A three-dimensional flexible modeling method for multi-layer reinforced corrugated pipes

Abstract

This invention discloses a three-dimensional flexible modeling method for multi-layer reinforced bellows, belonging to the field of liquid rocket engine overall design. This invention establishes three-dimensional models of the flexible bellows for each layer of sub-components and the reinforcing ring, assembling them to obtain a first-level assembly model. Through dynamic coordinate detection and analysis, dynamic parameter acquisition, and solid flexible drive design and dynamic parameter drive design, the flexible definition of the multi-layer reinforced bellows is realized. Furthermore, after assembly, it follows the engine's swaying flexible dynamic assembly, solving the problem of flexible dynamic deformation of multi-layer reinforced bellows. The unified three-dimensional model can synchronously guide production and assembly, laying the foundation for the simulation of the engine's overall dynamic swaying motion.

Description

Technical Field

[0001] This invention relates to a three-dimensional flexible modeling method for multi-layer reinforced bellows, belonging to the overall technical field of liquid rocket engines. Background Art

[0002] Multi-layered reinforced bellows is a crucial component for enabling the swaying function of a rocket engine. It is a rigid-flexible hybrid structure composed of overlapping thin metal layers and reinforcing rings. Its two ends connect to the engine's swaying components, and it dynamically deforms with these components to achieve displacement and angle compensation. Figure 2 As shown, the new generation of rocket engines fully adopts 3D modeling to replace traditional 2D drawings for assembly design and production. However, multi-layer reinforced bellows are in a free and inflexible state during production, but become flexible and swaying when assembled onto the engine. Furthermore, during engine model sway interference checks, the multi-layer reinforced bellows undergo flexible adaptive deformation. Currently, the 3D modeling method for multi-layer reinforced bellows cannot adapt to the various situations of production, model assembly, and engine swaying, and it cannot synchronously and dynamically adapt to engine swaying. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a three-dimensional flexible modeling method for multi-layer reinforced corrugated pipes. This method establishes three-dimensional models of each layer of reinforced corrugated pipe and a first-level assembly model formed after assembly. Through parameter-driven design, the flexible definition of multi-layer reinforced corrugated pipes is realized, thus solving the problem of flexible dynamic deformation of multi-layer reinforced corrugated pipes.

[0004] The technical solution of the present invention is:

[0005] A three-dimensional flexible modeling method for multi-layer reinforced bellows includes:

[0006] S1. Establish the task of multi-layer reinforced bellows primary assembly, and establish the starting coordinate system and the bellows swing end coordinate system in the task;

[0007] S2. Based on the design parameters of the bellows, establish flexible bellows models for each layer of sub-components according to the number of layers. The method for establishing the flexible bellows model for each layer of sub-components is as follows: first, establish the projection section, the coordinate system of the swing start point, and the coordinate system of the free state end point; then, establish spline curves based on the swing start point and the free state end point; finally, generate the bellows outer surface curve based on the spline curves; and finally, generate the bellows model. Based on the number of reinforcing rings, establish the installation coordinate system of each reinforcing ring on the spline curve of the outermost layer of sub-components flexible bellows.

[0008] S3. Establish a three-dimensional model of the reinforcing ring and define the design coordinate system for the reinforcing ring;

[0009] S4. In the task of assembling a multi-layer reinforced corrugated pipe into a primary assembly, set the assembly relationship of each layer of flexible corrugated pipe model and the three-dimensional model of the reinforcing ring to form a multi-layer reinforced corrugated pipe into a primary assembly model.

[0010] S5. Dynamically acquire the relative displacement and relative angle between the swing endpoint and the starting point in the coordinate system of the swing endpoint of the bellows in the assembly model. Use the above data to drive six parameters of the relative displacement and relative rotation angle of the endpoint relative to the starting point in the X, Y, and Z directions in the free state endpoint coordinate system. The six parameter values ​​are used as flexible dimensions to control the swing endpoint of the multi-layer reinforced bellows.

