CC BY
0УДК 7215.07.5
CALCULATING OF DETERMINING FORCE AND SPEED OF ROTARY SHAFTS
FOR GRINDING
Nematov Erkinjon Khamroyevich Tashkent State Technical University named after Islam Karimov, nav27ruz91 @mail. ru
Kalandarov Navruzbek Olimbayevich Tashkent State Technical University named after Islam Karimov, nav27ruz91 @mail. ru
Annotation. This article presents the types of devices used in the process of grinding raw materials and their operation schemes. The main elements of the shaft structure of the rotary shaft crusher are the dimensions and structure of the rifle, as well as the geometrical parameters. The main calculation formulas for the amounts of forces affecting the raw material during the grinding process, the rotational speeds of the shafts, the distance between the shafts and the levels of grinding are presented. The formula for calculating the forces affecting the grinding process was calculated.
Annotatsiya. Mazkur maqolada xomashyolarni maydalash jarayonida ishlatiladigan qurilmalarning turlari va ishlash sxemalari keltirilgan. Rotatsion valli maydalagichning val konstruksiyasining asosiy elementlari rifel o'lchamlari va tuzilishi hamda geometrik parametrlari berilgan. Maydalash jarayonida xomashyoga ta'sir qiluvchi kuchlarning miqdorlari, vallarning aylanish tezliklari, vallar orasidagi masofa hamda maydalash darajalari bo'yicha asosiy hisoblash formulalari keltirilgan. Maydalash jarayonida ta'sir qiluvchi kuchlarni hisoblash formulasi aniqlandi.
Аннотация. В данной статье представлены виды устройств, используемых в процессе измельчения сырья, и схемы их работы. Основными элементами конструкции вала роторной шахтной дробилки являются размеры и конструкция винтовки, а также геометрические параметры. Представлены основные формулы расчета величин сил, воздействующих на сырье в процессе измельчения, скоростей вращения валов, расстояния между валами и степеней измельчения. Рассчитана формула расчета сил, влияющих на процесс шлифования.
Keywords: flattening of grains, roller surfaces, mill, forces, corrugation, roundness of the roller, cutting angle, circumferential speed, particle capture by rollers, grain capture conditions, inter-roll zone, working gap width.
Kalit so'zlar: bug'doyni maydalash, val yuzasi, tegirmon, kuchlar, rifel, slindrik val, kesish burchagi, aylanma tezlik, donni vallarda qisish, bug'doyni qisish shartlari, vallar orasidagi masofa, ishchi yuza kengligi.
Ключевые слова: плющения зерен, поверхности вальцов, мельница, сила, рифел, округлости вальца, уголом резания, окружная скорость, захват частицы вальцами, условия захвата зерна, межвалковая зона, ширина рабочей щели.
Introduction.
In the flour-grinding industry machines and apparatus for grinding bulk food products are used, for instance, - for grinding grains of cereals into flour, in the feed industry - for grinding grain and hay into flour and various additives (salt, chalk) into powder, as well as for crushing cake ; in the production of food concentrates - for crushing grains of oats and corn, grinding dry vegetables, fruits and various additives (sugar, salt, etc.) into powders; in the confectionery industry - for grinding fat-containing half-ready products (cocoa nibs, kernels of nuts and
almonds, etc.), granulated sugar, chocolate production waste; in meat processing - for crushing ice, greaves; in fat extracting - for crushing oilseeds, as well as for crushing cake; in fermentation - for crushing barley, green malt, dry brewing malt and grinding potatoes; in fish -to obtain fishmeal; in salt production - for crushing salt.
The following types of machines are mainly used in food production (fig. 1):
1. Roller mills. These machines briefly act on the original product, which before destruction is subjected to compression and shear deformations at relatively low circumferential speeds (0.5^1.4 m/s) of cylindrical rolls (roller diameter 200^500 mm) rotating towards each other with different speeds. linear speed.
2. Disc mills. These machines have a relatively long effect on the original product also by compression and shear, the circumferential speed of the disc is 10^68 m/s relative to another fixed disc. These machines include, for example, millstones (mills).
