The purpose of this work is development and use of a mathematical apparatus for modeling the polypropylene fibrous filter elements (PFFE) production process control system based on the Petri net, which considers all stages of filter elements production at the enterprise. Real technological processes have a finite duration, which can be depicted graphically on Petri nets. This article reviews the possibility of using the Petri net for modeling the processes of polypropylene fibrous filter elements production, and also highlights a number of the Petri net advantages in modeling. Petri net; production management system; modeling; technological process; sequence The production of polypropylene filter elements by the method of pneumo-extrusion refers to process production, where each technological process is a sequence of technological operations, each of which cannot be interrupted at any time. It is very important to develop a model that considers all production processes and equipment operating cycle. Such model is necessary to increase the production process performance
diagram
and the entire pneumo-extrusion method polypropylene filter elements production process improvement as a whole.
The processing of polymers, in particular polypropylene, is preceded by the design of the product pattern, the choice of the optimal method of processing, technological equipment design and manufacturing, polymer composition formulation development, its preparation and formation arrangement.
The actual processing of the polymer involves the products formation and their further processing in order to improve the polymer material properties (heat treatment, radiative crosslinking, etc.).
Simulation is the main research method in all fields of knowledge and the complex systems
characteristics evaluation method for decision making in various fields of engineering is scientifically
rationalized. Existing and projected systems can be effectively researched
with the help of
mathematical models (analytical and simulation) implemented on modern computers, which in this
case act as the experimenter tool with system model [
The purpose of this work is development and use of a mathematical apparatus for modeling the polypropylene filter elements production process control system where filter elements are made by pneumo-extrusion method based on the Petri net. Petri net considers all stages of polypropylene filter elements production by the pneumo-extrusion method at the enterprise; not only the order of action, but also the temporal characteristics, construction of a Discrete Petri net, it simulates the process of polypropylene filter elements production by the pneumo-extrusion method at the enterprise.
2020 Copyright for this paper by its authors.
Petri net (PN) is a mathematical apparatus for modeling dynamic discrete systems. First described
by Carl Adam Petri in 1962. Most experts consider PN to be one of the most modern and most
effective means of different classes systems graphical and mathematical modeling [
Currently, there are the following main types of Petri nets(PN): discrete PN, stochastic PN,
functional PN, color PN, inhibitory PN, and hierarchical PN. There are advantages of PN in
modeling: the model lucidity, the ability to perform analysis using computer technology, the
hierarchical modeling possibility, as well as a high level of discrete event systems formalization. It
should be noted that in recent years interest in PN has increased significantly [
The technological polypropylene filter elements production process, made by the
pneumoextrusion method, consist of the following operations: production order placement, filter element
calculation, template and raw materials preparation, extrusion, spraying template with polypropylene
[
Getting information from the customer Scheduling of the order, pricing Transfer of production order Receiving an order from a manager Calculation of the filter element and the number of layers Loading raw materials into the bunker Milling of polypropylene granules
Cooling materials
Melting raw materials Moving materials between thermal zones
Keeping the temperature Moving the melting mass to the spray head Feed the hot air to the spray head Spraying on a rotating template
fulfillment, price formation
PW3, Raw
TP6, CT
TP6.3
An important issue for human life and activity is the efficient use of water resources of the planet. An important process for the research is the stage of filtration. Models for describing water filtration differ in supplying of data, the ability to check the adequacy in the real conditions.
It is known a technology which includes forming a backing layer of thick fibers and depositing
fine fibers thereon. [
The task of the proposed technology is the creation of an inexpensive multi-layer filter element of the filter-separator that provides a high degree of purification of gaseous and liquid media, such as natural gas and liquid fuel, both from mechanical impurities and free moisture contained in the filtered medium in the form of aerosols.
The setted task is achieved due to the fact that a known multilayer filter element for liquid and gaseous media made of fibers of a thermoplastic polymer, preferably polypropylene, and consisting of alternating thick-fiber and fine-fiber layers is made by extrusion in the form of a hollow cylinder with a thick-fiber outer layer, Thick-fiber layers consist of fibers with a diameter of 100-150 microns, and fine-fiber layers - from fibers with a diameter of 1-5 microns.