[0011] Furthermore, the origin of the swaying start coordinate system is [0, 0, 0], with the X-axis pointing in the swaying direction, the Z-axis pointing in the medium flow direction, and the Y-axis forming a right-handed system with the X and Z axes. The origin of the free state end coordinate system is [0, 0, L], and its direction is consistent with the swaying start coordinate system, where L is the distance between the swaying start and the free state end. The origin of the start coordinate system is [0, 0, 0], with the X-axis pointing in the swaying direction, the Z-axis pointing in the medium flow direction, and the Y-axis forming a right-handed system with the X and Z axes. The origin of the bellows swaying end coordinate system is set according to the bellows swaying position, with the X-axis pointing in the swaying direction, the Z-axis pointing in the medium flow direction, and the Y-axis forming a right-handed system with the X and Z axes.

[0012] Furthermore, in the multi-layer reinforced corrugated pipe primary assembly task, the assembly relationship of each layer of flexible corrugated pipe model and the three-dimensional model of the reinforcing ring is set. Among them, the swing starting point coordinate system of the outermost flexible corrugated pipe model coincides with the starting point coordinate system, and the reinforcing ring design coordinate system coincides with the reinforcing ring installation coordinate system.

[0013] Furthermore, a spline curve is established based on the swing start point and the free state end point, where the distance between the swing start point and the free state end point is the product of the wave number and the wave pitch of the flexible bellows.

[0014] Furthermore, the outer surface curve of the bellows is formed based on the spline curve, specifically as follows:

[0015] Using spline curves as the scanning trajectory, the center positions of the peaks and troughs on each projected section of the bellows are determined according to the trajectory equations. The trajectory equation for the peak center position is θ = 90 + trajpar·N·360, with the scanning radius being half the diameter of the bellows peak; the trajectory equation for the trough center position is θ = 90 + trajpar·N·360, with the scanning radius being half the diameter of the bellows trough; N is the wave number of the bellows, and trajpar is the parametric trajectory function.

[0016] Based on the crest radius and trough radius of the corrugated pipe, a flexible curve modeling and projection method is used to establish the outer surface curve of the corrugated pipe on each projection plane according to the established center position of the crest and trough, as well as the crest radius and trough radius.

[0017] Furthermore, by using the boundary blending method, the bellows outer surface is generated based on the bellows outer surface curves established on each projection plane. Then, the bellows model is generated using the thickening method, and the thickening offset is set to the single-layer bellows wall thickness.

[0018] Furthermore, a reinforcing ring mounting coordinate system is established on the spline curve of the outermost sub-part, the flexible bellows, with the Z-axis of the reinforcing ring mounting coordinate system being tangent to the spline curve.

[0019] Furthermore, a reinforcing ring for the sub-part is established using a rotation method, and the design coordinate system of the reinforcing ring is defined as the center of rotation, with the Z-axis perpendicular to the plane of rotation.

[0020] Furthermore, the relative displacement and relative angle between the swing endpoint and the starting point in the coordinate system of the bellows swing terminal in the assembly model are dynamically acquired. Using this data, six parameters—the relative displacement and relative rotation angle of the endpoint relative to the starting point in the X, Y, and Z directions—are driven in the free-state endpoint coordinate system. The driving method is as follows:

[0021] In the free state endpoint coordinate system, the relative displacements LEN_X, LEN_Y, and LEN_Z of the endpoint relative to the starting point in the X, Y, and Z directions are equal to the measured relative displacements in the X, Y, and Z directions, respectively.

[0022] The relative rotation angle ANGX of the endpoint relative to the starting point in the free state endpoint coordinate system is determined based on the measured angle between the two Z axes of the swing endpoint and the starting point coordinate system. If the angle between the two Z axes of the swing endpoint and the starting point coordinate system is less than 90°, then ANGX is equal to the difference between the angle between the two Z axes of the swing endpoint and the starting point coordinate system and the angle between the two X axes. Otherwise, it is equal to the difference between the angle between the two Z axes of the swing endpoint and the starting point coordinate system and the angle between the two X axes and 180°.

[0023] In the free state endpoint coordinate system, the relative rotation angle ANGY of the endpoint with respect to the starting point in the Y direction is equal to the angle between the measured swing endpoint and the two Z axes of the starting point coordinate system.

[0024] In the free-state endpoint coordinate system, the relative rotation angle ANGZ of the endpoint relative to the starting point in the Z direction is equal to the angle between the measured swing endpoint and the two Y axes of the starting point coordinate system.