3. Hammer crushers. In these machines, the material is destroyed due to hammer blows at their circumferential speed of 50^100 m/s and due to the interaction and friction of the crushed product relative to the inner surface of the machine casing.
I
a) b) c)
Fig. 1-Schemes of working bodies of machines for grinding food products
a) roller mills; b) disk mills; c) hammer mills
Roller mills are distinguished by the following features:
- according to the number of pairs of rollers - two-roller, three-roller, four-roller, five-roller, eight-roller;
- by size - different length and diameter of the rollers;
- on the side surface of the rollers - on smooth and corrugated.
Roller mills with two rollers and different side surfaces are most widely used.
The operation of such mills is based on the principle of cutting, splitting and crushing.
Both rollers are driven to each other in opposite directions and at different speeds. Along with cutting with corrugations, there is also a partial abrasion of the product.
By adjusting the width of the working gap, as well as by selecting the ratio of the circumferential speeds of the rollers and the use of different shapes of the flute, it is possible to obtain different degrees of grinding.
Methods.
When choosing a research method, the principles of operation of rotary grinders were studied, and the amount of power, which determines the available parameters in the production of shaft riffle sizes and rotation speeds, is theoretical when calculating the grinding power.
Materials.
These mills are suitable because they allow you to get food in the form of grits with a low quantitative content of mealy pulverized part.
Their disadvantages include quick sticking of the riffles when crushing wet (more than 18%), oily feed and heating the product.
Consider a cross section of a corrugated roller and its elements (Fig. 2).
Drum grooves are characterized by shape, slope, number per unit length of drum roundness and cutting angle.
In cross section, the corrugations have two unequal edges: a narrow edge of the tip (Fig. 2) and a wide edge of the back. Angle y, enclosed between these faces is called the taper angle and the standard is 90 The radius drawn through the top of the riffle divides the standard taper angle into two angles: a = 200 - acute angle and fi = 700 - back angle. Obtuse angle , enclosed between the edge of the corrugation and the tangent to the cylinder, drawn through the top of the corrugation, is conventionally called the cutting angle. Relying on the selected operating mode of the rollers, the cutting angle will be not similar. (90+ a or 90+ fi).
At the top of the riffle there is a platform with a width S = 0.15mm, necessary to maintain the exact shape of the cylinder after cutting the roller. The step t of the riffle along the circumference and their height h are connected by a certain ratio. To identify it, we shall depict the riffle elements. (fig.3)
S=0.I5MM
Edge point .—-—Edge о
Edge of the back
Fig. 2-Parameters of the corrugated roller
X
Fig. 3-Riffle elements
From the left right triangle we have:
And from the right: x = h • tga then
h =
(t — h ■ tga) ctga
or
At the end, we have:
t = h(ctga + tga) = -
sina ■ cosa
h = — ■ t ■ sin 2a 2
Number of nr riffle on 1 cm circumference n = _. On rollers for coarse grinding
r t
take n = 4 -10, and on the grinding rollers n =12 ^15.
To eliminate the uneven load and vibration of the rollers, the corrugations are applied at a certain angle 5 inclination to the generating of the cylinder; when they face with each other, they form an angle % friction. In this 25 = %< (p -angle of friction of the grain on the edge of the corrugation).
For the kinetics of grinding, the mutual emplacement of the grooves of the paired rollers is important. Of the four possible variants at mills in our country, it is customary to install rolls with corrugations in the "acute to acute" or "back to back" position. In the first case (Fig. 4 a), the most intense effect of the flute on the grain (coarse grinding) takes place, in the second case, the most "soft" one (Fig. 4 b).
The rollers of grain mills have the same diameters, but rotate at different speeds (highspeed and slow-rotating rollers) and subject the grain to complex deformation - compression and shear.
Peripheral speed ratio vf fast rotating drum to speed vx slowly rotating is called the speed differential and is denoted by k.
