Piston displacement prediction method for free piston Stirling generator

Abstract

The invention discloses a piston displacement prediction method for a free piston Stirling generator, and belongs to the field of generators. The implementation method comprises the steps that the arrangement structure and structure parameters of the free piston Stirling generator are determined; determining operation parameters of the free piston Stirling generator; a kinetic equation of the two pistons in the generator is established by combining the piston mass, the piston diameter, the plate spring rigidity and the friction coefficient; thermodynamic equations of a buffer cavity, a compression cavity, an expansion cavity and a heat exchanger in the generator are established according to the structural parameters of the piston diameter, the piston mass, the buffer cavity initial volume, the hot end temperature and the cold end temperature; establishing an electromagnetic equation of the linear motor by combining the internal resistance of the motor winding; the dynamic equation, the four thermodynamic equations and the electromagnetic equation are coupled to obtain a coupling equation, the coupling equation is solved to quantificationally obtain a displacement curve of the piston, and the accuracy and efficiency of displacement prediction of the Stirling generator piston are improved. The method can also be used for monitoring the running state of the generator in real time.

Description

Technical Field

[0001] The invention relates to a piston displacement prediction method, in particular to a free piston Stirling generator piston displacement prediction method, belonging to the field of generators. Background Art

[0002] The working principle of the piston Stirling generator is based on the Stirling cycle, which realizes energy conversion through the thermal expansion and cold contraction of the gas in the closed system. Unlike the traditional Stirling engine, the free piston Stirling generator cancels the mechanical transmission mechanism and adopts a free piston design, which enables it to convert between thermal energy and mechanical energy more efficiently. In the free piston Stirling generator. The working fluid (usually hydrogen, helium or air) is enclosed in the circulation loop, and the flow direction of the working fluid in the closed circulation loop is controlled by the ratio of the cylinder volume; the working fluid is compressed at a lower temperature and pressure, and expanded at a higher temperature and pressure, thereby obtaining positive cycle work. Its thermodynamic process is carried out according to the Stirling cycle.

[0003] Although the free-piston Stirling generator has the advantage of compact structure, it also brings challenges in displacement detection. Since there are no traditional mechanical transmission parts, the movement of the piston depends entirely on the change of gas pressure, which makes it particularly important to detect the piston position and movement state in real time. However, commonly used high-precision non-contact sensors (such as photoelectric or magnetic induction sensors) are expensive, which not only increases the cost of the overall system, but may also weaken its economy in some applications. In addition, the compact structure of the generator also makes it difficult to install these sensors, especially when accurate measurements need to be ensured in a limited space. The arrangement, maintenance and signal transmission of the sensors will encounter technical obstacles. These factors together increase the difficulty of achieving efficient and accurate displacement detection in free-piston Stirling generators.

[0004] During the operation of a free piston Stirling generator, the displacement of the piston is caused by the coupling of forces acting on it, including gas pressure, the elastic force of the rebound device, and the reaction force of the motor. The interaction between these forces determines the movement of the piston. Therefore, accurate prediction of the displacement of the piston is of great significance for optimizing the operating performance of the generator and improving its efficiency. The traditional method is to simply define the movement of the piston as a sine curve, which cannot describe the various processes inside the free piston Stirling generator. Therefore, the results calculated by the traditional method have large errors. Summary of the invention

[0005] In order to solve the problem that the prior art cannot accurately measure the displacement of a free piston Stirling generator, the purpose of the present invention is to provide a method for predicting the piston displacement of a free piston Stirling generator. During the operation of the free piston Stirling generator, the displacement of the piston is caused by the coupling of forces acting on it, and the forces include gas pressure, the elastic force of the rebound device, and the reaction force of the motor. The interaction between the forces determines the motion law of the piston. The displacement of the piston is accurately predicted based on the constructed motion law, and then the design parameters of the free piston Stirling generator can be adjusted according to the working conditions to improve the power generation efficiency and reduce energy loss. The present invention can also be used to monitor the operating status of the generator in real time and improve the reliability and stability of the power generation system.

