Energy‐saving methods in pneumatic actuator stroke using compressed air

Correspondence Wei Xiong, Ship Electromechanical Equipment Institute, Dalian Maritime University, Dalian, 116026, China. Email: xiongwei@dlmu.edu.cn Abstract The pneumatic systems have lower energy efficiency than the electric and hydraulic systems. Improving the utilisation rate of compressed air is an important aspect for increasing the energy efficiency in the pneumatic systems. This paper introduces two methods for reducing air consumption, including the quantitative air intake method and the optimisation of the air intake and exhaust duration method. The quantitative air intake method analyses the minimum air consumption volume in a specific pneumatic system based on the energy conservation theory. The optimisation of the air intake and exhaust duration method aims to find the best air intake and exhaust time schedule by the mathematical optimisation of the energy-saving and system stability of the pneumatic systems. An experimental equipment was established to verify the theoretical results of the two methods. Based on the experimental results, this paper analyses the characteristics and accuracy of the two methods and discusses the applicability of mathematical optimisation under some different boundary conditions. The experimental results show that both of the two methods can effectively reduce the air consumption in the piston stretching-out stroke and save 76% of the air consumption compared with continuous air intake during the whole stroke.


INTRODUCTION
The pneumatic systems are widely used in industrial productions because of their unique advantages. However, compared with the electric and hydraulic systems, their efficiencies are the lowest and less than 20% [1]. The national statistics show that the power consumption associated with the pneumatic systems accounts for about 10% of the total electric power consumption in China [2]. Therefore, it is of great significance to research on the energy-saving methods of the pneumatic systems to achieve energy conservation and emission reduction.
Usually, the energy-saving methods for the pneumatic systems are mainly composed of the following strategies.
(1) Improvement in the efficiency of the compressor: The screw compressors have higher efficiencies than the piston and sliding vane compressors. However, for specific compressor clusters, an increase in the load rate and the optimisation of the cluster control can reduce the power consumption [3,4]. Cai  pneumatic energy-saving theory on the flow power. This controller could achieve an energy saving of compressor groups by the flow and predictive controls [5,6]. The frequency conversion control was also employed to achieve the adjustment of the speed of an air compressor. The energy consumption of the compressor could be different for different load levels, which could save 30-40% of the energy consumption [7]. (2) Improvement in the hardware structure of pneumatic components: This method mainly focuses on the improvement in the compressor structure to reduce the friction and the gas resistance loss. For rotary compressors, energy saving can be achieved by improving the meshing profile and the belt transmission efficiency as well as reduction in the resistance loss of the oil-gas separator, valves, and other filtering devices [2,7]. (3) Heat recovery and utilisation: In the process of producing compressed air, around 80% of the electric power consumed is converted into heat [1]. 50-90% of this heat can be recycled except for the heat radiated to the environment and stored in the compressed air itself. The heat recovery of the pneumatic systems is usually achieved by heating other air or water through heat exchangers. The application of this method includes auxiliary heating and boiler water preheating etc. [8][9][10]. (4) Reduction in air leakage: This method is mainly applicable to the processes of supplying air with different pressures according to different applications [11]. This method aims to reduce the pressure loss along the air passage and to improve the ability to detect air leakage [6,12]. Some researchers introduced the method of connecting the overflow valve with the rod chamber so that the air supply pressure of the chamber during the piston retraction is lower than that during the piston stretching-out. When this method was employed in horizontal cylinders and vertical cylinders, the system energy saving of 25-75% could be achieved [13].
The above research mainly focused on energy saving in the air production and transportation periods. However, if the compressed air produced and delivered to an actuator cannot be effectively utilized, it will lead to a greater energy loss. In the traditional pneumatic systems, compressed air is continuously filled in the cylinder chamber during the whole stroke of the actuator, which mainly uses the expansion energy of compressed air to do works. One shortcoming of this traditional method is that compressed air is directly exhausted to the atmosphere at the start of the actuator's return stroke resulting in the loss of much expansion energy.
In order to fully utilize the energy of compressed air, many researchers are paying attention to the utilisation efficiency of compressed air during the working process of the pneumatic actuators. One method for improving the utilisation efficiency of compressed air is to store the exhausting compressed air into a container. Another method is to reuse the compressed air intake coming from higher pressure stroke in lower pressure stroke [14][15][16]. The practical application of these methods showed that nearly 50% of air consumption could be saved. Du et al. proposed a new type of closed pneumatic circuits, where an air compressor is connected to both the inlet and the outlet of the cylinder. By transferring the exhausted compressed air to the inlet directly, the system could save 70-74% of the air consumption [17]. In recent years, another method based on the bridge-type circuit and mathematical optimisation has been investigated. Some researchers [18,19] proposed the idea of controlling air intake and exhaust separately to make full use of the expansion energy of compressed air. The results showed that energy saving could reach 80%. Du et al. studied the method of scheduling the air intake and exhaust time by mathematical optimisation to reduce air consumption in the bridge-type pneumatic circuit. This method can not only save energy, but also improve motion stability [20].
Based on the above research achievements, this paper introduces two energy-saving methods for the piston stretching-out stroke in the bridge-type pneumatic circuit. These two methods are the quantitative air intake method and the optimisation of the air intake and exhaust duration method. Compared with pre-vious studies, the quantitative air intake method is a new method based on energy conservation. The optimisation of the air intake and exhaust duration method simplifies the model complexity of the bridge-type pneumatic circuit composed of four on-off valves instead of five on-off valves. The optimisation of the air intake and exhaust duration method simplifies the bridge-type pneumatic circuit composed of five on-off valves into that composed of four on-off valves, which can reduce the model complexity and improve the calculation speed. Both of the methods track the expansion energy of compressed air as effective work energy. The ways to fully utilize the effective energy of compressed air during the piston stretching-out stroke were mainly discussed in this work. Then, the amount of the minimum air needed for a specific pneumatic system was found through the theoretical calculation. Based on the experimental results of the two methods, this paper analyses the characteristics and applicability of each method.

