Structure design and deformation analysis of double hydraulic cylinder deep-sea pressure simulator

Because of the particularity of the deep-sea environment and the difficulty of on-site observation and research, it is particularly important to establish a deep-sea simulation system for research. Based on the high measurement accuracy requirement of deep-sea simulation equipment, a design scheme of a deep-sea pressure simulation device with a double hydraulic cylinder that can measure small water pressure changes is proposed. Firstly, the working parameters and pressure principle of the design are introduced, and then the deformation of the deep-sea pressure simulation device is analyzed. The mathematical model of piston feed and pressure without considering the deformation of the sealed pressure cylinder and the mathematical model of piston feed and pressure considering the deformation of the sealed pressure cylinder are established respectively. Finally, the relationship curve is analyzed by using origin software. The results show that when the deep-sea pressure simulator is used to simulate the underwater environment, it is necessary to consider not only the influence of liquid compression on the pressure but also the influence of deformation on the pressure.


Introduction
The reliability of underwater instruments and equipment must be tested and determined by experimental devices that simulate underwater environments.With the further development of underwater resources, higher requirements are put forward for the accuracy of deep-sea simulation experimental devices [1][2][3][4].Therefore, it is of great significance to design a deep-sea pressure simulation device with high accuracy.In [5][6], hydraulic pumps and electro-hydraulic servo valves are used for pressure control.However, due to the control accuracy of the electro-hydraulic servo valve and the fluctuation of motor speed, it was difficult to achieve relatively high precision pressure control.In [7][8], the liquid volume in the piston feed compression simulator is used for pressure control.The control accuracy of this method was high, but its pressure control range was limited, which made it difficult to achieve high-precision pressure control under a large pressure environment, so its application range was narrow.To simulate the underwater pressure environment with high precision, we should not only consider the high-pressure environment but also consider the precision control under the high-pressure environment.Based on the above factors, a pressure control method of a double hydraulic cylinder was proposed based on the compressibility of liquid [9][10].The pressurization scheme was realized by controlling the piston feed of the main and auxiliary hydraulic cylinders, in which the piston feed of the main pressurization system could make the pressure device reach the target pressure value range quickly.The piston feed of the auxiliary pressurization system could accurately control the small pressure, to achieve the goal of simulating the deep-sea pressure environment with high precision.

Mechanism design
To reduce the error caused by pressure fluctuation, a deep-sea pressure simulator with a double hydraulic cylinder is developed, which can measure the small water pressure change.The device can realize high-precision deep-sea environment simulation.The deep-sea pressure simulation device is shown in Figure 1.The device mainly consists of three parts: a sealed pressure cylinder for simulating an underwater environment, a feed rate control system for controlling pressure changes, and a support for supporting the simulation device.The sealed pressure cylinder comprises a cylinder cover, cylinder body, pressure gauge, and bolt group.The control system includes Motor 1, Reducer 1, ball screw 1, main hydraulic cylinder, Motor 2, Reducer 2, ball screw 2, and auxiliary hydraulic cylinder.The deep-sea pressure simulator can simulate the ocean depth of 0-500 m, and its main technical parameters are shown in Table 1.The device adopts a double hydraulic cylinder pressure system, which can realize the precise pressure requirement of 0-5.0 MPa through the coordinated feed of the main and auxiliary pressure system pistons.The structure block diagram of the pressure control system of the high-precision pressure simulation device is shown in Figure 2. The control object of the control system is the feed amount of the piston, and the purpose of control is to make the pressure inside the pressure cylinder reach the corresponding depth value of the marine environment, to simulate the depth of the marine environment to the greatest extent.The principle of its control is when the piston is fed, the pressure signal is converted into a digital signal through A/D conversion and is received by the data acquisition system.The current feed rate is calculated by detecting the control algorithm module of the data feed rate and is compared with the set feed rate.After calculation, the control signal is output.In Figure 2, the dotted boxes are the main components of the main and auxiliary pressurizing systems.The cross-sectional area of the piston of hydraulic cylinder 1 of the main pressurizing system is larger than that of the hydraulic cylinder 2 of the auxiliary pressurizing system.During the operation of the main pressurizing system, the internal pressure of the pressure device can quickly reach the target pressure range, while the auxiliary pressurizing system can accurately control the small pressure.Thus, the goal of simulating the deep-sea pressure environment with high precision is achieved.