[0006] The purpose of the present invention is achieved through the following technical solutions.

[0007] A free piston Stirling generator piston displacement prediction method disclosed in the present invention comprises the following steps:

[0008] Step S1: Determine the layout structure and structural parameters of the free piston Stirling generator; the structural parameters include the power piston mass m p , displacement plug mass m d , Power piston area A p , Replacement piston diameter A d , friction coefficient k, damping coefficient c, motor winding internal resistance r s , initial volume of buffer chamber V b0 ;

[0009] Step S2: Determine the operating parameters of the free piston Stirling generator; the operating parameters include the hot end temperature T h and the cold junction temperature T k ;

[0010] Step S3: combining the piston mass, piston diameter, leaf spring stiffness and friction coefficient, establishing the dynamic equations of the two pistons in the generator;

[0011] Step S4: combining the structural parameters of piston diameter, piston mass, initial volume of the buffer chamber, hot end temperature, and cold end temperature, respectively establishing thermodynamic equations of the buffer chamber, compression chamber, expansion chamber, and heat exchanger in the generator;

[0012] Step S5: Establishing the electromagnetic equation of the linear motor in combination with the internal resistance of the motor winding;

[0013] Step S6: The dynamic equation of S3, the four thermodynamic equations of S4, and the electromagnetic equation of S5 are coupled to obtain a coupling equation, and the coupling equation is solved to obtain the displacement curve of the piston, that is, to realize the piston displacement prediction of the free piston Stirling generator.

[0014] Furthermore, the arrangement structure in step S1 is divided into two different structures according to the different support forms of the displacement piston. Form 1: the support form is a gas spring; Form 2: the support form is that the displacement piston is connected to the leaf spring through a displacement piston rod passing through the power piston.

[0015] Furthermore, for a free piston Stirling generator supported by a gas spring, the dynamic equation is:

[0016]

[0017]

[0018] Where A is the cross-sectional area. refers to the piston acceleration, m refers to the piston mass, subscript d and subscript p refer to the displacement piston and power piston; A rod Refers to the displacement piston rod cross-sectional area, P e Refers to the expansion chamber pressure, P c Refers to the compression chamber pressure, P b Refers to the buffer chamber pressure, P d Refers to the gas spring pressure, F load Refers to the motor force acting on the power piston.

[0019] For a free piston Stirling generator supported by a piston rod and a leaf spring, the dynamic equation is:

[0020]

[0021]

[0022] Where x is the piston displacement, refers to the piston speed, c refers to the damping coefficient, k refers to the friction coefficient, and subscript d and subscript p refer to the displacement piston and power piston.

[0023] Furthermore, the thermodynamic equation in step S4 is:

[0024]

[0025]

[0026] P e =P c +ΔP (7)

[0027] Where P mean Refers to the initial inflation pressure, V b0 refers to the initial volume of the buffer chamber, ΔP refers to the pressure drop in the heat exchanger, γ refers to the specific heat ratio coefficient, S refers to the gas mass simplification coefficient, T eRefers to the expansion chamber temperature, T c Refers to the compression chamber temperature.

[0028] Furthermore, ΔP refers to the pressure drop in the heat exchanger. The heat exchanger consists of a hot end, a cold end, and a regenerator. Therefore, the pressure drop in the heat exchanger is equal to the sum of the pressure drops of these three parts. For the pressure drop of each part, the calculation formula is:

[0029]

[0030] In the formula, C fi refers to the Darcy friction coefficient, ρ refers to the density of the gas, l refers to the length, and d h refers to the hydraulic diameter, u refers to the gas velocity, and the subscripts h, r, and k refer to the hot end, regenerator, and cold end;

[0031] Darcy friction coefficient C fi , the corresponding relationship is shown in the following table, in which Re represents the Reynolds number, which is a dimensionless number used to characterize the flow of fluids; as a similar number to characterize the effect of viscosity in fluid mechanics, the smaller the Reynolds number, the more significant the effect of viscosity, and the larger the Reynolds number, the more significant the effect of inertia;

[0032]

[0033] Reynolds number Re calculation equation:

[0034]

[0035] Where μ is the fluid viscosity coefficient, ρ is the gas density, and d h is the hydraulic diameter and u is the gas flow rate.

