Method for analyzing and calculating thermodynamic geometric dimensions of slide valve pair of hydraulic valve in wide temperature range

Abstract

The invention relates to a method for analyzing and calculating the thermodynamic geometric dimension of a hydraulic valve slide valve pair in a wide temperature range, which comprises the following steps: S1, determining the parameters of the hydraulic valve slide valve pair, the parameters comprising the structural dimension, the part machining process, the working principle and the working condition; s2, constructing a simplified metal model of the slide valve pair according to the parameters determined in S1; s3, the radial clearance thermal deformation delta u and the key oil port thermal deformation delta w of the sliding valve pair are calculated; s4, when the radial clearance thermal deformation delta u in the wide temperature range is larger than or equal to the allowable maximum variable quantity, the clearance design size and the machining technology are updated; when the thermal deformation delta w of the key oil port is larger than or equal to the allowable maximum variable quantity, the machining process is updated; and S5, repeating the steps S2 and S3 until radial and axial design requirements are met. Compared with the prior art, the calculation method does not need to adopt finite element and other simulation calculation processes, optimizes the performance of the hydraulic valve in the wide temperature range on the basis of not changing part raw materials, and improves the precision.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic valves in a wide temperature range, and in particular to a method for analyzing and calculating the thermodynamic geometric dimensions of a sliding valve pair of a hydraulic valve in a wide temperature range. Background Art

[0002] Hydraulic valves, as key components for precise fluid dynamics control, directly impact the reliability, stability, and safety of electro-hydraulic control systems. The valve core, the core moving component of a hydraulic valve, plays a decisive role in precisely regulating the flow, pressure, and direction of the fluid. The quality of the spool pair is crucial for controlling hydraulic valve performance, including control accuracy, sealing, and responsiveness. Under actual operating conditions, subject to extreme high and low temperatures, such as within an automotive transmission, which can range from -40°C to 150°C, and reach as high as 90°C to 100°C under normal operating conditions, the spool pair experiences uneven thermal deformation at the spool-sleeve mating surfaces. This can lead to spool sticking and jamming, severely limiting hydraulic valve performance. To ensure hydraulic valve performance, it is necessary to analyze the extent and patterns of thermal deformation of the spool pair over a wide temperature range. This is crucial for temperature control and operational reliability.

[0003] The literature "CFD Study on the Temperature Field of the Radial Clearance of Hydraulic Slide Valve" (Liu Xiaohong, Ke Jian, Liu Huanlong. CFD Study on the Temperature Field of the Radial Clearance of Hydraulic Slide Valve [J]. Journal of Mechanical Engineering, 2006, (S1): 231-234.) aims to solve the problem of valve core sticking caused by throttling temperature rise. A two-dimensional CFD model is established to obtain the influence of working pressure, radial clearance and opening size on the temperature distribution in the radial clearance. The literature "Optimization Design of Valve Body Strength and Fitting Clearance of Large-Drift Slide Valve" (Liu Shuyin, Yang Shudong, Wu Liang, et al. Optimization Design of Valve Body Strength and Fitting Clearance of Large-Drift Slide Valve [J]. Hydraulics and Pneumatics, 2012, (05): 90-94.) establishes a thermo-stiff coupling finite element model to study the variation of the fitting clearance of a large-drift two-position four-way hydraulic reversing slide valve with pressure, temperature and valve body wall thickness, and optimizes the fitting clearance and valve body wall thickness. The literature "Research on the internal flow field and thermal deformation of U-type throttle valve" ([1] Wang Haibing. Research on the internal flow field and thermal deformation of U-type throttle valve [D]. China University of Mining and Technology, 2017.) uses a combination of theoretical analysis, numerical simulation and experimental research to conduct an in-depth study on the thermal deformation results of the valve core and valve body, establishes a theoretical model of flow field and thermal analysis, and discusses the influence of back pressure value, valve opening, etc. on temperature and thermal deformation. The literature "Numerical simulation for multi-way valves and fit clearance research based on heat-fluid-solid coupling" (Liping Xu; Haoyi Ma; Dezhi Ren. Numerical simulation for multi-way valves and fit clearance research based on heat-fluid-solid coupling [J]. The Journal of Engineering, 2019, 2019 (13): 247-252.) establishes a theoretical model of the fit clearance of multi-way valves, conducts numerical simulation of the thermal-solid-fluid coupling of multi-way valves, and obtains the thermal deformation and temperature characteristic curves of valve cores and valve bodies of various materials.