Fig. 4-Options for the relative position of the grooves of the rollers
For cutting rollers take k = 1.25 ^2.5; for smooth k = 1.25^1.5 ; for grain crushers k = 1. Relative speed v , characterizing the intensity of the impact of the working bodies on the material, is determined by the following expression:
h
vo = v/ - v. = v.(k -1)
and the average speed v movement of grain in the grinding zone will be equal to:
v/ + v*
vg = ~-
2
It is also important to know the condition of grain capture by rollers. Let we have two smooth rollers with a radius R (Fig.5). At the moment of entry into the slot, the particle perceives pressure at the point n P to roller.
Between the particle (conditionally shown in the form of a ball) and the roller there is a friction force F = f ■ P.
Fig. 5-Scheme for determining the conditions for capturing grain by rollers.
Force decomposition P and F into horizontal and vertical components (in the figure it is shown the decomposition of the forces acting from only one roller).
Horizontal forces cancel each other out. The vertical component of the friction force is directed downward. It draws a particle of the product into the working space. The vertical component of the force P is directed upward and prevents the particle from entering the working space.
The condition for capturing a particle by rollers with a sufficient degree of accuracy in general will look like this:
Where a - grip angle, from here
2 • f • P • cosa > 2 • P • sina
f = tgV> tga ,
a < Pyw .
Therefore, to ensure that the product is gripped by the surfaces of the rollers, it is necessary that the angle a was less than the angle of friction cp between product and roller.
The diameter of the rollers is determined by the particle size of the product and the angle of friction (Fig. 6).
From the scheme (Fig. 6) it can be seen that the center-to-center distance OO1 is equal:
OO = D + b = 2 • R • cosa + B
where B - exit particle size, b - largeness of the distance between rollers, D -diameter of the rollers.
The minimum diameter of the roller is distinguished by the formula:
o B - b
1 - cos«
But, since the limit value of the angle a equal to the angle of friction <p, then finally the result is:
d
mm л
1 - cos<
In existing designs of mills, the diameter D rollers are accepted within 250 ^ 350 mm.
The intensity of product processing is characterized by the length l processing paths (arcs) (Fig. 6). The more l, the more intense the crushing or grinding of the product.
It is distinguished l:
l = R ■a
^ e-%n , . a , a . . , , „
From expression —0 = l ■ si^— = l ■— (since the angle formed by a tangent and a
chord is measured by half the arc enclosed between them), it is found a
B - b
a =-
l
It is substituted in the expression to determine l values a
l = R-Bzb l
From that l = jR(B - b) .
Thus, the length of the processing path is greater, the larger the radius and the difference (B - b).
The theoretical productivity of one pair of rollers is determined taking into account the fact that the amount of grain equal to the second productivity passes through the gap per unit time. In this case, the productivity Q (kg/h) of the mill is determined by the formula
Q = b^Lvg ■p■y
where L -the length of the rollers (m), p - material density (kg/m3), y - coefficient taking into account the degree of material filling of the grinding zone (when grinding grain y = 0.1 -г- 0.2).
The performance will mainly depend on the size b, which means, on the degree of
grinding:
> with fine grinding b = 0.1^ 0.2mm;
> with medium grinding b = 0.2 ^ 0.3mm;
> with coarse grinding b = 0.1^ 0.2mm.
Fundamentals of calculation of roller working bodies for peeling products. If metal rollers in grain mills are replaced with rubber ones, then a machine for peeling cereal crops (rice, millet) can be obtained. Inside the body of such a machine there are two rubber rollers with a diameter of 200 mm rotating towards each other with different circumferential speed, a drive and other components. The gap between the rollers is regulated by a special mechanism. For the rubber surface of the rollers, rubber of a certain formulation is used, thanks to which the crushing of seeds during peeling is sharply reduced.
When entering the machine, the raw material from the feeder enters the gap between the rollers. Since the nature of the force effect on the seeds is based on a combination of compression and shear forces, and due to the different ratio of roller speeds, the seeds in the working area experience deformations and stresses that lead to the destruction of the outer covers, i.e. peeling of grain (seeds) occurs.
