An analytical analysis of the action of rolls on the medium and its behaviour at adhesion bonds with its surface are carried out. The methods and means of carrying out researches on determination of surface roughness are offered, and the experimental setting for determining the adhesion strength is developed. To reveal the essence and understanding of the general research execution, a number of hypotheses for the determination of adhesion are given and a generalized approach to the definition of adhesion is given. The physical nature of the influence of the roughness of the roller surface on the injection of the dies depends on the shape and angle of roughness, the application of mechanical forces, the degree of its previous dispersion (recipe) and its physical and mechanical properties. The nature of the contact interaction of the dough with the rough surface of the roller working organ in the injection nozzle of the fumigation machine is established. Violation of these mutual relations leads to the production of poorquality products and a reduction in the efficiency of the machine. The contact area of the adhesive and the component forming work for overcoming the adhesion and deformation of the environment in determining the criteria influencing the process according to each particular period of the deformation stage are substantiated. The obtained data give an answer to a number of questions about the possibility of interaction of the surface of the working bodies from the environment. On the basis of their data, the actual change in the contact adhesion in the roller unit of the molding machine with a comparative analysis of existing ones with the newly designed design is considered. It is established that in order to provide a constant area of actual contact, which contributes to better adhesion, and, accordingly, the passage of a qualitative process of tightening, compression and pouring, the necessary condition is the consistency of the specified criteria. This means that the actual contact area
In food technologies, in the preparation of raw materials, the receipt of semifinished products, finished products, their storage is important interaction product with various moving and stationary surfaces. Such interaction, as a rule, leads to the adhesion of the product to the surface of the working bodies, working chambers of technological equipment, as well as structural and technological materials etc. In technology, the phenomenon of sticking is called adhesion (
The adhesion of the elasticplastic food masses is realized at the boundary between the two solids. Elasticplastic bodies have abnormal viscosity, which varies depending on the shear stress, mass properties and other factors. The reason for the variability of viscosity is the peculiarities of the structure of elasticplastic bodies. Adhesion as a superficial phenomenon arises at the boundary of the distribution of two phases of heterogeneous condensed bodies: the food masses – one phase, the contact surface  the second phase (
Where:
Δ
The thermodynamic theory assumes that adhesion is always a reverse and distanceindependent process. This theory does not determine the influence of surface charge and the concentration of electrolytes in the environment. It is believed that this theory is most accurate when working with uncharged surfaces or in the presence of a large number of electrolytes in the medium (
Where:
The theory assumes that adhesion can be reciprocal and depends on distance. It is most accurate when electrostatic forces prevail, but it is limited in the case of ignoring the effect of polar interactions (
Where:
As in the case with the DLVO theory, the XDLVO model believes that adhesion can be reciprocal and depends on distance.However, researchers (
In production conditions, adhesion is a much more complicated process and its attachment to the surface may occur in different ways. Therefore, in our view, the process of adhesion to the surface in practice often differs from the above described theories. This is due to the fact that the surfaces of solid materials are exposed to various contacting media, adsorb organic and inorganic substances, thus forming a conditioning layer, to which the attachment of the contact medium comes. In the future, under the action of the driving forces, the formed air conditioning layer changes the physical and chemical properties of the surface, and this affects the process of adhesion.
On the basis of the above, we consider that the adhesion of the medium to solid surfaces is a twophase process, which consists of the initial inverse (physical) and the next irreversible (molecular or cellular) phase. Adhesion to the solid surface can also be passive or active, which depends on the driving forces and transport of cell media on the basis of gravity, diffusion, or hydrodynamic forces. In addition, the process of adhesion is influenced by the physical and chemical properties of the medium, phase composition and surface roughness.
Therefore, when studying adhesion, we pay attention to the surface roughness and the parameters of the topography. Thus, proceeding from this, the process of adhesion is closely related to the amplitude surface parameter (roughness) and its spatial changes, which are characterized by morphological features of the surface (topography). Therefore, the theory of attachment of the medium to the surface should consider mainly the physical and chemical aspects of the surface of materials, and to a lesser extent, pay attention to the morphological and physiological features of the medium.
A dough with a moisture content of 33%, for high quality wheat flakes on pressed yeast, was prepared in an opaque manner with a fermentation time of 60 minutes at a temperature of 32 – 33 °С. The quality of the pressed yeast corresponds to the DSTU. Characteristics of wheat flour:
mass fraction of moisture,% – 14.5;
the content of raw gluten,% – 28;
resistance gluten compression on the device IDK1, per.pril. – 54;
gluten stretch, cm – 14.