Modelling for minimum air consumption
In this part, the energy composition and conversion of compressed air during the processes of the compressed air production and the piston pushing out were analysed, as shown in Figure 1. Based on the principles of energy conservation and the ideal gas law, the equations of the energy composition and conversion of compressed air during its production and working processes were established. The main target of this section is to find out how much energy one stroke needs for pushing the piston and the load from the retracted state to the fully extended state. For this purpose, how much air (the volume V 0 in the standard condition) should be filled in the cylinder chamber to meet the work demand was investigated. Here, the thermodynamic law and the energy conservation method are used for modelling and calculating the minimum air consumption in this system.

Energy composition changes of air during the compressing process
According to the energy conservation equation of gas [21], the energy composition of air before and after compression can be expressed by where the subscripts 0 and 1 denote the values in the standard atmosphere and the tank, respectively, H is the enthalpy of air,

FIGURE 1
Thermodynamic processes during the production of compressed air and the piston stretching-out stroke m is the mass of the air, v is the air velocity, g is the gravitational acceleration, z is the height of the centre of the air mass, Q is the external heat exchange, and W is the work exchange between air and outside. Usually, during the production of compressed air, a compressor compresses the standard atmosphere into a tank. When the air in the tank becomes static and is under the standard temperature, this process is regarded as an isothermal process. Assuming that the air before and after the compression process is approximately static without flowing velocity, the kinetic energy of the air is equal to 0. Also, there is no heat exchange before the atmospheric air to be compressed, so Q 0 is equal to 0. After the compression process, the air will be stored in the constant volume tank without volume change, so W 1 is equal to 0. By ignoring the change of the potential energy of the air, (1) can be simplified as Because the process is isothermal, the enthalpies of the air before and after the compression process shall be the same, so H 0 = H 1 . Therefore, the work done by the compressor is equal to the heat that the compressed air releases.
From the above analysis, it can be concluded that compressed air with the volume of V 0 under the standard condition has the following enthalpy: where U 0 is the total internal energy of the compressed air stored in a tank, V 0 is the volume of the compressed air stored in a tank under the standard condition which shall be the minimum air consumption for a piston stretching-out stroke, V mol is the volume of one mole of air under the standard condition, and p 0 is the absolute atmospheric pressure under the standard condition.