[0004] However, existing thermal analysis of sliding valve pairs mostly focuses on finite element simulation analysis, and has not established a thermodynamic mathematical model of the sliding valve pair from a theoretical mechanism, especially considering the influence of parts processing, constraint force and temperature field distribution on the degree and law of thermal deformation of the sliding valve pair. It has not formed a theoretical model for thermal analysis and geometric dimension analysis under a wide temperature range. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above-mentioned defects of the existing technology and provide a method for analyzing and calculating the thermodynamic geometric dimensions of the hydraulic valve slide valve pair under a wide temperature range. This calculation method does not require the use of simulation calculation processes such as finite element analysis; it optimizes the performance of the hydraulic valve under a wide temperature range without changing the raw materials of the parts.

[0006] The present invention provides a method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve slide valve pair under a wide temperature range, comprising the following steps:

[0007] S1. Determine the hydraulic valve spool valve pair parameters, including: structural dimensions, parts processing technology, working principle and working conditions;

[0008] S2. Construct a simplified metal model of the slide valve pair based on the parameters determined in S1, including the parts processing technology, the temperature field of the working conditions, and the relationship between the slide valve pair constraints and the thermal deformation of the slide valve pair;

[0009] S3. Based on the theory of linear thermal stress and elastic mechanics, the valve sleeve of the spool valve pair is simplified into a metal cylinder with a cylindrical inner wall, and the valve core of the spool valve pair is simplified into a metal cylinder with a cylindrical outer wall. A thermodynamic mathematical model is established for this simplified metal model of the spool valve pair. The thermal deformation law of the spool valve pair over a wide temperature range is calculated, namely, the thermal deformation of the radial clearance Δu and the thermal deformation of the key oil port Δw of the spool valve pair are calculated.

[0010] S4. When the thermal deformation of the radial clearance Δu is greater than or equal to the maximum allowable variation under a wide temperature range, update the clearance design dimensions and processing technology; when the thermal deformation of the key oil port Δw is greater than or equal to the maximum allowable variation, update the processing technology;

[0011] S5. Recalculate the thermal deformation law of the sliding valve pair based on the updated dimensions and material parameters, and repeat steps S2 and S3 until the radial clearance thermal deformation Δu is less than the maximum allowable variation under a wide temperature range, and the critical oil port thermal deformation Δw is less than the maximum allowable variation, and the radial and axial design requirements are met.

[0012] Furthermore, in S2, during the construction of the simplified metal model, a polar coordinate system is established for the spatial axisymmetric object, and expressions representing each stress component in terms of displacement and temperature difference are obtained.

[0013] The expression is:

[0014]

[0015] Where, let μ1=1+μ, μ3=1-2μ;

[0016] Among them, σ r is the thermal stress in the radial direction, σ θ is the thermal stress in the tangential direction, σz is the thermal stress in the axial direction.

[0017] Furthermore, in S3, a thermodynamic mathematical model is established for the metal cylinder, and polar coordinates are established for the metal cylinder with spatial axisymmetry. The origin of the coordinate is located at the center of the metal cylinder. Any point P in the metal cylinder can be expressed as P(r,θ,z). The inner diameter and outer diameter of the metal cylinder are r1 and r2 respectively, and the length of the metal cylinder is l1.

[0018] Furthermore, after the metal cylinder has undergone quenching, grinding, and other processing processes, residual stresses generated by the processing will still exist within the material after cooling. Therefore, when the cylinder is in a temperature field, in addition to the thermal stress caused by the temperature, there are also residual stresses within the material. The superposition of the two stresses causes thermal deformation of the cylinder. In S3, if the material is not in a steady-state uniform temperature field, the stress inside the metal cylinder is:

[0019] σ=σ t +σ r ;

[0020] Among them, σ t is thermal stress, σ r is the residual stress, and σ is the stress after superposition.

