Corrugated pipe compensator with high compression strength

Abstract

The invention discloses a corrugated pipe compensator with high compression strength, and belongs to the technical field of corrugated pipe compensators. Comprising a corrugated pipe body and end pipes, the corrugated pipe body is of a U-shaped corrugated structure, and wave pitches of the corrugated pipe body are distributed in a non-uniform gradient mode in the axial direction. The corrugated pipe body is sequentially divided into an end area, a transition area, a middle area, a transition area and an end area in the axial direction, and a symmetrical gradient structure is formed. The minimum wave pitch is adopted in the end area to provide high rigidity, and the instability resistance of the end is enhanced; the maximum wave pitch is adopted in the middle area to provide high flexibility, the wave pitch of the transition area is calculated through a sine square function, smooth transition from the ends to the middle is achieved, and stress concentration caused by sudden rigidity change is avoided. According to the method, the wave pitch parameters of all the areas are reasonably configured, stress distribution of all the portions of the corrugated pipe is more uniform, the compression strength, the instability resistance and the fatigue life of the corrugated pipe are effectively improved on the premise that the material consumption is not increased, and the method is suitable for displacement compensation of a high-pressure pipeline system.

Description

Technical Field

[0001] This invention belongs to the technical field of bellows compensators, specifically relating to a bellows compensator with high pressure resistance. Background Technology

[0002] Bellows compensators are crucial flexible connecting elements in industrial pipeline systems, used to absorb displacements caused by thermal expansion and contraction, vibration, and misalignment. They are widely used in petrochemical, power, marine, and nuclear power plants. The core component of a bellows compensator is the bellows body, typically made of thin-walled stainless steel with a U-shaped corrugated structure. The elastic deformation of the corrugations compensates for axial displacement of the pipeline. With the development of offshore platforms, deep-sea pipelines, and high-pressure chemical plants, the operating pressure and temperature of pipeline systems are continuously increasing, placing higher demands on the pressure resistance and instability resistance of bellows compensators.

[0003] Existing bellows compensators typically employ a uniform pitch design, meaning all corrugations along the axial direction of the bellows body use the same pitch. While this design is simple and easy to manufacture, it suffers from uneven stress distribution. Because the welded joints between the bellows ends and end pipes are subject to significant boundary constraints, the stress at the end peaks is significantly higher than at the middle peaks under a uniform pitch design, resulting in obvious stress concentration. The ends become weak points under internal pressure, prone to column or planar instability, thus limiting the overall pressure resistance of the bellows.

[0004] Existing technologies also include bellows compensators with gradually changing wave pitch designs, but these mostly employ a linear gradual change method to achieve the wave pitch transition. While the linear gradual change design can improve stress distribution to some extent, due to the constant slope of the linear function, there are abrupt changes in the rate of change of wave pitch at the junctions of the end and transition regions, as well as at the junctions of the transition and middle regions. This leads to discontinuous changes in stiffness, and local stress concentrations still occur at the junctions. Stress concentrations accelerate the initiation and propagation of fatigue cracks, reduce the fatigue life of the bellows, and make it difficult to meet the requirements for use under high-cyclic fatigue conditions.

[0005] Current technologies lack systematic design methods and reasonable value ranges for selecting wavelength parameters, often relying on engineering experience, which can easily lead to problems such as excessively large or small wavelength ratios. Improper selection of the wavelength ratio can result in unsatisfactory stress homogenization or instability risks due to excessively low mid-section stiffness, making it difficult to achieve the optimal balance between compressive strength, compensation capacity, and anti-instability performance.

[0006] Therefore, there is an urgent need for a bellows compensator that can effectively homogenize stress distribution, improve compressive strength and fatigue life, and has a system design method. Summary of the Invention

[0007] To address the problems existing in the background art, the present invention provides a bellows compensator with high pressure resistance, comprising a bellows body and end pipes. The bellows body has a U-shaped corrugated structure with a non-uniform gradient distribution of the corrugation pitch along the axial direction. The bellows body is divided into five regions along the axial direction: end region I, transition region II, middle region III, transition region IV, and end region V; wherein:

[0008] End region I is located at the beginning of the bellows body and uses the minimum wave pitch. This provides high stiffness to enhance end-effector stability.

[0009] Transition region II is located between end region I and middle region III, with a wavelength ranging from... Smoothly increase to maximum wavelength This achieves a gradual transition in stiffness;

[0010] The central region III is located in the center of the bellows body and uses the maximum wave pitch. It serves as the main compensation zone, providing displacement compensation capability.

[0011] Transition region IV is located between central region III and end region V, with a wavelength ranging from... Smoothly decrease to This achieves a gradual transition in stiffness;

[0012] End region V is located at the tail end of the bellows body and uses the minimum wave pitch. This provides high stiffness to enhance end-effector stability.

[0013] The end pipe is configured as two pieces, which are welded and fixed to both ends of the corrugated pipe body respectively, for connection and transition with the pipeline system.

[0014] In the preferred scheme, the wavelength ratio The value range is 1.2-2.0.

[0015] In the preferred embodiment, the following parameters are defined for the bellows body:

[0016] The total number of corrugations in the bellows body; The wavenumber of the unilateral end regions, where end region I and end region V each contain One wave; The wavenumbers for the unilateral transition regions, where transition regions II and IV each contain... One wave; This refers to the last wave number of end region I; This refers to the last wave number in transition region II; This refers to the last wave number in the central region III; This refers to the last wave number in transition region IV; Wave number The value range is 1 to ; For the first Wavelength of each wave;

[0017] The boundary numbers for each region are calculated using the following formula: ; ; ; The first corrugated pipe body Wavelength of each wave Calculated using the following piecewise function:

[0018] when hour, Corresponding to end region I;

[0019] when hour, This corresponds to transition region II; where, This represents the change in wave distance, in mm.

[0020] when hour, This corresponds to the central region III.

[0021] when hour, This corresponds to transition region IV;

[0022] when hour, , corresponding to end region V.

[0023] In the preferred scheme, , , The boundary numbers for each region are: , , , Wavenumber in Central Region III .

[0024] In a preferred embodiment, the inner diameter of the bellows body is... The outer diameter of the corrugated pipe is 200mm. 230mm, wave height The effective wall thickness is 15mm. The minimum wavelength is 0.4 mm; The maximum wavelength is 16mm. It is 26mm, with a beamwidth ratio of 1.5mm. It is 1.625.

[0025] In the preferred embodiment, the outer diameter of the end tube is 219 mm, the wall thickness is 6 mm, and the length is 80 mm; the end tube and the corrugated pipe body are connected by TIG argon arc welding circumferential butt welding.

[0026] In a preferred embodiment, a flow-guiding inner sleeve is coaxially arranged inside the bellows body. The two ends of the flow-guiding inner sleeve are respectively fixed to the inner walls of the two end pipes. The flow-guiding inner sleeve and the inner wall of the bellows body maintain a clearance fit to protect the inner wall of the bellows and guide the flow of the medium.

[0027] In a preferred embodiment, a connecting flange is also included; the connecting flange is provided in two pieces, which are welded and fixed to the outer ends of the two end pipes respectively, for connection with the flange of the external piping system.

[0028] In a preferred embodiment, the connecting flange is equipped with a limit rod, the two ends of which pass through the two connecting flanges respectively and are fixed by a limit nut.

[0029] In a preferred embodiment, the outer diameter of the inner guide sleeve is 195mm, and it maintains a 2.5mm gap with the inner wall of the corrugated pipe body; the wall thickness of the inner guide sleeve is 3mm, and the length is 350mm; both the inlet and outlet ends of the inner guide sleeve are chamfered.