[0036] Furthermore, the electromagnetic equation in step S5 is expressed as:

[0037]

[0038]

[0039]

[0040] In the formula, r s Refers to the internal resistance of the motor winding, i a ,i b ,i c Refers to the three-phase current of A, B, and C, e a ,e b ,e c It refers to the back electromotive force of A, B, and C, u a ,u b ,u c Refers to the three-phase voltage of A, B, and C.

[0041] The three-phase back electromotive force is expressed as:

[0042]

[0043]

[0044]

[0045] In the formula, Ψ f refers to the three-phase flux of A, B, and C, v refers to the motor speed, θ refers to the motor rotation angle, and θ 0 It refers to the initial rotation angle of the motor, and τ refers to the motor pole pitch.

[0046] Furthermore, the method of coupling the dynamic equation of S3, the four thermodynamic equations of S4, and the electromagnetic equation of S5 in step S6 is:

[0047] When the linear motor is not connected to the power piston, the dynamic equation is:

[0048]

[0049] In the formula, m m Refers to the mass of the motor rotor, F e Refers to the external force applied to the motor rotor, B v refers to the coefficient of viscous friction;

[0050] For a free piston Stirling generator supported by a gas spring, the coupling equation is obtained by coupling equations (1), (2) and (5) to (16), which is:

[0051]

[0052]

[0053] Where V d Refers to the gas spring volume, T h ,T k Refers to the hot end temperature and the cold end temperature;

[0054] For the free piston Stirling generator supported by leaf springs, the coupling equation is obtained by coupling equations (3), (4) and (5) to (16), which is:

[0055]

[0056]

[0057] Beneficial effects:

[0058] 1. The present invention discloses a free piston Stirling generator piston displacement prediction method, which realizes accurate prediction of the piston displacement curve by combining the dynamic equation of the piston, the thermodynamic equation of the gas and the electromagnetic equation of the motor end, significantly improves the prediction accuracy and reduces the debugging time and cost in the design stage.

[0059] 2. The piston displacement prediction method proposed in the present invention adopts a coupling model to consider the mutual influence of multiple physical phenomena and makes full use of the unique properties of each equation, so as to more accurately reflect the actual motion state of the piston in a complex working environment. Compared with the traditional single equation prediction method, it reduces the prediction error and further optimizes the overall performance of the free piston Stirling generator.

[0060] 3. In view of the inaccuracy that may occur in existing piston displacement prediction methods under the influence of multiple variables, the present invention discloses a coupled prediction model that comprehensively considers dynamics, thermodynamics and electromagnetism. This model effectively overcomes the limitations of traditional methods through precise mathematical description, achieves higher prediction accuracy, and expands the scope of application of piston prediction.

[0061] 4. The free piston Stirling generator piston displacement prediction method disclosed in the present invention can provide a scientific basis for the free piston Stirling generator in the design stage on the basis of achieving the above-mentioned beneficial effects 1 and 2. This strategy ensures that the system can operate efficiently while reducing energy consumption, thereby improving overall economic benefits and environmental sustainability, and providing support for promoting the application and development of related technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The drawings constituting a part of this application are used to provide a further understanding of this application, so that other features, purposes and advantages of this application become more obvious. The schematic embodiment drawings and their descriptions of this application are used to explain this application and do not constitute an improper limitation on this application. In the drawings:

[0063] Figure 1 A free piston Stirling generator is a generator in which a displacement piston is connected to a leaf spring by a displacement piston rod passing through a power piston.