[0021] Furthermore, in S3, during the construction of the simplified metal model, it is assumed that the temperature field of the slide valve pair is independent of time, that is, the temperature field is a steady-state temperature field. Under the steady-state temperature field, the temperature distribution is only related to r and is symmetrical about the z axis;

[0022] Assuming that the temperature change ΔT is ΔT = ΔT(r), the thermal stress components generated inside the metal cylinder under the steady-state temperature field are calculated as follows:

[0023]

[0024] Among them, σ tr is the thermal stress in the radial direction of the metal cylinder, σ tθ is the thermal stress in the tangential direction of the metal cylinder, σ tz is the thermal stress in the axial direction of the metal cylinder; r1 and r2 are the inner diameter and outer diameter of the metal cylinder respectively, and l1 is the length of the metal cylinder.

[0025] Furthermore, in S3, the radial displacement deformation of the metal cylinder is calculated:

[0026]

[0027] ΔT = t2 - t1;

[0028] Among them, σ1 and σ2 are the surface stresses of the inner diameter and outer diameter of the metal cylinder respectively, σ1=σ t1 +σ r1 ,σ2=σ t2 +σ r2 ,σ t1 , σ t2 are the thermal stresses of the inner and outer diameters of the metal cylinder, σ r1 , σ r2 are the residual stresses on the inner and outer diameters of the metal cylinder, T1 and T2 are the temperature changes on the inner and outer surfaces of the metal cylinder, and η is the temperature coefficient of elastic modulus.

[0029] Furthermore, in S3, when the two ends of the metal cylinder are subjected to an axial constraint force F, the forces on both ends are equal in magnitude and directed toward the inside of the metal cylinder. Therefore, compressive stress is generated during high-temperature expansion, and no force is applied during low-temperature contraction. The two ends are in a free state, so the axial force generated by the axial stress is:

[0030]

[0031] The axial displacement deformation of the metal cylinder when it is subjected to axial constraint force is:

[0032]

[0033] σ1 and σ2 are the surface stresses of the inner and outer diameters of the metal cylinder, respectively. σ1=σ t1 +σ r1 ,σ2=σ t2 +σ r2 ,σ t1 , σ t2 are the thermal stresses of the inner and outer diameters of the metal cylinder, σ r1 , σ r2 are the residual stresses on the inner and outer diameters of the metal cylinder respectively; ΔT is the temperature change; η is the temperature coefficient of elastic modulus.

[0034] Furthermore, in S3, a mathematical model of thermodynamic geometric dimensions is established for the metal cylinder, and polar coordinates are established for the metal cylinder with spatial axisymmetry. The origin of the coordinate is located at the center of the metal cylinder, and any point Q in the cylinder is expressed as Q(r,θ,z); the outer diameter of the metal cylinder is r3, and the length of the metal cylinder is l2.

[0035] Furthermore, in S3, for a metal cylinder with residual stress on the surface, under the action of thermal load, the various thermal stress components generated inside are obtained as follows:

[0036]

[0037] σ tr is the thermal stress in the radial direction of the metal cylinder, σ tθ is the thermal stress in the tangential direction of the metal cylinder, σtz is the thermal stress in the axial direction of the metal cylinder, r3 is the outer diameter of the metal cylinder, l2 is the length of the metal cylinder, and ΔT is the temperature change.

[0038] Furthermore, in S3, under a steady-state uniform temperature field, that is, the temperature is independent of r, the temperature change ΔT = t2 - t1, and after considering the initial deformation of the metal cylinder at the initial temperature, the relative displacement changes in the radial and axial directions are obtained:

[0039]

[0040] Among them, σ3 is the stress on the outer surface of the metal cylinder, σ3=σ t3 +σ r3 ;

[0041] σ t3 is the thermal stress of the outer diameter of the metal cylinder, σ r3 is the residual stress of the outer diameter of the metal cylinder; η is the temperature coefficient of elastic modulus.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] (1) Engineering practicality: Through geometric simplification and axisymmetric assumption, the complex sliding valve pair is transformed into a model that can be solved analytically, avoiding the time-consuming problem of finite element simulation.

[0044] (2) Accuracy assurance: Considering residual stress, temperature field non-uniformity, and constraint force, their effects on thermal deformation are quantified. The relationship between residual stress on the part surface and thermal deformation is analyzed for problems that may occur during machining, such as tool blunting, excessive feed rate, or insufficient coolant. The axial constraint forces on the valve core during operation in the control valve, such as electromagnetic force and spring force, are considered, and the effect of constraint force on thermal deformation is analyzed. The effect of uneven temperature field distribution inside the valve core and valve sleeve on thermal deformation during heat exchange between the spool valve pair and the oil is considered. The relationship between the above factors and thermal deformation is comprehensively determined, and a mathematical model of thermodynamic geometric dimensions is established, which improves the accuracy of the geometric dimension analysis of thermal deformation of the spool valve pair.