[0030] The beneficial effects achieved by this invention are as follows:

[0031] This invention achieves uniform stress distribution across all parts of the bellows by designing the corrugation pitch of the bellows body as a non-uniform gradient distribution along the axial direction. This significantly improves the pressure resistance and service life of the bellows without increasing material usage. The invention uses the minimum corrugation pitch in the end region to achieve high stiffness, enabling the ends to withstand greater boundary constraint loads without instability. This effectively solves the technical problem of stress concentration at the ends, which easily becomes a weak point in the pressure-bearing structure, in traditional uniform corrugation designs. The invention uses the maximum corrugation pitch in the middle region to achieve high flexibility, allowing the middle region, as the main compensation zone, to fully utilize its displacement compensation capability and ensuring that the compensation performance of the bellows is not affected.

[0032] This invention uses a sine square function to calculate the wave pitch in the transition region. Utilizing the mathematical property that the sine square function is continuously differentiable and has zero derivative at its endpoints, it achieves a smooth, continuous transition of the wave pitch from the end to the middle, ensuring a continuous and smooth change in stiffness along the axial direction. Compared to linear transition methods, the sine square transition effectively avoids abrupt changes in stiffness at the boundary between the end and transition regions, eliminates local stress concentrations caused by discontinuous stiffness changes, reduces the risk of fatigue crack initiation, and thus extends the fatigue life of the bellows.

[0033] This invention controls the wavelength ratio within a reasonable range, ensuring sufficient stiffness contrast between the ends and the middle to achieve stress homogenization, while avoiding planar instability caused by excessively low stiffness in the middle due to an excessively large wavelength ratio. A wavelength ratio that is too small will result in an insignificant gradient effect, making it difficult to improve the uniformity of stress distribution; a wavelength ratio that is too large will make the middle region a new weak point for instability, thus reducing the overall load-bearing capacity. This invention achieves an optimal balance between high stiffness and instability resistance at the ends and high flexibility and compensation capability in the middle through a reasonable configuration of the wavelength ratio.

[0034] This invention also protects the inner wall of the bellows from direct erosion by high-speed fluid through the inclusion of a flow-guiding inner sleeve, reducing erosion and wear caused by eddies and turbulence, mitigating fatigue damage caused by pressure pulsation, and extending the service life of the bellows under high-speed media transport conditions. Furthermore, this invention limits the axial displacement range of the bellows by incorporating a limiting tie rod, preventing damage to the bellows body due to excessive stretching or compression, thus improving the safety and reliability of the compensator under abnormal pipeline system conditions. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the overall structure of the bellows compensator.

[0036] Figure 2 This is a schematic diagram showing the division of the wave pitch area of ​​the corrugated pipe body.

[0037] Figure 3 It is a curve showing the distribution of wave distance along the axial direction.

[0038] Figure 4 These are graphs showing the wavelength distribution of Examples 1 to 4. Figure 4 Subplot (a) shows the wavelength distribution of Example 1, subplot (b) shows the wavelength distribution of Example 2, subplot (c) shows the wavelength distribution of Example 3, and subplot (d) shows the wavelength distribution of Example 4.

[0039] Figure 5 This is a comparison curve of the equivalent stress distribution of each wave between Example 1 and Comparative Example 1.

[0040] Figure 6 This is a bar chart comparing the safety factors of Examples 1 to 4 and Comparative Examples 1 to 3.

[0041] Figure 7 This is a bar chart comparing the fatigue life of Example 1 with Comparative Examples 1 and 2.

[0042] Figure 8 This is a comparative bar chart of Example 1 and Comparative Examples 1 and 3 regarding the critical instability pressure.

[0043] Figure 9This is a comparison curve of axial stiffness distribution between Example 1 and Comparative Examples 1 and 2.

[0044] Figure 10 This is a comparative bar chart of Examples 1 to 4 and Comparative Examples 1 to 3 regarding stress uniformity.

[0045] Numbering on the map:

[0046] 1. Corrugated pipe body; 2. End pipe; 3. Connecting flange; 4. Inner guide sleeve; 5. Limiting tie rod. Detailed Implementation

[0047] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. In addition, the forms of the various structures described in the following embodiments are merely illustrative. The present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Reference Figures 1 to 3 This invention provides a high-pressure-resistant bellows compensator, comprising a bellows body 1 and end pipes 2. The bellows body 1 has a U-shaped corrugated structure, where the cross-section of the corrugations has a U-shaped profile. This structure has good flexibility and compensation capabilities, and is widely used in industrial pipeline systems to absorb displacements such as thermal expansion and contraction, vibration, and misalignment. Unlike traditional uniform pitch designs, the pitch of the bellows body 1 in this invention is distributed in a non-uniform gradient along the axial direction. By rationally configuring the pitch in different regions, the stress distribution is made more uniform, thereby improving the pressure resistance and instability resistance of the bellows.

[0049] The bellows body 1 is divided into five regions along the axial direction: end region I, transition region II, middle region III, transition region IV, and end region V. These five regions are symmetrically distributed along the axial direction of the bellows body 1, forming a gradient structure with high stiffness at both ends and high flexibility in the middle, which conforms to the stress distribution law of the bellows when subjected to internal pressure.

[0050] End region I is located at the beginning of the bellows body 1, and uses the minimum wave pitch. Wavelength refers to the axial distance between two adjacent wave crests. The smaller the wavelength, the more wavenumbers per unit length, and the higher the stiffness. Using the minimum wavelength in end region I can provide high stiffness to enhance the end's resistance to instability. When the bellows is subjected to internal pressure, the welded connection between the end and end pipe 2 is subjected to large boundary constraint stress. Using a high-stiffness design can effectively resist end column instability and planar instability.

[0051] Transition region II is located between end region I and middle region III, and its wavelength ranges from Smoothly increase to maximum wavelength The purpose of transition region II is to achieve a gradual transition in stiffness, avoiding stress concentration caused by abrupt changes in stiffness. If the transition is abrupt from the minimum to the maximum wavelength, a sudden change in stress will occur at the interface, which can easily lead to the initiation of fatigue cracks. The gradual transition design allows the stress to change smoothly along the axial direction, improving the overall integrity and reliability of the structure.

[0052] The central region III is located in the center of the bellows body 1 and uses the maximum wave pitch. The central region III serves as the main compensation zone, providing displacement compensation for the bellows. A larger corrugation pitch implies lower stiffness and stronger deformation capacity, making central region III the primary area for absorbing axial displacement of the pipeline. In actual operating conditions, axial displacement of the pipeline system caused by factors such as temperature changes and pressure fluctuations is mainly compensated by central region III.

[0053] Transition region IV is located between the middle region III and the end region V, and its wavelength ranges from... Smoothly decrease to The transition region IV and transition region II are symmetrically set to achieve a gradual transition in stiffness, ensuring that the stiffness distribution of the bellows body 1 along the axial direction exhibits a symmetrical gradient change.

[0054] End region V is located at the tail end of the bellows body 1 and uses the minimum wave pitch. This provides high stiffness to enhance the end's resistance to instability. End region V is symmetrically arranged with end region I, so that both ends of the bellows body 1 have the same stiffness characteristics and resistance to instability.

[0055] Two end pipes 2 are provided, welded and fixed to both ends of the bellows body 1 respectively. End pipes 2 serve as the connecting transition between the bellows body 1 and the external piping system, and their outer diameter matches the nominal diameter of the piping system. The end pipes 2 and the bellows body 1 are preferably connected by TIG argon arc welding (TIG) circumferential butt welding. TIG welding is a welding method that uses tungsten electrodes and inert gas as the shielding gas. It offers high weld quality, minimal deformation, and is suitable for welding thin-walled stainless steel, ensuring the airtightness and strength of the weld.

[0056] A flow-guiding inner sleeve 4 is coaxially installed inside the bellows body 1, with its two ends fixed to the inner walls of the two end pipes 2. A clearance fit is maintained between the flow-guiding inner sleeve 4 and the inner wall of the bellows body 1; the size of the clearance should ensure that the flow-guiding inner sleeve 4 does not interfere with the bellows during axial expansion and contraction of the bellows. The function of the flow-guiding inner sleeve 4 is to protect the inner wall of the bellows and guide the flow of the medium. When high-speed fluid is transported in the pipeline, eddies and turbulence easily form in the troughs of the bellows, causing erosion and wear on the inner wall of the bellows. Simultaneously, the pressure pulsation caused by the eddies exacerbates fatigue damage to the bellows. The flow-guiding inner sleeve 4 allows the medium to flow along a smooth inner surface, preventing the medium from directly scouring the inner wall of the bellows and extending the service life of the bellows. Both the inlet and outlet ends of the flow-guiding inner sleeve 4 are chamfered. The chamfer guides the medium to flow smoothly in and out, reduces flow resistance, and prevents eddies from forming at the sleeve ends.

