A Dimensionality Reduction Interference Analysis Method for Pipeline Bending

Abstract

The present invention discloses a pipeline bending interference dimensionality reduction analysis method, which belongs to the field of pipeline bending processing technology and solves the problem in the prior art that the pipeline cycle prolongs the product development timeline due to repeated iterations. The method includes simplifying the axis of the straight segment of the pipeline into a two-dimensional space distance curve through calculation; simplifying the center axis of the circular arc segment of the pipeline into a two-dimensional space angular distance curve through calculation; simplifying the roller used to process the circular arc segment of the pipeline and the mounting seat and motor housing of the processing equipment into a two-dimensional obstacle curve; judging whether the two-dimensional space distance curve and the two-dimensional space angular distance curve interfere with the two-dimensional obstacle curve. If interference exists, it indicates that the processing equipment is not suitable for the pipeline processing, marking the process and coordinates corresponding to the interference. If no interference exists, it indicates that the processing equipment is suitable for the pipeline processing. The present invention can be used for pipeline bending interference dimensionality reduction analysis.

Description

Technical Field

[0001] The invention belongs to the technical field of pipeline bending processing, and in particular relates to a pipeline bending dimensionality reduction interference analysis method. Background Art

[0002] At present, the more conventional process in the field of pipe bending processing is: three-dimensional digital model design, pipeline digital feature extraction, input or import of bending forming equipment, interference process simulation, adjustment of pipeline data, design model coordination, production of actual pipelines, actual interference adjustment, and forming and confirming the final sample pipe after multiple adjustments.

[0003] Among them, repeated iteration is the key to extending the process and cycle. The iterations include two-way contradictions such as manufacturing and assembly, manufacturing and design models, theoretical models and actual installation positions. The outbreak of problems is often concentrated in the processing, manufacturing and assembly pipeline periods, which leads to the extension of the pipeline cycle to the product R&D timeline. Summary of the Invention

[0004] In view of the above analysis, the present invention aims to provide a pipeline bending dimensionality reduction interference analysis method to solve the problem in the prior art that the pipeline cycle prolongs the product development timeline due to repeated iterations.

[0005] The purpose of the present invention is mainly achieved through the following technical solutions:

[0006] The present invention provides a pipeline bending interference dimensionality reduction analysis method comprising the following steps:

[0007] Step 1: Establish a curved rectangular coordinate system with the center point of the roller used to process the arc segment of the pipeline as the origin and the rotation axis of the roller as the z-axis;

[0008] Step 2: Based on the original XYZ data based on the original rectangular coordinate system, the straight line axis of the pipeline is simplified into a two-dimensional space distance curve through calculation. The horizontal coordinate is the vertical distance S from any point on the straight line axis of the pipeline to the xy plane. z , the vertical coordinate is the distance f(t) from any point on the straight line axis of the pipeline to the roller rotation axis;

[0009] Based on the original XYZ data of the pipeline's arc segment centerline, the pipeline's arc segment centerline is simplified into a two-dimensional space angle distance curve through calculation. The horizontal coordinate is the vertical distance S from any point on the pipeline's arc segment centerline to the xy plane. y , the vertical coordinate is the distance g(θ) from any point on the central axis of the arc segment of the pipeline to the rotation axis of the roller;

[0010] The roller used to process the arc section of the pipeline, as well as the mounting base and motor housing of the processing equipment are simplified into two-dimensional obstacle curves;

[0011] Step 3: Determine whether the two-dimensional space distance curve and the two-dimensional space angle distance curve interfere with the two-dimensional obstacle curve. If there is interference, it means that the processing equipment is not suitable for pipeline processing. Mark the process and coordinates corresponding to the interference. If there is no interference, it means that the processing equipment is suitable for pipeline processing.

[0012] Furthermore, after step 3, the following steps are also included:

[0013] Establish pipeline product models and processing equipment models;

[0014] Perform three-dimensional geometric assembly on the pipeline product model and the processing equipment model, compare the interference positions obtained by the pipeline bending interference dimensionality reduction analysis, and determine whether the interference processes and coordinates of the two are consistent. If they are consistent, it means that the pipeline bending interference dimensionality reduction analysis is credible. If not, it means that the pipeline bending interference dimensionality reduction analysis has errors and is unreliable.

[0015] Furthermore, in step 2, the original XYZ data of the pipeline is obtained using 3D modeling software. The original XYZ data is the starting point and intersection coordinate data P of the straight line segment axis in the pipeline. m =(X m ,Y m ,Z m ).

[0016] Furthermore, in step 2, the vertical distance S from any point on the axis of the straight segment of the pipeline to the xy plane is simplified and calculated based on the original XYZ data. z The distance f(t) from any point on the straight line axis of the pipeline to the roller rotation axis includes the following steps:

[0017] Step 21: Calculate the line vector T based on the original XYZ data n :

[0018] T n ={L n ,M n ,N n =P n+1 -P n ——Formula 1

[0019] m is any integer from 1 to m, and n is any integer from 1 to m-1;

[0020] Step 22: According to the straight line vector T n Calculate the straight line unit vector t respectively n The angle α between two adjacent straight line segments n :

[0021]

[0022]

[0023] Step 23: According to the straight line unit vector t n Calculate the angle bisector vector Vf respectively n The vector K of the rotation axis of the arc segment of pipeline 1 n , the solution formula using vector representation is as follows:

[0024] Vf n ={Lf n ,Mf n ,Nf n}={l n ,m n ,n n}-{l n+1 ,m n+1 ,n n+1}——Formula 4

[0025]

[0026] Step 24: Based on the original XYZ data, the arc radius R corresponding to the center axis of the arc segment n , the angle bisector vector Vf n Calculate the center position of the arc segment of pipeline 1, On = (X0 n ,Y0 n ,Z0 n ):

[0027]

[0028] Step 25: Calculate the first straight line segment and the first arc segment from the second bending process, and calculate the center position of the arc segment of the pipeline (X0 n ,Y0 n ,Z0 n ) and the vector K of the rotation axis of the arc segment of the pipeline n Calculate the axis equation (Xk, Yk, Zk):

