Three-dimensional flexible modeling method for multilayer reinforced corrugated pipe

Abstract

The invention discloses a three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe, and belongs to the field of overall design of liquid rocket engines. According to the method, a flexible corrugated pipe model and a reinforcing ring three-dimensional model of each layer of sub-parts are established and assembled to obtain a first-stage assembly body model, and flexible definition of the multi-layer reinforced corrugated pipe is realized through coordinate dynamic detection and analysis, dynamic parameter acquisition, entity flexible driving design and dynamic parameter driving design; and after being assembled, the multi-layer reinforced corrugated pipe is flexibly and dynamically assembled with the engine in a follow-up manner, the problem of flexible and dynamic follow-up deformation of the multi-layer reinforced corrugated pipe is solved, a unified three-dimensional model can synchronously guide production and assembly, and a foundation is laid for dynamic swing motion simulation of the whole engine.

Description

Technical Field

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

[0002] The multi-layer reinforced bellows is an important component for realizing the rocking function of rocket engines. The multi-layer reinforced bellows is a rigid-flexible hybrid structure composed of overlapping metal thin layers and reinforcing rings. Its two ends are connected to the engine rocking components. With the dynamic deformation of the components at both ends, displacement compensation and angle compensation are realized. 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, the multi-layer reinforced bellows are in a free and inflexible state during production, and in a flexible follow-up swing state when assembled on the engine. In addition, the multi-layer reinforced bellows are flexible and adaptively deformed during the engine model swing interference check. At present, the 3D modeling method of multi-layer reinforced bellows cannot adapt to various situations such as production, model assembly and engine swing, and cannot dynamically deform synchronously with the engine swing. Summary of the invention

[0003] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, propose a three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe, establish a three-dimensional model of each layer of reinforced corrugated pipe and a first-level assembly model formed after assembly, and through parameter-driven design, realize the flexible definition of the multi-layer reinforced corrugated pipe, and solve the problem of flexible dynamic follow-up deformation of the multi-layer reinforced corrugated pipe.

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

[0005] A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe, comprising:

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

[0007] S2. According to the design parameters of the bellows, the flexible bellows model of each layer of sub-parts is established according to the number of layers; the method for establishing the flexible bellows model of each layer of sub-parts is as follows: firstly, a projection section, a swing starting point coordinate system and a free state end point coordinate system are established, a spline curve is established according to the swing starting point and the free state end point, a bellows outer surface curve is formed based on the spline curve, and then an outer surface of the outer layer bellows is generated, and finally a bellows model is generated; according to the number of reinforcing rings, each reinforcing ring installation coordinate system is established on the spline curve of the outermost layer of the flexible bellows sub-part;

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

[0009] S4. In the multi-layer reinforced bellows primary assembly task, the assembly relationship between the flexible bellows models of each layer and the reinforcement ring three-dimensional model is set to form a multi-layer reinforced bellows primary assembly model;

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

[0011] Furthermore, the origin coordinates of the swing starting point coordinate system are [0, 0, 0], the X axis points to the swing direction, the Z axis points to the medium flow direction, and the Y axis forms a right-handed system with the X axis and the Z axis; the origin of the free state end point coordinate system is [0, 0, L], the coordinate system direction is consistent with the swing starting point coordinate system, and L is the distance between the swing starting point and the free state end point. The origin coordinates of the starting point coordinate system are [0, 0, 0], the X axis points to the swing direction, the Z axis points to the medium flow direction, and the Y axis forms a right-handed system with the X axis and the Z axis; the origin coordinates of the bellows swing terminal coordinate system are set according to the bellows swing position, the X axis points to the swing direction, the Z axis points to the medium flow direction, and the Y axis forms a right-handed system with the X axis and the Z axis.

[0012] Furthermore, in the multi-layer reinforced bellows primary assembly task, the assembly relationship between the flexible bellows models of each layer and the reinforcing ring three-dimensional model is set, wherein the swing starting point coordinate system of the outermost flexible bellows 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 according to the swing start point and the free state end point, and the distance between the swing start point and the free state end point is the product of the wave number and the wave distance of the flexible bellows.