[0064] Figure 2 It is a free piston Stirling generator supported by a gas spring.

[0065] Figure 3 This is a graph showing the results of Example 1.

[0066] Figure 4 This is a graph showing the results of Example 2.

[0067] Among them: 1-expansion chamber, 2-displacement piston, 3-heater, 4-heat exchanger, 5-cooler, 6-power piston, 7-displacer rod, 8-linear motor. DETAILED DESCRIPTION

[0068] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0069] Embodiment 1:

[0070] The following is an example of NASA's experimental data on the RE-1000 free piston Stirling generator.

[0071] like Figure 1 As shown, the RE-1000 free piston Stirling generator consists of an expansion chamber 1, a displacement piston 2, a heater 3, a heat exchanger 4, a cooler 5, a power piston 6, a displacer rod 7, and a linear motor 8.

[0072] Step S1: Select the internal layout of the free piston Stirling generator. RE-1000 is supported by a gas spring, so the gas spring is selected during the calculation process. The power piston mass of RE-1000 is 6.2 kg, the displacement piston mass is 0.426 kg, the power piston diameter is 5.72 cm, the displacement piston diameter is 5.67 cm, the friction coefficient is 400 N / m, and the damping coefficient is 258 N / m 2 , the initial volume of the buffer chamber is 2615cm 3 .

[0073] Step S2: Input the operating parameters of RE-1000 into the model, with the hot end temperature being 800K and the cold end temperature being 300K.

[0074] Step S3: The kinetic equation of RE-1000 is:

[0075]

[0076]

[0077] Where A is the cross-sectional area. refers to the piston acceleration, m refers to the piston mass, subscript d and subscript p refer to the displacement piston and power piston; A rod Refers to the displacement piston rod cross-sectional area, P e Refers to the expansion chamber pressure, P c Refers to the compression chamber pressure, P b Refers to the buffer chamber pressure, P d Refers to the gas spring pressure, F load Refers to the motor force acting on the power piston.

[0078] Step S4: combining the structural parameters of piston diameter, piston mass, initial volume of the buffer chamber, hot end temperature, and cold end temperature, respectively establishing thermodynamic equations of the buffer chamber, compression chamber, expansion chamber, and heat exchanger in the generator;

[0079]

[0080]

[0081] P e =P c +ΔP (25)

[0082] Where P mean Refers to the initial inflation pressure, V b0 refers to the initial volume of the buffer chamber, ΔP refers to the pressure drop in the heat exchanger, γ refers to the specific heat ratio coefficient, S refers to the gas mass simplification coefficient, T e Refers to the expansion chamber temperature, T c Refers to the compression chamber temperature.

[0083] ΔP refers to the pressure drop in the heat exchanger. The heat exchanger consists of a hot end, a cold end, and a regenerator. Therefore, the pressure drop in the heat exchanger is equal to the sum of the pressure drops of these three parts. For the pressure drop of each part, the calculation formula is:

[0084]

[0085] In the formula, C fi refers to the Darcy friction coefficient, ρ refers to the density of the gas, l refers to the length, and d h refers to the hydraulic diameter, u refers to the gas velocity, and the subscripts h, r, and k refer to the hot end, regenerator, and cold end;

[0086] Darcy friction coefficient C fi , the corresponding relationship is shown in the table, in which Re represents the Reynolds number, which is a dimensionless number that can be used to characterize the flow of fluids; as a similar number to characterize the effect of viscosity in fluid mechanics, the smaller the Reynolds number, the more significant the effect of viscosity, and the larger the Reynolds number, the more significant the effect of inertia;

[0087]

[0088]

[0089] Reynolds number Re calculation equation:

[0090]

[0091] Where μ is the gas viscosity coefficient, ρ is the gas density, and d h is the hydraulic diameter and u is the gas flow rate.

