Research and application of ultra-high pressure control system in strength tests

2.1. System composition

At present, there are mainly two strategies to obtain ultra-high pressure: using ultra-high-pressure components to obtain ultra-high pressure directly or using low pressure hydraulic components and a booster cylinder to obtain ultra-high pressure. The former strategy is expensive, with high flow, high internal leakage, and low efficiency [12]. The control accuracy of the ultra-high pressure with low flow is poor, and it is hard to control when reducing the pressure, which failed to meet test requirements. So, the latter strategy is selected for its convenience and low energy consumption in this paper.

1) Control system.

MOOG16 multi-channel coordinated loading control system is selected, which adopts PID algorithm [13], and can set the value of parameters in the computer according to the requirements of force, displacement, or pressure. Servo valves were used to control the action of the hydraulic system, and the input parameters were converted into weak electrical signals through force, displacement, or pressure sensors. After signal conditioning and A/D conversion, the signals are sent to the main controller, then compared with the instruction value to perform compensation coordination. Finally, the collected data and control status are transmitted to the computer, and the interface displays the working condition of the loading device at that moment. The system can carry out out-of-tolerance and out-of-limit settings according to the test requirements and modify test parameters to obtain desired control results.

2) Hydraulic system.

The hydraulic system provides 21 MPa working pressure for the system. It is composed of oil source, a pump station, hydraulic pipeline, servo valves, etc. The hydraulic system has an unloading module that can unload the pressure to zero manually or automatically in case of an emergency.

3) Booster cylinder.

The booster cylinder is the core of the whole system, which is responsible for converting low pressure oil of the low-pressure hydraulic system into high pressure oil.

Fig. 1Diagram of the booster cylinder

The structure of the booster cylinder is shown schematically in Fig. 1. It includes a low-pressure cavity C and a high pressure cavity D. The piston areas at both ends of the piston rod are different. The piston diameter of cavity C is 140 mm, While the diameter of cavity D is 80 mm, and the piston rod stroke is 500 mm. When the low-pressure oil is input to cavity C, the high pressure will be generated in cavity D. The value of the supercharging ratio is 3:1, which is equal to the ratio of piston areas at both ends. Therefore, the working pressure of cavity C is 21 MPa, and that of cavity D is 63 MPa. Like low pressure hydraulic system, the medium of the system is No. 46 anti-wear hydraulic oil.

2.2. Working principle

The working principle of the system is shown in Fig. 2.

When it is needed to raise the pressure, low-pressure oil output by the oil pump is pushed into the left rodless cavity of the booster cylinder through servo valve A, while hydraulic oil in the rod cavity of the booster cylinder flows back to the oil tank. By this way, the piston is pushed toward right, causing that cavity D and the actuating cylinder get high-pressure. At the same time, hydraulic oil in the rod cavity of the actuating cylinder flows back.

When it is needed to reduce the pressure, servo valve A reverses its direction, low-pressure oil output by the oil pump are pushed into the rod cavity of the booster cylinder through servo valve A and B, while hydraulic oil in the rodless cavity of the booster cylinder flows back to the oil tank. By this way, the piston retracts to the left, and the pressure of the actuating cylinder is reduced. At the same time, low pressure oil output by the oil pump enters the rod cavity of the retraction actuator to supplement oil to the rod cavity of the retraction actuator.

Before the test, a pressure sensor is connected to the pressurization cavity, so that flow of the servo valve can be controlled by the feedback of the sensor.

Fig. 2Diagram of pressurization circuit: 1 – oil tank, 2 – oil filter, 3 – oil pump, 4 – motor, 5 – servo valve A, 6 – servo valve B, 7 – booster cylinder, 8 – actuating cylinder, 9 – unloading valve

2.3. Calculation of the booster cylinder strength

In order to develop the potential for strength of the booster cylinder on the premise of safety, strength of the booster cylinder should be reasonably decided. Generally, the safety factor shall not be less than 5. The material of the cylinder is Quenching and tempering treatment 27SiMn, with tensile strength of 980 MPa and yield strength of 835 MPa. Main dimensions of the booster cylinder are shown in Table 1.

Strength of the cylinder is calculated by the theoretical method and finite element simulation respectively as follows.

1) Theoretical calculation.

For a thick-walled cylinder, the cylinder is in a state of three-dimensional stress, including radial compressive stress ${\sigma }_r$, tangential tensile stress ${\sigma }_{\theta }$, and axial tensile stress ${\sigma }_{\mathrm{s}}$, as shown in Fig. 3.

Fig. 3Stress analysis of thick-walled cylinder

According to the thick-walled cylinder theory [14], the stress is calculated by the following formula:

where, $p_{\mathrm{y}}$ – test pressure, $R_0$ – outside radius of the booster cylinder, $R_i$ – inner radius of the booster cylinder, $r$ – radius at any position of the cylinder, $K$ – $K=R_0/R_i$.