[0025] Furthermore, the relative displacement and relative angle between the swing endpoint and the starting point in the coordinate system of the bellows swing terminal in the assembly model are dynamically obtained. The method is as follows: in the assembly model, the coordinate system parameters of the starting point and the swing terminal are set according to the design requirements, and the relative displacement and relative angle between the swing endpoint and the starting point are measured.

[0026] The advantages of this invention compared to the prior art are:

[0027] 1) This invention is a flexible modeling method based on parameter dynamic driving, which simultaneously realizes the flexible definition of multi-layer reinforced bellows and allows for flexible dynamic assembly that follows the engine's swaying motion after assembly. Traditional 3D modeling methods for multi-layer reinforced bellows cannot achieve a unified production and assembly model; this invention's unified 3D model can simultaneously guide production and assembly.

[0028] 2) This invention solves the problem of flexible dynamic deformation of multi-layer reinforced corrugated pipes through flexible sensing design, namely, coordinate dynamic detection and analysis and dynamic parameter acquisition.

[0029] 3) This invention achieves the flexible definition of multi-layer reinforced bellows through solid flexible drive design, including advanced flexible curve modeling and projection, and flexible deformable surface hybrid generation, and after assembly, it can follow the engine swing flexible dynamic assembly.

[0030] 4) This invention uses dynamic parameter-driven design to synchronously drive multi-layer parts and drive component relationships across structures, laying the foundation for dynamic swaying motion simulation of the entire engine. Attached Figure Description

[0031] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present invention. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0032] Figure 1 This is a flowchart of the three-dimensional flexible modeling method for the multi-layer reinforced corrugated pipe of the present invention;

[0033] Figure 2 A schematic diagram for reinforcing a bellows;

[0034] Figure 3 In step S2 of this embodiment of the invention, a spline curve is established based on the swing start point and the free state end point;

[0035] Figure 4 This refers to step S2 of the present invention, which involves determining the center points of the peaks and troughs on each projected section of the bellows.

[0036] Figure 5The outer surface curve of the bellows in step S2 of this embodiment of the invention;

[0037] Figure 6 This is a schematic diagram of the corrugated pipe in step S2 of this embodiment of the invention.

[0038] Figure 7 This is the corrugated pipe production entity model in step S2 of the embodiment of the present invention;

[0039] Figure 8 This is the production entity model of the reinforcing ring in step S3 of the embodiment of the present invention;

[0040] Figure 9 The measurement group features are those described in step S5 of this embodiment of the invention.

[0041] Figure 10 This refers to the parameter relationship defined in step S5 of this embodiment of the invention;

[0042] Figure 11 These are the six parameters defined for the swing endpoint in step S1 of this embodiment of the invention;

[0043] Figure 12 This is a cross-sectional view of the swaying state of a multi-layer reinforced corrugated pipe according to an embodiment of the present invention;

[0044] Figure 13 This is a three-dimensional model of the swaying state of a multi-layer reinforced corrugated pipe according to an embodiment of the present invention. Detailed Implementation

[0045] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0046] This invention proposes a three-dimensional flexible modeling method for the design, production, assembly, and adaptation to engine swaying of multi-layer reinforced bellows. Applied to liquid rocket engines, it enables multi-state control of multi-layer reinforced bellows and allows it to follow the engine's flexible dynamic assembly after assembly, laying the foundation for the simulation of dynamic swaying motion of the entire engine.

[0047] A multi-layer reinforced corrugated pipe is constructed. The reinforced corrugated pipe structure has 2 layers, N=10 waves, a single-layer wall thickness δ=0.5mm, a wave pitch q=13mm, a wave crest radius rc=3.6mm, a wave trough radius rr=2.4mm, a wave crest diameter Dc, and a wave trough diameter Dr. The dynamic swaying requirement is that the upper end of the corrugated pipe is fixed, and the lower end sways accordingly.

[0048] The design is carried out according to the method proposed in this invention, and the process is as follows: Figure 1 As shown, it specifically includes:

[0049] S1. Establish the task of multi-layer reinforced corrugated pipe primary assembly.