[0092] Step S5: Establish the electromagnetic equations at the motor end:

[0093]

[0094]

[0095]

[0096] In the formula, r s Refers to the internal resistance of the motor winding, L s Refers to the winding self-inductance, i a ,i b ,i c Refers to the three-phase current of A, B, and C, e a ,e b ,e c It refers to the back electromotive force of A, B, and C, u a ,u b ,u c Refers to the three-phase voltage of A, B, and C.

[0097] The three-phase back electromotive force is expressed as:

[0098]

[0099]

[0100]

[0101] In the formula, Ψ f refers to the three-phase flux of A, B, and C, v refers to the motor speed, θ refers to the motor rotation angle, and θ 0 It refers to the initial rotation angle of the motor, and τ refers to the motor pole pitch.

[0102] Establish the motion equation of the motor end:

[0103]

[0104] In the formula, m m Refers to the mass of the motor rotor, F e Refers to the external force applied to the motor rotor, B v refers to the coefficient of viscous friction;

[0105] Step S6: The above formulas are coupled to obtain a coupling equation, which is:

[0106]

[0107]

[0108] Input the structural parameters and operating parameters into the formula to obtain the displacement results Figure 3 ,Comparing the calculated results with the experimental results, the relevant errors are also shown in Table 1. The maximum error is 4.8%, which proves the feasibility of the model.

[0109]

[0110]

[0111] Table 1 Comparison of calculated results and experimental results

[0112] Embodiment 2:

[0113] The experimental data of the GPU-3 free piston Stirling generator is used as an example to illustrate.

[0114] Step S1: Select the internal layout of the free piston Stirling generator. GPU-3 is supported by a displacement piston connected to a leaf spring through a displacement piston rod passing through the power piston. The power piston mass of GPU-3 is 0.22 kg, the displacement piston mass is 1.2 kg, the power piston diameter is 6.94 cm, the displacement piston diameter is 7.01 cm, the friction coefficient is 500 N / m, and the damping coefficient is 320 N / m. 2 , the initial volume of the buffer chamber is 2615cm 3 .

[0115] Step S2: Input the operating parameters of GPU-3 into the model, with the hot end temperature being 800K and the cold end temperature being 300K.

[0116] Step S3: The dynamic equation of GPU-3 is:

[0117]

[0118]

[0119] Where x is the piston displacement, refers to the piston speed, c refers to the damping coefficient, k refers to the friction coefficient, A refers to the cross-sectional area, m refers to the piston mass, and subscripts d and p refer to the displacement piston and power piston; A rod Refers to the displacement piston rod cross-sectional area, P e Refers to the expansion chamber pressure, P c Refers to the compression chamber pressure, P b Refers to the buffer chamber pressure, F load Refers to the motor force acting on the power piston.

[0120] Step S4: Combine the structural parameters piston diameter, piston mass, initial volume of the buffer chamber, initial volume of the compression chamber, initial volume of the expansion chamber, and hot end temperature and cold end temperature to establish the thermodynamic equations of the buffer chamber, compression chamber, expansion chamber and heat exchanger in the generator:

[0121]

[0122]

[0123] P e =P c +ΔP (41)

[0124] Where P mean Refers to the initial inflation pressure, V b0 refers to the initial volume of the buffer chamber, ΔP refers to the pressure drop in the heat exchanger, γ refers to the specific heat ratio coefficient, S refers to the gas mass simplification coefficient, T e Refers to the expansion chamber temperature, T c Refers to the compression chamber temperature.