[0029]

[0030] According to the original XYZ data and the straight line unit vector t n Calculate the equation of the line on which the first straight line segment lies:

[0031]

[0032] According to formula 8, the following formula is derived:

[0033]

[0034]

[0035]

[0036] Step 26: Vector K of the rotation axis according to the centerline of the arc segment of the pipeline n , the center position of the arc section of the pipeline (X0 n ,Y0 n ,Z0 n ) and the equation of the straight line where the first straight line segment is located, respectively calculate the distance f(t) from any point on the axis of the straight line segment of the pipeline to the roller rotation axis and the perpendicular distance S from any point on the axis of the straight line segment of the pipeline to the xy plane z :

[0037]

[0038]

[0039] Furthermore, after step 26, the following steps are also included:

[0040] Step 27: Set the starting point of the first straight line segment to

[0041] Set the endpoint of the first straight line segment to

[0042] Substituting Equation 9, Pq1, and Pq2 into Equation 10, we obtain the following formula:

[0043]

[0044]

[0045] Substituting Formula 9, Pq1, and Pq2 into Formula 11, we obtain the following formula: S z =(Xq1-X0 n+1 )Lk n+1 +(Yq1-Y0 n+1 )Mk n+1 +(Zq1-Y0 n+1 )Nk n+1 +t[(Xq 2 -Xq 1 )Lk n+1 +(Yq 2 -Yq 1 )Mk n+1 +(Zq 2 -Zq 1 )Nk n+1 ]——Formula 13

[0046] t∈[0,1];δ=(X0n+1 -Xq 1 )Mk n+1 -(Y0 n+1 -Yq 1 )Lk n+1 ;

[0047] β=(X0 n+1 -Xq1)Nk n+1 -(Z0 n+1 -Zq1)Lk n+1 ;

[0048] γ=(Y0 n+1 -Yq1)Nk n+1 -(Z0 n+1 -Zq1)Mk n+1 ;

[0049] λ=-(Xq2-Xq1)Mk n+1 +(Yq2-Yq1))Lk n+1 ;

[0050] μ=-(Xq2-Xq1)Nk n+1 +(Zq2-Zq1))Lk n+1 ;

[0051] η=-(Yq2-Yq1)Nk n+1 +(Zq2-Zq1)Mk n+1 .

[0052] Furthermore, in step 2, the vertical distance S from any point on the central axis of the arc segment of the pipeline to the xy plane is simplified and calculated based on the original XYZ data. y The distance g(θ) from any point on the center axis of the arc segment of the pipeline to the roller rotation axis includes the following steps:

[0053] Step 21': Calculate the line vector T based on the original XYZ data n :

[0054] T n ={L n ,M n ,N n =P n+1 -P n ——Formula 1

[0055] m is any integer from 1 to m, and n is any integer from 1 to m-1;

[0056] Step 22': According to the straight line vector T n Calculate the straight line unit vector t respectively n The angle α between two adjacent straight line segments n :

[0057]

[0058]

[0059] Step 23': According to the straight line unit vector t n Calculate the angle bisector vector Vf respectively n The vector K of the rotation axis of the arc segment of pipeline 1 n , the solution formula using vector representation is as follows:

[0060] Vf n ={Lf n ,Mf n ,Nf n}={l n ,m n ,n n}-{l n+1 ,m n+1 ,n n+1}——Formula 4

[0061]

[0062] Step 24': According to the original XYZ data, the arc radius R corresponding to the center axis of the arc segment n , the angle bisector vector Vf n Calculate the center position O of the arc segment centerline of pipeline 1 n =(X0 n ,Y0 n ,Z0 n ):

[0063]

[0064] Step 25': Calculate the first straight line segment and the first arc segment from the second bending process, and calculate the center position of the arc segment of the pipeline (X0 n ,Y0 n ,Z0 n ) and the vector K of the rotation axis of the arc segment of the pipeline n Calculate the axis equation (Xk, Yk, Zk):

[0065]

[0066] According to the rotation vector Vrot{Vrotx, Vroty, Vrotz}, the center position of the arc segment of the pipeline (X0 n ,Y0 n ,Z0 n ), the arc radius R corresponding to the center axis of the arc segmentn Calculate the equation of the first arc segment:

[0067]

[0068] Step 26': Based on the vector K of the rotation axis of the arc segment of pipeline 1 n , the center position of the arc section of the pipeline (X0 n ,Y0 n ,Z0 n ) and the first arc segment equation respectively calculate the vertical distance S from any point on the arc segment midline of the pipeline to the xy plane y The distance g(θ) from any point on the centerline of the arc segment of the pipeline to the roller rotation axis:

[0069]

[0070]

[0071] P c =(X c ,Y c ,Z c ), O n =(X0 n ,Y0 n ,Z0 n ).

[0072] Furthermore, the calculation formula of the rotation vector Vrot is as follows:

[0073] V rot =cosθV+sinθK n ×V+(1-cosθ)(V·K n )K n

[0074]

[0075]

[0076]

[0077]

[0078] θ is the angle between the rotation vector Vrot and the original vector V, and the original vector V{Vx, Vy, Vz} is the vector from the center of the circle to the starting point of the next straight line segment.

