Universal elbow winding path planning method

Abstract

The invention discloses a universal elbow winding path planning method, which realizes efficient winding design of complex elbows through multiple steps of discretizing the elbows, initializing path points, optimizing path lengths, checking bridges and the like. The method does not depend on a geodesic equation, adopts a'start point-end point 'two-point method to be combined with an iterative optimization algorithm, remarkably reduces calculation complexity, ensures path stability and adaptability, and can be widely applied to the field of composite material pipeline manufacturing.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic forming of fiber - reinforced composites, and particularly relates to a general winding path planning method for bent pipes, which is especially suitable for the efficient winding path design of bent pipes with complex shapes. Background Art

[0002] The fiber winding technology is one of the core processes for the automatic forming of composites and is widely used in the manufacture of pressure pipes. As an important connecting part in the pipeline system, bent pipes play a key role in adjusting the flow path direction and avoiding obstacles. To ensure the long - term stable operation of the pipeline system, bent pipes need to meet performance requirements such as high strength, corrosion resistance, pressure resistance, and fatigue resistance, and the realization of these performances is inseparable from an efficient and accurate winding path planning method.

[0003] Winding path planning is a key link in winding design, and its purpose is to generate a stable yarn - laying point path on the surface of the mandrel. A stable path must have the properties of non - bridging and non - slipping, which are important prerequisites for the smooth implementation of the winding process. Non - bridging means that there should be no phenomenon of yarn bridging during the winding process, and non - slipping means that the winding path should be as close as possible to the geodesic (the geodesic is the most stable winding path), so that the static friction force provided by the mandrel to the yarn is sufficient to maintain the stability of the yarn.

[0004] In the prior art, most of the winding path planning methods for bent pipes rely on the geodesic equation of the bent - pipe surface. Based on the "winding starting point + direction", the three - dimensional coordinates of subsequent yarn - laying points are obtained by solving the geodesic equation through the Runge - Kutta method. However, for bent pipes with complex shapes, even if the surface parametric equation is known, it is difficult to deduce its geodesic equation, resulting in low path - planning efficiency and limited applicability. Therefore, there is an urgent need for a path - planning method that does not rely on the geodesic equation and is suitable for complex bent pipes.

[0005] It should be noted that the information disclosed in this background - art section is only intended to deepen the understanding of the overall background technology of the present invention and should not be regarded as an admission or any form of implication that this information constitutes the prior art known to those skilled in the art. Summary of the Invention

[0006] The present invention aims at the deficiencies of the prior art and provides a "starting - point - end - point" two - point method winding path planning method based on length - shortest optimization. This method does not rely on the geodesic equation of the bent - pipe surface, realizes the generation of an efficient and stable winding path, is especially suitable for the winding design of complex bent pipes, and further expands the applicable scope of the fiber winding technology in the pipeline field.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A general bending pipe winding path planning scheme includes the following steps:

[0009] Step S1: Discretize the bending pipe into n frames along the guiding line

[0010] The bending pipe surface is used as a swept surface, which is formed by the generatrix g(u) (a space curve represented by the zonal parameter u) moving along the guiding line d(v) (a space curve represented by the meridional parameter v). The parametric equation of the swept surface can be expressed as:

[0011] S(u, v) = d(v) + T(v)·g(u) (1)

[0012] where S(u, v) is the position vector of any point on the swept surface, and T(v) is the transformation matrix related to the trajectory line v (including translation, rotation, and scaling).

[0013] Let L represent the length of the guiding line, and L can be written as:

[0014]

[0015] where v 1 and v n represent the starting point and the ending point of the guiding line respectively. Discretize the guiding line evenly into n points (including the starting and ending points), then the discrete length can be expressed as:

[0016] Δv = L / (n - 1) (3)

[0017] After discretization, the n points on the guiding line can be represented by the meridional parameter:

[0018] v i = (i - 1)·Δv, i = 1, 2, …, n (4)

[0019] Each point corresponds to a cross-section (also called a frame), and the homogeneous matrix of each frame is represented as T(v i ), so the point on the i-th frame can be represented as:

[0020] P(u) = d(v i ) + T(v i )·g(u) (5)

[0021] Step S2: Input the starting point u 1 of the path, and determine the ending point u n

[0022] First, calculate the area of the swept surface:

[0023]

[0024] where S u and Sv respectively represent the tangent vector along the generatrix direction and the tangent vector along the guide line direction.