Unlike the filter element according to the prior art, the present invention allows to create an inexpensive, efficiently operating filter element by: - performing the filter element in the form of a hollow cylinder by extrusion (in the prototype, the tubular filter element is obtained by folding a pre-fabricated multilayer sheet of complex structure); - the execution of the layer on the input side of the medium to be filtered with a thick -fiber, absorbing coarse mechanical impurities (in the prototype, the role of filter layers is performed by thin-fiber layers, and the thick-fiber layers serve as a spacer between them). The main purpose, as follows from the description, is to lining the fine- Its formation); - alternating layers of the same density from a fiber with a diameter of 100-150 microns with layers, whose density decreases along the path of the filtered medium, and which are made of a fiber with a diameter of 1-5 microns.
The essence of this method is illustrated by the following example.
Example: Polypropylene fibers were extruded by forming a filter element in the form of a hollow cylinder consisting of seven layers. The characteristics of the layers are given in the table 1.
When the first thick-fiber layer, made of a fiber with a diameter of 100-150 microns, having a density of 0.20 g / cc and a thickness of 20% of the thickness of the filter element, is filtered, the filtered medium / natural gas or liquid fuel is freed from coarse mechanical impurities. In the next, a thin-fiber layer, whose density is 0.40 g / cc and fiber diameter is 1-5 microns, a process of finer purification takes place, as well as coarsening of water droplets contained in the filtered medium in the form of aerosols and the formation of water films. When the filtered medium leaves the fine-fiber layer in the thick-fiber layer, the laminar process turns into a turbulent layer, which is accompanied by a significant loss of kinetic energy, especially the heavier fractions of the filtered medium (water and impurities contained in it). At the same time, under the action of gravity forces, partial drainage of heavy fractions occurs to the lower part of the filter element and about 70% of the dropping water is removed from the filtered medium.
This is facilitated by the change in the turbulent process to laminar when the filtered medium enters a denser, finer-fiber layer with a density of 0,30 g / cc (the fourth in the direction of motion). In this layer, drops of water partially reach the bottom of the filter element.
Each time when the filtered medium passes from the fine-fiber layer to the thick-fiber layer (from the denser layer to the less dense layer), the laminar process becomes turbulent and the water drops and the water is removed from the medium to be filtered. The density of the fine-fiber layers decreases along the motion of the medium to be filtered, while the density of the thick -fiber layers remains constant.
The proposed design provides almost complete removal of mechanical impurities and allows to purify natural gas or liquid oil products from drip water by 97-98%.
The multilayer fibrous structure of the filter element according to the invention provides an efficient cleaning of liquid and gas media from mechanical impurities and free water present in the filtered medium in the form of aerosols. The use of fibers of a thermoplastic polymer, advantageously of a polymer, gives the filter element a high chemical resistance to a wide range of chemicals.
Compared to similar filter elements, the filter element in question is of low cost, easy to assemble and dismantle.
Models for describing water filtration differ one from another in supplying of data. Explored model of water filtration makes it possible to evaluate the advantages and disadvantages of forming a model of the filter with Thermal polymers in which the filtering partition is formed by continuous fibers Thermal concluded on the winding core. Advantages include the fibrous structure of the filter (fibers with a size of about 20 μm) and its material (polypropylene) ensures the appearance of an induced electric potential when the liquid moves through the filter layer, which in turn helps to destroy the double electrical layer of colloidal microparticles and fix them inside the filter layer. This effect causes a sufficiently high degree of purification of liquids from colloidal microparticles in a wide range of sizes from 0.1 to 5 μm.