[0050] S2. Based on the design parameters of the bellows and the layer requirements, establish the sub-component flexible bellows.

[0051] 2.1) Establish the projection plane, the coordinate system of the swing starting point, and the coordinate system of the free state ending point as needed. The distance L between the swing starting point and the free state ending point satisfies L = N·q. The origin of the swing starting point coordinate system is [0, 0, 0], the X-axis points in the swing direction, the Z-axis points in the medium flow direction, and the Y-axis is right-handed with the X and Z axes. The origin of the free state ending point coordinate system is [0, 0, L]. The coordinate system orientation is consistent with the swing starting point coordinate system.

[0052] 2.2) Establish a spline curve based on the starting point of the swing and the ending point of the free state, such as... Figure 3 As shown.

[0053] 2.3) Using the spline curve established in step 2.2 as the scanning trajectory, the center points of the peaks and troughs on each projected section of the bellows are determined using the scanning method and trajectory equation, such as... Figure 4 As shown; the trajectory equation for the center position of the wave crest is θ=90+trajpar·N·360,r=0.5Dc; the trajectory equation for the center position of the wave trough is θ=90+trajpar·N·360,r=0.5Dr; trajpar is a parametric trajectory function, which controls the cross-sectional dimensions during the variable cross-section scanning process, varying from 0 to 1.

[0054] 2.4) Based on the curve modeling and projection method, establish the center positions of the peaks and troughs, and their corresponding values ​​rc and rr, on multiple projected planes according to step 2.3, as shown below. Figure 5 As shown, rc is the crest radius and rr is the trough radius. The connecting line is tangent to the crest and trough, forming the outer surface curve of the corrugated pipe.

[0055] 2.5) Using the boundary blending method and the boundary blending tool, based on the outline curves established on each projection plane in step 2.4, establish the outer corrugated pipe outline surface, such as... Figure 6 As shown. A solid model of the bellows is generated using a thickening method, as follows. Figure 7 As shown, the thickening offset is δ.

[0056] 2.6) Based on the spline curve established in step 2.2, establish uniformly distributed points on the spline curve according to the number of reinforcing rings, and establish a reinforcing ring installation coordinate system at each point. The origin coordinates of the reinforcing ring installation coordinate system are the uniformly distributed points, the X-axis is in the normal plane of the spline, and the Z-axis direction of the reinforcing ring installation coordinate system is tangent to the spline.

[0057] 2.7) In the part, the six parameters of the free state endpoint coordinate system are defined as the flexible dimensions.

[0058] Create a flexible bellows inner layer for the sub-part. The method is the same as step S2.

[0059] S3. Use rotation to create a reinforcing ring for the sub-part, such as... Figure 8 As shown, the design coordinate system of the reinforcing ring is defined as the center of rotation, with the Z-axis perpendicular to the plane of rotation.

[0060] S4. Define the assembly relationships between assemblies.

[0061] 4.1) Based on the bellows model established in step S2, set the starting coordinate system of the swing point of the flexible bellows of the sub-part established in S2 in the assembly body to coincide with the starting coordinate system in the assembly body.

[0062] 4.2) Set the reinforcing ring design coordinate system of step S3 to coincide with the reinforcing ring installation coordinate system of step S2 in the assembly body to realize the reinforcing ring follow-up.

[0063] S5. Through multi-layer part synchronous driving and component relationship cross-structure driving, dynamic acquisition of driving flexibility parameters and measurement group characteristics, such as... Figure 9 As shown;

[0064] 5.1) In the assembly of step S1, the coordinate system parameters of the starting point and the terminal are set according to the design requirements. In the starting point coordinate system, the origin coordinates are [0, 0, 0], the X-axis points in the swing direction, the Z-axis points in the medium flow direction, and the Y-axis forms a right-handed system with the X-axis and Z-axis. The bellows swing terminal coordinate system is a custom coordinate system, whose origin coordinates are set according to the bellows swing position, the X-axis points in the swing direction, the Z-axis points in the medium flow direction, and the Y-axis forms a right-handed system with the X-axis and Z-axis. Using the measurement method, the relative displacements of the swing terminal relative to the starting point in the X, Y, and Z directions [DISTANCE_X, DISTANCE_Y, DISTANCE_Z] and the relative angles between the X, Y, and Z axes of the two coordinates [ANGLE:FID_ID_5092, ANGLE:FID_ID_5093, ANGLE:FID_ID_5091] are obtained.

