Simulation of pneumatic actuator position system for long stroke mounting movements

The creation of new equipment and technical means for the implementation of promising processes and technologies is largely determined by the level of development of mechanical engineering. The most important requirements for technological equipment are an increase in work processes, flexibility and adaptability, automation, implementation of complex algorithms of executive movements. The mechanisms of executive movements ensure the operation of transporting, fixing and other target mechanisms, this largely determines the quality and efficiency of processing processes. Positional actuators have existing technical solutions. However, to a greater extent they relate to linear movements realized by rod cylinders, this does not allow adapting the results of existing research to the development of long-stroke positional movements. In the course of this work, an assessment was made of the existing types of drives and a displacement and position measurement sensors. The proposed positional pneumatic scheme allows solving the problem of positioning long-stroke displacements, its mathematical and computer models were built, and dynamic analysis and conclusions were made.


Assessment of the state of the issue
In order to achieve the linear movement of the output link of the technological equipment, pneumatic, electromagnetic and hydraulic drives are usually used. The latter two types of engine are more widespread. An electromagnetic drive, on the other hand, is clean and reliable to operate, but often requires a mechanical transmission, the combination of which can be quite expensive.
Pneumatic units have a number of advantages: they are fast, cheap, have outstanding power per unit weight, and are easy to maintain. A big problem when using a pneumatic cylinder is the presence of piston friction and non-linear characteristics of the compressed gas flow. Therefore, with long-stroke movements, there is a deterioration in the dynamics and positioning of the drive [1-3].
The use of existing sensors for measuring displacement and position is not always possible in industries where special attention is paid to fire and explosion safety. The use of electrical elements is not permitted there. The use of sensors with long travel distances can affect their cost or require feedback, which can also increase the cost of the drive.

Description of the principle of operation
The operator sets the required stop coordinate in the PLC, rapid traverse occurs. The pressure enters the nozzle N, then the pressure sensor PS. When the drive reaches the previously set coordinate, electromagnets Y1, Y2 are turned on. The cylinder rod PC4 switches the PV3 valve, the drive travel slows down. When the drive reaches the coordinate set by the operator through the N nozzle through the aligned hole, the pressure is supplied to the control line of the PV4 distributor and the PC4 tandem cylinder, and it switches the PV4, PV3 valves and blocks the inlet and outlet cavities, and activates the blocking brake.