[0057] The invention also includes connecting flanges 3, of which two are provided and welded to the outer ends of the two end pipes 2 respectively. The connecting flanges 3 are used for connection with mating flanges of external piping systems, enabling a detachable connection between the bellows compensator and the piping system. The specifications of the connecting flanges 3 should meet the requirements of relevant standards. Bolt holes are provided on the flanges, evenly distributed along the circumference, for installing connecting bolts.

[0058] Connecting flange 3 is equipped with limiting tie rods 5. Both ends of the limiting tie rods 5 pass through two connecting flanges 3 and are secured with limiting nuts. The limiting tie rods 5 are used to limit axial displacement and prevent excessive stretching or compression of the bellows body 1. During pipeline system operation, if the axial displacement of the bellows exceeds the design compensation amount, it can lead to excessive deformation or even damage to the bellows. The position of the limiting tie rods 5 can be adjusted by the limiting nuts to set the maximum stretching limit and maximum compression limit of the bellows. When the axial displacement reaches the limit value, the limiting tie rods 5 bear the axial load, protecting the bellows body 1 from excessive deformation. Multiple limiting tie rods 5 are generally provided, evenly distributed along the circumference to ensure uniform transmission of axial load.

[0059] For the piecewise function of the wave pitch of the bellows body 1, the following parameters are defined. The total number of corrugations in the bellows body 1 refers to the number of complete corrugations contained in the bellows body 1 along the axial direction. The wavenumber of the unilateral end regions, where end region I and end region V each contain A wave. The wavenumbers for the unilateral transition regions, where transition regions II and IV each contain... A wave. This refers to the last wave number in end region I. This refers to the final wave number in transition region II. This refers to the last wave number in the central region III. This is the sequence number of the last wave in transition region IV. Wave number The value range is 1 to . For the first The wave distance of each wave.

[0060] The boundary numbers of each region are calculated using the following formula. ; ; ; .in This refers to the last wave number in end region I; Wavenumber of the single-sided end region; The last wave number in transition region II; Wavenumber for the unilateral transition region; This refers to the final wave number of region III in the central area; Total wavenumber; This is the sequence number of the last wave in transition region IV.

[0061] The first in the bellows body 1 Wavelength of each wave Calculate according to the following piecewise function.

[0062] when hour, This corresponds to end region I. For the first The wave distance of each wave is in mm; Minimum wavelength, in mm; Wave number; This is the sequence number of the last wave in end region I.

[0063] when hour, This corresponds to transition region II. For the first The wave distance of each wave is in mm; Minimum wavelength, in mm; This represents the change in wave distance, in mm. ; Wave number; This refers to the last wave number in end region I; The wavenumber is for the single-sided transition region. The sine square function is used as the transition function because it is continuously differentiable and has a smooth change. Its derivative is zero at the endpoints, which can achieve a seamless transition of the wave pitch and make the stiffness change continuously along the axial direction.

[0064] when hour, This corresponds to Central Region III. Among them... For the first The wave distance of each wave is in mm; This represents the maximum wavelength, expressed in mm.

[0065] when hour, This corresponds to transition region IV. Among them... The last wave number in transition region IV; This is the wave index. This formula is structurally symmetrical to the formula for transition region II, causing the wave distance in transition region IV to... Smoothly decrease to .

[0066] when hour, , corresponding to end region V.

[0067] Wavelength ratio The definition of ,in It is the wavelength ratio; This is the maximum wavelength, in mm. Minimum wavelength, in mm. Wavelength ratio. This reflects the ratio between the maximum and minimum wave pitch in the bellows body 1; the wave pitch ratio The preferred value range is 1.2 to 2.0. A too-small wavelength ratio means that the wavelength differences between regions are not significant, the gradient effect is not obvious, and it is difficult to achieve stress homogenization. A too-large wavelength ratio will result in excessively low stiffness in the central region, making it prone to instability under internal pressure. Simultaneously, an excessively large stress gradient in the transition region is detrimental to the overall stability of the structure.

[0068] The design principle and process of the high-pressure-resistant bellows compensator of the present invention are as follows:

[0069] S1. Input design operating parameters. Obtain nominal diameter, design pressure, design temperature, total compensation, and material performance parameters. The design operating parameters are the basic inputs for bellows compensator design, determining the basic dimensions and performance requirements of the bellows.

[0070] Step S1 includes the following sub-steps.

[0071] S11. Obtain the nominal diameter. The unit is mm. The nominal diameter is the nominal inner diameter of the piping system and is the basic parameter for matching and connecting the bellows compensator with the piping system. This sub-step determines the basic diameter of the bellows.

[0072] S12, Obtain Design Pressure The unit is MPa. The design pressure is the maximum internal pressure that the bellows can withstand under normal operating conditions. It is the basis for strength design and pressure resistance verification. This sub-step determines the pressure rating of the bellows.

[0073] S13, Obtain the design temperature The unit is °C. The design temperature is the highest temperature of the bellows under working conditions. The design temperature affects the mechanical properties of the material and the allowable stress value. This sub-step determines the working temperature conditions of the material.

[0074] S14. Obtain the total compensation amount The unit is mm. The total compensation amount is the total axial displacement that the bellows needs to compensate for, including displacement caused by factors such as thermal expansion, cold contraction and installation errors. This sub-step determines the amount of axial displacement that the bellows needs to compensate for.

[0075] S15. Obtain material property parameters, including elastic modulus. Poisson's ratio and yield strength Elastic modulus Poisson's ratio represents the stiffness of a material during its elastic deformation phase, measured in MPa or GPa. Yield strength is the ratio of transverse strain to longitudinal strain in a material, and is a dimensionless parameter. This is the stress value at which the material begins to undergo plastic deformation, measured in MPa, and is the basis for determining the allowable stress. This sub-step generates a table of design working condition parameters.

[0076] S2. Determine the basic geometric parameters. Calculate the bellows' inner diameter, wave height, effective wall thickness, and total number of wavelets based on the design operating parameters. The basic geometric parameters determine the basic shape and pressure-bearing capacity of the bellows.

[0077] Step S2 includes the following sub-steps. S21: Determine the inner diameter of the bellows. .make .in This is the inner diameter of the bellows, in mm; This is the nominal diameter, in mm. The inner diameter of the corrugated pipe is taken to be equal to the nominal diameter to ensure that the flow area of ​​the corrugated pipe is consistent with that of the piping system. This sub-step generates the inner diameter value of the corrugated pipe.

[0078] S22. Determine wave height According to the formula Calculation. Among them... Wave height, in mm; This is the inner diameter of the bellows, in mm; The wave height coefficient is a dimensionless parameter, preferably ranging from 0.05 to 0.10. Wave height refers to the radial distance between the crest and trough of a wave. A larger wave height results in greater flexibility and compensation capability of the bellows, but a corresponding decrease in pressure resistance. Wave height coefficient The value of should be determined by comprehensively considering the balance between compensation capability and pressure resistance performance. This sub-step generates the wave height value.

[0079] S23. Determine the effective wall thickness According to the formula Calculation. Among them... Effective wall thickness, in mm; Design pressure, unit is MPa; This is the inner diameter of the bellows, in mm; The coefficient is derived from the circumferential stress formula for thin-walled cylinders; Allowable stress, in MPa, is the maximum working stress that a material can withstand after considering the safety factor. The welding coefficient is a dimensionless parameter, preferably ranging from 0.8 to 1.0. The welding coefficient reflects the degree of strength reduction of the welded joint relative to the base material. This sub-step generates the effective wall thickness value.

