Energy Analysis and Verification of a Constant-Pressure Elastic-Strain Energy Accumulator Based on Exergy Method

Abstract

Focusing on the low energy-storage efficiency and unstable energy output of existing accumulators, this paper proposes a novel constant-pressure elastic-strain energy accumulator based on the rubber material hyperelastic effect. The proposed accumulator can store and release energy at a constant pressure. Based on the exergy analysis method, the charging/discharging energy storage efficiency of a constant-pressure elastic-strain energy accumulator was analyzed. Then, the Mullins effect on the rubber airbag over multiple charging/discharging cycles was studied. Finally, a test platform was established to verify the energy storage efficiency, as well as the expansion and contraction pressure stability of the rubber accumulator during charging/discharging cycles. The experimental results showed that the energy storage efficiency calculation by the exergy analysis method was more accurate compared with the enthalpy analysis method. In tests with more than 200 cycles, the rubber airbag energy storage efficiency was always higher than 76%, and the expansion and contraction pressure errors at a steady state were less than 2.92 and 1.79 kPa, respectively. The results showed that the rubber airbag could be used as an effective energy storage component, which is very meaningful for energy recovery in pneumatic or hydraulic systems.

1. Introduction

As common energy storage elements, hydraulic accumulators are often used in systems for energy recovery. The airbag-type hydraulic accumulator is often used as an energy storage device in hydraulic hybrid systems to recover the energy generated when a car is braked and supply power when the car is restarted [1]. Studies have shown that when hydraulic hybrid technology has been applied to vehicles, fuel savings of 12–25% can be achieved in urban areas and fuel savings of 6–10% can be achieved during long-distance driving [2,3]. However, because the airbag type hydraulic accumulator cannot store and release energy at a constant pressure, the energy is often not fully recovered and is released due to the mismatch with the system pressure during the working process, resulting in energy waste [4]. Although the airbag accumulator is used as an auxiliary energy source and its power density meets usage requirements, the volume energy density and weight energy density are obviously not enough [5], which makes it difficult to apply hydraulic hybrid technology to small cars.

Many scholars have conducted research on hydraulic hybrid power systems and energy-storage element accumulators. Qingyong Zhang [6] conducted theoretical analysis on the airbag type hydraulic energy storage of hydraulically driven hybrid vehicles. The results showed that under the same initial braking pressure, the pressure growth rate and pressure variation range in the chamber were smaller when the accumulator volume was larger. Under the requirement of vehicle braking performance, reducing the accumulator volume and charging pressure increases the specific energy of the energy storage element. Bo Wang et al. [7] proposed a new configuration of a hydraulic hybrid electric vehicle based on compound accumulators. Simulation results showed that a hydraulic hybrid electric vehicle based on compound accumulators could switch the operation timing of large and small accumulators to take into account the energy recovery rate and braking performance. When the braking deceleration was 1.5 m/s², the energy recovery rate was 14.5% higher than that of a single accumulator. Eckert J [8] proposed a comprehensive optimization procedure of a series electric hydraulic hybrid vehicle powertrain and control through the interactive adaptive-weight genetic algorithm method. Battery aging is effectively reduced by using a high power density hydraulic accumulator, which acts as a peak power buffer unit. Hyukjoon K [9] introduced a thermodynamic theoretical method to analyze the energy characteristics of hydraulic hybrid systems. The method based on energy and exergy analysis is used in hydraulic hybrids.

Yunsong Lu [5] showed that the use of two-phase media could stabilize the output pressure of the accumulator and increase the energy density of the accumulator by 3–5 times. The difficulty was that it was difficult for the saturated vapor pressure to meet the ideal requirements. Yunsong Lu raised a cylinder accumulator using a multi-layer structure of carbon fiber and high-strength metal. When the working pressure was 1 × 10⁵ kPa, the energy density and specific energy were 1.05 × 10² kJ/m³ and 14 Wh/kg, respectively, which were 10 and 20 times greater than those of existing rigid accumulators. However, this still did not solve the problem of constant-pressure energy storage and release, and the production cost was higher. Alexander P and Eric J. Barth [10] put forward a hydraulic-strain-energy accumulator by using elastomer with a strain-energy-storage mechanism to obtain a higher energy storage efficiency and energy density. On this basis, John T. Tucker [11] evaluated and verified the materials, built a pressure prototype (the maximum filled liquid pressure was 3.8 × 10² kPa), and found that the energy storage efficiency of polyurethane in the accumulator exceeded 88%. Daniel N. Cramer and Eric J. Bart [12] conducted charging/discharging tests on rubber airbags of different materials and concluded that the latex airbag had ideal expansion and contraction behavior. They also determined the energy efficiency of the airbag with different inner diameters and materials. John M. Tucker and Eric J. Barth [13] established a mathematical model of the energy density of a hydraulic strain energy accumulator, analyzed the factors that affected the energy density, and presented corresponding solutions. Joshua J. Cummins et al. [14] established a mathematical model of the charging/ discharging energy storage efficiency of pneumatic strain energy accumulators based on the enthalpy analysis method, and they explored the influence of the rubber Mullins effect on the expansion pressure, contraction pressure, and energy storage efficiency of the device.