Depending on the type of processed product, the gap between the rollers can be adjusted from 0.35 to 1.0 mm. The peripheral speed of the rapidly rotating roller is vr = 12.5 ^15 m/s,
slow rotating v = 8.7 ^10.5.
For the effective course of the process of peeling raw materials in a sheller with rubber rollers, it is very important to establish the optimal forces for compressing seeds in the interroller working area, the length of the path for the particle to pass through the working area, which should be minimal with a high technological effect of peeling.
It is shown (Fig. 7) the length of the path (L) inter-roller working area, where the working bodies act on the grain. If it is denoted the angle between the center line and the radius (grip angle) drawn through the point of contact of the grain with the surface of the rollers at the point where the grain enters the working area of the roller, through a , and at the exit point of the rollers (entry angle) - through ax, roller diameter D mm, distance between rolls (gap) 5 mm
OC
and seed size (grains) d mm, then from the considered right triangle AOC, cosa =-.
OA
From the scheme it is seen that OC = D + 5 , and OA = Ob+BA = D+d. In this
2
conclusion, the grain is assumed to be spherical, therefore
OC D + 5
cosa =-=-
OA D + b
A similar situation exists for ax.
The length of the working section of compression L grains in the working inter-roll zone will be equal to:
( D + 5^ a = arccoS -
\ D + d )
From where
D ( D + = 2-arccoS-I
com 360 \ D + d J
As can be seen from the formula L does not depend on the circumferential speed of the rollers and their differential.
Since the rolls (rollers) rotate at different peripheral speeds, one of them (fast) is ahead of the other (slow) by some certain amount in the working area L . It is determined the value of this advance, which we will call the shift length Zmov (Fig.8).
Fig. 8-Scheme for determining the amount of advance (shifting) Zmov of the rollers
With steady motion, the fast roller ue for a certain period of time, the path from the moment of capture (point F ) until the exit of the grain from the working area (point C ), is equal to L . In the same section, a slowly rotating roll travels a path equal to F1 q1 (for the same period of time). From the design scheme (Fig. 8) it can be seen that the rapidly rotating roll is ahead of the slowly rotating roll by the length of the arc q Q or L :
- L_
L„
From where
Lmov
L (vf - v )
com\f s /
Studies have shown that applying a differential is higher k = 3 impractical, since it can
only slightly affect the increase in the peeling coefficient kp .
As it is known, one of the main requirements for peeling the grain of cereal crops is the maximum preservation of the integrity of the kernel. Therefore, the forces in the working area of
v
v
s
v
s
the machine should not cause the destruction of the grain itself with an effective separation of the film (shells).
After contact of the grain with the rubber surface of the rolls, it moves in the working area, as shown in Fig. 8, along the axis y — y. The center of the roll O is connected with grain center O and consider a right triangle OOB, in which % - the current value of the angle, which
determines the position of the grain at the moment. Line segment
OB D + —
OO3 =
cos x 2cosx
where O1B =
D + 8 2
The value of the absolute deformation of the rubber surface is characterized by the segment CF, which is defined in the following way.
A preliminary segment is found FO3 = Ofl3 — OF, where Ofi3 = cosx but OXF = — ,
i.e. the radius of the rubber roll
FO3 =
D + 8 D
whence the segment
where CO = ~ 2
then,
cos x 2
CF = CO3 - FO3
™ d D+8 D
CF =---+ — = Ah0
2 2cosx 2
Corner x can vary from zero to % = a ■
Fig. 9-Scheme for determining the compression force of the grain in
inter-roll zone
This conclusion is also true for cases when the grain is below the line of roll centers.
When the grain is on the center line of the windrows (% = 0), = d — — , i.e. the
greatest absolute deformation of the rubber surface of the rolls is observed.
In the diagram (Fig. 9) of the interaction of a roll and a grain when it passes through the working area. In this scheme, the power P represents the action of the second roll on the grain. The amount of absolute deformation (Ah0) the rubber surface of the roll is determined by
the following dependence on the applied force Ah0 =
9n2k,2 (R + 2R^ v R1 ' r2 j
32
P2
.2
where ^ = 1 -—— characterizes the mechanical features of rubber, /u = 0.5 - Poisson's
n E
ratio, E-modulus of elasticity of rubber (equal to 7.5^8.0 MPa), R = d - grain radius (m),
R2 = D - rubber roll cylinder radius (m),
Results and discussion.