[0080] S24. Determine the total wavenumber. According to the formula Calculation. Among them... Total wavenumber; This is the floor function, which means rounding the result to the smallest integer not less than this value; Total compensation amount, in mm; The single-wave compensation coefficient is a dimensionless parameter, preferably ranging from 0.15 to 0.25. The single-wave compensation coefficient represents the ratio of the displacement that a single ripple can compensate to the wave height. The wave height is in mm. Using an up-rounding function ensures the total wave number is an integer and the compensation capability is not less than the design requirements. This sub-step generates the total wave value.

[0081] S3. Divide the wave pitch regions and determine the boundary numbers. Divide the bellows along the axial direction into end regions, transition regions, and middle regions, and determine the wave number and boundary wave number for each region. Region division is the basis for realizing the wave pitch gradient distribution.

[0082] Step S3 includes the following sub-steps. S31: Determine the wavenumber of the unilateral end region. According to the formula Calculation. Among them... For the wavenumber of a single-sided end region, end region I and end region V each contain One wave; This is the rounding function; Total wavenumber; The end wavenumber ratio is a dimensionless parameter, preferably ranging from 0.10 to 0.20. The end wavenumber ratio reflects the proportion of the end region wavenumber to the total wavenumber. If the ratio is too small, the end stiffness will be insufficient, and if the ratio is too large, the compensation capability of the middle region will be sacrificed. This sub-step generates the wavenumber of the end region on one side.

[0083] S32. Determine the wavenumber of the unilateral transition region. According to the formula Calculation. Among them... The wavenumbers for the single-sided transition region are: Transition Region II and Transition Region IV each contain... One wave; This is the rounding function; Total wavenumber; The transition wavenumber ratio is a dimensionless parameter, preferably ranging from 0.10 to 0.20. The transition wavenumber ratio reflects the proportion of the transition region wavenumbers to the total wavenumbers. A sufficient number of transition region wavenumbers should be generated to ensure a smooth transition in stiffness. This sub-step generates the wavenumbers for the unilateral transition region.

[0084] S33, Calculate the wavenumber in the central region According to the formula Calculation. Among them... The wavenumber for the central region III; 1 represents the total wavenumber; 2 is a coefficient indicating bilateral symmetry, meaning there are two waves in both the end region and the transition region. Wavenumber of the single-sided end region; This is the wavenumber for the single-sided transition region. The wavenumber for the central region should have sufficient compensation capability; this sub-step generates the wavenumber for the central region.

[0085] S34. Calculate the boundary wave number for each region. Use the following formula: , , , .in This refers to the last wave number in end region I; The last wave number in transition region II; This refers to the final wave number of region III in the central area; This refers to the final wave number of transition region IV. The boundary wave number is used to determine the region to which each wave belongs in the piecewise function; this sub-step generates the region division scheme.

[0086] S4. Establish the wave distance piecewise function and calculate the wave distance for each wave. Set the minimum and maximum wave distances, and calculate the wave distance value for each wave according to the piecewise function. The wave distance piecewise function is the core algorithm for achieving stress homogenization in this invention.

[0087] Step S4 includes the following sub-steps. S41: Set the minimum beam distance. According to the formula Calculation. Among them... Minimum wavelength, in mm; Wave height, in mm; The minimum wave distance coefficient is a dimensionless parameter, preferably ranging from 1.0 to 1.2. The minimum wave distance coefficient reflects the ratio of the minimum wave distance to the wave height. A ratio that is too small will result in overly dense waveforms, increasing processing difficulty. This sub-step generates the minimum wave distance value.

[0088] S42, Set maximum beam distance According to the formula Calculation. Among them... This is the maximum wavelength, in mm. Wave height, in mm; The maximum wavelength factor is a dimensionless parameter, preferably ranging from 1.5 to 2.0. The maximum wavelength factor reflects the ratio of the maximum wavelength to the wave height. The maximum wavelength determines the stiffness and compensation capability of the central region. This sub-step generates the maximum wavelength value.

[0089] S43, Verification of Wavelength-to-Span Ratio According to the formula Calculation. Among them... It is the wavelength ratio; This is the maximum wavelength, in mm. Minimum wavelength, in mm. Verification. If the beamwidth ratio exceeds the range of 1.2 to 2.0, the minimum beamwidth factor should be adjusted back to its original value. or maximum wave distance coefficient The step generates the verified wavelength ratio.

[0090] S44. Calculate the change in wave distance According to the formula Calculation. Among them... This represents the change in wave distance, in mm. This is the maximum wavelength, in mm. The minimum wavelength is expressed in mm. The wavelength variation is the magnitude of the wavelength variation in the transition region; this sub-step generates the wavelength variation.

[0091] S45. Calculate the wave distance of each wave based on the piecewise function. For end regions I and V, For Central Region III, For transition region II, according to the formula... Calculation. Among them... For the first Wave distance, in mm; Minimum wavelength, in mm; This represents the change in wave distance, in mm. It is a sine square function; Pi; The current wave number; This refers to the last wave number in end region I; Wavenumber for the unilateral transition region; The coefficient is used. For the transition region IV, according to the formula... Calculation. Among them... This is the last wave number in transition region IV. The piecewise function uses a sine square function to achieve a smooth transition in wave distance. The sine square function has a range of 0 to 1, and its derivative is zero at the endpoints of the interval, ensuring the continuity and smoothness of the wave distance change from the end region to the middle region. This sub-step generates a table of wave distance values ​​for each wave.

[0092] S5. Calculate stress distribution and evaluate stress uniformity. Calculate the equivalent stress of each wave, statistically analyze the characteristic values ​​of stress distribution, and calculate the stress uniformity index. Stress analysis is a crucial step in verifying the rationality of the design.

[0093] Step S5 includes the following sub-steps: S51, Calculate the equivalent stress of each wave. According to the formula Calculation. Among them... For the first Wave equivalent stress, in MPa; Design pressure, unit is MPa; This is the inner diameter of the bellows, in mm; Effective wall thickness, in mm; This is the pressure correction factor; For position correction factor. For pressure correction factor. According to the formula Calculate. Where 1 and 0.5 are empirical coefficients; Wave height, in mm; For the first Wavelength, in mm; superscript 2 indicates squaring. The pressure correction factor reflects the influence of waveform geometry on stress; the smaller the wavelength, the larger the correction factor, and the higher the stress. Position correction factor. Considering the amplification effect of boundary constraints on end wave stress, the preferred value range for the end wave position correction factor is 1.2 to 1.4, while the value for the middle wave is 1.0. This sub-step generates the equivalent stress array for each wave.

[0094] S52. Statistical stress eigenvalues. Extracting the maximum stress. and minimum stress According to the formula Calculate the average stress. Wherein The average stress is expressed in MPa. For the first Wave equivalent stress, in MPa; This represents the total wavenumber. Stress eigenvalues ​​are used to evaluate the uniformity of stress distribution; this sub-step generates stress eigenvalues.

[0095] S53, Calculation of stress uniformity index According to the formula Calculation. Among them... This is an index of stress uniformity, expressed as a percentage. This represents the maximum stress, expressed in MPa. Minimum stress, in MPa; The stress is the average stress, expressed in MPa; 100% is a percentage conversion factor. The stress uniformity index reflects the dispersion of stress distribution. The smaller the index value, the more uniform the stress distribution, and the higher the utilization rate of the pressure-bearing capacity of the bellows. This sub-step generates the stress uniformity index.

[0096] S6. Optimize wavelength parameters. Determine if the stress uniformity meets the target requirements. If not, adjust the wavelength parameters and recalculate. The optimization process achieves convergence of the design target through iterative adjustments.

[0097] Step S6 includes the following sub-steps. S61: Determine whether the target requirement is met. If... Then proceed to step S7. Wherein... The target stress uniformity is preferably set between 15% and 25%. The target stress uniformity is the convergence criterion for design optimization, and this sub-step generates the convergence judgment result.