Deformation analysis
The deformation of the sealed pressure cylinder, pipeline, and bolt will all lead to the reduction of the internal pressure of the whole device.However, due to the slight influence of pipeline deformation and bolt deformation, only the deformation of sealed pressure cylinders is studied [11].
Firstly, the assembly model of the sealed pressure cylinder is imported into ANSYS software, and then a 5.0 MPa pressure load is added.Finally, the results can be obtained through analysis, as shown in Figure 3.
Figure 3 shows the deformation analysis result of the sealed pressure cylinder under the pressure of 5.0 MPa.The deformation of the pressure gauge is not required to be considered in the analysis, so only the deformation result of the pressure cylinder is observed.According to the analysis of Figure 3 (a), the maximum deformation of the pressure cylinder is located in the center area of the cylinder cover, which is the orange area shown in Figure 3 (a).The maximum deformation is 0.041627 mm, and the average deformation of the lid is about 0.0258 mm.The maximum deformation of the cylinder is located in the inner wall of the cylinder, and it is difficult to directly observe the result of its deformation in the left figure, so it is necessary to pull the cylinder out separately to analyze the result, as shown in Figure 3 (b).It is concluded that the maximum deformation of the cylinder is located in the middle area of the inner wall of the cylinder, that is, the red area shown in Figure 3

The relationship between piston feed and pressure without considering the deformation
The main parameters of the main and auxiliary pressurization systems are shown in Table 2. Initial liquid volume (V/mm 3 ) 1.32u10 7   The piston feed of the main and auxiliary pressure systems can compress the liquid and thus play the role of pressure.According to the compressibility conditions of the liquid, it can be obtained: where ݇ is the coefficient of liquid compression (MPa -1 ); ܸ is the initial liquid volume (mm 3 ); οܸ ᇱ is the volume compression of liquid (mm 3 ) under the action of Pressure P; ܸ is the corresponding volume of the piston (mm 3 ) when it is fed a certain stroke, and ܸ = ‫ܮ‬ ଵ ‫ܣ‬ ଵ + ‫ܮ‬ ଶ ‫ܣ‬ ଶ , in which ‫ܮ‬ ଵ and ‫ܮ‬ ଶ refer to the feed stroke of the main and auxiliary hydraulic cylinder pistons (mm), and ‫ܣ‬ ଵ and ‫ܣ‬ ଶ refer to the cross-sectional area of the main and auxiliary hydraulic cylinder pistons (mm 2 ).Thus, the relationship between piston feed and pressure is obtained.
The relationship curve is shown in Figure 4.As shown in Figure 4, the black box line is the relationship curve between the feed rate and pressure when the piston of the main hydraulic cylinder is fed, and the red dot line is the relationship curve between the feed rate and pressure when the piston of the auxiliary hydraulic cylinder is fed.It can be seen from the figure that the change of pressure inside the pressure cylinder caused by the piston feed of the auxiliary hydraulic cylinder is an order of magnitude smaller than that of the piston feed of the main hydraulic cylinder, and the relationship between the piston feed and pressure is approximately linear in the range of 0-140 mm, so accurate pressure control can be carried out through this relationship curve.