[0079] Furthermore, the original vector V{Vx, Vy, Vz} is calculated based on the vector K of the rotation axis of the arc segment of the pipeline. n and the straight line unit vector t n The calculation formula is as follows:

[0080]

[0081] Furthermore, step 26' further includes the following steps:

[0082] Step 27': Simplify Equation 18 to the following formula:

[0083]

[0084] Simplify Equation 19 to the following formula:

[0085]

[0086] θ∈[0,α n ];Δ1=(Y0 n+1 -Y0 n )Nk n+1 -(Z0 n+1 -Z0 n )Mk n+1 ;

[0087] Δ2=(Z0 n+1 -Z0 n )Lk n+1 -(X0 n+1 -X0 n )Nk n+1 ;

[0088] Δ3=(X0 n+1 -X0 n )Mk n+1 -(Y0 n+1 -Y0 n )Lk n+1 ;

[0089] A=Mk n n n+1 -Nk n m n+1 ; B=-Lk n n n+1 +Nk n l n+1 ; C=Lk n m n+1 -Mk n l n+1 ;

[0090] D=Mk n *Lk n m n+1 -Mk n *Mk n l n+1 +Nk n *Lk n nn+1 -Nk n Nk n l n+1 ;

[0091] E=-Lk n *Lk n m n+1 +Lk n Mk n l n+1 +Nk n *Mk n n n+1 -Nk n Nk n m n+1 ;

[0092] F=-Lk n *Lk n n n+1 +Lk n Nk n l n+1 -Mk n *Mk n n n+1 +Mk n Nk n m n+1 ;

[0093] a=-BNk n+1 +CMk n+1 , b=-CLk n+1 +ANk n+1 , c=-AMk n+1 +BLk n+1 ,

[0094] d=-ENk n+1 +FMk n+1 , e=-FLk n+1 +DNk n+1 , f=-DMk n+1 +ELk n+1 .

[0095] Furthermore, the processing equipment includes a chuck, a roller, a mounting seat and a motor housing. The mounting seat is arranged on the upper surface of the motor housing, the roller is arranged on the upper surface of the mounting seat and is rotatably connected to the mounting seat, the forming end of the chuck cooperates with the outer peripheral surface of the roller, and the pipeline is bent by rotating the forming end of the chuck around the rotating axis of the roller.

[0096] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0097] The pipeline bending interference dimensionality reduction analysis method provided by the present invention can replace the motion simulation, post-calculation data comparison, and pipeline optimization processes of pipeline forming process review, by establishing a bending rectangular coordinate system with the center point of the roller used for processing the pipeline arc segment as the origin and the rotation axis of the roller as the z-axis, and simplifying the straight segment axis and the center axis of the circular segment of the pipeline into two-dimensional coordinates through calculation, wherein the straight segment axis is simplified to a curve of the distance from any point on the pipeline straight segment axis to the roller rotation axis and the perpendicular distance from any point on the pipeline straight segment axis to the xy plane, and the center axis of the circular segment is simplified to the distance from any point on the pipeline circular segment center axis to the roller rotation axis and the perpendicular distance from any point on the pipeline circular segment center axis to the xy plane. distance, so that the direction of the axis of the straight segment and the center axis of the arc segment of the pipeline can be intuitively seen in the two-dimensional coordinate system. By comparing the above two curves with the two-dimensional obstacle curve (that is, the curves of the roller used to process the arc segment of the pipeline and the mounting base and motor housing of the processing equipment in the above two coordinate systems), it can be intuitively seen whether there is interference between the pipeline and the processing equipment, and the dimensionality reduction analysis of the pipeline bending interference can be achieved, which can effectively reduce the difficulty of the feasibility review of pipeline forming, reduce the number of simulations and experiments, provide strong data and intuitive graphics, and provide a high-speed and accurate method for identifying unprocessable pipelines, thereby greatly advancing the start time of pipeline optimization direction, helping to ensure production progress and reduce production costs.

[0098] Other features and advantages of the present invention will be described in the following description, and part of them will become obvious from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0100] Figure 1 A schematic diagram of the flow chart of the pipeline bending dimensionality reduction interference analysis method provided by the present invention;

[0101] Figure 2 A schematic diagram of the geometric structure of a pipeline before bending in the pipeline bending dimensionality reduction interference analysis method provided by the present invention;

[0102] Figure 3 A schematic diagram of the geometric structure of a pipeline after bending in the pipeline bending dimensionality reduction interference analysis method provided by the present invention;

[0103] Figure 4 Schematic diagram of the catheter axis model for the pipeline bending dimensionality reduction interference analysis method provided by the present invention;

[0104] Figure 5 A two-dimensional distance curve obtained by the pipeline bending dimensionality reduction interference analysis method provided in Example 1 of the present invention;

[0105] Figure 6 A two-dimensional spatial angle distance curve obtained by the pipeline bending dimensionality reduction interference analysis method provided in Example 1 of the present invention;

[0106] Figure 7 A three-dimensional geometric assembly drawing in the pipeline bending dimensionality reduction interference analysis method provided in the first embodiment of the present invention;

[0107] Figure 8a The two-dimensional space distance curve and the two-dimensional space angular distance curve of the second bend obtained by the pipeline bending dimensionality reduction interference analysis method provided in the second embodiment of the present invention;

[0108] Figure 8b The two-dimensional space distance curve and the two-dimensional space angular distance curve of the seventh bend obtained by the pipeline bending dimensionality reduction interference analysis method provided in the second embodiment of the present invention;

[0109] Figure 8c The two-dimensional space distance curve and the two-dimensional space angular distance curve of the fourth bend obtained by the pipeline bending dimensionality reduction interference analysis method provided in the second embodiment of the present invention;

[0110] Figure 9a A three-dimensional geometric assembly diagram of the second bend in the pipeline bending dimensionality reduction interference analysis method provided in the second embodiment of the present invention;

[0111] Figure 9b A three-dimensional geometric assembly diagram of the third bend in the pipeline bending dimensionality reduction interference analysis method provided in the second embodiment of the present invention;

[0112] Figure 9c This is a three-dimensional geometric assembly diagram of the fourth bend in the pipeline bending dimensionality reduction interference analysis method provided in Example 2 of the present invention.

[0113] Reference numerals:

[0114] 1-Pipeline; 2-Chuck; 3-Roller; 4-Bent rectangular coordinate system; 5-Mounting seat; 6-Motor housing; 7-Original rectangular coordinate system. DETAILED DESCRIPTION

[0115] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein the accompanying drawings constitute a part of the present invention and are used to explain the principles of the present invention together with the embodiments of the present invention.

[0116] To minimize adverse impacts on quality, cost, cycle time, and schedule, the product development process can be divided into two parallel timelines: the physical manufacturing timeline and the mathematical twin timeline. These two interconnected and mutually reinforcing processes can bring the discovery of machining problems forward while also enabling rapid solutions. This can determine the need for 3D model simulation, prioritize forming equipment and methods, and perform local optimization of design dimensions to ensure machinability.