[0045] (3) Design guidance: The degree of thermal deformation is calculated to provide theoretical and technical support for the structural dimension design and processing technology of the hydraulic valve. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The figure is a flow chart of the thermodynamic geometrical dimension analysis and calculation method of the hydraulic valve spool pair under a wide temperature range;

[0047] Figure 2 A schematic diagram of a hydraulic valve slide valve simplified as a metal cylinder;

[0048] Figure 3 A schematic diagram of a hydraulic valve slide valve simplified as a metal cylinder;

[0049] Figure 4 This is the working principle diagram of the electro-hydraulic proportional valve;

[0050] Figure 5 Schematic diagram of the change of radial clearance with temperature under normal processing conditions and abnormal processing conditions;

[0051] Figure 6 Schematic diagram of the zero point of the axial deformation of the valve core and valve sleeve. DETAILED DESCRIPTION

[0052] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0053] Example 1:

[0054] This embodiment provides a method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range. Figure 1 shown.

[0055] In this embodiment, Figure 4 The electro-hydraulic proportional valve slide shown is used to describe the solution of the present invention.

[0056] like Figure 4 The figure shows the slide valve structure of the electro-hydraulic proportional valve. This valve is used in automobile transmissions. During normal operation, the oil temperature can reach 90℃~100℃. However, under extreme ambient temperatures, the maximum temperature range that the electro-hydraulic proportional valve can withstand is -40℃~150℃. Figure 4 The mating surface marked in the figure shows sticking in a wide temperature range. The radial clearance of this mating surface is analyzed below.

[0057] The valve core and valve sleeve are made of aluminum alloy 6061T, and the parameters such as density, elastic modulus, Poisson's ratio and linear expansion coefficient are clearly defined. The valve sleeve of the sliding valve pair is simplified to a metal cylinder, and the valve core of the sliding valve pair is simplified to a metal cylinder, such as Figure 2 、 3 shown.

[0058] Among them, the elastic modulus of metal will change with temperature, that is, the elastic modulus decreases with increasing temperature in a complex exponential law. The elastic modulus of aluminum alloy changes with temperature. At the extreme temperature T = -40℃ ~ 150℃, assuming 20℃ as room temperature and assuming that the thermal deformation of metal at room temperature is zero, the reduction coefficients of different mechanical properties can be calculated based on the modified coefficient fitting model:

[0059] When T=20℃~150℃, β T =-2.977×10 -6(T+24) 2 +1.009

[0060] When T=-40~20℃, β T =1.0814-0.00381T-1.28882×10 -5 T 2

[0061]

[0062] Among them, β T is the reduction coefficient of different mechanical properties, and η is the temperature coefficient of elastic modulus.

[0063] According to the different manufacturing processes of the core valve sleeve, the residual stress generated during processing is determined. The outer circle of the valve core is generally quenched and ground to generate compressive stress. The direction points to the center of the circle and takes a negative sign. When calculating, take σ 2、3 =-220MPa; the inner hole of the valve sleeve needs to be finely ground and honed, which will produce tensile stress, the direction of which is away from the center of the circle, and the positive sign is taken. When calculating, σ1 = 270MPa. This processing is normal processing. However, if the tool becomes blunt, the feed rate is too large, or the coolant is insufficient during the external grinding of the valve core, the external circle will burn and produce phase change stress, and the compressive stress will become tensile stress, and the direction will be away from the center of the circle. When calculating, σ 2、3 =290MPa; However, the inner hole space of the valve sleeve is small, and the heat dissipation is poor during grinding, which makes it easy to burn and generate phase change stress. The compressive stress turns into tensile stress, and the direction points to the center of the circle. When calculating, take σ1 = -290MPa. This processing is abnormal processing.

[0064] Determine whether the temperature field is a steady-state uniform temperature field, and calculate the internal stress of the valve core and valve sleeve.