The study of the dough injection process was carried out on the molding machine B54 of the confectionery factory (Ternopil). It is known from work (
The problem that complicates the determination of adhesion strength is the establishment of the actual contact area. After all, the size of the area of actual contact is influenced by many factors: normal pressure, the nature of the contacting bodies, as well as external factors  temperature, tenseness, duration of the previous load, speed of growth separation effort. These factors have a different effect on the change in the actual contact area.
An analysis of existing methods of studying the adhesion properties of food products showed that all the methods considered have their advantages and disadvantages. In this regard, an experimental device was developed for the study of adhesion properties of the dough consisting of vessel 1 (Figure
Scheme of the installation for the study of adhesion propertiesprotein dispersed phase:1 – a vessel; 2 – plate; 3 – stock; 4 – cargoes; 5 – measuring vessel; 6 – capacity; 7 – flexible hose; 8 – valve: 9 – cable: 10 – pulleys;11 – tripod; 12 – guiding; 13 – valve.
This installation worked as follows. A bowl of uniform dough was placed in the vessel 1, on top of which a wide plate 2 with a rigidly fixed rod 3 was installed. The previous loading was carried out by measuring loads 4 which were mounted on the plate 2. In a measuring vessel 5, a liquid from the container 6 was fed by means of a flexible hose 7 and thus created the separation effort that was transmitted to the plate 2 by means of a rope 9, which is one end attached to the rod 3, and the other to a measuring vessel 5. In the vessel 6, a constant level of liquid was maintained. The valve 8 made it possible to adjust the flow rate of the liquid to the measuring vessel 5 and thus adjust the rate of application of the force to the plate 2.
The change in the direction of the force by 180 ° was carried out with the help of pulleys 10 which are attached with the possibility of rotation around their axis on the tripod 11. As a previous load so and the separation effort acted at right angles to the plate 2.
This was provided by means of a guide 12 rigidly attached to the tripod 11. After the complete separation of the plate, the 2meter vessel 5 moved down and the valve 13 blocked the feeds in the liquid from the vessel 6. The separation effort was determined through the volume of the liquid that was in the measuring vessel 5 after the plate was detached.
The developed experimental setup allowed to regulate parameters that influence the adhesion interactions: the pressure of the previous loading (0 – 10 kPa), the separation effort (0 – 100 N), the rate of growth of the separation effort (0.2 – 2 N.s^{1}) and contact area
The quarrying of the experimental setup was to determine the force to be applied to rod 3 to ensure that the plate 2 is detached from the bottom of the vessel 1 provided there is no layer of the protein disperse phase in vessel 1.
The dough was applied uniformly to the bottom of a rigid vessel with cylindrical walls in such a way that the height of the layer was 1.2 x 10^{2} m. The area of the bottom of the vessel corresponded to the area of the plate and amounted to 7.8 x 10^{3} m^{2}.
Adhesion strength was determined by substituting data obtained during the experiment into the following formula:
Where:
F_{0} – separation effort in the absence of the test material in the vessel, Н.
Experimental researches were carried out using modern technical and standard methods (determination of surface roughness of steel), microscopic (light and electron microscopy of the process of formation and degradation of dough residues), spectrophotometric (optical density (density), mathematical and theoretical modelling, statistical). Used plates of stainless corrosionresistant nickelchrome austenitic steel in the size of 30 × 30 mm and 5 mm thick, with roughness of the surface R_{a} = 2.687 ±0.014 microns, R_{a} = 0.95 ±0.092 microns, shown in Figure.
The appearance of the stainless plates with different roughness: a native appearance of the plates; Bappearance of plates using microinterferometer MII4U4.2 (increase 1500 times).
The roughness of the surfaces of the stainlesssteel plates was determined using a profiler of the mark 296. The profile of the profile (Figure
Ploofilometer mark 296.
Electronic block 2 is executed in a desktop version. On the block front panel there are: a digital scoreboard for the measured R_{a} value; indicator of the working area; power button.
Considering the chaotic interaction of the dough during its displacement, where the change of interaction occurs between the broadwalled surface in the surface of the roll, the task planning experiment with the use of a full factor experiment of the second order is compiled. With two factors, the model of the experiment's function has the form:
According to the results of the experiment, we obtain a regression equation of the second order.