Let us dwell on Petri nets with time constraints to analyze the polypropylene filtering fibrous
elements production process. Real technological processes have a finite duration, which can be
depicted graphically on time schedules. Because for the chemists who develop systems of periodic
action and flexible automated production systems, the apparatus of Petri nets is little known [
Graphically, the Petri net is denoted as follows. Positions are represented by places, transitions are
by thickened bars (barriers), marking by points inside places, and any number of points inside a place
is allowed.
vertices represented by natural numbers [
Discrete Petri nets is a two-part oriented graph supplemented by the characteristics of arcs and = ( , , , 0, ′, ′′) where Р = {pi}– positions set; T = {tj} – transitions set; 0, ⊆ ( × ) (
× ) – finite arcs set (indeterminacy function); → {0, 1, 2, … } – initial network markup; ′ = { 1′ , 2′, … , ′, } – transitions minimum delay times set; ′′ = { 1′′, 2′′, … , ′′, } – transitions minimum delay times set.
Petri nets are mainly used to model so-called interactive operations or interactions when several (at
least two) technological devices are involved in the operation. The interaction simulations are
performed in order to identify additional system resources, conflict situations for the further device
interaction process control. However, Petri nets can successfully model much simpler operations,
such as sequential processes in periodic devices. Of course, the Petri network models not its own
technological processes but only their sequence as a result of the certain conditions fulfillment [
Discrete Petri nets are one of the known extensions of basic Petri nets used to model systems and processes. Analysis of which must consider not only the order of action but also temporal characteristics.
Such networks are widely used in the research of technological and organizational management systems.
We define the technological operations (conditions) for modeling using Petri nets, presented in the form of a Table 2.
We define the states: - the start of the technological process(TP) and - the finish of the technological process.
Draw up a table of input and output conditions (Table 3, Table 4).
Designation of operations О1 О2
The described situation is modeled by the Petri net, which is presented in the form of a table (Table 4) and its graphical representation (Fig.3). As can be seen from table 3, there is a one-to-one P1 P2 t1
t2 P3 { P4 t9 t3 P14 P15
}; }; t4 t5
t6 P5
P6 t7
P10 P9 P8
P7 t9
t8 P13
P12
P11 correspondence is established between technological operations and network positions, as well as between equipment states and network transitions: {Technological operation} ↔ { { } ↔ { }; { } ↔ { }; } ↔ {
Conducted experimental and theoretical researches have made it possible to form a universal algorithm (Fig. 4) for obtaining the optimum fiber thickness, depending on the technological process physical characteristics. The presented algorithm allows solving the following problems: supports the creation of polypropylene fibrous filtering elements formulations with specified consumer characteristics, depending on the application field and optimal cost; forms recommendations on the filtering characteristics of the received polypropylene fibrous filter elements according to current standards (DSTU, TU, etc.); provides search of optimum physical characteristics at all stages of technological process; analyzes the final product quality, identifies technological problems and suggests solutions.
The algorithm of the optimum polypropylene fibrous filter elements fibers thickness as the main task requiring automation is presented as a block diagram in Fig. 3.
The presented algorithm can be used to select the fiber structure of a polypropylene filter element depending on the application field.
Models of water filtration makes it possible to evaluate the advantages and disadvantages of forming a model of the filter with Thermal polymers in which the filtering partition is formed by continuous fibers Thermal concluded on the winding core.
Advantages include the fibrous structure of the filter.
The disadvantages are when we form a pore with a gas bubble, we can more accurately determine the diameter of the pore that we want to get. And in a fiber filter this is achieved by increasing or decreasing the packing density of the fibers in the layers of the filter and the thickness of the fiber itself. And it can be programmed only in the laboratory by an experimental method. Not every production can afford the choice of parameters through laboratory research.
We have reviewed the polypropylene fibrous filter elements technological production process control system modeling using the Petri net. Modeling is one of the main research methods in all fields of knowledge and a scientifically justified method for evaluating the complex systems characteristics used in various fields of engineering decision making. Petri nets are simple but effective in analyzing production systems method. A model of the polypropylene fibrous filter elements production process has been constructed where all technological processes are managed. This made it possible to construct an algorithm for designing the polypropylene filtering elements fiber optimum thickness.