[0014] Furthermore, the bellows outer surface curve is formed based on the spline curve, and the specific method is as follows:

[0015] The spline curve is used as the scanning trajectory, and the center position points of the crests and troughs on each projection section of the bellows are determined according to the trajectory equation; the trajectory equation of the crest center position is θ=90+trajpar·N·360, and the scanning radius is half of the crest diameter of the bellows; the trajectory equation of the trough center position is θ=90+trajpar·N·360, and the scanning radius is half of the trough diameter of the bellows; N is the number of waves of the bellows, and trajpar is the parameter trajectory function;

[0016] According to the crest radius and trough radius of the bellows, the flexible curve modeling and projection method is adopted to establish the bellows outer surface curve on each projection section according to the established crest and trough center positions and the crest radius and trough radius.

[0017] Furthermore, a boundary blending method is used to generate a bellows outer surface according to the bellows outer surface curves established on each projection section, and then a bellows model is generated using a thickening method, and the thickening offset is set to be the wall thickness of a single-layer bellows.

[0018] Furthermore, a reinforcement ring installation coordinate system is established on the spline curve of the outermost sub-component flexible bellows, and the Z-axis direction of the reinforcement ring installation coordinate system is tangent to the spline curve.

[0019] Furthermore, the sub-part reinforcement ring is established by using the rotation method, and the reinforcement ring design coordinate system is defined as the rotation center point, and the Z axis is perpendicular to the rotation plane.

[0020] Furthermore, the relative displacement and relative angle of the swing end point relative to the starting point in the swing terminal coordinate system of the bellows in the assembly model are dynamically obtained. The six parameters of the relative displacement and relative rotation angle of the end point relative to the starting point in the free state end point coordinate system in the X direction, Y direction, and Z direction are driven by the above data. The driving method is:

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

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

[0023] The relative rotation angle ANGY of the end point relative to the starting point in the Y direction in the free state end point coordinate system is equal to the measured angle between the two Z axes of the swing end point and the starting point coordinate system;

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

[0025] Furthermore, the relative displacement and relative angle of the swing end point relative to the starting point in the coordinate system of the bellows swing terminal in the assembly model are dynamically obtained. The acquisition method is: in the assembly model, the coordinate system parameters of the starting point coordinate system and the swing terminal 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.

[0026] The advantages of the present invention compared with the prior art are:

[0027] 1) The present invention is a flexible modeling method based on parameter dynamic drive, which realizes the flexible definition of multi-layer reinforced bellows and moves with the engine swing flexible dynamic assembly after assembly. The traditional multi-layer reinforced bellows three-dimensional modeling method cannot achieve the unified production and assembly model. The unified three-dimensional model of the present invention can guide production and assembly simultaneously.

[0028] 2) The present invention solves the problem of flexible dynamic follow-up deformation of multi-layer reinforced bellows through flexible sensing design, namely dynamic detection and analysis of coordinates and acquisition of dynamic parameters.

[0029] 3) The present invention realizes the flexible definition of multi-layer reinforced bellows through entity flexible drive design, including advanced flexible curve modeling and projection, and flexible deformation surface hybrid generation, and after assembly, it moves with the engine swing flexible dynamic assembly.

[0030] 4) The present invention uses dynamic parameter driven design to synchronously drive multi-layer parts and drive component relationships across structures, laying the foundation for dynamic swing motion simulation of the entire engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

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

[0033] Figure 2 Schematic diagram for strengthening the bellows;

[0034] Figure 3 Establishing a spline curve based on the swing starting point and the free state end point in step S2 of the embodiment of the present invention;

[0035] Figure 4 Determine the center points of the crests and troughs on each projection section of the corrugated tube in step S2 of the embodiment of the present invention;

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

[0037] Figure 6 This is a physical appearance diagram of the bellows in step S2 of the embodiment of the present invention;

[0038] Figure 7 A physical model for producing the corrugated pipe in step S2 of the embodiment of the present invention;

[0039] Figure 8 Producing a solid model for the reinforcement ring in step S3 of the embodiment of the present invention;

[0040] Fig. 9 The measurement group characteristics in step S5 of the embodiment of the present invention;

[0041] Fig.10 is the parameter relationship defined in step S5 of the embodiment of the present invention;

[0042] Fig.11 The six parameters defined for the swing endpoint in step S1 of the embodiment of the present invention;

[0043] Fig.12 This is a cross-sectional view of a multi-layer reinforced bellows in a swinging state according to an embodiment of the present invention;

[0044] Fig.13 This is a three-dimensional model of the swing state of the multi-layer reinforced bellows according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0046] The present invention proposes a three-dimensional flexible modeling method for designing, producing, assembling and adapting to engine swing of a multi-layer reinforced bellows, which is applied to liquid rocket engines to achieve multi-state control of the multi-layer reinforced bellows, and after assembly, it moves with the engine's flexible dynamic assembly, laying the foundation for dynamic swing motion simulation of the entire engine.