For experiments a plan with corresponding matrices of experiment planning with the number of experiments and boundaries of factor changes has been drawn up. The matrix is a list of options taken in this series of experiments. Independent variables were selected from the analysis of the nature of the effect on the change in the contact angle of the dough with the roll (forums number 5). As a parameter of optimization, the side a and the contact area of the broadened surface S are used respectively.
Х_{1} – side length
Х_{2} – the contact area of the broad surface
The main factors and their variation equation.
Characteristics of the plan  Variable factors  Variable factors  

side length a X_{1}, mm  the area of contact of the broader surface S X_{2},mm^{2}  


Basic level, X_{1} ^{(0)}  4.5  12  
The step of variation  1.5  3  
Lower level X_{1}^{()}(1)  3  9  
Upper level, X_{1} ^{(+)}(+1)  6  16 
The experiment plan and its results.
X_{1}(a, mm)  X_{2}(S, mm^{2})  У_{1}  У_{2} 
3  9  30  5.6 
4.5  9  35  7 
6  9  40  9 
3  12  45  9.8 
4.5  12  50  10 
6  12  64  10.8 
3  16  60  11 
4.5  16  68  11.6 
6  16  75  12.4 
Output parameters were:
У_{1} – change in the angle of interaction of the dough in height of its movement in the gap between the burrs. The displacement height of the test mass was recorded by the visual control method on a scale applied to the working roller;
У_{2} – change the angle of interaction of the dough on its contact area on the roll surface. The weight of the test was fixed by the method of visual inspection according to the photographs.
Using the obtained data of the regression coefficients, we make a regression equation for У_{1} and У_{2}
The analysis of the impact of the surface roughness of the roll confirms our opinion about the activity of adhesion at the injection stage and its dependence on the driving forces. From the graphical dependencies of Figure
General view of the profile mod. 296: drive – 1; block electronic – 2; rack – 3; sensor – 4; prism – 5; nut – 6.
Twodimensional section of the surface of the response as a function.
Surface response У_{1} = f (a, S).
Twodimensional section of the surface of the response as a function У _{2} = f (a,
Surface response У_{2} = f (a, S).
The optimum values are within the range of 50 – 600 at the values а = 4.5 – 5.5 mm, S = 11 – 13.5 mm^{2}. To change the angle of interaction of the dough along its contact plane У2 – the optimal values are at the corner 6 – 90 at values а = 5 – 6 mm, S = 10.5 – 12.5 mm^{2}.
Thus, the surface of the roll really creates conditions for the movement of the mass of the dough both on its surface and in the layers placed in the working chamber.
The formed adhesion on the surface of the roll consists of an inhomogeneous structure, resulting in a gas concentration gradient, in particular, reducing the amount of oxygen from the periphery to the depth of the environment, pH gradients and temperature. Such gradients of functioning provide contact between the two bodies, resulting in phenotypic resistance to abrupt change in environmental factors. Data from the scientific literature (
Studies on the effect of terrain and surface roughness on adhesion are not straightforward. Thus, according to (
Therefore, the conflicting data obtained by scientists regarding the effect of the surface roughness of stainless steel on the adhesion process are obviously related to the experiments under different conditions using different media, materials and methods of study. However, scientists have concluded that such elements of the surface topography as scratches, cracks, holes, protrusions, cracks play an important role in the adhesion process (
The results of the analytical review and the conducted research and statistical modelling made it possible to approach the development of methods for determining the surface and adhesion strength by mathematical modelling. Based on the above and the data processing, two mathematical modelling approaches are proposed that can be used to determine the adhesion strength and strength.
The results of the computational experiments allowed to investigate the effect of changing the angle of roughness of the roll surface on the interaction with the dough. From the studies it is clearly seen that the angle of roughness of the surface when interacting with the dough affects the adhesion properties. This approach allows us to determine rational design parameters that will contribute to the intensification of the dough injection process. Based on previous studies (
Interaction on the boundary of two phases, that is, the dough and the surface of the rolls, occurs from the first seconds of the molding machine. Therefore, the phenomenon of wetting the roller surface is related to the ratio of surface tensions (σ) of the adhesive and substrate. To achieve wetting on the surface of a welladhesive roller, it must be ensured that the surface tension of the substrate is greater than the surface tension of the adhesive. This will accelerate the process as a whole with a corresponding reduction in energy costs.