[0098] S62, if Then adjust the beam distance parameter. According to the formula... Update the minimum beam distance coefficient. This is the updated minimum beam distance coefficient; 1 represents the current minimum beam distance coefficient; 1 represents the baseline value. The step size is a dimensionless parameter, preferably ranging from 0.05 to 0.15. By reducing the minimum wavelength coefficient, the stiffness of the end region can be increased, and the stress distribution can be adjusted. This sub-step generates the adjusted wavelength coefficient.

[0099] S63. Return to step S41 and recalculate using the updated parameters. This sub-step implements an iterative optimization loop. The iteration process continues until the stress uniformity meets the target requirement or the upper limit of the number of iterations is reached.

[0100] S7. Verify pressure resistance. Calculate the critical buckling pressure and verify whether the safety factor meets the requirements. Pressure resistance verification is a necessary step to ensure the safe operation of the bellows.

[0101] Step S7 includes the following sub-steps: S71, Calculate the total length of the corrugated portion. According to the formula Calculation. Among them... This represents the total length of the corrugated section, in mm. For the first The corrugation pitch is in mm. The total length of the corrugated section is an important parameter of the axial dimension of the bellows; this sub-step generates the total length of the corrugated section.

[0102] S72. Calculate the critical instability pressure According to the formula Calculation. Among them... The critical instability pressure is expressed in MPa. This is an empirical coefficient, preferably ranging from 0.3 to 0.5. The empirical coefficient is determined based on the boundary conditions and instability mode of the bellows. This refers to the elastic modulus, expressed in MPa. Effective wall thickness, in mm; Minimum wavelength, in mm; This is the inner diameter of the bellows, in mm; Wave height is expressed in mm; 1000 is a unit conversion factor. The critical buckling pressure is the critical pressure at which the bellows becomes unstable. This invention effectively increases the critical buckling pressure by using the minimum wave pitch in the end region. This sub-step generates the critical buckling pressure value.

[0103] S73, Verify the safety factor According to the formula Calculation. Among them... For safety factor; The critical instability pressure is expressed in MPa. Design pressure, unit: MPa. Verification. If the conditions are not met, return to step S41 to adjust the parameters and recalculate. The safety factor is the ratio of the critical buckling pressure to the design pressure, characterizing the safety margin of the bellows against buckling. This sub-step generates the pressure resistance performance verification results.

[0104] S8. Output Design Results. Summarize and output the optimized geometric parameters and performance indicators of the bellows compensator. The design results serve as the basis for bellows processing and manufacturing.

[0105] Step S8 includes the following sub-steps. S81: Summarize geometric parameters, including the bellows inner diameter. , wave height Effective wall thickness Total wavenumber Minimum wave distance Maximum wave distance Wavelength of each wave and the total length of the corrugated part Geometric parameters are the dimensional basis for the processing and manufacturing of bellows. This sub-step generates a summary table of geometric parameters.

[0106] S82. Summary of performance indicators. This includes stress uniformity. Critical instability pressure and safety factor Performance indicators are used to evaluate the design quality of bellows; this sub-step generates a summary table of performance indicators.

[0107] S83. Output Design Report. This includes design conditions, geometric parameters, region division, wave pitch distribution, and performance verification results. As a complete technical document, the design report serves as the technical basis for bellows processing, manufacturing, and quality inspection. This sub-step generates a complete bellows compensator design scheme.

[0108] This invention designs the corrugated pipe body 1 with a non-uniform gradient distribution of the corrugation pitch along the axial direction. A smaller pitch is used in the end region to improve stiffness and resistance to instability, while a larger pitch is used in the middle region to ensure compensation capability. A smooth transition in stiffness is achieved through a transition region, resulting in a more uniform stress distribution throughout the corrugated pipe. This avoids the stress concentration problem at the ends in traditional uniform pitch designs, improving the pressure resistance and service life of the corrugated pipe without increasing material usage. Through iterative optimization, automatic adjustment of stress uniformity is achieved, allowing for rapid acquisition of the optimal pitch distribution scheme according to different operating conditions.

[0109] Example 1: This example is applied to a high-pressure pipeline system of a certain marine platform. For the working conditions of nominal diameter DN200mm, design pressure 2.5MPa, design temperature 300℃, and total compensation amount of 25mm, a corrugated pipe compensator with high pressure resistance is designed and manufactured.

[0110] The overall structure of the bellows compensator in this embodiment includes a bellows body, end pipes, connecting flanges, a flow-guiding inner sleeve, and a limiting tie rod. The bellows body is the core pressure-bearing and compensation element, made of 316L stainless steel, which has good corrosion resistance and high-temperature mechanical properties. The bellows body has an inner diameter of 200mm, an outer diameter of 230mm, a wave height of 15mm, and an effective wall thickness of 0.4mm. It consists of six single-layer structures stacked together to form a total wall thickness of 2.4mm, with a total of 12 wave counts. The bellows body has a U-shaped corrugated structure, and its core innovation lies in the non-uniform gradient distribution of the wave pitch along the axial direction, forming a symmetrical structure with high end stiffness and high middle flexibility.

[0111] The bellows body is divided into five regions along the axial direction: end region I, transition region II, middle region III, transition region IV, and end region V. End regions I and V each contain two corrugations with a minimum corrugation pitch of 16 mm, providing high stiffness to enhance end stability. Transition regions II and IV each contain two corrugations with pitches of 18.5 mm and 23.5 mm respectively, achieving a smooth transition in stiffness from the end to the middle. Middle region III contains four corrugations with a maximum corrugation pitch of 26 mm, serving as the main compensation zone to provide sufficient displacement compensation. The corrugation pitch ratio is 1.625, and the total length of the corrugated section is 252 mm.

[0112] Two end pipes are provided, each with an outer diameter of 219mm, a wall thickness of 6mm, and a length of 80mm. They are welded and fixed to both ends of the bellows body, and connected to the bellows body using TIG argon arc welding for transition to the piping system. Two connecting flanges are provided, each with a specification of DN200PN4.0, and are welded and fixed to the outer ends of the two end pipes for connection to the external piping system flanges. A flow-guiding inner sleeve is coaxially installed inside the bellows body, with an outer diameter of 195mm, maintaining a 2.5mm gap from the inner wall of the bellows, a wall thickness of 3mm, and a length of 350mm. Its two ends are fixed to the inner walls of the two end pipes, protecting the inner wall of the bellows and guiding the flow of the medium. Four limiting tie rods are provided, evenly distributed along the circumference, with both ends passing through the two connecting flanges and fixed by limiting nuts, to limit axial displacement and prevent excessive stretching or compression of the bellows body.

[0113] This embodiment is a design based on an in-depth analysis of the stress distribution law of traditional uniform pitch bellows. In traditional uniform pitch bellows, the welded connection between the bellows end and the end pipe bears a large boundary constraint stress, and the stress at the end peak is significantly higher than that in the middle, forming stress concentration and becoming a weak link in the load-bearing capacity. This invention increases the local stiffness by using a smaller pitch in the end region, enabling the end to withstand higher boundary constraint loads without instability. At the same time, a larger pitch is used in the middle region to ensure sufficient flexibility and compensation capacity, and a gradual transition of stiffness is achieved through a transition region to avoid stress concentration caused by abrupt changes in stiffness.

[0114] The wave pitch variation in the transition region is calculated using a sine square function, a design based on mechanical analysis. The sine square function is continuously differentiable and exhibits smooth variation; its derivative is zero at the endpoints, enabling a seamless transition of the wave pitch. This allows for continuous stiffness variation along the axial direction, avoiding the abrupt stiffness changes and stress concentrations that occur at the interface in linear transition methods. This results in a more uniform stress distribution throughout the bellows, significantly improving its pressure resistance and instability resistance without increasing material usage.

[0115] In this embodiment, the wavelength ratio is set to 1.625. If the wavelength ratio is too small, the wavelength differences between regions will be small, the gradient effect will be insignificant, and it will be difficult to achieve the goal of stress homogenization. If the wavelength ratio is too large, the stiffness of the central region will be too low, making it prone to instability under internal pressure. This embodiment achieves the best balance between high stiffness and instability resistance at the ends and high flexibility and compensation capability in the middle through a reasonable wavelength ratio design.

