curvimeter, after each experiment these compartments must be cleaned with a small stick with a bristle brush; for this purpose the curvimeter is turned bottom upward.

C. Drawing cumulative curves in the absence of a reducer.

If there is no reducer with the granograph, then, according to the instructions, an imprint is made as of an ordinary particle-size curve. The drawing of the cumulative curve, reduced to a definite height, is carried out as follows:

1) Taking a paper strip (300 mm. × 15 mm.), one marks on it, along the side, with a pencil and by successively adding them one to another, the heights of the ordinates of the obtained particle-size curve;

2) The slip of paper with the marks of the ordinates is placed on millimeter paper, on which vertical lines have been drawn corresponding to the width of the columns of the curvimeter, and two horizontal lines at the distance of the adopted constant height of the reduced cumulative curve being drawn, obliquely in such a way that the extreme marks on it coincide with these limiting lines (see drawing), and at the intersections of the horizontal lines drawn from the marks on the slip of paper with the above-mentioned verticals, a series of points of the reduced cumulative curve is obtained.

Labels in the drawings: “fractions”; “paper strip”; “curve ordinates”; “reduced curve.”

D. Determination of the particle-size coefficient.

The particle-size coefficient is determined by planimetering the area \(acb\), bounded by the cumulative particle-size curve, and taking its ratio to the entire area of the rectangle \(abcd\).

Note 1. In the absence of a planimeter, the area may be determined by multiplying the sum of the heights of the individual trapezia \(ef\), \(gh\), etc., by the total sum of their bases \(ad\).

Note 2. If standard cumulative particle-size curves have been established for the given kind of product, it is possible to determine the particle size by superimposing the cumulative curve obtained in the experiment and drawn on transparent paper upon the standard one.

E. Engineer S. Balakshin’s farinogranometer.

Established color of the farinograms:

White:

Mill-run flour, siftings (wheat), and various products: cement, sugar, peas, molding sand, etc.

Pink:

Semolina flour and products of semolina mills (bran shorts, middlings, dust, etc.).

Yellow:

Rye flour, buckwheat flour, millet flour, etc.

Fig. 9. Change in cumulative fineness curve as a function of sieving duration.

Legend:

— — — moistened

——— unmoistened

Fig. 10. Influence of the moisture content of the product under study (mukul) on the cumulative size curve.

To Senior Engineer S. N. Belanishin.

Graph annotations: 100%; 90; 80; 70; 60; 50; 40; 30; 20; 10; 1–15; \(\eta = 32.5\%\); \(\eta = 31.6\%\).

— curve of the granulometer.
- - - weight curve.

Fig. 11. Comparison of the cumulative curve
(of flour) of the granulometer with the weight curve.

Inst. of Eng. S. A. Bogatkina

Legend:

— cumulative diameter curve

• • • cumulative weight curve

$\eta = 11.5\%$

$\eta = 10.9\%$

Fig. 12. Comparison of the cumulative diameter curve (cement) with the cumulative weight curve.

Fig. 13. Cumulative fineness curves obtained by a granometer for various products.

Legend:

• granulated sugar
• wheat flour, coarse
• wheat flour, medium
• wheat flour, fine
• tooth powder
• semolina
• rye flour, medium
• potato flour
• cement
• rice powder

For the article by Eng. S. A. Balabin.

Solid line — before casting
Dashed line — after casting

\(\eta = 44.9\%\)

\(\eta = 32.1\%\)

Fig. 14. Molding sand.