The studies carried out by the authors found that the strength of the adhesion of the dough at speeds of its separation from the roller working body of the molding machine was not determined more than 1 m.s^{1}. This is due, first of all, to the lack of simulation of the existing processes of formation, transport of the dough, which is mainly due to relatively small speeds of movement of the working bodies of the molding machine.
Power interaction of the medium with a roll occurs on its surfaces after the discrete injection of the mass of the test. Since the method of formation and the shape of the interaction profiles of the dough with the surface of the roll has a significant impact on the quality characteristics and the injection process, a number of comparative studies have been carried out to determine the rational roughness section of the roll.
To increase the force of adhesion between the viscous medium and the leading roller working body is possible by increasing the angle of coverage in accordance with the wellknown law of Euler:
Where:
S_{nab} and s_{nag} – respectively, tightening at the points of the runoff of the medium and its coincidence with a rough surface; α – the angle of coverage of the medium; f – coefficient of friction in a pair of materials.
The change in the angle of coverage of the medium is achieved due to the geometric orientation of the tightening and its injection. The problem of geometric synthesis of the system with an increase in the angle of coverage of the medium is solved on the basis of geometric bonds. Consider cases of power interaction, in which the line of vertices of roughness of a roll: parallel to the vector of injection velocity υ_{р} and the circular power R_{KB} (angle α = 0 °);
 not parallel to the velocity vector injection υr and circular power R_{KB} (angle α >0°).
The angle α depends on the lifting of roughness (Figure
 rectilinear horizontal in the direction from the axis of the roll to the inner surface of its body, due to centrifugal force Рvb;
 rotational horizontal in the direction of rotation of the roll due to the force of the knee
 straight vertical from the force of gravity on the dough layer of the dough that is above it
Due to these movements, the friction forces (adhesion) appear on the upper and lower front roughness of the roller surface. The three components of the dice movement described above correspond to the coordinate axes of the XYZ Cartesian coordinate system (Figure
Coordinate system, which considered power interaction: R_{VB}– centrifugal force; Rg– gravity force; R_{KB} – the force acting on the dough; P_{CT} is a compressive force; υ_{KB}– circular speed.
In the case of α = 0 °, the vertical coordinate plane XOY will be perpendicular to a plane passing through lines of roughness to its front surface. If α >0 °, then the angle between the abovementioned planes will be 90 °±α.
For comparison, two triangles were chosen (an equilateral triangle, an equilateral triangle with an angle at the vertex of 75, crosssections of roughness with an area of 1.2 mm^{2} each (Figure
Crosssections of roughness of different profiles with an area of 1.2 mm2 each: a) triangular, equilateral; b) triangular, equidistant.
For an equilateral triangle S, the length of a side is determined by the formula:
For an isosceles triangle, the area (S) will be determined by the formula:
Where:
a – side of the triangle; b – the basis of the triangle; α – is the angle between the side and the base (for an isosceles triangle with an angle at the apex 75 ° α = 52.5 °).
We will define the projection theorem
Substituting equation (
Where:
At the moving surface of the rotary rollers, a general work is performed which consists of elastic forces and changes in the contact of the rolling dough:А_{z} = А_{pr} + А_{k}.
Work of elastic forces:
Specific work 1 kg of dough (in J) can be calculated by the formula:
Where:
Where:
The work that is spent on changing the contact of a moving layer of the medium with the surface of the working chamber and rollers to overcome the adhesion and deformation of the medium А_{d}, will be:
Where:
F_{ad}, А_{d} – the efforts of adhesion and deformation;
h – the thickness of the medium on the surface of the roll when the separation of its layer on the subsequent process formation;
F_{vid} – the effort of separating a piece of medium from the surface of the roll.
Consider the components forming the work of the separation:
Deformation of the environment is determined:
Where:
Given the length of the contact area, we obtain the expression:
Work determined by the separation effort is spent on overcoming adhesion F_{ad} and deformation of the medium, when exiting through a rectangular molding surface between rotating rolls F_{def}
When studying the process of dough injection, one of its conditions was to change the gap between the rolls and the angular velocity of their rotation. Knowing the mass of the dough, the area of its contact with the surface of the mixing drum, with the help of the proposed method and computer symbolic mathematics, the strength of adhesion is determined.
Initial speeds are selected at three values of the crack (δ = 20 mm; δ = 25 mm; δ = 30 mm). Trajectory of the mass of the test for three cases in the car chamber:
Where:
K – factor of resistance.