[0047] A multi-layer reinforced bellows is established. The reinforced bellows structure has the following characteristics: the number of layers n=2, the number of waves N=10, the single-layer wall thickness δ=0.5mm, the wave pitch q=13mm, the peak radius rc=3.6mm, the trough radius rr=2.4mm, the peak diameter Dc, the trough diameter Dr, and the dynamic swing requirement is that the upper end of the bellows is fixed to achieve follow-up swing at the lower end.

[0048] According to the method proposed in the present invention, the design process is as follows Figure 1 As shown, specifically including:

[0049] S1. Establish the first-level assembly task of multi-layer reinforced bellows.

[0050] S2. Create the sub-component flexible bellows according to the design parameters of the bellows and the number of layers required

[0051] 2.1) Establish the projection surface, the swing start coordinate system and the free state end coordinate system as needed. The distance between the swing start and the free state end is L, satisfying L = N·q. Among them, the origin coordinates of the swing start coordinate system are [0, 0, 0], the X axis points to the swing direction, the Z axis points to the medium flow direction, and the Y axis forms a right-hand system with the X axis and the Z axis. The origin of the free state end coordinate system is [0, 0, L]. The direction of the coordinate system is consistent with the swing start coordinate system.

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

[0053] 2.3) Use the spline curve established in step 2.2 as the scanning trajectory, and use the scanning method and trajectory equation to determine the center position points of the crests and troughs on each projection section of the bellows, such as Figure 4 As shown; the trajectory equation of the center position of the wave peak is θ=90+trajpar·N·360, r=0.5Dc; the trajectory equation of the center position of the wave trough is θ=90+trajpar·N·360, r=0.5Dr; trajpar is a parameter trajectory function, which controls the cross-sectional size during the variable cross-sectional scanning process and changes between 0-1.

[0054] 2.4) According to the curve modeling and projection method, the center positions of the peaks and valleys and rc and rr are established on multiple projection sections according to step 2.3, such as Figure 5 As shown, rc is the crest radius, rr is the trough radius, and the connecting line is tangent to the crest and trough to form the outer surface curve of the bellows.

[0055] 2.5) By using the boundary blending method and the boundary blending tool, the outer bellows outer surface is established according to the outer surface curves established on each projection surface in step 2.4, such as Figure 6 The bellows solid model is generated by thickening method, as shown in Figure 7 As shown, where the thickening offset = δ.

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

[0057] 2.7) The six parameters of the free state end point coordinate system in the part are defined as flexible dimensions.

[0058] Create the inner layer flexible bellows of the sub-part in the same way as step S2.

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

[0060] S4. Set the assembly relationship between assemblies

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

[0062] 4.2) The reinforcement ring design coordinate system of step S3 is set in the assembly to coincide with the reinforcement ring installation coordinate system of step S2 to achieve the reinforcement ring following motion.

[0063] S5, through multi-layer parts synchronous driving, component relationship cross-structure driving, dynamic acquisition of driving flexibility parameters, measurement group features such as Fig. 9 As shown;

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

[0065] 5.2) Using the defined parameter relationship, such as Fig.10As shown, the measurement data in step 5.1 is used to drive the flexible dimension set in step S2, LEN_X, LEN_Y, LEN_Z are equal to the measured relative displacements in the X direction, Y direction, and Z direction, respectively, ANGY is equal to the measured angle between the two Z axes of the coordinate system of the swing end point and the starting point, ANGZ is equal to the measured angle between the two Y axes of the coordinate system of the swing end point and the starting point, ANGX is determined according to the measured angle between the two Z axes of the coordinate system of the swing end point and the starting point, if the measured angle between the two Z axes of the coordinate system of the swing end point and the starting point is less than 90°, then ANGX is equal to the difference between the angle between the two Z axes of the coordinate system of the swing end point and the starting point 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 coordinate system of the swing end point and the starting point and the angle between the two X axes and 180°. Among them, LEN_X, LEN_Y, LEN_Z, ANGX, ANGY, and ANGZ correspond to the six parameters defined by the swing end point, as shown in Fig.11 As shown in FIG. 1 , these parameters are used as overall driving parameters to control the swing end point of the flexible member, thereby realizing the swing of the multi-layer reinforced bellows assembly, as shown in FIG. Fig.12 , 13 shown.