[0125] ΔP refers to the pressure drop in the heat exchanger. The heat exchanger consists of a hot end, a cold end, and a regenerator. Therefore, the pressure drop in the heat exchanger is equal to the sum of the pressure drops of these three parts. For the pressure drop of each part, the calculation formula is:

[0126]

[0127] In the formula, C fi refers to the Darcy friction coefficient, ρ refers to the density of the gas, l refers to the length, and d h refers to the hydraulic diameter, u refers to the gas flow rate, and the subscripts h, r, and k refer to the hot end, regenerator, and cold end;

[0128] Darcy friction coefficient C fi , the corresponding relationship is shown in the table, in which Re represents the Reynolds number, which is a dimensionless number that can be used to characterize the flow of fluids; as a similar number to characterize the effect of viscosity in fluid mechanics, the smaller the Reynolds number, the more significant the effect of viscosity, and the larger the Reynolds number, the more significant the effect of inertia;

[0129]

[0130] Reynolds number Re calculation equation:

[0131]

[0132] Where μ is the gas viscosity coefficient, ρ is the gas density, and d h is the hydraulic diameter and u is the gas flow rate.

[0133] Step S5: Establish the electromagnetic equations at the motor end:

[0134]

[0135]

[0136]

[0137] In the formula, r s Refers to the internal resistance of the motor winding, L s Refers to the winding self-inductance, i a ,i b ,i c Refers to the three-phase current of A, B, and C, e a ,e b ,e c It refers to the back electromotive force of A, B, and C, u a ,u b ,u c Refers to the three-phase voltage of A, B, and C.

[0138] The three-phase back electromotive force is expressed as:

[0139]

[0140]

[0141]

[0142] In the formula, Ψ f refers to the three-phase flux of A, B, and C, v refers to the motor speed, θ refers to the motor rotation angle, and θ 0 It refers to the initial rotation angle of the motor, and τ refers to the motor pole pitch.

[0143] Establish the motion equation of the motor end:

[0144]

[0145] In the formula, m m Refers to the mass of the motor rotor, F e Refers to the external force applied to the motor rotor, B v refers to the coefficient of viscous friction;

[0146] Step S6: The above formulas are coupled to obtain a coupling equation, which is:

[0147]

[0148]

[0149] Input the structural parameters and operating parameters into the formula to obtain the displacement results Figure 4 ,Comparing the calculated results with the experimental results, the relevant errors are also shown in Table 2.,The maximum error is 6.2%, which proves the feasibility of the model.

[0150]

[0151] Table 2 Comparison of calculated results and experimental results

[0152] Those skilled in the art may make various modifications and variations to the present invention. If these modifications and variations are within the scope of the claims of the present invention and their equivalents, then these modifications and variations are also within the protection scope of the present invention.

[0153] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting piston displacement of a free piston Stirling generator, characterized in that: The following steps are included: Step S1: Determine the layout structure and structural parameters of the free piston Stirling generator; the structural parameters include the power piston mass m p 、Displacement plug mass m d , Power piston area A p , Replacement piston diameter A d , friction coefficient k, damping coefficient c, motor winding internal resistance r s , initial volume of buffer chamber V b0 ; Step S2: Determine the operating parameters of the free piston Stirling generator; the operating parameters include the hot end temperature T h and the cold junction temperature T k ; Step S3: combining the piston mass, piston diameter, leaf spring stiffness and friction coefficient, establishing the dynamic equations of the two pistons in the generator; Step S4: combining the structural parameters of piston diameter, piston mass, initial volume of the buffer chamber, hot end temperature, and cold end temperature, respectively establishing thermodynamic equations of the buffer chamber, compression chamber, expansion chamber, and heat exchanger in the generator; Step S5: Establishing the electromagnetic equation of the linear motor in combination with the internal resistance of the motor winding; Step S6: The dynamic equation of S3, the four thermodynamic equations of S4, and the electromagnetic equation of S5 are coupled to obtain a coupling equation, and the coupling equation is solved to obtain the displacement curve of the piston, that is, to realize the piston displacement prediction of the free piston Stirling generator.

2. The displacement prediction method according to claim 1, characterized in that: The arrangement structure described in step S1 is divided into two different structures according to the different support forms of the displacement piston. Form 1: the support form is a gas spring; Form 2: the support form is that the displacement piston is connected to the leaf spring through the displacement piston rod passing through the power piston.