[0117] The present invention provides a pipeline bending interference dimensionality reduction analysis method, see Figure 1 , including the following steps:

[0118] Step 1: Establish a curved rectangular coordinate system 4 with the center point of the roller 3 used for processing the arc segment of the pipeline 1 as the origin and the rotation axis of the roller 3 as the z-axis;

[0119] Step 2: Based on the original XYZ data based on the original rectangular coordinate system 7, the original XYZ data requires that the straight segment axis of the pipeline 1 be simplified into a two-dimensional space distance curve by calculation in the same original rectangular coordinate system 7, and the horizontal coordinate is the vertical distance S from any point on the straight segment axis of the pipeline 1 to the xy plane. z , the ordinate is the distance f(t) from any point on the axis of the straight segment of pipeline 1 to the rotation axis of roller 3;

[0120] Based on the original XYZ data of the center axis of the arc segment of pipeline 1, the center axis of the arc segment of pipeline 1 is simplified into a two-dimensional space angle distance curve through calculation. The horizontal coordinate is the vertical distance S from any point on the center axis of the arc segment of pipeline 1 to the xy plane. y , the vertical coordinate is the distance g(θ) from any point on the midline of the arc segment of pipeline 1 to the rotation axis of roller 3;

[0121] The roller 3 used for processing the arc segment of the pipeline 1, as well as the mounting base 5 and the motor housing 6 of the processing equipment are simplified into a two-dimensional obstacle curve;

[0122] Step 3: Use the reduced-dimensional image of pipeline 1 to replace the original three-dimensional image of pipeline 1, and determine whether the two-dimensional space distance curve and the two-dimensional space angle distance curve interfere with the two-dimensional obstacle curve. If interference exists, it means that the above-mentioned processing equipment is not suitable for this type of pipeline 1 processing. Mark the process and coordinates corresponding to the interference. If there is no interference, it means that the above-mentioned processing equipment is suitable for this type of pipeline 1 processing, thereby simplifying the output to realize the data visualization of pipeline 1.

[0123] It should be noted that, during the pipeline bending process, to determine whether the processing equipment can be used for the bending of a certain type of pipeline 1, the most important thing is to ensure that the pipeline 1 will not interfere with the components of the processing equipment (for example, the roller 3, the mounting base 5 and the motor housing 6) during the bending process. The pipeline bending dimensionality reduction interference analysis method of this embodiment is to check in two-dimensional space whether the three-dimensional pipeline 1 will collide with the processing equipment during the bending and rotation process.

[0124] Compared with the prior art, the pipeline bending interference dimensionality reduction analysis method provided by the present invention can replace the motion simulation, post-calculation data comparison, and optimization process of the pipeline 1 forming process review, by establishing a bending rectangular coordinate system 4 with the center point of the roller 3 used for processing the circular arc segment of the pipeline 1 as the origin and the rotation axis of the roller 3 as the z-axis, and simplifying the straight segment axis and the central axis of the circular arc segment of the pipeline 1 into two-dimensional coordinates by calculation, wherein the straight segment axis is simplified to a curve of the distance from any point on the straight segment axis of the pipeline 1 to the rotation axis of the roller 3 and the vertical distance from any point on the straight segment axis of the pipeline 1 to the xy plane, and the central axis of the circular arc segment is simplified to the distance from any point on the central axis of the circular arc segment of the pipeline 1 to the rotation axis of the roller 3 and the vertical distance from any point on the central axis of the circular arc segment of the pipeline 1 to the xy plane. The vertical distance of the y plane can be used to intuitively see the direction of the axis of the straight segment and the center axis of the arc segment of the pipeline 1 in the two-dimensional coordinate system. By comparing the above two curves with the two-dimensional obstacle curve (i.e., the curves of the roller 3 used to process the arc segment of the pipeline 1 and the mounting base 5 and motor housing 6 of the processing equipment in the above two coordinate systems), it can be intuitively seen whether there is interference between the pipeline 1 and the processing equipment, and the dimensionality reduction analysis of the pipeline bending interference can be achieved, which can effectively reduce the difficulty of the feasibility review of the pipeline 1 forming, reduce the number of simulations and experiments, provide strong data and intuitive graphics, and provide a high-speed and accurate method for identifying the unprocessable pipeline 1, thereby greatly advancing the start time of optimizing the direction of the pipeline 1, helping to ensure production progress and reduce production costs.

[0125] In order to verify the results of the above pipeline bending interference dimensionality reduction analysis, the following steps are also included after the above step 3:

[0126] Establish pipeline 1 product model and processing equipment model;

[0127] Perform three-dimensional geometric assembly on the pipeline 1 product model and the processing equipment model, compare the interference positions obtained by the pipeline bending interference dimensionality reduction analysis, and determine whether the interference processes and coordinates of the two are consistent. If they are consistent, it means that the pipeline bending interference dimensionality reduction analysis is credible. If they are inconsistent, it means that there are errors in the pipeline bending interference dimensionality reduction analysis and it is not credible.

[0128] For example, in the above pipeline bending interference dimensionality reduction analysis method, the arrangement of each component is as follows: Figures 2 to 3,in Figure 2 This is a schematic diagram of the geometric structure before the pipe is bent. Figure 3 This is a schematic diagram of the geometric structure of the pipe after bending. The processing equipment includes a chuck 2, a roller 3, a mounting seat 5 and a motor housing 6. The mounting seat 5 is provided on the upper surface of the motor housing 6. The roller 3 is provided on the upper surface of the mounting seat 5 and is rotatably connected to the mounting seat 5. The forming end of the chuck 2 cooperates with the outer peripheral surface of the roller 3. The forming end of the chuck 2 rotates around the rotating axis of the roller 3 to bend the pipe. For example, the radius of the mounting seat 5 is 144mm, and the radius of the motor housing 6 is 244mm. It should be noted that Figure 2 Also shown are the positions of the original rectangular coordinate system 7 and the positions of the newly created curved coordinate system used for simplification.

