The results of the measurements on the individual systems are presented below.
Figure 5 shows the results of the measurements on the hydraulic system with a system pressure of 50 bar, 100 bar and 200 bar.
Figure 5Charts of hydraulic measurements; (a) displacement, (b) force, (c) velocity, (d) hydraulic power, (e) acceleration and (f) electric power verses time.
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Since velocity is the first derivative and acceleration the second derivative of displacement, the deviations are clearly visible in both Fig. 5a, c and e. The maximum deviation from the expected (linear) value occurs at a system pressure of 200 bar in the unloaded state, with the highest velocity and acceleration and the lowest velocity and acceleration occurring at a system pressure of 50 bar in the unloaded state.
Figure 5c shows curves representing the measurements with and without load, and the measurements with load differ significantly. The oscillation frequency is significantly higher in the unloaded measurements than in the loaded measurements. The unloaded carriage settles after one period at constant velocity (0.2 m/s), while the period of oscillation of the loaded carriage decreases towards constant velocity (0.2 m/s) due to the influence of the inertial mass (acceleration and deceleration). At a system pressure of 200 bar, where this phenomenon is most pronounced, the period of oscillation is 0.15 s for the unloaded measurement. However, when the platform is loaded, three periods of oscillation occur, with the first period lasting 0.51 s, the second 0.17 s (about 35% of the first period) and the last period 0.16 s (about 32% of the first period). When the piston rod of the hydraulic cylinder moves towards the starting point, a similar behaviour as described above occurs. The loaded measurements show a lower oscillation frequency than the unloaded measurements, where the oscillation frequency decreases up to a constant velocity of 0.3 m/s. The backward velocity is higher due to the differential hydraulic cylinder (smaller surface area for the same flow). All this can also be seen in Fig. 5e (acceleration curves).
In Fig. 5b it can be seen that at the beginning of the movement of the piston rod there is a compressive force because the piston rod "pushes" the carriage away from itself, but soon the compressive force turns into a tensile force and the "belly" can be clearly seen in Fig. 5a. This means that the piston rod stops for a moment and the accelerated inertial mass wants to continue moving in the direction of the initial movement. For unloaded measurements, the compressive or tensile force is quite small, but increases as the system pressure increases. For measurements with load, the initial compressive force is much higher (20%) because the piston rod of the hydraulic cylinder has to push the load away from itself in addition to all the expected friction (seals, friction in the piping, etc.). After the initial compressive force, a higher tensile force occurs due to the greater inertia, but at the same time there is an oscillation between the tensile and compressive forces, with the frequency of the oscillation decreasing until the proportional valve is switched and the piston rod moves towards the starting point. During the measurements with the load, there is a sharp increase in the tensile force, which is due to inertia. At this point, the valve switches to the position where the piston rod starts to move back to the starting point, but the inertial mass continues to move in the other direction for a few moments. When approaching the starting point, the inertial mass "bumps" again, which is shown by the oscillation or transition between compressive and tensile force (the oscillation frequency decreases in the direction of constant friction).
The hydraulic power (Fig. 5f) depends on the flow rate and the pressure. When the valve is switched, the pressure drops to the value required to overcome pressure losses, friction, etc., and at this point flow enters the system. The oil begins to fill one chamber of the hydraulic cylinder and flows out of the other through the valve into the reservoir. At the beginning of the movement, the hydraulic power is "zero", which is mainly due to the energy or potential energy stored in the lines, even if the hydraulic accumulators have not been used. When the system pressure is increased, the hydraulic power also increases. In unloaded measurements, the hydraulic power was constant when the piston rod moved from the starting position (20 W), the increase only occurs at the beginning of the movement, but is very significant at a system pressure of 200 bar. Another immediate increase occurs when the valve is switched, when there is a small increase in pressure. When measuring with the load, the potential energy or pressure difference is so great that the hydraulic power is zero. This phenomenon is best observed at a system pressure of 200 bar, where the pressure difference is greatest. In the unloaded measurements, the power increase occurs after approx. 0.1 s, followed by a short increase and constant power; in the loaded measurements, the power increase only occurs after approx. 0.5 s. Similar to the unloaded measurements, there is a short power increase, after which the oscillation frequency drops to a constant power. As can be seen in Fig. 5f, when the system pressure is increased, the electric motor is loaded more before the valve is switched from the zero position, because the hydraulic pump generates a higher pressure. At a system pressure of 200 bar, the electrical power was about 1500 W before the piston rod started to move, while at 50 bar the electrical power was more than twice as much, i.e. about 740 W. After the valve was switched and the piston rod of the hydraulic cylinder started to move, the power dropped to about 650 W.
Figure 6 shows the results of the measurement with a pneumatic system. The system pressure was set at 6 bar and 8 bar. With increasing system pressure, a similar displacement of the piston rod of the pneumatic cylinder was obtained. Figure 6a shows the influence of the compressibility of the air, especially for measurements with load.
Figure 6Charts of pneumatic measurements; (a) displacement, (b) force, (c) velocity, (d) hydraulic power, (e) acceleration and (f) electric power verses time.
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The results of using the pneumatic system were surprising, as it was expected that the compressor would not be able to supply enough air because the reservoir (pressure vessel) was not used.