[0116] Example 2: This example is applied to a heat exchange system in a petrochemical plant, designed for operating conditions with a nominal diameter of DN150mm, a design pressure of 1.6MPa, a design temperature of 250℃, and a total compensation of 20mm. The corrugated pipe body is made of 304 stainless steel, with an inner diameter of 150mm, a wave height of 12mm, and an effective wall thickness of 0.35mm. Five layers are stacked together to form a total wall thickness of 1.75mm, and the total number of wavelets is 10.

[0117] Considering the lower design pressure and fewer total corrugations in this embodiment, a more compact configuration is adopted for the regional division. End regions I and V each contain two corrugations with a minimum corrugation pitch of 14mm. Transition regions II and IV each contain only one corrugation with a pitch of 17mm, achieving rapid transition with a single corrugation. The central region III contains four corrugations with a maximum corrugation pitch of 20mm. The corrugation pitch ratio is 1.43, which is at the lower end of the recommended range and suitable for medium and low pressure conditions. The total length of the corrugated section is 170mm.

[0118] This embodiment employs a smaller wavelength ratio design. Although the stiffness difference between the ends and the middle is relatively small, it still effectively improves the uniformity of stress distribution. Due to the lower design pressure, the requirements for end instability resistance are correspondingly reduced. Using a smaller wavelength ratio can achieve better compensation performance while ensuring safety.

[0119] Example 3: This example is applied to an LNG cryogenic pipeline system, designed for extreme operating conditions with a nominal diameter of DN300mm, a design pressure of 4.0MPa, a design temperature of -162℃, and a total compensation of 40mm. The corrugated pipe body is made of 316L stainless steel to meet the cryogenic toughness requirements. The corrugated pipe has an inner diameter of 300mm, a wave height of 20mm, and an effective wall thickness of 0.5mm. Seven layers are stacked to form a total wall thickness of 3.5mm, and the total number of waves is 16.

[0120] To address the characteristics of high-pressure, large-diameter pipelines, this embodiment employs a more comprehensive regional division scheme to achieve a smoother stiffness transition. End regions I and V each contain three waves with a minimum wave pitch of 20mm, providing ample end stiffness reserves. Transition regions II and IV each contain three waves, achieving a smoother stiffness transition through the gradual change of these three waves. The central region III contains four waves with a maximum wave pitch of 40mm. The wave pitch ratio is 2.0, taking the upper limit of the recommended range of this invention, to obtain the maximum contrast between end and central stiffness. The total length of the corrugated portion is 480mm.

[0121] This embodiment effectively addresses the stringent requirements for instability resistance in high-pressure, large-diameter applications by increasing the wave number at the ends and transition regions and employing a design strategy that utilizes the maximum recommended wave pitch ratio. The larger wave pitch ratio results in significantly higher stiffness at the ends compared to the middle, substantially increasing the critical instability pressure, while the multi-wave transition ensures the continuity of stiffness changes.

[0122] Example 4: This example is applied to the main piping system of a nuclear power plant, designed for operating conditions with a nominal diameter of DN250mm, a design pressure of 3.2MPa, a design temperature of 350℃, and a total compensation of 30mm. The corrugated pipe body is made of 321 stainless steel to meet high-temperature stability requirements. The corrugated pipe has an inner diameter of 250mm, a wave height of 18mm, and an effective wall thickness of 0.45mm. Six layers are stacked to form a total wall thickness of 2.7mm, and the total number of waves is 14.

[0123] This embodiment employs a balanced regional configuration scheme. End regions I and V each contain 2 waves with a minimum wave pitch of 18mm. Transition regions II and IV each contain 2 waves. The central region III contains 6 waves with a maximum wave pitch of 28mm; the higher number of waves in the central region provides ample compensation capability. The wave pitch ratio is 1.56, and the total length of the corrugated portion is 322mm.

[0124] Example 1: Total number of wavelengths 12, with wavelengths increasing from 16mm to 26mm and then decreasing back to 16mm, resulting in a wavelength-to-span ratio of 1.625. Example 2: Total number of wavelengths 10, with wavelengths increasing from 14mm to 20mm and then decreasing back to 14mm, resulting in a wavelength-to-span ratio of 1.43. Example 3: Total number of wavelengths 16, with wavelengths increasing from 20mm to 40mm and then decreasing back to 20mm, resulting in a wavelength-to-span ratio of 2.0. Example 4: Total number of wavelengths 14, with wavelengths increasing from 18mm to 28mm and then decreasing back to 18mm, resulting in a wavelength-to-span ratio of 1.56.

[0125] The wavelength distribution in each embodiment exhibits a symmetrical sinusoidal square transition shape, achieving a gradient structure with high stiffness at both ends and high flexibility in the middle. Specifically, as follows... Figure 4 As shown, Figure 4 (a) is Example 1. Figure 4 (b) is Example 2. Figure 4(c) is Example 3. Figure 4 (d) is Example 4. From Figure 4 It can be seen from this that Figure 4 The sub-figure (a) shows that the wavelength of Example 1 smoothly increases from 16 mm at the end to 26 mm in the middle and then decreases back to 16 mm, exhibiting a symmetrical distribution. Figure 4 (b) shows that the wave pitch of Example 2 increases from 14 mm to 20 mm and then decreases, with only one wave in the transition region, which is suitable for low-pressure, small-diameter applications. Figure 4 (c) shows that the wave pitch of Example 3 increases from 20mm to 40mm and then decreases. The transition region contains 3 waves, and the transition is smoother, which is suitable for high-pressure and large-diameter working conditions. Figure 4 The middle (d) shows that the wave distance of Example 4 increases from 18mm to 28mm and then decreases. The middle region contains 6 waves, which provides sufficient compensation capability. Figure 4 This indicates that the wavelength distribution in each embodiment exhibits a symmetrical sinusoidal square transition shape, forming a gradient structure with high stiffness at both ends and high flexibility in the middle. This verifies that the wavelength segmentation function design method of the present invention can flexibly configure the region division and wavelength parameters according to different working conditions, and has good engineering adaptability.

[0126] Comparative Example 1 employs a traditional uniform wave pitch design scheme and is used for comparison and verification with Example 1. The design parameters, material parameters, bellows inner diameter, wave height, effective wall thickness, and total wave number of Comparative Example 1 are the same as those of Example 1, with the only difference being the wave pitch distribution method.

[0127] In Comparative Example 1, all 12 waves used a uniform wave pitch of 21 mm. This value was taken as the midpoint between the minimum wave pitch of 16 mm and the maximum wave pitch of 26 mm in Example 1, to ensure that the total length of the corrugated portion was similar. Comparative Example 1 did not have regional divisions or wave pitch gradient distributions, and all waves had the same stiffness. The advantage of traditional uniform wave pitch design is its simple structure and convenient processing, but its disadvantage is that the ends and the middle use the same stiffness, making it impossible to specifically enhance the end's resistance to instability, thus causing the ends to become weak points under pressure.

[0128] Comparative Example 2 employs a linearly varied wavelength design to verify the superiority of the sinusoidal square transition function of this invention. The design parameters, material parameters, and basic geometric parameters of Comparative Example 2 are the same as those of Example 1, and the region division method is also the same; the only difference lies in the wavelength calculation method for the transition region.

[0129] In Comparative Example 2, the wavelength in the transition region is calculated using a linear function, meaning the wavelength increases or decreases in an arithmetic progression from the end region to the middle region. A characteristic of a linear transition is a constant rate of change in wavelength. Abrupt changes in the rate of change in wavelength occur at the boundaries between the end region and the transition region, as well as at the boundaries between the transition region and the middle region, leading to discontinuous changes in stiffness and resulting in localized stress concentrations.

[0130] Comparative Example 3 employs a design scheme with an excessively large wavelength range to verify the rationality of the recommended wavelength range range of this invention. The design parameters, material parameters, and basic geometric parameters of Comparative Example 3 are the same as those of Example 1, using a sinusoidal square transition function; the only difference is that the wavelength range exceeds the recommended range.