Energy conversion of compressed air during the piston stretching-out process
The piston stretching-out process is that the compressed air in the tank enters the chamber without a rod in the cylinder and pushes the piston and the load to move the piston to the stroke end. The analysis and calculation were carried out based on the energy conservation equation of gas expressed by where the subscripts 1 and 2 denote the values in the tank and in the chamber without a rod in the cylinder, respectively. The piston stretching-out process completes quickly without heat exchange. This is an isentropic process, and the air has no kinetic energy after finishing the process. So (4) can be simplified into In order to save the air consumption and make full use of the expansion energy of compressed air, the pressure in the chamber without a rod should be equal to the ambient atmospheric pressure when the piston reaches the end of the stroke. Then, the air enthalpy in the chamber without a rod at the end of the stroke can be expressed by where T is the absolute temperature of air, d is the internal diameter of the chamber without a rod, and L is the stroke distance. According to the ideal gas law, the state equation of air, in this case, can be described by The work W 2 done by the compressed air is composed of two parts where W e is the work done by the volume expansion of air and W f is the work against friction during the whole stroke.
W e and W f can be expressed by (9) and (10), respectively where k is the ratio of specific heat, which is 1.4 for air where is the friction coefficient. Based on the above analysis, the minimum air consumption volume V 0 under the standard condition, which is just enough for pushing the piston with the load to the stroke end, should satisfy the following equation: For a pneumatic system with given values of the air supply pressure, the load, and the cylinder structure parameters, the minimum volume of air consumption V 0 under the standard condition can be calculated by (11). Based on (11) and the parameters of an actual pneumatic system shown in Table 1, the minimum volume of air consumption was calculated to be 2.7 L under the standard condition.

Verification experiment for the quantitative air intake method
In order to verify the accuracy and applicability of the theoretical calculation results shown above, an experimental system was established. This experimental system was mainly composed of the bridge-type pneumatic circuit, the signal acquisition system, and the software system based on the LabVIEW. The detailed equipment specifications are listed in Table 2, and a photo of the equipment is shown in Figure 2. Three pressure sensors were installed on the air supply pipe and the intake and exhaust ports of the cylinder, respectively. These sensors could monitor the air pressures in the air supply pipe and chambers. Two flow sensors were installed on the intake and exhaust pipes, which could detect the intake and exhaust flow. The displacement sensor was installed under the cylinder with a detector fixed on the rod end, which could detect the displacement of the piston.
In the experiment, the intake air volumetric flow rateV in can be measured by the flow meter, and the real-time intake air volume V ′ 0 under the standard condition can be obtained by the following equation: When the intake air volume V ′ 0 was equal to the required air volume V 0 , the inlet valve closed automatically, while the piston continued to move under the work of the air expansion energy until reaching the stroke end. This method demonstrated a reduction in the consumption of compressed air and achieved the purpose of saving energy. Figure 3 shows the experimental results of the pressure in the cylinder chambers, the intake air flow rate, the piston displacement, and the piston speed. The results show that the experimental equipment could detect and calculate the standard volume of the air being filled in the cylinder chambers in real time. When the air intake reached the required minimum air volume, the inlet valve closed and the piston kept moving until arriving at the stroke end. Figure 3(c) shows that the piston reached the stroke end at 0.63 s, and the speed of the piston was smooth without obvious impact. By analysing the flow data, the total air consumption was 2.58 L, which is 4.4% different from the theoretical value of 2.7 L. Compared with the traditional continuous air supply method, the quantitative air intake  method could save 76% of the air consumption. So, the experimental results confirmed the correctness of the theoretical analysis and calculation, which could achieve the required energy saving of the bridge-type pneumatic circuit.
In order to verify the applicability and accuracy of this method, more experiments with different air supply pressures and loads were carried out using the same experimental equipment. Table 3 shows three sets of experimental parameters and a comparison between the calculated intake air volume and the   Figure 4 shows the time change of the piston displacement and the intake air volume flow rate in the case of the first set of parameters shown in Table 3. From Table 1 and Figure 4, it can be found that the actual air intake was less than the calculated value in most of the time resulting in the piston not fully reaching the end of the stroke. The reason is that the flow was detected by the flow meter, and the intake volume was obtained by integrating the signals with much noise, as shown in Figure 5. So, the calculated intake air volume was different from the actual one. Also, the collection of multiple signals for the real-time calculation requires complicated software and hardware resulting in higher cost and lower accuracy. This is one of the disadvantages of the quantitative air intake method. In the following section, another energy-saving method based on the optimisation of the air intake and exhaust duration will be introduced.