[0025] The equivalent perimeter is:

[0026]

[0027] Let the reference winding angle be α, representing the angle between the path and the meridional parametric curve. Then the latitudinal angle experienced by the helical winding path can be expressed as:

[0028]

[0029] The latitudinal angle of the first frame is represented by u 1 (as an input parameter), then the latitudinal angle of the path point of the nth frame is u n = u 1 + Δu.

[0030] Step S3: Initialization of the path for the intermediate frames

[0031] The latitudinal angle of the path points of the intermediate frames should be between u 1 and u n and show a monotonic change. For example, it can be simply set to change uniformly and monotonically. The latitudinal angle of the path points of the intermediate frames can be expressed as:

[0032] u i = u 1 + (i - 1), i = 2, 3,..., n - 1 (9)

[0033] Step S4: Optimization of path length minimization

[0034] First, represent the total length of the path. The starting point u 1 and the ending point u n of the path are both determined. Then the total path length φ is a function of the latitudinal angles of the path points of the intermediate frames:

[0035] φ = f(u 2 , u 3 , …, u n-1 ) (10)

[0036] Specifically, the total length of the path can be expressed as the sum of the lengths of each line segment, that is:

[0037] φ = ||P 1 P 2 || + … + ||P i-1 P i || + … + ||P n-1 P n || (11)

[0038] where the coordinates of P i are ui The function, namely

[0039] P i (u i ) = d(v i ) + T(v i )·g(u i ) (12)

[0040] Express the coordinate components of P i in x i , y i and z i respectively. Then the length of the line segment ||P i-1 P i || can be written as:

[0041]

[0042] The length minimization optimization is to minimize φ. The L - BFGS optimization method is adopted. When the difference between the total lengths of two adjacent iterations of φ is less than ε, the optimization is terminated. Otherwise, the iterative optimization process continues. After the optimization is completed, the updated intermediate frame meridional angle is obtained. Substitute the meridional angle into Equation (12) to obtain the three - dimensional Cartesian coordinates of the path points.

[0043] Step S5: Bridging inspection

[0044] For the path point P i , the normal direction of the elbow surface can be expressed as

[0045]

[0046] Then the non - bridging condition at P i can be written as:

[0047]

[0048] If no bridging occurs at all path points, the stability requirement of the winding path is satisfied. Conversely, the winding angle should be increased and the above steps should be executed again until the obtained winding path satisfies the non - bridging condition.

[0049] The beneficial effects of the present invention are:

[0050] 1. It does not require geodesic equations and is applicable to elbows with complex shapes;

[0051] 2. The optimization algorithm reduces the computational complexity;

[0052] 3. It can be flexibly adapted to various elbow shapes;

[0053] 4. It ensures that the path does not bridge and does not slip. Description of the drawings

[0054] Figure 1 According to some embodiments of the present invention, a flowchart of a general bending pipe winding path planning method is shown;

[0055] Figure 2 According to some embodiments of the present invention, a geometric model of a bending pipe is shown;

[0056] Figure 3 According to some embodiments of the present invention, a uniformly initialized winding path and a geodesic spiral path optimized by the method of the present invention are shown;

[0057] Figure 4 According to some embodiments of the present invention, a non-uniformly initialized winding path and a geodesic spiral path optimized by the method of the present invention are shown. Detailed implementation manners

[0058] The technical features and advantages of the present invention will be described in more detail below with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making the protection scope of the present invention more clearly defined.

[0059] Please refer to Figure 1 , which is a flowchart of a general bending pipe winding path planning method according to an embodiment of the present invention, and will be described in detail below with reference to a specific embodiment.