[0066] The sub-parts are produced according to the three-dimensional models established in step S2 and step S3, and the flexible follow-up swing of the multi-layer reinforced bellows can be achieved according to step S5.

[0067] The above-described embodiments are only preferred specific implementations of the present invention. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope of the present invention.

Claims

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

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

3. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 2, characterized in that: In the first-level assembly task of the multi-layer reinforced bellows, the assembly relationship between the flexible bellows model of each layer and the three-dimensional model of the reinforcement ring is set. The setting method is: coincide the swing starting point coordinate system of the outermost flexible bellows with the starting point coordinate system, and coincide the reinforcement ring design coordinate system with the reinforcement ring installation coordinate system.

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

5. The three-dimensional flexible modeling method of a multi-layer reinforced corrugated pipe according to claim 1, characterized in that: The bellows outer surface curve is formed based on the spline curve. The specific method is as follows: The spline curve is used as the scanning trajectory, and the center position points of the crests and troughs on each projection section of the bellows are determined according to the trajectory equation; the trajectory equation of the crest center position is θ=90+trajpar·N·360, and the scanning radius is half of the crest diameter of the bellows; the trajectory equation of the trough center position is θ=90+trajpar·N·360, and the scanning radius is half of the trough diameter of the bellows; N is the number of waves of the bellows, and trajpar is the parameter trajectory function; According to the crest radius and trough radius of the bellows, the flexible curve modeling and projection method is adopted. On each projection section, according to the established crest and trough center position and crest radius and trough radius, the connecting line is tangent to the crest and trough to form the bellows outer surface curve.

6. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 5, characterized in that: The boundary blending method is used to generate the bellows outer surface according to the bellows outer surface curves established in each projection section, and then the bellows model is generated using the thickening method. The set thickening offset is the wall thickness of the single-layer bellows.

7. The three-dimensional flexible modeling method of a multi-layer reinforced corrugated pipe according to claim 1, characterized in that: Uniformly distributed points are established on the spline curve of the outermost sub-part, the flexible bellows, 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 direction is tangent to the spline curve.

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

9. A three-dimensional flexible modeling method for a multi-layer reinforced corrugated pipe according to claim 1, characterized in that: Dynamically obtain the relative displacement and relative angle of the swing end point relative to the starting point in the swing terminal coordinate system of the bellows in the assembly model. The six parameters of the relative displacement and relative rotation angle in the X, Y and Z directions of the end point relative to the starting point in the free state end point coordinate system are driven by the above data. The driving method is: The relative displacements LEN_X, LEN_Y, and LEN_Z of the end point relative to the starting point in the free state end point coordinate system in the X, Y, and Z directions are respectively equal to the measured relative displacements in the X, Y, and Z directions; The relative rotation angle ANGX of the end point relative to the starting point in the free state end point coordinate system in the X direction is determined according to the measured included angle between the two Z axes of the swing end point and the starting point coordinate system. If the included angle between the two Z axes of the swing end point and the starting point coordinate system is less than 90°, ANGX is equal to the difference between the included angle between the two Z axes of the swing end point and the starting point coordinate system and the included angle between the two X axes. Otherwise, ANGX is equal to the difference between the included angle between the two Z axes of the swing end point and the starting point coordinate system and the included angle between the two X axes and 180°. The relative rotation angle ANGY of the end point relative to the starting point in the Y direction in the free state end point coordinate system is equal to the measured angle between the two Z axes of the swing end point and the starting point coordinate system; The relative rotation angle ANGZ of the end point relative to the starting point in the Z direction in the free state end point coordinate system is equal to the measured included angle between the two Y axes of the swing end point and 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: Dynamically obtain the relative displacement and relative angle of the swing end point relative to the starting point in the swing terminal coordinate system of the bellows in the assembly model. The acquisition method is: 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 of the swing terminal relative to the starting point are measured.

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