From the above analysis, it is known that the expansion pressure of the strain energy accumulator based on rubber material is an effective energy storage device with high energy density and steady pressure output. The pressure is determined by the material, wall thickness, and radial expansion radius. However, two problems that the above studies did not consider require further focus. On the one hand, in order to adapt to different system pressures, it is necessary to customize the airbag. On the other hand, the device’s performance depends heavily on the rubber material characteristics. With the increase in the number of uses, the rubber material damage will increase, which will inevitably lead to a decline in the performance of the whole device.

The key to solving these two problems is to perform accurate energy analysis, which should be carried out simultaneously from the perspectives of energy quantity and quality. The common enthalpy energy analysis method only analyzes the energy storage efficiency from the perspective of the amount of energy, and it cannot reveal the qualitative changes in the energy during the conversion or transfer process. At the same time, the method cannot fully reflect the loss within the system [15]. At present, an energy-saving analysis method widely used in industry is the exergy analysis method, which combines the “quantity” and “quality” of energy, scientifically analyzes the utilization of energy conversion and transmission, and truly reflects the external and internal losses in the process of energy utilization [16]. Kaiser F. [17] analyzed the optimized energy-saving scheme of an industrial compressed air system based on the combination of the exergy analysis method and the energy efficiency method. The results showed that the exergy analysis method was more in line with the actual situation and could be used to make more accurate decisions on the energy savings of compressed air systems. Chen L. [18] used exergy analysis to study the performances of the main components of a single-stage adiabatic compressed air energy storage system under different working conditions.

In summary, the strain-energy accumulator based on the study by Joshua J. Cummins et al. [14] was further investigated in this paper. One aspect that has not been studied is examined: accurate energy analysis to solve the problem of the energy loss inside the accumulator and the fatigue of the rubber airbag. Therefore, this paper mainly focuses on an accurate energy storage efficiency model and the influence of the Mullins effect during the process of rubber airbag charging/discharging by exergy analysis, and then built a test platform to verify the energy storage efficiency. First, the structure of the constant-pressure elastic-strain energy accumulator and the principle of constant pressure is explained. Then, the specific modeling process is given, and a constant-pressure elastic-strain energy accumulator charging/discharging test platform is built to verify the difference between the exergy analysis method and the enthalpy analysis method. Finally, combined with uncertainty analysis, the influence of the Mullins effect on the charging/discharging performance of the rubber airbag is explored.

2. Elastic-Strain Energy Accumulator Design

The structure of a constant-pressure strain-energy accumulator [19,20] is shown in Figure 1, which is mainly composed of a rubber airbag, rigid shield, fixed ring, quick coupling, etc. The rubber airbag is used to store energy. Additionally, the principle is that when the airbag is charged with gas, the compressed gas performs work on the airbag so the airbag is expanded and the gas pressure energy can be converted into strain energy and stored in the elastic body. When the airbag contracts and performs work on the gas, the elastic body strain energy can be converted into pressure energy and released the stored energy. The rigid shield limited the rubber airbag radial strain. On the one hand, it could increase the pressure during the charging/discharging process; on the other hand, it could prevent the rubber airbag from reaching the ultimate strain every expanded time and causing premature fatigue to ensure the device performance. The fixing ring was connected with the rigid shield and the quick coupling by an interference fit, which limited the position of the rigid shield and the quick coupling.

The constant-pressure elastic-strain energy accumulator’s characteristic is that it can expand and contract at a relatively constant pressure when charging/discharging. The charging/discharging pressure-volume curve is shown in Figure 2, and a typical rubber material stress–strain curve is shown in Figure 3. It can be seen from the figure that the volume changes continuously during the process of charging and discharging, while the expansion pressure and contraction pressure remain relatively constant.