[0065] 5.2) Using defined parameter relationships, such as Figure 10As shown, the measurement data in step 5.1 drives the flexible dimensions set in step S2. LEN_X, LEN_Y, and LEN_Z are equal to the measured relative displacements in the X, Y, and Z directions, respectively. ANGY is equal to the angles between the measured swing endpoint and the two Z-axis of the starting coordinate system. ANGZ is equal to the angles between the measured swing endpoint and the two Y-axis of the starting coordinate system. ANGX is determined based on the measured angles between the measured swing endpoint and the two Z-axis of the starting coordinate system. If the measured angles between the measured swing endpoint and the two Z-axis of the starting coordinate system are less than 90°, then ANGX is equal to the difference between the angles between the measured swing endpoint and the two Z-axis of the starting coordinate system and the angles between the two X-axis; otherwise, it is equal to the difference between the difference between the angles between the measured swing endpoint and the two Z-axis of the starting coordinate system and the angles between the two X-axis and 180°. LEN_X, LEN_Y, LEN_Z, ANGX, ANGY, and ANGZ correspond to the six parameters defined for the swing endpoint, as follows: Figure 11 As shown, these parameters, as overall driving parameters, control the swing endpoint of the flexible component, thereby realizing the swing of the multi-layer reinforced bellows assembly, such as... Figure 12 , 13 As shown.

[0066] The sub-parts are manufactured according to the three-dimensional models established in steps S2 and S3, and the flexible follow-up swaying of the multi-layer reinforced corrugated pipe can be realized according to step S5.

[0067] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A three-dimensional flexible modeling method for multi-layer reinforced corrugated pipes, characterized in that, include: S1. Establish the task of multi-layer reinforced bellows primary assembly, and establish the starting coordinate system and the bellows swing end coordinate system in the task; S2. Based on the design parameters of the bellows, establish flexible bellows models for each layer of sub-components according to the number of layers. The method for establishing the flexible bellows model for each layer of sub-components is as follows: first, establish the projection section, the coordinate system of the swing start point, and the coordinate system of the free state end point; then, establish spline curves based on the swing start point and the free state end point; finally, generate the bellows outer surface curve based on the spline curves; and finally, generate the bellows model. Based on the number of reinforcing rings, establish the installation coordinate system of each reinforcing ring on the spline curve of the outermost layer of sub-components flexible bellows. S3. Establish a three-dimensional model of the reinforcing ring and define the design coordinate system for the reinforcing ring; S4. In the task of assembling a multi-layer reinforced corrugated pipe into a primary assembly, set the assembly relationship of each layer of flexible corrugated pipe model and the three-dimensional model of the reinforcing ring to form a multi-layer reinforced corrugated pipe into a primary assembly model. S5. Dynamically acquire the relative displacement and relative angle between the swing endpoint and the starting point in the coordinate system of the swing endpoint of the bellows in the assembly model. Use the above data to drive six parameters of the relative displacement and relative rotation angle of the endpoint relative to the starting point in the X, Y, and Z directions in the free state endpoint coordinate system. The six parameter values ​​are used as flexible dimensions to control the swing endpoint of the multi-layer reinforced bellows.

2. The three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that, The origin of the swaying starting point coordinate system is a point with coordinates [0, 0, 0]. The X-axis points in the swaying direction, the Z-axis points in the medium flow direction, and the Y-axis forms a right-handed system with the X-axis and Z-axis. The origin of the free state endpoint coordinate system is [0, 0, L], and the coordinate system direction is consistent with the starting point coordinate system of the swing. L is the distance between the starting point of the swing and the endpoint of the free state. The origin of the starting point coordinate system is the point [0, 0, 0]. The X-axis points in the swing direction, the Z-axis points in the medium flow direction, and the Y-axis is right-handed with the X-axis and Z-axis. The origin of the bellows swing terminal coordinate system is set according to the swing position of the bellows. The X-axis points in the swing direction, the Z-axis points in the medium flow direction, and the Y-axis is right-handed with the X-axis and Z-axis.