Modelling and optimisation
Due to the limitation in the accuracy of the sensor and realtime calculation, the quantitative air intake method should have some errors. The main purpose of saving energy is to reduce Original intake volume flow data without filtering the amount of air intake by controlling valve switching. The method discussed in Section 2 is to monitor the air intake volume through real-time signals, whose accuracy depends on the sensor accuracy. So, in this section, we propose another method to control the air intake volume by controlling the opening and closing state of the valves, which shall make the system control more efficient and improve the system accuracy. In order to obtain the on-off schedule of the valves, the system dynamics models of the bridge-type pneumatic circuit were established. Then, the mathematical optimisation method was used to obtain appropriate results. It should be pointed out that the optimisation objectives include not only air consumption, but also the stroke time and the piston speed. Therefore, during the piston stretching-out stroke, both of the intake and exhaust valves shall have switch action, and sometimes, they will switch several times in one stroke.

Air volume flow rate into the cylinder chamber
The air volume flow rate coming into the cylinder chamber can be described byV where j is the flow direction coefficient (air intake into the cylinder chamber: j = 0, exhaust to the atmosphere: j = 1), i is the valve symbol (inlet value: i = l, exhaust value: i = r), u is the onoff state of a valve (valve open: u = 1, valve close: u = 0), and G(p s ,p 1 ,b) is the air volume flow rate calculated by where C i is the sonic conductance, ρ is the air density, p s is the upstream pressure of the valve, p i is the downstream pressure of the valve, and b is the critical pressure ratio usually taken as 0.528. Then, the air volume flow in the two chambers in the cylinder during the piston stretching-out stroke can be expressed by (15) and (16), respectivelyV

Dynamic equation for the chamber pressure
The chamber pressure can be described bẏ where n is the gas polytropic index, V li (x) is the volume change during working, V ti is the dead zone volume of the chamber, R is the gas constant, and t 0 is the gas absolute temperature under the standard condition, which is 293 K.

Piston displacement state equation
The piston dynamic displacement can be expressed bÿ whereẍ is the piston acceleration, A l is the cross-sectional area of the chamber's inner cavity, A o is the cross-sectional area of the piston rod, F f is the ambient atmospheric pressure, which is equal to standard atmospheric pressure, and F f is the friction force with the external support when the piston is moving horizontally.
In order to simplify the complex model and improve the calculation speed, F f is described by

Optimisation function establishment
For the optimisation required, the state vectors are defined by where x 1 is the piston displacement, x 2 is the piston speed, x 3 is the pressure in the chamber without a rod, x 4 is the pressure in the chamber with a rod.
The input vectors are defined by Then, the system state model can be expressed by Furthermore, the optimisation function can be expressed by and This is a dynamic optimisation problem in the form of differential-algebraic equations. The state variables shall satisfy certain boundary conditions at the beginning time t 0 and the ending time t e . For the actual experimental conditions shown in Table 1, the optimisation model can be expressed by This is a mixed-integer nonlinear dynamic optimisation problem with nonlinear differential equations, so it is difficult to solve by general methods. Based on some research studies [20,22], by employing the methods of "dynamic optimisation model discretisation" and "SQP algorithm", the optimisation tool AMPL can determine the intake and exhaust time by the IPOPT solver. According to the parameters shown in Table 1, the optimisation results of the on-off status of intake and exhaust valves are shown in Figure 6.
According to the optimisation objectives and constraints, it can be seen that the intake valve keeps open from the beginning to 0.17 s and opens again after a period of time. On the other hand, the exhaust valve keeps open except for the short time close at 0.62 s. Table 4 shows the detailed on-off duration of these valves.