[0065] After calculation, from Figure 5 It can be seen that under normal processing conditions, the radial clearance of mating surface B increases with increasing temperature; under abnormal processing, the radial clearance decreases with increasing temperature. Assuming that metal does not undergo thermal deformation at a normal temperature of 20°C, the two curves in the figure intersect at (20°C, 0 μm). The different fitting models for the elastic modulus coefficients of metal materials during cooling and heating result in an inflection point at 20°C. Based on these values, the minimum radial design clearance must be greater than 10.6 μm to avoid valve core sticking and jamming over a wide temperature range.

[0066] If the calculated minimum design clearance of the mating surface is 2.5μm < 10.6μm, the design dimensions need to be updated, the processing technology needs to be improved, and the above calculation process needs to be repeated until the minimum value of the radial design clearance is greater than 10.6μm.

[0067] like Figure 1 As shown in the figure, the thermodynamic analysis calculation of the axial opening of the slide valve auxiliary oil inlet is as follows:

[0068] According to the structural characteristics of the electro-hydraulic proportional valve mentioned above, since the valve sleeve is fixed to the electromagnet housing, the axial deformation of the left end of the valve sleeve is zero; the axial deformation of the left end of the valve core in contact with the moving iron core is zero. The zero point of the axial deformation of the valve core and valve sleeve is set as follows: Figure 6 shown.

[0069] Determine whether the temperature field of the valve core and valve sleeve is a steady-state uniform temperature field, and calculate the internal stress.

[0070] Since the two ends of the valve core in this embodiment are subject to axial constraint force F,

[0071] The calculation results show that at temperatures between -40°C and 150°C, the thermal deformation Δw at the oil inlet ranges from -19 to 14.1 μm. Under normal machining, this variation is less than 4% of the oil inlet. If burns or other problems occur during machining, the variation is less than 6%. This indicates that improper machining can increase the deformation of the oil inlet. Therefore, during grinding of the valve sleeve inner bore, the coolant flow rate can be increased to accelerate heat dissipation. Furthermore, controlled stress shot peening can be performed on the outer surface of the valve core and sleeve. The variation is minimal and has little impact on the performance of the electro-hydraulic proportional valve. The calculation process ends.

[0072] Compared with the traditional temperature analysis of hydraulic valve slide valve pairs, the present invention theoretically and comprehensively analyzes the geometric size law of thermal deformation of the slide valve pairs under the influence of factors such as parts processing technology and constraint force, which is of great significance to the design, manufacture and operation reliability of hydraulic valve slide valve pairs.

[0073] Components not described in detail in this embodiment are all existing components that can be purchased through public channels.

[0074] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range, characterized in that: The following steps are involved: S1. Determine the hydraulic valve spool valve pair parameters, including: structural dimensions, parts processing technology, working principle and working conditions; S2. Construct a simplified metal model of the slide valve pair based on the parameters determined in S1, including the parts processing technology, the temperature field of the working conditions, and the relationship between the slide valve pair constraints and the thermal deformation of the slide valve pair; S3. Based on the theory of linear thermal stress and elastic mechanics, the valve sleeve of the spool valve pair is simplified into a metal cylinder with a cylindrical inner wall, and the valve core of the spool valve pair is simplified into a metal cylinder with a cylindrical outer wall. A thermodynamic mathematical model is established for this simplified metal model of the spool valve pair. The thermal deformation law of the spool valve pair over a wide temperature range is calculated, namely, the thermal deformation of the radial clearance Δu and the thermal deformation of the key oil port Δw of the spool valve pair are calculated. S4. When the thermal deformation of the radial clearance Δu is greater than or equal to the maximum allowable variation under a wide temperature range, update the clearance design dimensions and processing technology; when the thermal deformation of the key oil port Δw is greater than or equal to the maximum allowable variation, update the processing technology; S5. Recalculate the thermal deformation law of the sliding valve pair based on the updated dimensions and material parameters, and repeat steps S2 and S3 until the radial clearance thermal deformation Δu is less than the maximum allowable variation under a wide temperature range, and the critical oil port thermal deformation Δw is less than the maximum allowable variation, and the radial and axial design requirements are met.

2. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S2, during the construction of the simplified metal model, a polar coordinate system is established for the spatial axisymmetric object, and expressions representing each stress component in terms of displacement and temperature difference are obtained.

3. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, a thermodynamic mathematical model is established for the metal cylinder, and polar coordinates are established for the metal cylinder with spatial axisymmetry. The origin of the coordinate is located at the center of the metal cylinder. Any point P in the metal cylinder can be expressed as P(r,θ,z). The inner diameter and outer diameter of the metal cylinder are r1 and r2 respectively, and the length of the metal cylinder is l1.

4. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, if the material is not in a steady-state uniform temperature field, the stress inside the metal cylinder is: s = s t +s r ; Among them, σ t is thermal stress, σ r is the residual stress, and σ is the stress after superposition.

5. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, during the construction of the simplified metal model, it is assumed that the temperature field of the slide valve pair is independent of time, that is, the temperature field is a steady-state temperature field. Under the steady-state temperature field, the temperature distribution is only related to r and is symmetrical about the z axis; Assuming that the temperature change ΔT is ΔT = ΔT(r), the thermal stress components generated inside the metal cylinder under the steady-state temperature field are calculated as follows: Among them, σ tr is the thermal stress in the radial direction of the metal cylinder, σ tθ is the thermal stress in the tangential direction of the metal cylinder, σ tz is the thermal stress in the axial direction of the metal cylinder; r1 and r2 are the inner diameter and outer diameter of the metal cylinder respectively, and l1 is the length of the metal cylinder.

6. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, the radial displacement deformation of the metal cylinder is calculated: ΔT = T2 - T1; Among them, σ1 and σ2 are the surface stresses of the inner diameter and outer diameter of the metal cylinder respectively, σ1=σ t1 +σ r1 ,σ2=σ t2 +σ r2 , σ t1 , σ t2 are the thermal stresses of the inner and outer diameters of the metal cylinder, σ r1 , σ r2 are the residual stresses of the inner and outer diameters of the metal cylinder, T1 is the initial temperature of the metal cylinder surface before thermal deformation, T2 is the final temperature of the metal cylinder surface after thermal deformation; η is the temperature coefficient of elastic modulus.

7. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, when the two ends of the metal cylinder are subject to an axial constraint force F, the forces on both ends are equal in magnitude and directed toward the inside of the metal cylinder. Therefore, compressive stress is generated during high-temperature expansion, and no force is applied during low-temperature contraction. The two ends are in a free state, so the axial force generated by the axial stress is: Combining the axial strain component of the metal cylinder and the axial compressive stress it experiences during high-temperature expansion, the axial displacement deformation of the metal cylinder under axial constraint force is obtained as follows: σ1 and σ2 are the surface stresses of the inner and outer diameters of the metal cylinder, respectively. σ1=σ t1 +σ r1 ,σ2=σ t2 +σ r2 , σ t1 , σ t2 are the thermal stresses of the inner and outer diameters of the metal cylinder, σ r1 , σ r2 are the residual stresses on the inner and outer diameters of the metal cylinder respectively; ΔT is the temperature change; η is the temperature coefficient of elastic modulus.

8. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, a mathematical model of thermodynamic geometric dimensions is established for the metal cylinder, and polar coordinates are established for the metal cylinder with spatial axisymmetry. The origin of the coordinate is located at the center of the metal cylinder, and any point Q in the cylinder is expressed as Q(r,θ,z); the outer diameter of the metal cylinder is r3, and the length of the metal cylinder is l2.

9. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, for a metal cylinder with residual stress on the surface, the components of internal thermal stress generated under thermal load are calculated as: σ tr is the thermal stress in the radial direction of the metal cylinder, σ tθ is the thermal stress in the tangential direction of the metal cylinder, σ tz is the thermal stress in the axial direction of the metal cylinder, r3 is the outer diameter of the metal cylinder, l2 is the length of the metal cylinder, and ΔT is the temperature change.

10. The method for analyzing and calculating the thermodynamic geometric dimensions of a hydraulic valve spool pair under a wide temperature range according to claim 1, characterized in that: In S3, under a steady-state uniform temperature field, that is, the temperature is independent of r, the temperature change ΔT = t2 - t1, and after considering the initial deformation of the metal cylinder at the initial temperature, the relative displacement changes in the radial and axial directions are obtained: Among them, σ3 is the stress on the outer surface of the metal cylinder, σ3=σ t3 +σ r3 ; σ t3 is the thermal stress of the outer diameter of the metal cylinder, σ r3 is the residual stress of the outer diameter of the metal cylinder; η is the temperature coefficient of elastic modulus.

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