3. The three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 2, characterized in that, In the task of assembling a multi-layer reinforced corrugated pipe, the assembly relationship of each layer of flexible corrugated pipe model and the three-dimensional model of the reinforcing ring is set. The setting method is as follows: the coordinate system of the swing starting point of the outermost flexible corrugated pipe is coincident with the starting point coordinate system, and the design coordinate system of the reinforcing ring is coincident with the installation coordinate system of the reinforcing ring.

4. The three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 2, characterized in that, A spline curve is established based on the swing start point and the free state end point. The distance between the swing start point and the free state end point is the product of the wave number and the wave pitch of the flexible bellows.

5. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that, The method for generating the outer surface curve of the bellows based on spline curves is as follows: Using spline curves as the scanning trajectory, the center positions of the peaks and troughs on each projected section of the bellows are determined according to the trajectory equations. The trajectory equation for the peak center position is θ = 90 + trajpar·N·360, with the scanning radius being half the diameter of the bellows peak; the trajectory equation for the trough center position is θ = 90 + trajpar·N·360, with the scanning radius being half the diameter of the bellows trough; N is the wave number of the bellows, and trajpar is the parametric trajectory function. Based on the crest radius and trough radius of the corrugated pipe, a flexible curve modeling and projection method is adopted. On each projection plane, according to the established center position of the crest and trough, as well as the crest radius and trough radius, the connecting lines are tangent to the crest and trough to form the outer surface curve of the corrugated pipe.

6. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 5, characterized in that, Using the boundary blending method, the bellows outline surface is generated based on the bellows outline curves established on each projection plane. Then, the bellows model is generated using the thickening method, with the thickening offset set to the single-layer bellows wall thickness.

7. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that, On the spline curve of the outermost sub-part flexible bellows, uniformly distributed points are established according to the number of reinforcing rings, and a reinforcing ring installation coordinate system is established at each point. The origin coordinates of the reinforcing ring installation coordinate system are the uniformly distributed points, the X-axis is in the normal plane of the spline, and the Z-axis is tangent to the spline curve.

8. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that, The reinforcing ring of the sub-part is established using a rotation method, and the design coordinate system of the reinforcing ring is defined as the center of rotation, with the Z-axis perpendicular to the plane of rotation.

9. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that, The relative displacement and relative angle between the swing endpoint and the starting point in the coordinate system of the bellows swing terminal in the assembly model are dynamically acquired. Using this data, six parameters—the relative displacement and relative rotation angle of the endpoint relative to the starting point in the X, Y, and Z directions—are driven in the free-state endpoint coordinate system. The driving method is as follows: In the free state endpoint coordinate system, the relative displacements LEN_X, LEN_Y, and LEN_Z of the endpoint relative to the starting point in the X, Y, and Z directions are equal to the measured relative displacements in the X, Y, and Z directions, respectively. The relative rotation angle ANGX of the endpoint relative to the starting point in the free state endpoint coordinate system is determined based on the measured angle between the two Z axes of the swing endpoint and the starting point coordinate system. If the angle between the two Z axes of the swing endpoint and the starting point coordinate system is less than 90°, then ANGX is equal to the difference between the angle between the two Z axes of the swing endpoint and the starting point coordinate system and the angle between the two X axes. Otherwise, it is equal to the difference between the angle between the two Z axes of the swing endpoint and the starting point coordinate system and the angle between the two X axes and 180°. In the free state endpoint coordinate system, the relative rotation angle ANGY of the endpoint with respect to the starting point in the Y direction is equal to the angle between the measured swing endpoint and the two Z axes of the starting point coordinate system. In the free-state endpoint coordinate system, the relative rotation angle ANGZ of the endpoint relative to the starting point in the Z direction is equal to the angle between the measured swing endpoint and the two Y axes of the starting point coordinate system.

10. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that, The relative displacement and relative angle between the swing endpoint and the starting point in the coordinate system of the bellows swing endpoint in the assembly model are dynamically obtained as follows: In the assembly model, the coordinate system parameters of the starting point and the swing end are set according to the design requirements, and the relative displacement and relative angle of the swing end point relative to the starting point are measured.

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