3. The displacement prediction method according to claim 2, characterized in that: For a free piston Stirling generator supported by a gas spring, the dynamic equation is: Where A is the cross-sectional area. refers to the piston acceleration, m refers to the piston mass, subscript d and subscript p refer to the displacement piston and power piston; A rod Refers to the displacement piston rod cross-sectional area, P e Refers to the expansion chamber pressure, P c Refers to the compression chamber pressure, P b Refers to the buffer chamber pressure, P d Refers to the gas spring pressure, F load Refers to the motor force acting on the power piston; For a free piston Stirling generator supported by a piston rod and a leaf spring, the dynamic equation is: Where x is the piston displacement, refers to the piston speed, c refers to the damping coefficient, k refers to the friction coefficient, and subscript d and subscript p refer to the displacement piston and power piston.

4. The motion prediction method according to claim 3, wherein: The thermodynamic equation in step S4 is: Where P mean Refers to the initial inflation pressure, V b0 refers to the initial volume of the buffer chamber, ΔP refers to the pressure drop in the heat exchanger, γ refers to the specific heat ratio coefficient, S refers to the gas mass simplification coefficient, T e Refers to the expansion chamber temperature, T c Refers to the compression chamber temperature.

5. The displacement prediction method according to claim 4, characterized in that: ΔP refers to the pressure drop in the heat exchanger. The heat exchanger consists of a hot end, a cold end, and a regenerator. Therefore, the pressure drop in the heat exchanger is equal to the sum of the pressure drops of these three parts. For the pressure drop of each part, the calculation formula is: In the formula, C fi refers to the Darcy friction coefficient, ρ refers to the density of the gas, l refers to the length, and d h refers to the hydraulic diameter, u refers to the gas velocity, and the subscripts h, r, and k refer to the hot end, regenerator, and cold end; Darcy friction coefficient C fi , the corresponding relationship is shown in the following table, in which Re represents the Reynolds number, which is a dimensionless number used to characterize the flow of fluids; as a similar number to characterize the effect of viscosity in fluid mechanics, the smaller the Reynolds number, the more significant the effect of viscosity, and the larger the Reynolds number, the more significant the effect of inertia; Reynolds number Re calculation equation: Where μ is the fluid viscosity coefficient, ρ is the gas density, and d h is the hydraulic diameter and u is the gas flow rate.

6. The motion prediction method according to claim 5, characterized in that: The electromagnetic equation in step S5 is expressed as: In the formula, r s Refers to the internal resistance of the motor winding, L s Refers to the winding self-inductance, i a ,i b ,i c Refers to the three-phase current of A, B, and C, e a ,e b ,e c It refers to the back electromotive force of A, B, and C, u a ,u b ,u c Refers to the three-phase voltage of A, B, and C; The three-phase back electromotive force is expressed as: In the formula, Ψ f It refers to the three-phase flux of A, B, and C, v refers to the motor speed, θ refers to the motor rotation angle, θ0 refers to the initial rotation angle of the motor, and τ refers to the motor pole pitch.

7. The motion prediction method according to claim 1, wherein: The method of coupling the dynamic equation of S3, the four thermodynamic equations of S4, and the electromagnetic equation of S5 in step S6 is: When the linear motor is not connected to the power piston, the dynamic equation is: In the formula, m m Refers to the mass of the motor rotor, F Load Refers to the external force applied to the motor rotor, B v refers to the coefficient of viscous friction; For a free piston Stirling generator supported by a gas spring, the coupling equation is obtained by coupling equations (1), (2) and (5) to (16), which is: Where V d Refers to the gas spring volume, T h ,T k Refers to the hot end temperature and the cold end temperature; For the free piston Stirling generator supported by leaf springs, the coupling equation is obtained by coupling equations (3), (4) and (5) to (16), which is:

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