Figure 6c shows that the pneumatic system behaved better when the measurements were made with load. After switching the valve, the velocity increased to a constant value (0.35 m/s), while in the measurements without load, the velocity oscillated to the maximum value until the valve was switched. When the piston rod moved towards the starting point, an oscillation was detected in the unloaded measurements, which could be due to the compressibility of the air or to a lack of air. The lack of air can be seen in Fig. 6e, where the piston rod of the pneumatic cylinder accelerates and then cannot follow the movement due to the lack of air, resulting in oscillation. In the measurements with load, the velocity increased slowly (lower slope of the curve). Due to the slower acceleration at the beginning of the movement towards the end position, there was no sign of air shortage or oscillation, but the velocity was higher (0.6 m/s) than in the measurements without load, which is due to the inertial mass. When the valve was switched to the zero position, the effect of compressibility can be clearly seen in Fig. 6c and e, as the oscillation of the carriage with the inertial mass at the end can be seen.
In Fig. 6b, the compressive force is very low (− 20 N) in unloaded measurements where the piston rod has moved from its initial position, as the piston rod pushes the carriage away from itself. After switching the valve, there was an immediate increase in the tensile force, as the carriage continued to move in the direction of the initial movement for a few moments, after which the tensile force was very low again. In the measurements with load, the compressive force was ten times higher than in the unloaded measurements, but after the initial increase at the beginning, it decreased to very low values, very similar to those of the unloaded measurements. Due to the inertia of the mass, which continued to move in the direction of the initial position for a short time after the valve was switched (the piston rod began to move in the direction of the initial position), the tensile force increased sharply (480.5 N). The influence of the compressibility of the air is clearly noticeable in the measurements under load when the valve is switched to the zero position, as the movement of the inertial mass causes an oscillation between the compressive and tensile force (damped oscillation phenomenon, in which the oscillation frequency decreases towards zero with time).
Pneumatic power (Fig. 6d) is related to flow and pressure. In unloaded measurements, when the valve is switched, the pressure drops to the value required to overcome the friction in the guides, seals, etc. Therefore, the pneumatic power is quite constant (70 W), the increase only occurs when switching the valve due to a short pressure rise. With loaded measurements, the values of the pneumatic power are greater, because, in addition to the friction in guides, seals, etc., additional pressure is required to push or pull the carriage with weights.
The values of the electrical power (Fig. 6f) after the measurements with or without load do not differ, only with movement the power decreases. From this it can be concluded that the system is not overloaded.
Figure 7 shows the results of the measurements on the electrical system.
Figure 7Charts of electric measurements; (a) displacement, (b) force, (c) velocity, (d) electric power, (e) acceleration and (f) electric power on controller time.
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At the limiting acceleration of 0.1 m/s2, a soft start can be seen in Fig. 7a. The piston rod of the electric cylinder begins to move slowly to the end position, while it reacts more jerkily when the limit acceleration is increased. Increasing the limit acceleration causes a similar displacement of the piston rod or the threaded spindle of the electric cylinder. Unlike the similar displacement, the permissible acceleration 0.1 m/s2 required 3.5 s to travel from the starting position to the end position and back without bumping. With the maximum permissible acceleration of 5 m/s2 and 10 m/s2, the extension and retraction was five times shorter and with the maximum permissible acceleration of 15 m/s2 almost six times shorter.
In addition to acceleration, the electrical system is also limited by velocity, which is about 0.3 m/s. This limitation can be seen in Fig. 7c. With a permissible acceleration of 0.1 m/s2, the maximum velocity was not reached because the piston rod or spindle accelerated so slowly and evenly that the maximum velocity was not reached. The maximum velocity was 0.1 m/s. Figure 7e shows that the measured values are within the configurable values, at the maximum permissible acceleration of 15 m/s2 the acceleration was not exceeded.
At a maximum permissible acceleration of 0.1 m/s2 as shown in Fig. 7a, c and 7e see also Fig. 7b), the acceleration was so smooth and slow that the force value is very low (from − 10 to 16 N). A different behaviour is visible when the maximum permissible acceleration is increased, especially for measurements under load. In unloaded measurements, a low compressive force (35 N) occurs initially, because the piston rod of the electric cylinder pushes the carriage out of itself, but at the same time friction in the guides, friction on the spindle in the electric cylinder etc. must be overcome. In the direction of the end position, the compressive force is very low. From the end position to the initial position, the piston rod pulls the carriage behind it, creating a tensile force. The initial tensile force is somewhat higher (35–45 N), but after the initial pull, the values drop to about 13 N. When the movement stops (deceleration), the carriage "bumps" against the piston rod, creating a compressive force. When measuring with the load, much greater compressive and tensile forces occur. The compressive force increases with the increase of the maximum permissible acceleration. Due to the inertia of the mass and the inability to follow the acceleration or movement of the inertial mass, there is an oscillation between the compressive and tensile forces (damped oscillation phenomenon). When the movement starts in the direction of the starting point, a high tensile force occurs due to the short movement of the inertial mass in the other direction. Here, too, an oscillation between the compressive and tensile forces occurs, because the inertial mass wants to move faster than the system allows due to the acceleration and "bumps" against the piston rod of the electric cylinder.
Figure 7d shows that the power increases with the increase of the maximum permissible acceleration, whereby the load has an additional influence on the power increase.
A similar effect can be observed with power measurements directly at the controller (Fig. 7f).
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