Introduction. The efficiency of the drives used in modern processing equipment is determined by the speed of movement of the actuating element along the coordinate axes, and the accuracy of positioning the actuators of the drive in real time during the implementation of the required work cycles [1]. These cycles, as a rule, consist of a rapid approach of the actuator, its deceleration to the positioning speed, precise stopping, and rapid withdrawal [2].

Pneumatic drives are characterized by high speed of movement and protection against fire. They also have explosion safety, environmental friendliness, reliability and flexibility in confined spaces [3]. They are effectively used in mechanical engineering, as well as in the food, chemical and woodworking industries, where the combination of speed and positioning accuracy of the power elements of the drive is important [4].

Modern transport and production machines are equipped with various actuators based on pneumatic drives [5]. Such systems are constantly subject to ever higher demands on the speed, accuracy and reliability of their operation [6]. In this context, pneumatic automation offers universal approaches to the control of similar systems.

Most modern industrial drive equipment operates on the basis of automatic pneumatic drives with long-stroke movements of the actuators [7]. These industrial positioning drives guarantee positioning accuracy of about 1% (in some special designs, it can reach up to 0.4%) of the maximum stroke length. This has a negative impact on the accuracy of pneumatic long-stroke drives [8]. Air compressibility and complex thermodynamic processes occurring in air flows have a significant impact on the control of air flows in the drive lines and cavities of the pneumatic cylinder, which limits the positioning accuracy of the drive [9].

Research by D.V. Shilin [10] demonstrated that the implementation of a hybrid control system significantly increased the accuracy of positioning the carriage of a rodless pneumatic cylinder. Experiments made it possible to reduce the error to 0.2% of the stroke length, which was a good result. In [11], the authors proposed a new controller circuit based on fuzzy logic, used to monitor the actuator trajectory following of a robot manipulator with two degrees of freedom.

A promising direction is the development of flexible rodless pneumatic cylinders for long-stroke McKibben-type actuators [12]. Pneumatic cylinders with a self-holding function were tested, providing precise positioning even without applying pressure. Dao The Anh [13] developed and investigated an automated positioning pneumatic actuator with increased accuracy and operating speed, identifying the dependence of the actuator characteristics on the mass of the objects being moved, the deceleration coefficient, relative displacement, and braking force.

Paper [14] presents an adaptive second-order sliding mode tracking control scheme for robotic manipulators. A new control law is proposed that allows for the transition of the robotic manipulator trajectories from all initial conditions to the switching surface of the proportional-integral derivative in a finite time with subsequent retention on this surface.

There is a jet positioning numerical control system [15] based on a cylinder with a piston and a rod connected to a measuring scale. The system uses a “nozzle-receiving channel” sensor to generate a control signal. The device operates on a pneumatic sensor that measures the gap between the sensor and the inclined measuring bar, whose angle is adjusted by a screw. The sensor output is connected to the control input of a threshold device that generates a signal to stop the piston, whose position is adjusted by a throttle [15].

The key drawback of the modern technical solutions under consideration is that they are designed exclusively for the use of standard cylinders [16] with a working stroke not exceeding three meters. When attempting to implement mechanisms with an increased stroke of over three meters, developers encounter a set of serious technical obstacles [17]. The main problem is that to provide the functioning of such systems, it is required to modernize the control system, which causes a significant increase in the costs of manufacturing the end product. The increase in cost occurs in two main areas: the first is associated with the introduction of more complex control electronics, the second is due to the need for additional elements for reliable operation at increased distances [18]. Under such conditions, it is critically important to create an innovative approach capable of effectively solving problems associated with long strokes (more than three meters). At the same time, the new solution must not only provide the required technical characteristics, but also remain economically justified for potential users, while maintaining a high level of operational qualities [19].

This research objective was to experimentally verify the results of mathematical modeling of a positioning long-stroke rodless pneumatic actuator, as well as to confirm the degree of influence of key factors on positioning accuracy.

Materials and Methods. Experimental studies were aimed at validating the results obtained through the mathematical modeling of pneumatic drive systems, which was carried out earlier in paper [8].

During preliminary calculations, the element base of the stand was selected, and its assembly drawing was made, which is presented in Figure 1.

The stand, as a technical model of a pneumatic drive for experimental research, assembled on the basis of design documentation, is shown in Figure 2. To study the pneumatic and kinematic characteristics of the drive, an original control system was developed and applied, including a jet sensor and an external brake device [20].

In the course of the development of the experimental setup, a Camozzi 52G2P40A0400 rodless pneumatic cylinder with a working stroke of 400 mm and a piston diameter of 40 mm was mounted on the testing stand. The proposed original control system, developed as part of previous studies, was fixed on the movable carriage of this device [20].

This system included a jet sensor of an original design, consisting of two nozzle elements and a special rack with holes, as well as an external brake device, represented by two Camozzi 31F4A040A005 pneumatic cylinders with friction linings on the rods [8]. Friction linings of Argolon-TX material were selected due to their friction coefficient of 0.4 and linear wear, which is up to 5.5 μm/brake [13].

Additionally, a standard Camozzi 40M2L050A0400 pneumatic cylinder with a stroke length of 400 mm and a piston diameter of 50 mm was installed on the stand, which made it possible to simulate external loads on the drive. To verify the operability and accuracy of the jet sensor readings, a spillage method was used using a Camozzi MF4008-10-R-BV-A flow sensor located after the element under study, and two Camozzi SWCN-P10-P3-2 pressure sensors placed before and after this element. The tests of the jet sensor showed high reliability and stability of operation in various operating modes.