The stress–strain curve in Figure 3 was divided into four regions. Region_(a), corresponds to the initial elastic modulus of the rubber, which corresponds to the gas pressure rise stage in Figure 2. As more gas is filled in, the stress on the rubber airbag increases, and the elastic modulus begins to decrease, corresponding to region_(b) in Figure 3. At this time, the rubber airbag undergoes hyperelastic deformation and begins to expand, resulting in a sudden increase in the airbag volume. The gas pressure decreases, as shown in Figure 2. Subsequently, the pressure continues to decrease until the elastic modulus of the expansion zone of the rubber airbag increases, as shown in the region_(d), and the elastic modulus in this stage is the same as that in region_(a). The local increase in the elastic modulus is caused by the local strain hardening of the rubber material. At this time, the expansion area of the rubber airbag begins to move along the axial direction of the airbag with the minimum elastic modulus in region_(c). When the expansion area moves in the axial direction, the pressure is not changed, while the volume continues to increase, corresponding to the flat area in Figure 2.

The energy loss during the charging/discharging process is mainly caused by three factors: (1) the rubber material’s mechanical properties (such as the Mullins effect, hysteresis effect, etc. which can cause material deterioration); (2) the friction between the airbag and rigid shield during the charging/discharging process, causing energy loss; (3) pressure loss due to thermal changes. The impact of these three factors on the rubber airbag is directly reflected in the value of its contraction pressure, which is lower than the expansion pressure and leads to energy loss. The relationship between the expansion and contraction pressure is very important to consider when analyzing the energy storage efficiency.

3. Exergy Storage Efficiency Analysis

3.1. Enthalpy Analysis Method

The calculation of the strain energy generated by the charging/discharging of the airbag by the enthalpy analysis method was based on the idea of converting the expansion energy into work, as shown in Figure 4.

During charging, the gas expands, work is performed on the airbag, and the airbag volume is charged. The gas pressure energy is converted into elastic material strain energy and stored in the elastic body. Based on the enthalpy analysis method of the first law of thermodynamics, the mathematical model of the energy storage efficiency of the device is established. The energy is calculated as shown in Equation (1).

$$E_{Tot}=E_s+E_p={\displaystyle {\int }_{V_0}^{V_{full}}{P}_{\exp }dv}+P_{\exp }{V}_{full}\ln \left(\frac{P_{\exp }}{P_{atm}}\right)$$

(1)

where E_tot is the total energy of entering the airbag, E_s is the strain energy produced by the expansion of the rubber material, E_P is the gas pressure energy stored inside the airbag, V₀ is the initial volume of the airbag, V_full is the volume of the airbag after inflation, P_exp is the inflation pressure, and P_atm is the atmospheric pressure.

The discharging process is similar to the above expression, and only the corresponding integral limit needs to be modified. The ratio of the discharging energy to the charging energy is the energy storage efficiency of the airbag during the charging/discharging process, as shown in Equation (2).

$$\eta =\frac{-{\displaystyle {\int }_{V_{full}}^{V_0}{P}_{con}dv+P_{con}{V}_{full}\ln \left(\frac{P_{con}}{P_{atm}}\right)}}{{\displaystyle {\int }_{V_0}^{V_{full}}{P}_{\exp }dv+P_{\exp }{V}_{full}\ln \left(\frac{P_{\exp }}{P_{atm}}\right)}}$$

(2)

where P_con is the contraction pressure.

As shown in Equation (2), when calculating the charging/discharging energy storage efficiency, it is necessary to know the expansion pressure, contraction pressure, and expansion volume. An airbag’s volume undergoes a dynamic variation process, and the expansion and contraction volumes at any time cannot be obtained by measurement. Thus, the ideal gas state equation was used to calculate the airbag volume at any time during the charging/discharging process, which would result in a certain error. At the same time, the enthalpy analysis method cannot reflect the thermal variation’s influence on the energy storage efficiency, so it was necessary to analyze the energy storage efficiency of the rubber airbags based on the exergy analysis method.

3.2. Exergy Analysis Method

Since energy conversion is related to the environmental conditions and process characteristics, in order to measure the maximum energy conversion capacity, it is necessary to determine the zero energy state when calculating the exergy balance. The environmental standards specified in GB/T 14909-94 were adopted in this paper, with P₀ = 1 × 10⁵ Pa, T₀ = 298.15 K.