[0129] Figure 4 A schematic model diagram of the simplified axis of the corresponding curved pipeline 1 (including the axis of the straight segment and the center axis of the arc segment).

[0130] Specifically, in the above step 2, 3D modeling software (including but not limited to UG, CATIA software) is first used to conveniently obtain the pipeline 1 data. The above pipeline 1 data is the original XYZ data, that is, the starting point and intersection coordinate data P of the straight line segment in the pipeline 1 guide line. m =(X m ,Y m ,Z m ).

[0131] In step 2 above, the vertical distance S from any point on the axis of the straight segment of pipeline 1 to the xy plane is simplified and calculated based on the original XYZ data. z The distance f(t) from any point on the axis of the straight segment of the pipeline 1 to the rotation axis of the roller 3 includes the following steps:

[0132] Step 21: Calculate the line vector T based on the original XYZ data n :

[0133] T n ={L n ,M n ,N n =P n+1 -P n ——Formula 1

[0134] Here, m is any integer from 1 to m, and n is any integer from 1 to m-1.

[0135] Step 22: According to the straight line vector T n Calculate the straight line unit vector t respectively n The angle α between two adjacent straight line segments n :

[0136]

[0137]

[0138] Step 23: According to the straight line unit vector t n Calculate the angle bisector vector Vf respectively n The vector K of the rotation axis of the arc segment of pipeline 1 n , the solution formula using vector representation is as follows:

[0139] Vf n ={Lf n ,Mf n ,Nf n}={l n ,m n ,n n}-{l n+1 ,m n+1 ,n n+1}——Formula 4

[0140]

[0141] Step 24: Based on the original XYZ data, the arc radius R corresponding to the center axis of the arc segment n , the angle bisector vector Vf n Calculate the center position On(X0 of the central axis of the arc segment of pipeline 1 n ,Y0 n ,Z0 n ):

[0142]

[0143] It should be noted that X00=X1, Y00=Y1, and Z00=Z1.

[0144] Step 25: After obtaining the spatial parameters of pipeline 1, analyze the distance between each part of pipeline 1 and the rotation axis of the processing equipment. When bending the first bend, it is obvious that no calculation is required based on the structure of the processing equipment. Therefore, the calculation of the first straight line segment and the first arc segment is carried out during the second bend processing. According to the center position of the central axis of the arc segment of pipeline 1 (X0 n ,Y0 n ,Z0 n ) and the vector K of the rotation axis of the arc segment of pipeline 1 n Calculate the axis equation (Xk, Yk, Zk):

[0145]

[0146] According to the original XYZ data and the straight line unit vector t nCalculate the equation of the line on which the first straight line segment lies:

[0147]

[0148] According to formula 8, the following formula is derived:

[0149]

[0150]

[0151]

[0152] Step 26: Vector K of the rotation axis based on the centerline of the arc segment of pipeline 1 n , the center position of the arc segment of pipeline 1 (X0 n ,Y0 n ,Z0 n ) and the equation of the line where the first straight line segment is located, respectively calculate the distance f(t) from any point on the axis of the straight line segment of pipeline 1 to the rotation axis of roller 3 and the perpendicular distance S from any point on the axis of the straight line segment of pipeline 1 to the xy plane z :

[0153]

[0154]

[0155] Among them, P z =(X z ,Y z ,Z z ), O n =(X0 n ,Y0 n ,Z0 n ).

[0156] Alternatively, in order to simplify the calculation process, a simple algorithm may be used. It should be noted that such a simple algorithm can be implemented by programming (for example, C language, etc.). That is, the following steps are further included after step 26:

[0157] Step 27: Set the starting point of the first straight line segment to

[0158]

[0159] Set the endpoint of the first straight line segment to

[0160]

[0161] Substituting Equation 9, Pq1, and Pq2 into Equation 10, we obtain the following formula:

[0162]

[0163]

[0164] Substituting Equation 9, Pq1, and Pq2 into Equation 11, we obtain the following formula:

[0165] S z =(Xq1-X0 n+1 )Lk n+1 +(Yq1-Y0 n+1 )Mk n+1 +(Zq1-Y0 n+1 )Nk n+1 +t[(Xq2-Xq1)Lk n+1 +(Yq2-Yq1)Mk n+1 +(Zq2-Zq1)Nk n+1 ]

[0166] ——Formula 13

[0167] Where t∈[0,1];δ=(X0 n+1 -Xq1)Mk n+1 -(Y0 n+1 -Yq1)Lk n+1 ;

[0168] β=(X0 n+1 -Xq1)Nk n+1 -(Z0 n+1 -Zq1)Lk n+1 ;

[0169] γ=(Y0 n+1 -Yq1)Nk n+1 -(Z0 n+1 -Zq1)Mk n+1 ;

[0170] λ=-(Xq2-Xq1)Mk n+1 +(Yq2-Yq1))Lk n+1 ;

[0171] μ=-(Xq2-Xq1)Nk n+1 +(Zq2-Zq1))Lk n+1 ;

[0172] η=-(Yq2-Yq1)Nk n+1 +(Zq2-Zq1)Mk n+1 .

[0173] In step 2 above, the vertical distance S from any point on the centerline of the arc segment of pipeline 1 to the xy plane is simplified and calculated based on the original XYZ data. y The distance g(θ) from any point on the central axis of the arc segment of the pipeline 1 to the rotation axis of the roller 3 includes the following steps:

[0174] Step 21': Calculate the line vector T based on the original XYZ data n :

[0175] T n ={L n ,M n ,N n =P n+1 -P n ——Formula 1

[0176] Here, m is any integer from 1 to m, and n is any integer from 1 to m-1.