The graph of the relationship between the coefficient of resistance K and the length of the dough movement at the output of the rollers (x) is shown in Figure
Charts of functions K (x) for an initial speed of 0.18 m.s1.
Experimentally determining the value of length (x), substituting it into an approximation equation, one can determine the coefficient of resistance K, which is the sum:
Where:
The air resistance coefficient is 0.11.
Consequently, considering the trajectory of the dough movement at m.s^{1} the most favourable (gap of 30 mm), we will substitute x = 0.3 into the approximation equation:
We find the coefficient of adhesion, which in our case will be:
In accordance with the chosen model of motion, we consider that due to adhesion, the strength of resistance appeared, directed against the movement of the mass of the test, equal to:
Since xaxis is chosen for calculations, then:
Substituting this equation in (в), we obtain:
Knowing the magnitude
Where:
Area of the nominal contact
Where:
R – roll radius;
b – roller width (Figure
Scheme of Roll.
considering relations (6) and (7) – (8), the separation effort will be in the form:
With these conditions, it is possible to determine the actual adhesion by the results of an adhesion test at insignificant discontinuation rates when Vv → 0.
These conditions are fully consistent with the processes taking place at the pumping stage. In addition, we know the actual contact area of the phases. Minimum actual contact area S_{nk}, formed by a contact of a dough with a roll surface, where α = 1. The maximum contact area is equal to the surface area of the roll (substrate) Sc (Figure
Scheme of the injection site: 1–working chamber, 2–dough, 3–rolls; Adetermination of the actual contact area of the roller working body and the dough: 2–adhesive (dough); 3 – substrate; 4 – surface of the substrate.
The nominal contact area is easily determined by the geometry of the adhesive or substrate. The area of the substrate, considering the relief surface (depends on the frequency and type of its processing, Figure
Where:
Z – the value of the height of the inequalities;
x, y – Cartesian coordinates;
m, n – Harmonic numbers.
The forces of adhesion in these cases are very small.
Expression (
Knowing the profile form, i.e. dz/dx and dz/dy, it is possible by means of integration to define Sc based on the topography of the surface. So, as the relief of the surface of the roller working body has grooves with the appropriate angle, the angle of the vertex between the groove protrusion γ = 60° at the top of the trapeze. In any arbitrarily selected slit, the relief has the form of an equilateral trapezoid (Figure 16). Then the length of the profile formed by the surface in 2 times will increase the length of the middle line of the profile. Accordingly, the surface area of the substrate will be 2 times greater than the nominal contact area.
In real conditions, the dough does not fully contact the surface of the roller working body. According to the work (
It can be assumed that the dough is in contact with a broadwalled surface at a contact pressure Pk. The width of the roll is characterized by the mean square value of the inequalities Rz. In this case, the cavity on the surface of the roll is filled with a dough. If the size of the macromolecules of the dough is much smaller than the slit of the surface, the law of the mechanics of continuous media propagates in the car's current and the twodimensional flow motion passes.
In this case, the forces of inertia are small, and the forces of hydrostatic pressure, viscous friction and capillary are mutually balanced. In such conditions, to obtain the basic criteria for the similarity of the current, it is sufficient to consider the onedimensional equation of the dough movement. In isothermal flow, when the values of the temperature of the dough and rolls are equal (this is evident from the experiments of (
Where:
p – pressure;
x, y – Cartesian coordinates;
On the free surface of the dough, the conditions of continuity of the normal and the absence of tangential stresses are fulfilled.
We denote the radius of curvature of the adhesive on the surface of the substrate (Figure
Filling the cavity on the substrate surface 1 with adhesive 2.
Where:
The rheological properties of the dough in the region of small deformation velocities, namely, when passing through the gap between rotating roller working bodies, is characterized by the ShvedovBingam equation (
Where:
j – gradient of strain rate.
The tensile stress in the xx direction is determined accordingly
Where:
А – the second invariant of the strain rate tensor, obtained for a onedimensional flow from the ratio:
Considering (
Replacing differentials with characteristic values
we get dimensionless components:
Criterion
Photo of adhesion of the dough to the surface of the roll of a new design: 1 – roll with screw grooves; 2 – car body.
To ensure a constant area of actual contact, which contributes to better adhesion and, accordingly, the passage of a qualitative process of tightening, compression and pouring, the necessary condition is the consistency of the criteria (18). This means that the actual contact area