The energy storage efficiency exergy analysis of the rubber airbag was based on the open thermal system exergy equation, and the following assumptions were made: (1) the charging/discharging process is adiabatic, and there is no heat exchange with the external environment; (2) the gas is assumed to be ideal gas, and the kinetic and potential energy exergy of the gas are ignored; (3) during the discharging phase, the gas can be completely discharged from the airbag; (4) the entire charging/discharging process occurs under steady-state and steady-flow conditions.

Based on the above assumptions, the system exergy change during charging can be obtained using Equation (3).

$$e_{x.1}-e_{x.2}=w_s+l$$

(3)

where w_s is the output work in the charging stage, that is, the work performed by the gas being charged into the airbag, which is equivalent to the strain energy e_s generated by the airbag inflation converted from the pressure energy. e_x.1 and e_x.2 are the specific flow exergies before and after the gas enters the airbag, respectively, which are calculated with Equations (4) and (5); l is the exergy loss, which mainly includes the damage of the rubber material during the conversion of pressure energy to strain energy.

$$e_{x.1}=c_p\left(T_1-T_0\right)-T_0(c_p\ln \frac{T_1}{T_0}-R_g\ln \frac{p_1}{p_0})$$

(4)

$$e_{x.2}=c_p\left(T_2-T_0\right)-T_0(c_p\ln \frac{T_2}{T_0}-R_g\ln \frac{p_2}{p_0})$$

(5)

where P₀ and T₀ are the pressure and temperature of the reference environment, respectively; P₁ and T₁ are the pressure and temperature before the gas enters the airbag, respectively; P₂ and T₂ are the pressure and temperature after the gas enters the airbag to perform work on the airbag; Rg = 0.287 kJ/(kg·K) is the gas constant of air; and c_p = 1.004 kJ/(kg·K) is the constant pressure specific heat of air.

In the first stage, the gas is charged in the accumulator to perform work on the airbag. Assuming that the specific flow of the gas entering the airbag through the inlet of the control surface at this stage is denoted as e_x.1, the gas is charged the airbag and works on the airbag. The strain energy generated after the airbag is stably expanded is e_s.1, where e_s.1 is defined as the exergy revenue of the system, e_x.1 is defined as the exergy expenditure, and the ratio of the two is defined as the exergy efficiency of the inflation stage as shown in Equation (6).

$${\eta }_{ex.1}=\frac{e_{s.1}}{e_{x.1}}$$

(6)

In the second stage, the gas is discharged. The work performed by the airbag on the gas to convert strain energy into pressure the airbag through the outlet of the control surface at this stage is e_x.2, where e_s.1 is defined as the payment exergy of the system, e_x.2 is the revenue exergy of the system, and the ratio of the two is defined as the exergy efficiency in the discharging stage, as shown in Equation (7).

$${\eta }_{ex.2}=\frac{e_{x.2}}{e_{s.1}}$$

(7)

Regarding the two stages as a whole—that is, the gas works on the airbag after charging to expand the airbag and the airbag contracts when discharging—the exergy efficiency of the entire system is shown in Equation (8).

$${\eta }_{ex.3}={\eta }_{ex.1}\cdot {\eta }_{ex.2}=\frac{e_{s.1}}{e_{x.1}}\cdot \frac{e_{x.2}}{e_{s.1}}=\frac{e_{x.2}}{e_{x.1}}$$

(8)

4. Experimental Verification

Through the cyclic charging/discharging tests of the rubber airbag, this paper mainly examined the following: (1) the steady-state value of the expansion pressure, contraction pressure, and energy storage efficiency during the cyclic charging/discharging process; (2) the comparison of the exergy analysis method and the enthalpy analysis method to verify the advantages of the exergy analysis method in calculating the rubber airbag energy storage efficiency.

4.1. Experimental Device and Principle

The test platform is shown in Figure 5, which was composed of a two-way mass flow sensor, a pressure sensor, a throttle valve, a temperature sensor, a power supply, a three-position five-way solenoid valve, and a data acquisition card and control procedure (the acquisition control terminal is not shown in the figure). The constant-pressure elastic-strain energy accumulator used in the test was composed of a rubber airbag with an inner diameter of 5 × 10⁻³ m and an outer diameter of 10mm, as well as a rigid protective cover with an inner diameter of 2.9 × 10⁻² m.

The air supply pressure was adjusted to 4 × 10⁵ Pa by the pressure regulator. The compressed gas flowed through the three-position five-way solenoid valve through the bidirectional mass flowmeter, pressure sensor, and temperature sensor and then entered the rubber airbag. The opening and closing of the solenoid valve and data acquisition were programmed in Simulink (

Table 1. Main components and specifications.