Knowing that M0, determine the magnitude of the force P , compressing grain
P = 4^ki 3
Ahl ' R ' R
R
2 + R2
Number of grains (n ), situated in the working inter-roll zone, is determined by the size of its thickness c (for an elliptical grain) or diameter d (for a spherical grain), as well as the length of the roll (L):
Lr
n = — d
In the process of shell removal, in addition to compressive forces, shear forces are of great importance. The fast swath is ahead of the slow swath by L . At the same time, as a result of pressing the grain into the rubber surface, the high-speed roll not only destroys the shell of the compressed grain, but also separates it, that is, it produces peeling.
The resultant force acts on the grain in the inter-roll zone
P = P - P
P0 P/ Ps
where P and P - force, with which the fast and slow rolls act on the grain, respectively. The value of P0 is defined on the basis of quantity of motion:
m(v1 - v2) = P0 • t
vf + vs
where m -weight of grain (kg), v1 = —-— - grain speed at the point when it leaves the
working area (m/s), v2 =yj2gH - grain speed at the moment of contact with the rolls (m/s), H -
2L
grain fall height (m), t = —- the time of passage of the grain of the working area (s).
v1 + v2
Knowing that m and t determine the shear force required to remove the outer covers from the caryopsis
Po =
m(vi + V2)
t
Conclusions.
Set energy costs ( E )for the peeling process. Since the fast roll is ahead of the slow one by
3
Lmov = Lcom ^ k —1 j, then on this segment in the inter-roll working zone, energy is expended on
the removal and destruction of the caryopsis shells. Then the work spent on the peeling process will be equal to:
Ec = Po- Lmov , JOU1 or taking into account the work of compression ( Ec)
Ee = P0 •Lmov + Ecom ,
The peeling coefficient of grain in a sheller with rubber rolls for a single pass is k^ = 0.88 ^ 0.92 with a minimum amount of crushed kernel 0,3^0,5 %.
REFERENCES
1. Ivanov, V.V. Improving the Operating Modes of a Disk Grinder of Feed Grains: Extended Abstract of a Dissertation of the Candidate of Technical Sciences; FSBEI HPE "Don State University", 2014; p. 132
2. Ahmad, F.; Weimin, D.; Qishou, D.; Rehim, A.; Jabran, K. Comparative Performance of Various Disc-Type Furrow Openers in No-Till Paddy Field Conditions. Sustainability 2017, 9, 1143.
3. Academicia Globe: Inderscience Research. Volume 3, Issue 3, Mar, 2022. P. 177-181. MILL SYSTEM ROTARY ROLLER CYLINDERS Nematov Erkinjon Khamroevich, Kalandarov Navruzbek Olimbaevich, Sadillaeva Saodat Juraevna.
4. Eurasian Scientific Herald. Volume 6| March, 2022. P.70-72. Requirements for the Use of Rotary Shafts Used on Roller Looms. Nematov Erkinjon Khamroevich, Kalandarov Navruzbek Olimbaevich, Sadillaeva Saodat Juraevna
5. Dynamic stress-strain states in viscoelastic half-spaces from the effects of cylindrical inclusion loads. Cite as: AIP Conference Proceedings 2467, 060024 (2022); https://doi.org/10.106375.0092396 Published Online: 22 June 2022. Ismoil Safarov, Muhsin Teshaev, Sharif Axmedov, Navruzbek Qalandarov and Abdurakhim Marasulov
6. Seismic Vibrations of Spherical Bodies in a Viscoelastic Deformable Medium. Part 2. AIP Conference Proceedings 2432, 030125 (2022); https://doi.org/10.106375.0091187 Published Online: 16 June 2022. A.O. Umarov, U.Sh. Jurayev, T.O. Zhuraev, F.F. Khamidov and N. Kalandarov