[0060] Step S1: Discretize the bending pipe into n frames along the guiding line

[0061] As Figure 2 shown, moving the generatrix 1 along the guiding line 2 can form the bending pipe core mold 3. In this embodiment, the generatrix 1 is a circle and the guiding line 2 is an arc, which can be expressed as:

[0062]

[0063] In formula (1), y c and z c are the y and z coordinates of the center of the generatrix 1, R is the radius of the arc of the guiding line 2, v is the meridional parameter (also used as the arc length parameter in this embodiment), θ 1 and θ 2 respectively represent the phase angles of the starting point 4 and the ending point 5 of the guiding line 2 in the YZ plane. (In this embodiment, the values of the above parameters are: R = 100, y c = 0, z c = -100, θ 1 = 3π / 4, θ 2 = π / 4)

[0064] Let L represent the length of the guiding line 2, and L can be written as:

[0065] L = R(θ 1 - θ 2 )(2)

[0066] The guiding line 2 is evenly discretized into n (n = 91 in this embodiment) discrete points 6 (including the starting point 4 and the ending point 5), then the distance between two adjacent discrete points can be expressed as:

[0067] Δv = L / (n - 1) (3)

[0068] After discretization, the n discrete points on the guiding line 2 can be represented by the arc length parameter:

[0069] v i = (i - 1)·Δv, i = 1, 2, …, n (4)

[0070] The homogeneous matrix T(v i ) corresponding to each point can be written as:

[0071]

[0072] Among them, represents the phase angle of each discrete point on the guiding line 2, Rotx(θ vi ) represents the rotation matrix of rotating by θ vi around the x-axis, and when expanded, it is written as:

[0073]

[0074] t(v i ) represents the translation vector of the i-th point relative to the starting point 4, t(v i ) = d(v i ) - d(v 1 ).

[0075] Each point on the guiding line 2 corresponds to a cross-section 7 (also called a frame 7). In this embodiment, the bus bar 1 is a circle with a fixed size, which can be expressed as:

[0076]

[0077] Among them, r represents the radius of the circle of the bus bar 1 (r = 10 in this embodiment), and u represents the latitudinal angle parameter. Then any point on the i-th frame can be expressed as:

[0078] P(u) = d(v i ) + T(v i )·g(u), u ∈ [0, 2π] (8)

[0079] According to equation (8), each frame of the bent pipe can be drawn (see each frame on the bent pipe 3 in Figure 2 ).

[0080] Furthermore, the parametric equation of the swept surface can be expressed as:

[0081] s(u, v) = d(v) + T(v)·g(u) (9)

[0082] In equation (9), S(u, v) is the position vector of any point on the swept surface.

[0083] Step S2: Input the starting point u of the path 1 , and determine the ending point u of the path according to the reference winding angle n

[0084] First, find the surface area of the bent pipe:

[0085] A = 2π(θ 1 - θ 2 )rR (10)

[0086] The equivalent perimeter of the bent pipe is:

[0087] C eq = 2πr (11)

[0088] Let the reference winding angle be α (α = 53° in this embodiment), representing the angle 9 between the path and the meridional parameter direction 8. Then the latitudinal angle experienced by the helical winding path can be expressed as:

[0089]

[0090] The latitudinal angle of the starting point 10 of the path is represented by u 1 (as an input parameter, u 1 = 0 in this embodiment). Then the latitudinal angle of the ending point 11 of the path in the nth frame is u n = u 1 + Δu.

[0091] Step S3: Initialization of the path for intermediate frames

[0092] The latitudinal angle of the path points in the middle should be between u 1 and u n . Usually, it can be set to change uniformly and monotonically. That is, the latitudinal angle of the path points on the intermediate frames can be expressed as:

[0093] u i = u 1 + Δu(i - 1) / (n - 1), i = 2, 3,..., n - 1 (13)

[0094] The obtained uniformly initialized path 12 is the dotted line as shown in Figure 3 .

[0095] To clearly show that the winding path calculated by the present invention is not affected by path initialization, this embodiment also provides an initialization path with non-uniform variation of the weft angle, which is expressed as follows:

[0096]

[0097] The obtained non-uniform initialization path 14 is as shown by the dashed line in Figure 4 Figure.