Pneumatic Components	Equipment Type	Specification Parameter
Relay Board	ADVANTECH: PCLD-785B	16 optically isolated digital input channels; 0–24 V direct current (DC)
Flow sensor	FESTO: SFAH IO-Link IODD	–90 to 1000 kPa, 0.1–200 L/min
Temperature sensor	ZC SENSOR: ZPT-1607A	PT100 1/3B; 0–30 °C; 24 V DC
Pressure sensor	SMC: ISE40-C6-22L-M	−0.100 to 1.000 MPa
Three-position five-way solenoid valve	WSNS: 4V230C-08	DC24V 4.8 W; 1.5–8 Kgf/cm2

).

A charging/discharging cycle took 5 s, including a charging time of 0.8 s, holding for 2 s, and then discharging. Five charging/discharging periods were set for the tested airbag, and each period included 40 charging/discharging cycles, and a 10 min recovery period was set between each period. The data of five periods were processed as independent samples. In order to weaken the Mullins effect, 15 pre-inflation cycles were performed before the test. All pressures were converted to absolute pressures.

The airbag volume dynamic change in the charging stage is shown in Figure 6. It should be noted that the bubble location was not fixed. When the bubble appeared at the top (away from the charging end) or the middle of the airbag, it led to the rubber airbag’s undesirable expansion behavior, as shown in Figure 7. In this way, the rubber airbag could not expand completely, and the energy storage capacity was greatly reduced. Daniel N Cramer [12] observed the same phenomenon when experimenting with different rubber airbags. To obtain the ideal expansion behavior, the airbag basement (gas inlet) was pre-strained before charging to ensure that the bubble appear at the airbag basement. At the same time, a medical lubricant was used to lubricate the airbag and the rigid shield to reduce the friction.

The pressure, flow, and temperature of the airbag were obtained from the sensor. The value of a certain cycle is shown in Figure 8, Figure 9 and Figure 10.

In Figure 8, it can be seen that in the initial charging stage, gas continued to enter the airbag, the pressure continued to rise, and the entered the pressure peak when the bubble formed. Additionally, the pressure then began to drop. A slight decrease in the pressure during the maintenance phase indicated that a gas leakage existed. The airbag experienced a relatively constant-pressure contraction when discharging. The positive and negative peaks of the mass flow curve represent the charging and discharging phases, respectively. The temperature change in a charging/discharging cycle is shown in Figure 10.

4.2. Data Processing and Calculation

It is necessary to know the expansion pressure, contraction pressure, gas temperature, and gas quality of each cycle when calculating the rubber airbag energy storage efficiency. The quality of the gas entering and leaving the airbag could be obtained by integrating the mass flow. The integration of the mass flow would cause data to drift [14]. The integrated gas quality was adjusted based on three adjustment principles proposed in the literature [14]: (1) the total mass of each cycle should start and end at zero; (2) the later data points have a larger uncertainty range than the previous data points; (3) the overall shape of the data can be scaled but should remain unchanged. The quality and adjusted data of the gas entering and exiting the airbag are shown in Figure 11.

After integrating the mass flow rate, the airbag volume change at any time can be obtained by the ideal gas equation of state, and then the pressure-volume curve of the charging/discharging cycle can be obtained by combining the volume and pressure at each time, as shown in Figure 12. The red solid line represents the charging stage, and the blue dotted line represents the discharging stage. It can be seen that the airbag volume experienced continuous expansion/contraction and relatively constant pressure in the charging/discharging stage, indicating that the rubber airbag had constant-pressure charging/discharging characteristics.

The average pressure value between two squares represents expansion pressure, and the average pressure value between two triangles represents contraction pressure. The expansion/contraction pressure values of the airbag in five cycles are shown in Figure 13.

From Figure 13, it can be seen that the expansion and contraction pressures decreased over the five test periods, which indicated that the Mullins effect influenced them. The expansion and contraction pressures in the initial charging/discharging stage of a latter test cycle were both greater than those in the latter half of the previous cycle because the airbag experienced a 10 min recovery period after each test period, and the rubber material had certain resilience.

The expansion pressure, contraction pressure, and temperature data obtained from each charging/discharging cycle were substituted into Equations (6) and (7) to obtain the exergy changes in the gas inside and outside the airbag, as shown in Figure 14. The exergy storage efficiency of the airbag charging/discharging cycle can be calculated from Equation (8), as shown in Figure 15.