It can be seen that the stress reaches the maximum on the inner wall of the cylinder, where $r=R_i$. According to the fourth strength theory, the stress of the cylinder is as follows:

As a result, the following results are achieved:

Stress of the cylinder’s high-pressure cavity, $\left[\sigma \right]=$ 146 MPa, the factor of safety, $n=\sigma /\left[\sigma \right]=$ 835/146$=$ 5.7.

Stress of the cylinder’s low-pressure cavity, $\left[\sigma \right]=$ 155 MPa, the factor of safety, $n=\sigma /\left[\sigma \right]=$ 835/155 = 5.3.

2) Finite element simulation.

A finite element model of the pressurized cylinder was established in Abaqus. The model was discretized into 35188 elements, the main type of which is hexahedral linear reduction integration element C3D8R. The high-pressure cavity is loaded a pressure of 63 MPa, while pressure of the low-pressure cavity is 21 MPa.

The FEM results show that peak stress on the inner wall of the high-pressure cavity reaches 132.4 MPa, and the safety factor is 6.6, while peak stress on the inner wall of the low-pressure cavity reaches 149.6 MPa, with a safety factor of 5.6. The stress cloud picture is shown in Fig. 4.

It can be seen from the above analysis that the theoretical calculation results are close to the finite element analysis results, as shown in Table 2. The results demonstrate that the strength safety factor of the booster cylinder is greater than 5, which meets the strength requirement.

Fig. 4FEM results of the booster cylinder

3.1. Test overview

During aircraft take-off and landing phases, the actuating cylinder is the main core component to control the retraction and extension of the landing gear [15]. The actuating cylinder is a two-force hinged support rod, one end of which is hinged to the main strut of the landing gear, and the other end of which is hinged to the wing (or fuselage). Extension and retraction of the piston are controlled by the hydraulic system of the aircraft.

During retraction and extension of the landing gear, the actuating cylinder joint on the wing is subjected to an axial force from the actuating cylinder. The joint is made of aluminum alloy and is connected with the wing by screws, so its strength is weaker than that of the landing gear and the actuating cylinder. Therefore, the structural strength of the joint and its diffusion area is necessary to be tested. The actuating cylinder has two working states: retracted state and extended state, which are shown in Fig. 5.

Fig. 5Diagram of a landing gear in retracted and extended states

a) Retracted state

b) Extended state

Generally, the force shall be applied to the joint in the specified direction. But a loading actuator and a force sensor cannot be arranged in this test, due to the limitation of loading space. Therefore, pressurization directly in the actuating cylinder was considered, and the force value is calculated according to oil pressure and cross-sectional area of the piston, so as to achieve the purpose of checking the strength of the joint.

The oil circuit was connected as shown in Fig. 2 before the test. For retracted state of the landing gear, rod cavity of the actuating cylinder related to the booster cavity (cavity D shown in Fig. 1). For extended state of the landing gear, rodless cavity of the actuating cylinder related to the booster cavity.

Before the test, the actuating cylinder was disconnected from the connecting structure, and the booster cylinder was used to apply pressure to the working cavity of the actuating cylinder. When piston rod of the actuating cylinder was observed to move, the value of the pressure sensor was recorded, which was the starting pressure for the actuating cylinder. Then the value of the pressure sensor was set to zero.

The test was completed in the Full-Scale Aircraft Structure Static/Fatigue Aeronautic Science and Technology Laboratory, Aircraft Strength Research Institute of China. 100 % and 150 % limited load tests were carried out in retracted state and extended state of the landing gear, respectively. The test loading process was stable, and the control system worked well during the test.

According to the test load, pressure in the rodless cavity of the actuating cylinder in the 100 % limited load test is 28.98 MPa in extended state, and pressure in the rod cavity of the actuating cylinder in the 100 % limited load test is 28.98 MPa in retracted state.

3.2. Test results

High loading accuracy was obtained in the test, and the control accuracy of 100 % and 150 % limited load tests in both cases is shown in Table 3. In fact, the relative error is far less than 0.5 % in the whole process of the test.

Six strain gages were pasted on the actuating cylinder joint to monitor stress state of the joint. Variation of strain with load obtained from the test are shown in Fig. 6 and Fig. 7.

Fig. 6Variation of strain with load in retracted state of the landing gear

a) 100 % limited load test

b) 150 % limited load test

Fig. 7Variation of strain with load in extended state of the landing gear

a) 100% limited load test

b) 150% limited load test

In the limited load tests of 100 % and 150 % in retracted state of the landing gear and 100 % limited load test in extended state, strain increased linearly with the load, and the maximum strain was below 5000 με. In the 150 % limited load test with the landing gear extended, strain increased linearly with the load before 120 % limited load, while the strain curve was basically flat after 120 % limited load, as shown in Fig. 7(b). It indicates that the load greater than 120 % was not transmitted to the actuating cylinder joint. The reason may be that the piston travel of the actuating cylinder is limited and can no longer be extended. It can be seen that the actuating cylinder joint will not bear more than 120 % of the load in actual case.