[0177] Step 22': According to the straight line vector T n Calculate the straight line unit vector t respectively n The angle α between two adjacent straight line segments n :

[0178]

[0179]

[0180] Step 23': According to the straight line unit vector t n Calculate the angle bisector vector Vf respectively n The vector K of the rotation axis of the arc segment of pipeline 1 n , the solution formula using vector representation is as follows:

[0181] Vf n ={Lf n ,Mf n ,Nf n}={l n ,m n ,n n}-{l n+1 ,m n+1 ,n n+1}——Formula 4

[0182]

[0183] Step 24': According to the original XYZ data, the arc radius R corresponding to the center axis of the arc segment n , the angle bisector vector Vf n Calculate the center position of the arc segment of pipeline 1 (X0 n ,Y0n ,Z0 n ):

[0184]

[0185] It should be noted that X00=X1, Y00=Y1, and Z00=Z1.

[0186] Step 25': After obtaining the spatial parameters of pipeline 1, analyze the distance between each part of pipeline 1 and the rotation axis of the processing equipment. When bending the first bend, it is obvious that no calculation is required based on the structure of the processing equipment. Therefore, the calculation of the first straight line segment and the first arc segment is carried out during the second bend processing. According to the center position of the central axis of the arc segment of pipeline 1 (X0 n ,Y0 n ,Z0 n ) and the vector K of the rotation axis of the arc segment of pipeline 1 n Calculate the axis equation (Xk, Yk, Zk):

[0187]

[0188] According to the rotation vector Vrot{Vrotx, Vroty, Vrotz}, the center position of the arc segment of pipeline 1 (X0 n ,Y0 n ,Z0 n ), the arc radius R corresponding to the center axis of the arc segment n Calculate the equation of the first arc segment:

[0189]

[0190] The calculation formula of the rotation vector Vrot is as follows:

[0191] V rot =cosθV+sinθK n ×V+(1-cosθ)(V·K n )K n

[0192]

[0193]

[0194]

[0195]

[0196] Among them, θ is the angle between the rotation vector Vrot and the original vector V, and the original vector V{Vx, Vy, Vz} is the vector from the center of the circle to the starting point of the next straight line segment, which can be calculated based on the vector K of the rotation axis of the arc segment of pipeline 1n and the straight line unit vector t n The specific formula is as follows:

[0197]

[0198] Step 26': Based on the vector K of the rotation axis of the arc segment of pipeline 1 n , the center position of the arc segment of pipeline 1 (X0 n ,Y0 n ,Z0 n ) and the first arc segment equation respectively calculate the vertical distance S from any point on the arc segment centerline of pipeline 1 to the xy plane y The distance g(θ) from any point on the midline of the arc segment of pipeline 1 to the rotation axis of roller 3 is:

[0199]

[0200]

[0201] Among them, P c =(X c ,Y c ,Z c ), O n =(X0 n ,Y0 n ,Z0 n ).

[0202] Alternatively, in order to simplify the calculation process, a simple algorithm may be used. It should be noted that such a simple algorithm can be implemented by programming (for example, C language, etc.). That is, the following steps may be further included after step 26':

[0203] Step 27': Simplify Equation 18 to the following formula:

[0204]

[0205] Simplify Equation 19 to the following formula:

[0206]

[0207] Among them, θ∈[0,α n ];Δ1=(Y0 n+1 -Y0 n )Nk n+1 -(Z0 n+1 -Z0 n )Mk n+1

[0208] Δ2=(Z0 n+1 -Z0<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> )Lk<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -(X0<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -X0<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> )Nk<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0209] <h2 style=";text-align:left;direction:ltr"> Δ3 = (X0<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -X0<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> )Mk<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -(Y0<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Y0<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> )Lk<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0210] <h2 style=";text-align:left;direction:ltr"> A=Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> m<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> (B) - Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> +Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> ;C=Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> m<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> ;<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0211] <h2 style=";text-align:left;direction:ltr"> D=Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> m<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> +Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0212] <h2 style=";text-align:left;direction:ltr"> E=-Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> m<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> +Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> MK<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> +Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> m<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0213] <h2 style=";text-align:left;direction:ltr"> F=-Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> +Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1+Mk n Nk n m n+1

[0214] a=-BNk n+1 +CMk n+1 , b=-CLk n+1 +ANk n+1 , c=-AMk n+1 +BLk n+1 ,

[0215] d=-ENk n+1 +FMk n+1 , e=-FLk n+1 +DNk n+1 , f=-DMk n+1 +ELk n+1 .

[0216] Example 1

[0217] The pipeline data of this embodiment are shown in Table 1, and the two-dimensional space distance curve obtained by dimensionality reduction analysis is shown in Figure 5 , the two-dimensional space angle distance curve obtained by dimensionality reduction analysis can be found in Figure 6 , see the 3D geometric assembly drawing Figure 7 , combined with the judgment criteria (i.e., two-dimensional obstacle curve) [-25, 25) Dp ≤ 59 mm, [25, 75) Dp ≤ 159 mm, [75, 125] Dp ≤ 259 mm, the preliminary obstacle range is the area surrounded by the dotted line segment in the figure. By analyzing the intersection, the process and location of the collision can be determined.

[0218] Table 1 Pipeline digital model data (length in mm)

[0219] Point number Xn Yn Zn R P1 0 0 0 - P2 350 350 0 44 P3 350 350 250 44 P4 700 70 250 -

[0220] from Figure 5 and Figure 6 It can be clearly seen that there is interference between the straight section of the pipeline and the processing equipment, while there is no interference between the arc section and the processing equipment. However, in general, this type of processing equipment is not suitable for the processing of this type of pipeline.

[0221] Obviously, when the point of the perpendicular line between two lines lies outside the endpoints of the line segment, the shortest distance to be calculated is the distance between the portion of the line segment between the endpoints and the axis. The calculation result should also reflect the value of t, which can be used to determine the collision point, the part of the device that collided, and where on the line segment the collision occurred. Therefore, further analysis is needed regarding distance calculation methods involving the start and end points, as well as the parameter t.