[0098] Step S4: Path length minimization optimization

[0099] First, represent the total length of the path. The starting point u 1 and the ending point u n of the path have both been determined. Then, the total path length φ can be expressed as a function of the weft angles of the intermediate frame path points, that is:

[0100] φ = f(u 2 , u 3 , …, u n-1 ) (15)

[0101] Specifically, the total length of the path can be expressed as the sum of the lengths of each line segment, that is:

[0102] φ = ||P 1 P 2 || + … + ||P i-1 P i || + … + ||P n-1 P n || (16)

[0103] The coordinates of P i are a function of u i , that is:

[0104] P i (u i ) = d(v i ) + T(v i ) · g(u i ) (17)

[0105] where the arc length parameter v i was determined in step S1. The coordinate components of P i (u i ) are represented by x i , y i and z i respectively. Then, the length of the line segment ||P i-1 P i || can be written as:

[0106]

[0107] According to equations (16) to (18), the length of the entire path can be fully represented. Next, the L-BFGS optimization method is used to minimize φ. When the difference between the total lengths of two adjacent iterations is less than ε (in this embodiment, ε = 10 -6 ), the optimization is terminated. Otherwise, the iterative optimization process continues. After the optimization is completed, the intermediate frame's latitudinal angle is obtained. Substituting the latitudinal angle into equation (17) can obtain the three-dimensional Cartesian coordinates of the path points.

[0108] In this embodiment, the optimized results of the latitudinal angles of 89 intermediate path points are as follows (separated by commas):

[0109] Point number Optimization results of the latitudinal angles of each path point 2～10 0.296964,0.588387,0.869679,1.13778,1.39126,1.63008,1.85514,2.06795,2.27029 11-20 2.46405,2.65114,2.83341,3.01265,3.19063,3.36909,3.54978,3.73448,3.92502,4.12328 21-30 4.33116,4.55052,4.78301,5.02985,5.29148,5.56713,5.85449,6.14961,6.44729,6.74184 31-40 7.02815,7.30244,7.56256,7.8079,8.03897,8.25707,8.46387,8.66125,8.8511,9.0353 41-50 9.21568,9.39401,9.57205,9.75152,9.9342,10.1219,10.3164,10.5198,10.7338,10.9602 51-60 11.2005,11.4555,11.725,12.0075,12.2997,12.597,12.8936,13.1842,13.4642,13.7309 61-70 13.9828,14.2202,14.4439,14.6556,14.8569,15.0499,15.2364,15.4183,15.5973,15.7753 71-80 15.9539,16.1349,16.3201,16.5114,16.7105,16.9195,17.1401,17.3741,17.6224,17.8855 81-90 18.1625,18.4509,18.7465,19.0442,19.3381,19.6233,19.8962,20.1548,20.3986,20.6283

[0110] For the uniformly initialized path 12, after optimizing for the shortest length, the geodesic spiral path 13( Figure 3 ) is obtained. Optimizing and solving the non-uniformly initialized path 14 yields the geodesic spiral path 15( Figure 4 ). The two results shown by paths 14 and 15 are consistent (not listed one by one here), indicating that the optimization results do not depend on the selection of the initialized path.

[0111] Step S5: Bridging inspection

[0112] For the path point P i , the normal direction of the elbow surface can be expressed as

[0113]

[0114] where S u and S v respectively represent the tangent vector along the generatrix direction and the tangent vector along the guide line direction. Then the condition for no bridging at Pi is:

[0115]

[0116] If no bridging occurs at all path points, the stability requirement of the winding path is satisfied. Conversely, the winding angle should be increased and the above steps should be re-executed until the obtained winding path satisfies the non-bridging condition. After inspection, all path points in this embodiment satisfy the non-bridging condition.

[0117] The embodiment of the present invention realizes the following beneficial effects by proposing a path planning method based on the "start point - end point" two-point method with the shortest length optimization:

[0118] 1. This method does not depend on the geodesic equation of the elbow surface and can efficiently and stably generate the winding path of the elbow, especially suitable for complex elbows.