The relationship between piston feed and pressure when considering deformation
Volume before deformation: where ‫ݎ‬ is the inside diameter of the pressure cylinder (mm); ݄ is the inside height of the pressure cylinder (mm).Volume after deformation: where ݂(݄) is the inside diameter of the pressure cylinder at different heights (mm); ο݄ is the elongation of the pressure cylinder cap (mm).Thus, the total deformation is: Because the volume deformation of the sealed pressure cylinder is small, the deformation of the sealed pressure cylinder can be simplified into axial and radial deformation.Thus, the deformation of the simplified model οܸ is as follows: where ο‫ݎ‬ is the amount of increase in the inside diameter of the pressure cylinder under a certain pressure (mm); ο݄ is the amount of increase in the inside height of the pressure cylinder under a certain pressure (mm).
Through the above deformation analysis, it has been obtained that under the pressure environment of 5.0 MPa, the average deformation of the cylinder body and the average deformation of the cylinder cover are about 0.0114 mm and 0.0258 mm respectively.Therefore, axial deformation: ο݄ = 0.0258 ݉݉; radial deformation: ο‫ݎ‬ = 0.0114 ݉݉.The deformation of the sealed pressure cylinder is calculated by Formula (6): οܸ ൎ 3, 749 ݉݉ ଷ .
The above analysis is the deformation of the pressure cylinder under 5.0 MPa pressure.According to the same steps, the deformation analysis of the assembly of the pressure cylinder by ANSYS analysis software can be analyzed within the range of 0-5.0 MPa, and the average axial deformation ο݄ and radial deformation ο‫ݎ‬ of pressure cylinder can be also analyzed.The greater the pressure is, the greater the deformation οܸ of the pressure cylinder is.Therefore, to obtain the target pressure, we should not only consider the effect of liquid compression on the pressure but also consider the reverse effect of the deformation of the pressure cylinder on the pressure.Therefore, it can be concluded that the deformation of the pressure cylinder should be considered to simulate the deeper underwater pressure environment.
At this time, the formula of liquid volume compression should be revised as follows: The corrected relationship between piston feed and pressure is thus obtained.
The relationship curve is shown in Figure 5.It can be seen from Figure 5 that when considering the deformation of the pressure cylinder, the pressure of the piston of the main hydraulic cylinder can reach 5.0 MPa only when the piston of the auxiliary hydraulic cylinder is fed to more than 135 mm, and the pressure value changes slightly when the piston of the auxiliary hydraulic cylinder is fed.Compared with Figure 4, when pressurizing to the same target pressure value, the piston needs more feed considering the deformation of the pressure cylinder.Therefore, the previous conclusion is verified: when using the deep-sea pressure simulator to simulate the deep-sea environment, it is necessary to consider the reverse influence of the deformation of the pressure cylinder on the pressure.

Conclusion
To improve the simulation accuracy of the deep-sea pressure simulator, based on the compressibility of the liquid, a design scheme of a double-hydraulic cylinder deep-sea pressure simulator that can measure small water pressure changes is proposed.The pressurization scheme is realized through the coordinated feed of the main and auxiliary hydraulic cylinder pistons, in which the main hydraulic cylinder piston can make the pressure device reach the target pressure value range quickly while the auxiliary hydraulic cylinder piston can accurately control the small pressure, to achieve the goal of simulating the deep-sea pressure environment with high precision.This provides a new solution for the development of a high-precision deep-sea simulator.
Through the deformation analysis of the deep-sea pressure simulator, it is concluded that the deformation οܸ of the pressure cylinder is also different under different pressures within the pressure range of 0-5.0 MPa.Therefore, to obtain the target pressure value, it is necessary to consider not only the influence of liquid compression on the internal pressure of the deep-sea pressure simulator but also the reverse influence of the deformation of the deep-sea pressure simulator on the internal pressure.However, as the above analysis mainly stays in theory and there are some errors, the subsequent work needs to develop experimental equipment to further verify and optimize the control method, to obtain higher dynamic pressure simulation accuracy.

Figure 2 .
Figure 2. Block diagram of pressure control system structure.

Figure 4 .
Figure 4.The relation between piston feeding and pressure without considering deformation.

Figure 5 .
Figure 5.The relation between piston feeding and pressure with considering deformation.

Table 2 .
The main parameters of the main and auxiliary pressurization system.