[0222] Example 2

[0223] The pipeline data of this embodiment are shown in Table 2. The two-dimensional space distance curve and two-dimensional space angle distance curve of the second bend obtained by dimensionality reduction analysis are shown in Table 2. Figure 8a , the three-dimensional geometric assembly diagram of the second bend is shown in Figure 9a The 2D distance curve and 2D angle distance curve of the third bending obtained by dimensionality reduction analysis can be found in Figure 8b , the three-dimensional geometric assembly drawing of the third bend is shown in Figure 9b The 2D distance curve and 2D angular distance curve of the fourth curvature obtained by dimensionality reduction analysis can be found in Figure 8c , the 3D geometric assembly diagram of the fourth bend is shown in Figure 9c , combined with the judgment criteria (i.e., two-dimensional obstacle curve) [-25, 25) Dp ≤ 59 mm, [25, 75) Dp ≤ 159 mm, [75, 125] Dp ≤ 259 mm, the preliminary obstacle range is the area surrounded by the red line segment in the figure. By analyzing the intersection, the process and location of the collision can be determined.

[0224] Table 2 Pipeline digital data (length in mm)

[0225] point Xn Yn Zn R P1 334.026197 111.645991 58.758156 - P2 431.989667 188.361403 227.926428 44 P3 600 355 0 44 P4 350 350 0 44 P5 350 350 350 44 P6 599.878019 150.097585 350 -

[0226] from Figure 8a and Figure 8c It can be clearly seen that the second, third and fourth bending processes of the pipeline will interfere with the processing equipment, and this processing equipment is not suitable for the processing of this type of pipeline.

[0227] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A pipeline bending interference dimensionality reduction analysis method, characterized in that: The steps include: Step 1: Establish a curved rectangular coordinate system with the center point of the roller used to process the arc segment of the pipeline as the origin and the rotation axis of the roller as the z-axis; Step 2: Based on the original XYZ data based on the original rectangular coordinate system, the straight line axis of the pipeline is simplified into a two-dimensional space distance curve through calculation. The horizontal coordinate is the vertical distance S from any point on the straight line axis of the pipeline to the xy plane. z , the vertical coordinate is the distance f(t) from any point on the straight line axis of the pipeline to the roller rotation axis; Based on the original XYZ data of the pipeline's arc segment centerline, the pipeline's arc segment centerline is simplified into a two-dimensional space angle distance curve through calculation. The horizontal coordinate is the vertical distance S from any point on the pipeline's arc segment centerline to the xy plane. y , the vertical coordinate is the distance g(θ) from any point on the central axis of the arc segment of the pipeline to the rotation axis of the roller; The roller used to process the arc section of the pipeline, as well as the mounting base and motor housing of the processing equipment are simplified into two-dimensional obstacle curves; Step 3: Determine whether the two-dimensional space distance curve and the two-dimensional space angle distance curve interfere with the two-dimensional obstacle curve. If there is interference, it means that the processing equipment is not suitable for the pipeline processing. Mark the process and coordinates corresponding to the interference. If there is no interference, it means that the processing equipment is suitable for the pipeline processing.

2. The pipeline bending interference dimensionality reduction analysis method according to claim 1 is characterized in that: The step 3 further includes the following steps: Establish pipeline product models and processing equipment models; Perform three-dimensional geometric assembly on the pipeline product model and the processing equipment model, compare the interference positions obtained by the pipeline bending interference dimensionality reduction analysis, and determine whether the interference processes and coordinates of the two are consistent. If they are consistent, it means that the pipeline bending interference dimensionality reduction analysis is credible. If not, it means that the pipeline bending interference dimensionality reduction analysis has errors and is unreliable.

3. The pipeline bending interference dimensionality reduction analysis method according to claim 1, characterized in that: In step 2, the original XYZ data of the pipeline is obtained using 3D modeling software. The original XYZ data is the starting point and intersection coordinate data P of the straight line axis in the pipeline. m =(X m ,Y m ,Z m ).