[0119] 2. This method effectively reduces the computational complexity during the winding path planning process through the shortest length optimization algorithm, while ensuring the accuracy and reliability of the path.

[0120] 3. In the path planning based on the shortest length optimization, the L-BFGS method has the characteristics of high efficiency, stability, and memory-friendliness, and can obtain a high-precision winding path within fewer iterations.

[0121] 4. This method has strong versatility and can adapt to various elbow shapes and sizes without the need to re-adjust the calculation model for different shapes.

[0122] 5. It provides higher flexibility in path planning, allowing the setting of the winding start and end points according to actual needs to achieve customized winding path planning.

[0123] In summary, the present invention provides an innovative and practical elbow winding path planning method, which combines stability and efficiency, and provides an efficient and reliable solution for the fiber winding process in actual production.

[0124] In the description of the embodiments of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "center", "top", "bottom", "top part", "bottom part", "inner", "outer", "inner side", "outer side", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. Among them, the "inner side" refers to the internal or enclosed area or space. The "periphery" refers to the area surrounding a specific component or a specific area.

[0125] In the description of the embodiments of the present invention, the terms "first", "second", "third", "fourth" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first", "second", "third", "fourth" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0126] In the description of the embodiments of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection", "linkage", and "assembly" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a direct connection or an indirect connection through an intermediate medium, and it may be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0127] In the description of the embodiments of the present invention, specific features, structures, materials, or characteristics may be combined in any one or more embodiments or examples in a suitable manner.

[0128] In the description of the embodiments of the present invention, it should be understood that "-" and "~" represent the range between two values, and this range includes the endpoints. For example, "A - B" represents a range greater than or equal to A and less than or equal to B. "A ~ B" represents a range greater than or equal to A and less than or equal to B.

[0129] In the description of the embodiments of the present invention, the term "and / or" herein is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " herein generally represents an "or" relationship between the associated objects before and after.

[0130] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A general method for planning a curved pipe winding path, characterized in that: The following steps are involved: S1. Discretize the curved pipe surface into n frames along the guide line, and each frame is generated by sweeping the mother line along the guide line; S2. Input the starting point u1 of the winding path and determine the end point u according to the winding angle α n ; S3. Initialize the latitude angle u of the intermediate frame i ; S4. Using an iterative optimization algorithm to minimize the total length of the winding path, and obtain the optimized coordinates of the middle point; S5. Check whether the winding path meets the no-bridge condition. If not, adjust the parameters and re-optimize; The curved pipe surface is a swept surface formed by moving the generatrix along the guide line; the winding angle α represents the angle between the winding path and the longitudinal parameter curve, and the latitudinal angle u i Represents the angle traversed by the helical winding path.

2. The method according to claim 1, characterized in that The guide line is a space curve, and the parametric equation of the curved pipe surface can be expressed as: S(u,v)=d(v)+T(v)·g(u); Among them, S(u,v) is the position vector of any point on the curved surface of the pipe, T(v) is the transformation matrix related to the trajectory line v, including rotation, translation and scaling transformations, d(v) is the spatial curve equation of the guide line expressed by the radial parameter v, and g(u) is the spatial curve equation of the mother line expressed by the latitudinal parameter u.

3. The method according to claim 1, characterized in that In step S2, the end point u n The calculation formula is: n =u1+Δu; in, L represents the length of the guide line, C eq is the equivalent circumference of the elbow.

4. The method according to claim 1, characterized in that In step S3, the latitudinal angle of the intermediate frame path point can be expressed as: i =u1+(i-1),i=2,3,…,n-1; u i The initialization methods include uniform distribution or nonlinear distribution.

5. The method according to claim 1, characterized in that: In step S4, the iterative optimization algorithm is a gradient descent method or a quasi-Newton method.

6. The method according to claim 1, characterized in that In step S5, the no-bridging condition is: Among them, P i is u i The function of P i (u i )=d(v i )+T(v i )·g(u i ); N(u i ,v i ) is the normal vector of the curved pipe surface, 7. The method according to claim 1, characterized in that The method is suitable for manufacturing fiber-wound pipelines in the fields of petrochemical industry and aerospace.

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