Ensuring conditions for the squeezed fluid flowing from the skin along the conveyor of the technological machine

. The conditions for the free flow of the squeezed fluid from a wet semi-finished product along an inclined feed conveyor are studied in the article. The condition of fluid flow against the movement of the feed conveyor is determined. The average rate of fluid flow along the conveyor is determined depending on the thickness of the fluid layer. The dependence of the angle of fluid flow off on the lifting angle and inclination angle of the feed conveyor is determined analytically. The results obtained in the study contribute to the choice of geometric parameters of the transporting device, taking into account its rational lifting angle and inclination angle. Using a numerical method, a graph of the dependence of the angle of the fluid flow along the conveyor on its lifting angle and inclination angle was obtained.


Introduction
The design of technological machines for processing fibrous materials requires knowledge of the process itself and numerous factors that affect its quality performance.Below, we consider the well-known publications devoted to the study of fluid flow along planes.
In [1], the mechanical behaviour of three types of hard wood impregnated with various swelling fluids, compressed at a high strain rate, was studied.Variations in modulus of elasticity, proportional limit, and maximum stress were studied depending on the type of treatment.It was found that saturated samples could be as hard as dry ones.This result was explained by the behaviour of the fluid present in the large cavities of the wood, i.e. in the pores; the results differ from the ones observed at low strain rates.At high strain rates, fluid cannot flow out of the pores and must behave like a solid, so the structure of the material is strengthened.
The study in [2] is devoted to the research of the mechanical properties of leather.It is noted that at ambient temperature and humidity, most types of leather exhibit mainly elasticity, although delayed elasticity can impart plasticity to leather.The dependence of the stress relaxation time under constant linear strain showed that the stress decreases linearly with time.The stress-strain ratio for the leather specimens stretching was non-linear and fixed even at low strains.
In [3], composite materials made from natural rubber with industrial leather waste were studied.The microstructure, mechanical properties, and rheological properties of these composites were studied.The results showed that leather waste increased tensile strength and hardness with good reproducibility and uniform distribution of residues as fillers.The authors concluded that the investigated composite material could be used as raw material for the manufacture of shoes and other products.
One of the factors influencing the process of fluid squeezing from a semi-finished product is its feeding.The feeding is conducted by a belt conveyor; a significant drawback in the designs of squeezing machines is the draining of the squeezed fluid to the workplace of attendants.In this regard, the authors of [4][5][6][7][8][9][10][11][12][13] proposed devices and performed studies, the results of which make it possible to eliminate these drawbacks.
In [14], experiments were conducted, where a fibrous layer covering the primary cavity was observed during the invasion of a fluid of higher density into a less dense medium and a fluid of lower density into a heavier one.The thickness of the fibrous shell of the primary cavity increases with the growth of the drop rate.
The method for modeling the destruction of river dams was developed in [15].The authors considered two sets of Lagrangian material points that represent soil and pore water layers.
In [16], a method was obtained for modeling flows of a non-viscous fluid with a large deformation of the free surface.To simulate turbulent flows with a free surface, the particle displacement method was introduced into this method.This method was used to simulate extremely large deformation and free surface re-connection.
In [17], the fluid flow in industrial pumps was studied.The results of the study showed that with an increase in the concentration of solids in the pump, its casing was subjected to the greatest wear.
An experimental device was developed in [18] for testing a two-phase flow of solid and liquid phases in a centrifugal pump.The test results showed that the device allows measuring the flows of solid and liquid phases in a centrifugal pump with high reliability.
In [19], a sludge pump of a mining-and-processing plant was studied.The Euler method was used to analyze the slurry flow for various particle concentrations and low-volume flow rates.
The study in [20] describes the wear mechanisms related to various types of materials that affect them.Theoretical and empirical models were given to predict wear.
In reference [21], the properties of leather processed in water were investigated.The tanning process was carried out with natural tannin at different duration of the process.Leather samples were processed by traditional methods in liquids and treated.The results showed that the 2-hour and 4-hour tanning was insufficient in terms of the expected physical properties, however, the 6-hour and 8-hour tanning resulted in leather of good quality.
The authors of article [22] investigated the process of tanning leather without chromium.An environmental impact analysis showed that the developed process resulted in a significant reduction (compared to chrome tanning) in total solids content and improved biodegradability of organic compounds present in wastewater.
The flow along a flat plate was experimentally studied in [23] using different fluids.The results showed that the decrease in surface tension has a stabilizing effect on the flow, damping the capillary waves that would otherwise have to occur.As the slope increases, the fluid film thickness decreases and as the fluid flow rate increases, it increases too.
In [24], the characteristics of regeneration of a liquid desiccant on multi-row vertical cylindrical surfaces were experimentally studied.The method of mechanical surface modification was researched to improve the performance level of the cylinder surface.It was determined that the regeneration rate of the surface of a conventional cylinder exceeds the regeneration rate of the surface of a conventional plate by 50.5%.The authors proposed an empirical correlation to evaluate the efficiency of regenerators with falling films.An analysis of the studies discussed above showed that in the formulation of the problems of these studies, the flow of fluid against the motion of the plane was not considered.In this paper, for the first time, the problem of fluid flow under its own weight along a moving plane inclined relative to the horizontal and vertical lines is considered.