Formation of a generalized mathematical model
The mathematical model of the pneumatic drive demonstrates a system of differential equations describing the movement of the working body and the change in pressure in the cavities of the actuator, the mathematical model of the pneumatic drive includes the following equations: 1. The equation of motion of the actuator of the pneumatic cylinder. 2. Equations of pressure change in the discharge cavity. 3. Equations of pressure change in the exhaust cavity.
The design diagram of the pneumatic drive is shown in Figure 2. When designing, one of the main conditions is to confirm the functionality of the developed drive, as well as to analyze the processes occurring in it when positioning the pneumatic cylinder. When forming the mathematical model of the drive, the following assumptions were made:  the pressure of the compressed air source is constant over time;  the thermodynamic process of gas behavior in the pneumatic system is assumed to be adiabatic;  in the description of pneumatic devices, the ideal gas model is used, since the pressure in the pneumatic system is below 10 bar;  leaks are not taken into account;  the force of viscous friction is proportional to the speed;  the coefficients of expenses are taken as averaged;  the mass of the moved parts is assumed constant;  force Fc at the output link of the pneumatic drive is constant;  relay control of pneumatic valves;  the time of forming the control signal from the displacement sensor is not taken into account [4][5]. During the calculation of the pneumatic actuator, the initial data for the modeling were calculated and presented in Table 1.  (2) where is the effective area of the cavities, m2; 1 , 2 -air pressure, respectively, in the discharge and exhaust cavities of the cylinders, Pa; − speed of movement of moving masses, m / s; вн -the force of external forces, N; вт -coefficient of viscous friction; -mass of moving parts of the drive, kg. т -braking force, N; where is the coefficient of friction; -normal force, N; -supply pressure, Pa; т -the area of the piston cavity in the pneumatic brake,.
Where р is the effective area of the valve end of the distributor, m 2 ; м , 1 , т -Pressure at the inlet and outlet of the distributor, Pa; -Pressure in the control channel, Pa; с -forces of resistance to movement of the distributor spool, N; -thrust reaction forces, N; м -force of action of the electromagnet on the valve spool, N; с пр р -spring compression ratio, N / m; р -mass of the distributor spool, kg. 7. Equation in the discharge cavity. Based on the first law of thermodynamics, the amount of energy supplied with the gas into the discharge cavity from the main goes to change the internal energy of the gas in the cavity 1 and to perform the work of the drive = 1 + ; (9) = • , (10) The specific energy of a gas is determined by its body content -enthalpy. Enthalpy is related to the specific and temperature of the gas in the pipeline by the dependence: = = • (11) Elementary mass of gas express it in terms of expense : = • (12) Substituting (11) and (12) into equation (10), we find the amount of energy that enters the piston cavity = • • • (13) After the transformation, we obtain the equation for the change in the internal energy of the gas: Where − specific heat capacity of a gas at a constant volume; 1 − gas temperature in the discharge cavity; 1 −mass of gas in the discharge cavity. The mass of gas is determined in the size and volume of the cavity 1 1 : 1 = 1 • 1 (15) Next, we substitute (15) into formula (14) and obtain an expression for determining the change in the internal energy of the gas 1 in the cavity: At constant pressure and constant volume, the specific heat capacities of the gas are interconnected by dependencies: Substituting equation (18) into (17) we get: To simplify the expression, the adiabatic exponent for air, we multiply the entire equation by R and divide by, as a result we get: = = 1.4 Let us find expressions for the components of this equation. The volume of the discharge cavity 1 consists of the working (variable) volume of the working cavity 1 of the pneumatic cylinder and the initial (constant) volume 01 of the pneumatic drive: The working volume of the discharge cavity 1 is expressed through the area of the piston 1 in the discharge cavity and the coordinate : The initial volume 01 includes the structural volume of the discharge cavity in the extreme position of the piston and the volume of the supply line, which consists of the volumes of the pipeline and the connected pneumatic equipment.
The initial volume 01 of the supply line can be written, as is customary in some works [6-8], as follows: where 01 is the reduced initial coordinate of the piston position. Finally, substituting (25) and (26) into equation (24), we find the volume of the injection cavity 1 1 = 1 ( + 01 ) (27) Gas flow in pneumatic industrial drives. Coming into the discharge cavity depends on the nature of the process.
In pneumatic industrial drives, the gas flow is close to the isothermal process [7-9]. Therefore, the gas flow rate is determined from the equation which we write in the following form, bearing in mind that. = м м = 1 • √ м 2 − 1 2 , Substituting the values and from (27)  (37) The volume of gas in the exhaust cavity, taking into account the volume of the outlet pipeline and pneumatic equipment, is: 2 = ( + 2 − ) • 2 (38) The outflow of gas from the exhaust cavity through the pipeline is close to the isothermal process. Therefore, the flow rate is determined from the simplified equation corresponding to the isothermal gas outflow: Substituting the values 2 and 2 from (38) and (39) into equation (37), we obtain the equation for the pressure change in the exhaust cavity: where is the adiabatic index; R -gas constant, J / К кg  ; where is the adiabatic index; R -gas constant, J / К кg  ; м air temperature in the discharge line, K; а atmospheric pressure, Pa; -1 , 3 pressure in the flowing part of the pipeline, Pa; 1 , 2 -the volume of the flow parts, 3 / -3 , 4 the coefficient of resistance of the supply and exhaust lines. 3 , 4 -pipeline section area, m2; We obtain the system of equations of the mathematical model of this pneumatic system: The system of differential equations can be solved by various numerical methods (Euler, Runge-Kutta, etc.) for given initial conditions, drive parameters and control actions that functionally depend on the coordinate of the output link [10-13]. The study of the model was carried out in the SimIntech program by numerical methods.

Сomputer model
The computer model is shown in Figure 3. Oscillographic analysis of the positioning process has established that the dynamic and control characteristics of the proposed drive are significantly improved when using a pneumatic brake. The drive run-out is significantly reduced, while providing a reliable fixation of the mechanism, which maintains accuracy under subsequent external influences [14][15].The speed of movement of the pneumatic cylinder has a decisive influence on the processes of deceleration, stopping and positioning of the control object [16][17]. So for a better stop, a deceleration was added at the penultimate coordinate.