Verification experiment for the optimising the intake and exhaust duration method
The experimental equipment shown in Figure 1 has the function of setting the switching time of the valves. This function can control the valves to open and close at certain times. This function was mainly used to verify the accuracy of the on-off time sequence of the valves that were determined by the optimisation. Especially, for the case of the discrete optimisation results, better intake and exhaust durations could be obtained by experiments to integrate or adjust the on-off time sequence of the valves. In order to verify the accuracy of the theoretical research, the optimized duration of the intake and exhaust valves shown in Table 4 was put into the experimental system. The piston displacement and the air intake volume flow rate in the experiment are shown in Figure 7.
The experimental results show that when the intake valve closed at 0.37 s, the piston kept moving by the energy of air expansion and reached the end of the stroke smoothly at 0.93 s. Different from the quantitative air intake method, the piston fully reached the end of the stroke at this time. The total air consumption was 2.71 L, which is closer to the theoretical value of 2.7 L than the value of 2.58 L obtained by the quantitative air intake method. This method could also save 76% of compressed air, but because the intake valve closed for some time, the whole stroke time was longer than that of the quantitative air intake method.
The above results show that the applicability of the optimisation results greatly depends on the air supply pressure and the load value. It should be noted that the ideal air intake and exhaust time sequence cannot be obtained under all boundary conditions. For example, under fixed stroke time and air supply pressure, if the load is too high, the piston cannot reach the stroke end even though the air intake is enough for the whole assumed stroke time. Then, the optimized result is not available. We define the applicability level as "1" when the optimisation results are inapplicable to practical applications, and define the applicability level as "5" when the optimized on-off status is clear and the application results are accurate for the actual pneumatic circuit. If the optimized on-off status is discrete and can be applied to the actual system after conducting some manual adjustments, as shown in Figure 8, its applicability is defined as "2", "3", and "4" according to the discrete situation.  In order to identify which boundary values are suitable for the optimization method and what is the relationship between the boundary values, and the applicability of the optimization method under different conditions, are evaluated here. Table 5 shows the scale of the boundary values.
The applicability levels of the optimisation results were verified under different air supply pressures and loads for varying stroke time, as shown in Figures 9 and 10, respectively. As shown in Figure 9, at the fixed load of 38.48 kg, when the air supply pressure is in the range from 0.3 to 0.7 MPa and the whole stroke time is in the range between 0.5 and 0.85 s, the optimized results have high applicability levels. But when the air supply pressure is 0.2 MPa, the on-off status of the valves obtained by the optimisation has a low applicability level and is difficult to be used in the actual bridge-type pneumatic circuit. The applicability levels of the optimisation results drop quickly when the boundary conditions will be out of the effective range. The main reason is that, at a fixed stroke time, if the air supply pressure is too low or the load is too high, the assumed stroke time is impossible to be achieved.
When the applicability level is between 2 and 4, the optimized results can also be used after conducting some adjustments. As shown in Figure 8, the on-off time sequence of the intake and exhaust valves can be obtained by the optimisation method under the boundary conditions shown in Table 6.
The optimisation method gives the air intake duration from the beginning to 0.35 s, but the exhaust start time is relatively discrete around 0.35 s. In order to find out a reasonable exhaust start time, experiments with three different exhaust start times were carried out. Table 7 shows the experimental design.    Figure 11 shows the air intake flow rate and the piston speed with different exhaust start times. As shown in Figure 11(a), the air intake volume flow rates were the same for the exhaust start time of 0.3, 0.35, and 0.38 s. But as shown in Figure 11(b), different exhaust start times led to different piston speeds. In this case, the later the exhaust start time was, the smoother the piston speed became. So, by adjusting the exhaust start time to 0.38 s, the pneumatic system could have better motion stability.

CONCLUSIONS
This paper introduces two energy-saving methods for the bridge-type pneumatic circuit. The main idea of the methods is to find out how much compressed air is needed for a piston stretching-out stroke and to control the air intake at the minimum required level. The first method is the quantitative air intake method, where the energy content of air from the atmosphere to the compressed state is analysed to calculate the minimum air consumption in a specific pneumatic system based on the state equation of air and the energy conservation principle. The modelling and calculation of the quantitative air intake method are simple and easy. But the accuracy of this method is affected by the accuracy of sensors and real-time calculation so some errors in practical applications are inevitable. The second method is to achieve energy saving by controlling the intake and exhaust duration. This method uses mathematical optimisation to obtain the opening and closing times of the intake and exhaust valves and achieves saving energy by controlling the switching time of the valves. Furthermore, by setting the optimisation objectives of the piston speed and the stroke time, the second method can improve the running stability of a pneumatic system by avoiding the stroke end impact and adjusting the full stroke time as required. The applicability of the optimisation algorithm was also verified by some experiments. Some discrete optimisation results can also be used after conducting some adjustments and experimental verifications. So, compared with the traditional way to fill in compressed air in the cylinder chamber during the whole stroke, both methods can achieve the target of saving energy. The experimental results showed that 76% of the air consumption could be reduced compared with the traditional way. In further study, there are some works needed to be done. Especially, when the applicability levels of the optimisation results are below "5", the on-off time of the valves cannot be directly applied to the actual pneumatic system without some manual adjustments. Therefore, future research should focus on the precise system dynamic model to improve the optimisation method to get better on-off time intervals of the valves.