Material and method of research
To justify the choice of the parameters of the squeezing rollers of a feeding conveyor, it is necessary to know the dependence of the flowing off of the squeezed liquid on the parameters of the feeding conveyor (Figures 1, 2).Therefore, we consider the dependence of the angle of draining of the squeezed fluid in the plane of the conveyor on the angles of inclination of the plane of the conveyor in two coordinate axes (Figures 3, 4).
Squeezing fluid from a water-saturated semi-finished leather product occurs under the pressure created by the squeezing rollers during their rotation.Therefore, the pressure between the squeezing rollers varies from the smallest values to the largest ones.
We rotate the coordinate frame ox1y1z1 by an angle θ relative to the ox1-axis, then . Now we rotate the coordinate frame ox2y2z2 by an angle φ relative to the oy2-axis, then

 
Substituting the values of x2, y2, z2 from (2) into expression (1), we obtain the connection of coordinate frames ox1y1z1 and ox3y3z3 . We determine the coordinates of point B in the coordinate frame ox1y1z1.
. For point O, the coordinates in the frame ox1y1z1 are x1=0, y1=0, z1=0.Let us find the intersection of the OBC plane with the ox1y1z1 plane, which represents the form of equation C2z=0; we assume that C2=1.
Then the equation of the line of intersection will be expressed in the following form: which we denote by OD, where Let us find the equation of the plane passing through point B perpendicular to line O1D: , where, We define the angle between line BC and perpendicular BK as: here . Substituting these values into (6), we obtain: Let us define line KM of the intersection of the OKB plane with the x1oy1 plane.
. The equation of this straight line is written in the following form: where Then we find the angle between the lines BK and KM: where  Thus, the dependence of the angle of fluid flow off along the conveyor on its lifting angle and lateral inclination was numerically revealed; graphically it is shown in Figure 4.
Analysis of the graph in Figure 5 shows that the angle of fluid flow on the conveyor increases with an increase in the angle of lateral inclination from 0 to 30 degrees, and the lifting angle of the conveyor -from 0 to 45 degrees.At that, with an increase in the angle of lateral inclination from 30 to 45 degrees and the lifting angle of the conveyor -from 0 to 45 degrees, the angle of fluid flow off decreases.

Results
An equation for a plane passing through three points O, C, B is obtained.Now we determine the equation for the plane:  (12) Therefore, the equation of the plane passing through points O, B, C and B, K, M will have the following form Then, we determine the one-dimensional flow of fluid along an inclined conveyor when the velocity of its motion is opposite to the fluid flow (Figure 3).So, in our case, it is: U is the velocity of the conveyor, ν is the fluid viscosity, α1 is the angle of inclination of the conveyor, h is the thickness of the fluid layer, z is the coordinate, β is the angle of inclination of the fluid flow off on the plane of the conveyor.
From expression (14), we find the thickness h of the film: Fluid flow rate is: A condition for the fluid flow off against the movement of the conveyor is obtained; it depends on the lifting angle, the velocity of the conveyor, the thickness of the removed fluid layer, the angle of fluid flow off, and the fluid viscosity.
On the basis of the study, a rational condition was determined that ensures the flow off of the squeezed fluid from the processed wet semi-finished product from the inclined feed conveyor: .
If h1>h, then the fluid squeezed out of the semi-finished product flows off, and if h1<h, then it does not flow off.
Thus, analytical expressions were obtained that make it possible to determine the dependence of the angle of flowing off of the squeezed fluid from a wet semi-finished product on the lifting angle relative to the movement of the semi-finished product and the lateral inclination of the feed conveying device.1.The dependence (7) of fluid flowing off on the lifting angle and lateral inclination angle of the conveyor was analytically determined.
2. Formula ( 14) was obtained for the dependence of the fluid flow rate on the velocity of motion, the conveyor inclination angle, the fluid viscosity, the fluid flow inclination angle, and the fluid layer thickness.
3. From the point of view of the efficiency of the squeezed fluid flow along the conveyor, the flow angle equal to β=70°-80° is considered rational.To prevent premature slipping of the semi-finished product from the conveyor belt during its movement, the angle of lateral inclination φ=5° and the lifting angle θ=15°-25° of the conveyor are considered rational.

Fig. 1 .
Fig. 1.Scheme of the inclined conveying device for feeding the skin between the squeezing rolls.

Fig. 2 .
Fig. 2. Scheme of the accumulation of fluid squeezed from wet hides in front of the squeezing rolls.   sin sin cos 3 3 1 b y x x     ,   y b b y x y y sin cos cos sin cos sin cos 3 3 3 1

3 VFig. 3 .
Fig. 3. Scheme of the fluid flow off in front of the working shaft.The coordinates of point C in the coordinate frame ox3y3z3 are x3=l, y3=0, z3=0.Substituting x3y3z3 into equation (4), we obtain the coordinates of point C in the coordinate frame ox1y1z1:

.Fig. 4 .
Fig. 4. Scheme of fluid flow off on the plane of the feed conveyor.

Fig. 5 .
Fig. 5. Dependence of the fluid flow angle in front of the squeezing roll on the inclination angles of the feed conveyor.