[0131] Comparative Example 3 has a minimum wavelength of 12 mm and a maximum wavelength of 30 mm, resulting in a wavelength-to-span ratio of 2.5, which exceeds the recommended range of 1.2 to 2.0 of this invention. An excessively large wavelength-to-span ratio means that the wavelength in the middle region is too large and the stiffness is too low. Although the end regions achieve higher stiffness, the middle region is prone to planar instability under internal pressure, thus becoming a new weak point. Simultaneously, an excessively large wavelength-to-span ratio leads to an excessively large stress gradient in the transition region, which is detrimental to the overall stability of the structure.

[0132] Experiment Example 1: Stress Distribution Comparison Experiment; The stress distribution of Example 1 and Comparative Example 1 was simulated using the finite element method. A three-dimensional finite element model of the bellows was established, with 20-node hexahedral elements used for mesh generation, and the mesh size was approximately 1 / 3 of the wall thickness. The boundary conditions were a fixed constraint at one end and an axial displacement constraint at the other end, with an internal pressure of 2.5 MPa. The equivalent Von Mises stress at each wave crest position was extracted, and the stress uniformity index was calculated.

[0133] In Example 1, the equivalent stresses of each wave were 185.2 MPa, 182.6 MPa, 168.4 MPa, 155.3 MPa, 148.7 MPa, 147.2 MPa, 148.1 MPa, 149.5 MPa, 156.8 MPa, 169.2 MPa, 183.4 MPa, and 186.1 MPa, respectively. The maximum stress was 186.1 MPa, the minimum stress was 147.2 MPa, the average stress was 165.0 MPa, and the stress uniformity was 23.6%. The equivalent stresses of each wave in Comparative Example 1 were 218.5 MPa, 196.3 MPa, 175.2 MPa, 162.8 MPa, 155.6 MPa, 152.1 MPa, 151.8 MPa, 154.9 MPa, 163.5 MPa, 176.8 MPa, 198.2 MPa, and 221.3 MPa, respectively. The maximum stress was 221.3 MPa, the minimum stress was 151.8 MPa, the average stress was 176.4 MPa, and the stress uniformity was 39.4%. The results are as follows... Figure 5 As shown, from Figure 5As can be seen, the equivalent stress curves of each wave in Example 1 exhibit a gentle U-shaped distribution, with relatively small differences between the stress at the ends and the stress in the middle. The stress values ​​of waves 1 to 12 fluctuate between 147.2 MPa and 186.1 MPa. In contrast, the stress curve of Comparative Example 1 exhibits a steep U-shaped distribution, with the stresses at the ends of waves 1 and 12 reaching as high as 218.5 MPa and 221.3 MPa, respectively, significantly higher than the 151.8 MPa in the middle, indicating a substantial difference in stress between the ends and the middle. Figure 5 This indicates that after adopting the gradient wavelength design in Example 1, the local stiffness in the end region is increased by using a smaller wavelength, which effectively reduces the stress concentration at the end and makes the stress distribution along the axial direction more uniform.

[0134] Experimental Example 2: Comparative Test of Pressure Resistance; The pressure resistance of Examples 1 to 4 and Comparative Examples 1 to 3 were tested using the water pressure burst test method. The test medium was room temperature clean water, the pressurization rate was 0.5 MPa / min, and the pressure value at which the bellows failed was recorded as the burst pressure. The safety factor was the ratio of the burst pressure to the design pressure.

[0135] The experimental results are as follows: Example 1: Design pressure 2.5 MPa, burst pressure 12.8 MPa, safety factor 5.12; Example 2: Design pressure 1.6 MPa, burst pressure 8.5 MPa, safety factor 5.31; Example 3: Design pressure 4.0 MPa, burst pressure 19.2 MPa, safety factor 4.80; Example 4: Design pressure 3.2 MPa, burst pressure 15.6 MPa, safety factor 4.88; Comparative Example 1: Design pressure 2.5 MPa, burst pressure 9.6 MPa, safety factor 3.84; Comparative Example 2: Design pressure 2.5 MPa, burst pressure 10.8 MPa, safety factor 4.32; Comparative Example 3: Design pressure 2.5 MPa, burst pressure 7.2 MPa, safety factor 2.88. The results are as follows... Figure 6 As shown, from Figure 6 As can be seen, the safety factors of Examples 1 to 4 are 5.12, 5.31, 4.80 and 4.88 respectively, all higher than 4.5, far exceeding the requirement of a lower safety factor limit of 2.5. The safety factor of Comparative Example 1 is 3.84, Comparative Example 2 is 4.32, and Comparative Example 3 is only 2.88, close to the lower safety factor limit. Figure 6 This indicates that all embodiments employing the gradient wave pitch design of the present invention have a high pressure resistance safety margin, while the safety factors of traditional uniform wave pitch design, linear transition design, and excessively large wave pitch ratio design are significantly lower. The safety factor of Embodiment 1 is improved by 33% compared to Comparative Example 1. This is because the gradient wave pitch design effectively improves the overall pressure resistance of the bellows by enhancing end stiffness, demonstrating the significant effect of the present invention in improving pressure resistance.

[0136] Experiment Example 3: Fatigue Life Comparison Experiment; The fatigue life of Example 1, Comparative Example 1, and Comparative Example 2 was tested using the axial displacement fatigue test method. The test conditions were: ambient temperature, axial displacement ±5mm, cycle frequency 0.5Hz, internal pressure maintained at 1.0MPa, and the number of cycles was recorded until leakage occurred in the bellows.

[0137] The experimental data are as follows: Example 1 had a fatigue life of 8520 cycles, Comparative Example 1 had a fatigue life of 5680 cycles, and Comparative Example 2 had a fatigue life of 6850 cycles. Example 1 showed a 50.0% increase in fatigue life compared to Comparative Example 1, and a 24.4% increase compared to Comparative Example 2. The results are as follows... Figure 7 As shown, from Figure 7 As can be seen from the data, the fatigue life of Example 1 reached 8520 cycles, Comparative Example 1 was 5680 cycles, and Comparative Example 2 was 6850 cycles. Figure 7 The results show that Example 1 improves fatigue life by 50% compared to Comparative Example 1 and by 24% compared to Comparative Example 2. The improvement in fatigue life is due to the uniformity of stress distribution. Example 1 achieves a smooth transition of wave pitch through a sinusoidal square function, avoiding local stress concentration caused by abrupt changes in stiffness. This strengthens the weak points of the bellows under cyclic loading, thereby significantly extending fatigue life. This demonstrates that the sinusoidal square transition function design of the present invention has a significant effect on extending service life.

[0138] Experiment Example 4: Comparative Experiment of Critical Instability Pressure; The instability performance of Example 1, Comparative Example 1, and Comparative Example 3 was tested using the critical instability pressure test method. The test method involved slowly applying pressure and observing the deformation of the bellows. When obvious radial or axial instability deformation occurred, the pressure value was recorded as the critical instability pressure.

[0139] The experimental data are as follows: Example 1 had a critical buckling pressure of 8.6 MPa, Comparative Example 1 had a critical buckling pressure of 6.2 MPa, and Comparative Example 3 had a critical buckling pressure of 4.8 MPa. Example 1 showed a 38.7% increase in critical buckling pressure compared to Comparative Example 1, and a 79.2% increase compared to Comparative Example 3. The results are as follows... Figure 8 As shown, from Figure 8 As can be seen, the critical instability pressure of Example 1 is 8.6 MPa, that of Comparative Example 1 is 6.2 MPa, and that of Comparative Example 3 is 4.8 MPa. Figure 8 The results show that Example 1 exhibits a 38.7% increase in critical buckling pressure compared to Comparative Example 1, and a 79.2% increase compared to Comparative Example 3. Example 1 employs a minimum wavelength of 16mm in the end region, resulting in significantly higher end stiffness than the middle region, effectively resisting end column buckling and planar buckling. Comparative Example 3, due to its excessively large wavelength ratio, suffers from excessively low stiffness in the middle region, which ironically becomes a weak point for buckling. This verifies the scientific validity of the recommended wavelength ratio range of 1.2 to 2.0 in this invention, demonstrating that the high-stiffness design at the ends helps improve buckling resistance.