For the water drawing, a Camozzi MF4008-10-R-BV-A flow sensor was used, which had the following technical characteristics: analog output 0.5–4.5 V; measured value — volumetric flow rate; initial value of the flow measurement range — 0 l/min; final value of the flow measurement range — 10 l/min; accuracy (1.5+0.2∙FS/MV) %; operating pressure — 0–5 bar. Camozzi SWCN-P10-P3-2 pressure sensors were also used for the tests, which had the following technical characteristics: maximum measurement pressure — 10 bar; minimum measurement pressure — 1 bar; measurement pressure drop — 0.01 bar; maximum error — no more than 2.01%; scaling factor — 1.543. Additionally, Camozzi M043R-12 pressure gauges were used to provide measurement accuracy and pressure control in various drive units. The experimental stand was equipped with a modern electronic control unit, which included a Giga Device GD32F103VET6 microcontroller. It was responsible for collecting and processing data from all sensors of the pneumatic system, as well as for controlling the pneumatic distributors. To improve the accuracy of the actuator positioning, an encoder of the New Hong OVW6-10-2HC model was used, which had the following technical parameters [21]: power supply — DC 5–12 V, 12–24 V; response frequency — 0–100 kHz; consumption current — 80 mA. All data from the pressure sensors and the encoder were recorded in the system using the Modbus protocol [22]. Information from all measuring devices was collected by a personal computer synchronized with the microcontroller via the W5500 interface.

The DD1 controller interacted with the system, generating control signals for electromagnetic relays via a Unisonic Technologies ULN2003 transistor unit. This provided precise and reliable control of the pneumatic distributor solenoids, as well as maintaining the specified operating parameters of the drive in various operating modes [23].

Figure 3 shows the research complex appearance. The principle of its operation is described in [8, 20], etc. The control system of this complex consists of a contactless jet sensor and an external brake device.

The contactless jet sensor transmits information about the current position of the actuator of the pneumatic cylinder, switches the drive controls for its deceleration and precise stopping.

The external braking device performs the work of fixing the actuator of the pneumatic drive when it is out of operation and precisely stops at a given coordinate. Then the actuator switches to the positioning speed.

Experimental studies were conducted under the following conditions:

During the field experiment, the following were investigated:

Research Results. The graphs of the movement of the drive power elements, their speed, as well as the dependence of the air pressure in the drive pneumatic system, in comparison to the graphs of the same drive parameters obtained during the simulation, are presented in Figures 4–6.

The maximum discrepancy between the experimental data and the mathematical modeling data (Fig. 4–6) does not exceed 18%, which confirms the reliability of the research results [24].

The discrepancy between the research results was determined for all the data obtained (Fig. 4–6) using the following formula [25]:

(1)

where aэ — data obtained during the experimental study (displacement, speed, pressure), aт — data obtained as a result of the theoretical study [26].

In Figures 7 and 8, the captions “Lexp” and “Lmod” denote oscillograms obtained as a result of full-scale and computational experiments, respectively.

Figure 7 shows the result of the study on the effect of mass M of the moving structure on the value of the positioning accuracy of the pneumatic cylinder.

The studies have shown that the positioning accuracy of the drive depends on the mass of the moving object. With an increase in mass from 10 to 30 kg, the positioning accuracy decreased by 1.47 times, and with an increase in mass to 60 kg, the accuracy worsened compared to a mass of 10 kg by 1.37 times.

Figure 8 shows the result of the study on the effect of the stop coordinate of the drive actuator on the accuracy of its positioning at the same maximum speed of movement. It was found that the accuracy of the drive positioning depends on the length of its working stroke to a complete stop (stop coordinates): when changing the stop coordinate from 0.1 m to 0.22 m, the positioning accuracy worsened by 3.2 times, and when changing the stop coordinate from 0.22 m to 0.35 m, the positioning accuracy increased by 2.2 times. This is due to the fact that during the operation of the drive, back pressure is created in the air cavity of the pneumatic cylinder when the piston approaches its extreme walls (and the closer to the wall, the greater the pressure) [27]. Back pressure also increases additionally during throttling due to the narrowing of the flow section of the channels of the holes intended for pumping and bleeding gas [28]. The narrowing of the flow sections of the channels causes the deceleration of gas flows [29]. This is observed when the actuator of the drive is moved at the positioning speed [30].

Discussion. The conducted experimental studies allowed obtaining good results in the development of long-stroke pneumatic drives. Successful verification of the mathematical model confirmed the correctness of the theoretical studies carried out in previous works [8][19].

The obtained positioning accuracy of the drive is 77 µm at a distance of over three meters. This figure significantly exceeds similar results presented in [13][15], which demonstrates high potential of the developed design, since the economic efficiency of the proposed solution is due to the absence of an electronic component base in the control system [31]. This not only reduces initial production costs, but also significantly simplifies maintenance of the drive during operation [32]. Comparative analysis with existing developments [2][13] confirms the superiority of the developed system in terms of cost criteria.

Conclusion. The main research results are as follows:

The conducted studies confirmed the efficiency of the developed solutions for long-stroke rodless pneumatic actuators.

The practical significance of the study is validated by the possibility of using the obtained results in the creation of high-precision long-stroke mechanisms in various industries [33]. The developed design can be used in automated production lines, robotic complexes, and other areas where precise positioning over significant distances is required.

Promising areas for further research include optimizing the parameters of the control system to obtain even higher positioning accuracy, as well as developing calculation methods for positioning long-stroke pneumatic drives.