4. The pipeline bending interference dimensionality reduction analysis method according to claim 3 is characterized in that: In step 2, the vertical distance S from any point on the axis of the straight segment of the pipeline to the xy plane is simplified and calculated based on the original XYZ data. z The distance f(t) from any point on the straight line axis of the pipeline to the roller rotation axis includes the following steps: Step 21: Calculate the line vector T based on the original XYZ data n : m is any integer from 1 to m, and n is any integer from 1 to m-1; Step 22: According to the straight line vector T n Calculate the straight line unit vector t respectively n The angle α between two adjacent straight line segments n : Step 23: According to the straight line unit vector t n Calculate the angle bisector vector Vf respectively n The vector K of the rotation axis of the arc segment of pipeline 1 n , the solution formula using vector representation is as follows: Vf n = {Lf n , Mf n , Nf n} = {l n , m n , n n} - {l n+1 , m n+1 , n n+1} —— Formula 4 Step 24: According to the original XYZ data, the arc radius R corresponding to the center axis of the arc segment n , the angle bisector vector Vf n Calculate the center position O of the arc segment centerline of pipeline 1 n =(X0 n ,Y0 n ,Z0 n ): Step 25: Calculate the first straight line segment and the first arc segment from the second bending process, and calculate the center position of the arc segment of the pipeline (X0 n ,Y0 n ,Z0 n ) and the vector K of the rotation axis of the arc segment of the pipeline n Calculate the axis equation (Xk, Yk, Zk): According to the original XYZ data and the straight line unit vector t n Calculate the equation of the line on which the first straight line segment lies: According to formula 8, the following formula is derived: Step 26: Vector K of the rotation axis according to the centerline of the arc segment of the pipeline n , the center position of the arc section of the pipeline (X0 n ,Y0 n ,Z0 n ) and the equation of the straight line where the first straight line segment is located, respectively calculate the distance f(t) from any point on the axis of the straight line segment of the pipeline to the roller rotation axis and the perpendicular distance S from any point on the axis of the straight line segment of the pipeline to the xy plane z : P z =(X z ,Y z ,Z z ), O n =(X0 n ,Y0 n ,Z0 n )。 5. The pipeline bending interference dimensionality reduction analysis method according to claim 4 is characterized in that: The step 26 further includes the following steps: Step 27: Set the starting point of the first straight line segment to Pq1 = (Xq1, Yq1, Zq1) Set the endpoint of the first straight line segment to Pq2 = (Xq2, Yq2, Zq2) Substituting Equation 9, Pq1, and Pq2 into Equation 10, we obtain the following formula: Substituting Equation 9, Pq1, and Pq2 into Equation 11, we obtain the following formula: t∈[0，1]； δ=(X0 n+1 -Xq1)Mk n+1 -(Y0 n+1 -Yq1)Lk n+1 ; β=(X0 n+1 -Xq1)Nk n+1 -(Z0 n+1 -Zq1)Lk n+1 ; γ=(Y0 n+1 -Yq1)Nk n+1 -(Z0 n+1 -Zq1)Mk n+1 ; λ=-(Xq2-Xq1)Mk n+1 +(Yq2-Yq1))Lk n+1 ; μ=-(Xq2-Xq1)Nk n+1 +(Zq2-Zq1))Lk n+1 ; η=-(Yq2-Yq1)Nk n+1 +(Zq2-Zq1)Mk n+1 。 6. The pipeline bending interference dimensionality reduction analysis method according to claim 3, characterized in that: In step 2, the vertical distance S from any point on the central axis of the arc segment of the pipeline to the xy plane is simplified and calculated based on the original XYZ data. y The distance g(θ) from any point on the center axis of the arc segment of the pipeline to the roller rotation axis includes the following steps: Step 21': Calculate the line vector T based on the original XYZ data n : T n ={L n ,M n ,N n =P n+1 -P n ——Formula 1 m is any integer from 1 to m, and n is any integer from 1 to m-1; Step 22': According to the straight line vector T n Calculate the straight line unit vector t respectively n The angle α between two adjacent straight line segments n : Step 23': According to the straight line unit vector t n Calculate the angle bisector vector Vf respectively n The vector K of the rotation axis of the arc segment of pipeline 1 n , the solution formula using vector representation is as follows: Vf n = {Lf n , Mf n , Nf n} = {l n , m n , n n} - {l n+1 , m n+1 , n n+1} —— Formula 4 Step 24': According to the original XYZ data, the arc radius R corresponding to the center axis of the arc segment n , the angle bisector vector Vf n Calculate the center position O of the arc segment centerline of pipeline 1 n =(X0 n ,Y0 n ,Z0 n ): Step 25': Calculate the first straight line segment and the first arc segment from the second bending process, and calculate the center position of the arc segment of the pipeline (X0 n ,Y0 n ,Z0 n ) and the vector K of the rotation axis of the arc segment of the pipeline n Calculate the axis equation (Xk, Yk, Zk): According to the rotation vector Vrot{Vrotx, Vroty, Vrotz}, the center position of the arc segment of the pipeline (X0 n ,Y0 n ,Z0 n ), the arc radius R corresponding to the center axis of the arc segment n Calculate the equation of the first arc segment: Step 26': Based on the vector K of the rotation axis of the arc segment of pipeline 1 n , the center position of the arc section of the pipeline (X0 n ,Y0 n ,Z0 n ) and the first arc segment equation respectively calculate the vertical distance S from any point on the arc segment midline of the pipeline to the xy plane y The distance g(θ) from any point on the centerline of the arc segment of the pipeline to the roller rotation axis: P c =(X c ,Y c ,Z c ), O n =(X0 n ,Y0 n ,Z0 n )。 7. The pipeline bending interference dimensionality reduction analysis method according to claim 6, characterized in that: The calculation formula of the rotation vector Vrot is as follows: Vrot=cosθV+sinθK n ×V+(1-cosθ)(V·K n )K n θ is the angle between the rotation vector Vrot and the original vector V, and the original vector V{Vx, Vy, Vz} is the vector from the center of the circle to the starting point of the next straight line segment.

8. The pipeline bending interference dimensionality reduction analysis method according to claim 7, characterized in that: The original vector V{Vx, Vy, Vz} is based on the vector K of the rotation axis of the arc segment of the pipeline n and the straight line unit vector t n The calculation formula is as follows: K n ={Page n Mk. n No n }。 9. The pipeline bending interference dimensionality reduction analysis method according to claim 6, characterized in that: The step 26' further includes the following steps: Step 27': Simplify Equation 18 to the following formula: Simplify Equation 19 to the following formula: θ∈[0,α n ]; Δ1=(Y0 n+1 -Y0 n )Nk n+1 -(Z0 n+1 -Z0 n )Mk n+1 ; Δ2=(Z0 n+1 -Z0 n )Lk n+1 -(X0 n+1 -X0 n )Nk n+1 4 Δ3=(X0 n+1 -X0 n )Mk n+1 -(Y0 n+1 -Y0 n )Lk n+1 ; A=Mk n n n+1 -Nk n m n+1 ; B=-Lk n n n+1 +Nk n l n+1 ; C=Lk n m n+1 -Mk n l n+1 ; <h2 style=";text-align:left;direction:ltr">D=Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> m<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Mk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> +Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> *Lk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> n<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> -Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> Nk<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> l<h2 style=";text-align:left;direction:ltr"> n+1 <h2 style=";text-align:left;direction:ltr"> ; E=-Page n *Page n m n+1 +Page n Mk. n l n+1 +Nk n *Mk n n n+1 -N.K. n No n m n+1 ; F=-Page n *Page n n n+1 +Page n No n l n+1 -Mk n *Mk n n n+1 +Mk n No n m n+1 ; a=-BNk n+1 +CMk n+1 ,b=-CLk n+1 +ANk n+1 ,c=-AMk n+1 +BLk n+1 , d=-ENk n+1 +FMk n+1 ,e=-FLk n+1 +DNk n+1 ,f=-DMk n+1 +Each n+1 。 10. The pipeline bending interference dimensionality reduction analysis method according to any one of claims 1 to 9, characterized in that: The processing equipment includes a chuck, a roller, a mounting seat and a motor housing. The mounting seat is arranged on the upper surface of the motor housing. The roller is arranged on the upper surface of the mounting seat and is rotatably connected to the mounting seat. The forming end of the chuck cooperates with the outer peripheral surface of the roller. The pipeline is bent by rotating the forming end of the chuck around the rotating axis of the roller.

Images