[0140] Experiment Example 5: Stiffness Distribution Comparison Experiment; The axial stiffness distribution of Example 1, Comparative Example 1, and Comparative Example 2 was simulated using the finite element method. A unit axial displacement was applied, and the axial stiffness values ​​of each wave region were extracted.

[0141] Axial stiffness of each region in Example 1: End region I: 385 N / mm; Transition region II, wave 3: 312 N / mm; Transition region II, wave 4: 248 N / mm; Middle region III: 186 N / mm; Transition region IV, wave 9: 245 N / mm; Transition region IV, wave 10: 315 N / mm; End region V: 382 N / mm. The stiffness of each wave in Comparative Example 1 with a uniform pitch is approximately 265 N / mm. Comparative Example 2 shows a sudden change in stiffness in the transition region, with a stiffness change rate of 28.5% from wave 2 to wave 3, while the stiffness change rate from wave 2 to wave 3 in Example 1 is only 19.0%. The results are as follows... Figure 9 As shown, from Figure 9 As can be seen, the axial stiffness curve of Example 1 exhibits a symmetrical ∩-shaped distribution, with an end stiffness of approximately 385 N / mm and a middle stiffness of approximately 186 N / mm, showing a smooth change in stiffness along the axial direction. Comparative Example 1 shows a horizontal straight line, with a stiffness of 265 N / mm for each wave, exhibiting no gradient change. Although the stiffness curve of Comparative Example 2 shows a gradient change, there is a clear inflection point between the second and third waves, with a stiffness change rate reaching 28.5%. Figure 9 The results show that, after adopting a sinusoidal square transition in Example 1, the stiffness change rate at the same location is only 19.0%, and the stiffness change is more continuous and smooth. The derivative of the sinusoidal square function is zero at the endpoints of the interval, achieving a seamless transition in both wave distance and stiffness, avoiding the abrupt stiffness changes that occur at the boundaries in linear transition methods. This demonstrates that the sinusoidal square transition function of this invention is significantly more effective than linear transition in achieving smooth stiffness changes.

[0142] Experimental Example 6: Comprehensive Comparison of Stress Uniformity; Based on the stress distribution data of Experimental Example 1, a comparative analysis of stress uniformity indices was conducted on Examples 1 to 4 and Comparative Examples 1 to 3. Stress uniformity is defined as the difference between the maximum and minimum stress divided by the average stress and then multiplied by 100%. The smaller the index, the more uniform the stress distribution.

[0143] The experimental data are as follows: Example 1: stress uniformity 23.6%; Example 2: stress uniformity 21.8%; Example 3: stress uniformity 24.5%; Example 4: stress uniformity 22.3%; Comparative Example 1: stress uniformity 39.4%; Comparative Example 2: stress uniformity 32.6%; Comparative Example 3: stress uniformity 45.2%. The stress uniformity of each example is better than the target value of 25%, while the comparative examples did not reach this target. The results are as follows... Figure 10 As shown, from Figure 10As can be seen, the stress uniformity of Examples 1 to 4 was 23.6%, 21.8%, 24.5%, and 22.3%, respectively, all lower than the target value of 25%. The stress uniformity of Comparative Example 1 was 39.4%, Comparative Example 2 was 32.6%, and Comparative Example 3 was 45.2%, all failing to reach the target value. Figure 10 The results show that the stress uniformity of each embodiment using the design method of this invention is better than that of the comparative example, and the improvement effect on stress distribution uniformity is significant. The stress uniformity of comparative example 3 is the worst, indicating that an excessively large wavelength ratio not only fails to improve stress distribution but also exacerbates stress non-uniformity, suggesting that the wavelength ratio should be controlled within an appropriate range.

[0144] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A corrugated pipe compensator with high pressure resistance, comprising a corrugated pipe body and end pipes, characterized in that: the corrugated pipe body is a U-shaped corrugated structure with a non-uniform gradient distribution of wave distance along the axial direction; the corrugated pipe body is divided into five regions along the axial direction in sequence: end region I, transition region II, middle region III, transition region IV and end region V; wherein: End region I is at the leading end of the bellows body, with the smallest wave pitch , providing high stiffness to enhance the end instability resistance Transition region II is located between end region I and middle region III, the wave distance from Smoothly increasing to the maximum wave distance , realizing the gradual transition of stiffness; The middle region III is located in the center of the bellows body, adopts the maximum wave distance , and provides displacement compensation capacity as the main compensation region. Transition region IV is located between middle region III and end region V, the wave distance from smoothly decreases to , realizing the gradual transition of stiffness; End region V is located at the tail end of the bellows body, with the smallest wave pitch , providing high stiffness to enhance the end instability resistance the end pipes are provided in two pieces and are welded and fixed at both ends of the corrugated pipe body respectively, for connecting transition with the pipeline system.

2. The corrugated pipe compensator with high pressure strength according to claim 1, characterized by Wave distance ratio is in the range of 1.2-2.

0.

3. The corrugated pipe compensator with high pressure strength according to claim 1, characterized by For the corrugated pipe body, the following parameters are defined: total number of waves for the bellows body; number of waves for the single-sided end region, wherein end region I and end region V each comprise waves; number of waves for the single-sided transition region, wherein transition region II and transition region IV each comprise waves; last wave number for end region I; last wave number for transition region II; last wave number for middle region III; last wave number for transition region IV; wave number, ranging from 1 to ; wave pitch for the th wave; The boundary numbers for each region are calculated using the following formula: ; ; ; The first corrugated pipe body Wavelength of each wave Calculated using the following piecewise function: When time, to the corresponding end region I; When Time, corresponding transition region II; wherein, is the wave distance variation, in mm; When time, corresponding middle region III; When time, corresponding transition region IV; When time, corresponding end region V.

4. The corrugated pipe compensator with high pressure strength according to claim 3, characterized by , , , the region boundary serial number is: , , , ; the wave number of the middle region III .

5. The corrugated pipe compensator with high pressure strength according to claim 2, characterized by, The bellows inner diameter of the bellows body was 200 mm, the bellows outer diameter was 230 mm, the bellows height was 15 mm, the effective wall thickness was 0.4 mm; the minimum bellows pitch was 16 mm, the maximum bellows pitch was 26 mm, the bellows pitch ratio was 1.

625.

6. The corrugated pipe compensator with high pressure strength according to claim 1, characterized by the outer diameter of the end pipe is 219 mm, the wall thickness is 6 mm, and the length is 80 mm; the end pipe and the corrugated pipe body are connected by TIG argon arc welding ring joint butt welding mode.

7. The corrugated pipe compensator with high pressure strength according to claim 1, characterized by A flow guide inner sleeve is coaxially arranged inside the corrugated pipe body, both ends of the flow guide inner sleeve are fixed to the inner walls of the two end pipes, and the flow guide inner sleeve and the inner wall of the corrugated pipe body are gap fitted, for protecting the inner wall of the corrugated pipe and guiding the flow of medium.

8. The corrugated pipe compensator with high pressure strength according to claim 1, characterized by, It also includes connecting flanges; the connecting flanges are provided in two pieces and are welded and fixed at the outer ends of the two end pipes respectively, for flange connection with the external pipeline system.

9. The corrugated pipe compensator with high pressure resistance according to claim 8, the connecting flanges are provided with a limiting pull rod in a matched manner, both ends of the limiting pull rod pass through the two connecting flanges and are fixed by limiting nuts.

10. The corrugated pipe compensator with high pressure strength according to claim 7, characterized by, The outer diameter of the flow guide inner sleeve is 195 mm, and the inner wall of the corrugated pipe body maintains a gap of 2.5 mm; the wall thickness of the flow guide inner sleeve is 3 mm, and the length is 350 mm; both the inlet end and the outlet end of the flow guide inner sleeve are provided with chamfers.

Images