According to Figure 14, the energy storage efficiency in the first cycle was lower, improved, and tended to be stable in the subsequent cycles, because the rubber airbag was not softened under the loaded before the first charging/discharging cycle. Thus, in the first cycle, the pressure energy had a large loss when transforming into strain energy. In the subsequent cycles, because the rubber airbag had been softened, the energy loss was reduced when the gas overcame the elastic force of the rubber airbag and worked to was converted the pressure energy into the strain energy. Additionally, the energy storage efficiency was significantly improved and stabilized in the subsequent cycles.

5. Steady-State Characteristic Analysis

The main indexes used to evaluate the constant-pressure elastic-strain energy accumulator quality was whether the expansion pressure, contraction pressure and energy storage efficiency can be maintained consistently during the charge/discharge cycles.

As an energy storage component, due to the Mullins effect and the hysteresis effect, the rubber airbag performance inevitably decreased during the charging/discharging cycles. The performance changes were affected by the changes in the expansion pressure, contraction pressure, and energy storage efficiency. Uncertainty analysis was performed to determine whether the airbag performance after multiple charging/discharging cycles met the use requirements.

The calculation of the average μ, standard deviation σ, and standard deviation of the mean value SD _μ during 40 cycles of each test is shown in Equations (9)–(11).

$$\mu =\frac{1}{n}{\displaystyle \sum _{n=1}^n{x}_i}$$

(9)

$$\sigma ={\left[\frac{1}{n-1}{\displaystyle \sum _{i=1}^n{\left(x_i-{\mu }_x\right)}^2}\right]}^{1/2}$$

(10)

$$SD\mu =\sigma /\sqrt{n}$$

(11)

where n is the total number of data points and x_i is the value of the i-th data point. Due to the Mullins effect, the data obtained from the first charging/discharging cycle will be very different from the subsequent data. Therefore, the first charging/discharging cycle data in every period was discarded in the uncertainty analysis. The average value and standard deviation of each parameter in the charging/discharging cycle are shown in Figure 16, Figure 17 and Figure 18.

From Figure 16 and Figure 17, it can be seen that the expansion pressure average value decreased by 6 kPa and the contraction pressure average value decreased by 4 kPa in the five test periods, and the standard deviations were 2.92 kPa and 1.79 kPa, respectively. According to Figure 18, it can be seen that the energy storage efficiency average value change in five test periods was 0.2%, and the standard deviation was 0.317%. The above data indicate that after multiple cycles, the rubber airbag still had good mechanical properties.

In previous work, the energy storage efficiency model was established based on the enthalpy analysis method, and the experimental analysis was conducted (the results are shown in Figure 19). In 200 charging/discharging cycles, the energy storage efficiency error was 0.584%, and the average energy storage efficiency was 76.9%.

From Figure 18 and Figure 19, it can be seen that the standard deviation of the average energy storage efficiency calculated based on enthalpy analysis is 0.317%, and the standard deviation of the average energy storage efficiency calculated based on exergy analysis is 0.584%, which indicates that the accuracy of the energy storage efficiency calculated by exergy analysis is higher than that calculated by enthalpy analysis.

6. Conclusions

Aiming at the insufficient energy-storage efficiency modeling with the enthalpy analysis, this paper mainly focuses on establishing a rubber airbag charging/discharging energy storage efficiency model based on the exergy analysis method, studies the influence of the Mullins effect during the process of rubber airbag charging/discharging by exergy analysis, and builds a test platform to discuss the energy storage efficiency. The main conclusions are as follows:

(1) The experiments confirm that the error of the energy storage efficiency model based on the exergy analysis method is reduced by 0.267% compared with the enthalpy analysis method, which proves that the exergy analysis method is relatively accurate.

(2) The Mullins effect is mainly reflected in the expansion and contraction pressure changes during the charging and discharging cycles. The expansion pressure average value decreases by 6 kPa, and the contraction pressure average value decreases by 4 kPa. The corresponding standard deviations are 2.92 kPa and 1.79 kPa, respectively.

This paper verifies that a constant-pressure strain-energy accumulator can store and release energy at relatively constant pressure with high energy-storage efficiency. Future work will explore other structures, such as different sizes of the rigid shield and the rubber airbag, to maximize the energy storage efficiency and energy density. Ultimately, this will achieve the goal of meeting the needs of strain energy accumulators in medical rehabilitation equipment, stable gas sources, and other more extensive applications.