A method for continuously and comprehensively predicting the thickness of fiber-wound pressure vessel heads.

Abstract

This invention provides a method for continuously and comprehensively predicting the thickness of fiber-wound pressure vessel heads. It acquires the fiber bundle distribution area of ​​the pressure vessel head and represents it as a planar surface region. The overlap of the fiber bundle distribution area is detected, and the number of fiber bundle layers is obtained comprehensively based on the distribution of fiber bundle layers. The surface region of the pressure vessel head is remapped to three-dimensional space, and the thickness at corresponding points is calculated using the layer values. This invention provides a continuous and comprehensive method for predicting the thickness of fiber-wound pressure vessel heads, taking into account the theoretically designed surface region covered by each cycle in the entire fiber winding process. By detecting the overlap between surface regions, the overall thickness distribution at the fiber-wound pressure vessel head is obtained, providing accurate thickness data for fiber-wound composite pressure vessels and improving the design optimization efficiency of fiber-wound composite pressure vessels.

Description

Technical Field

[0001] This invention belongs to the field of pressure vessel design and manufacturing technology based on fiber winding, specifically relating to a method for continuously and comprehensively predicting the thickness value of the end cap of a fiber-wound pressure vessel. Background Technology

[0002] Continuous fiber reinforced composite materials possess excellent corrosion resistance, lightweight properties, and high specific strength, leading to their widespread application in numerous fields such as aerospace, defense, sporting goods, and energy. Among these, fiber-wound composite pressure vessels play a crucial role in improving the performance and reliability of aircraft while reducing costs and maintenance requirements, contributing significantly to the development of satellites, spacecraft, rockets, and other aerospace vehicles. Accurate prediction of the composite layer thickness at the cylinder and head sections is essential during the design and manufacturing of pressure vessels to ensure the correctness of the design theory and effectively improve the efficiency of pressure vessel structural optimization design.

[0003] During fiber winding, the pressure vessel head exhibits a complex fiber distribution due to variations in radius and winding pattern, making accurate thickness prediction difficult. Currently, the main methods for predicting the thickness of fiber-wound composite pressure vessel head segments include the general single-formula method, the double-formula method, and the cubic spline function method. The single-formula method predicts an infinitely large thickness near the polar hole; the double-formula method divides the analysis area into two regions—one within a bandwidth near the polar hole and one outside—and performs analytical analysis on both regions to predict the thickness, but its prediction performance is poor at a distance of one bandwidth from the polar hole; the cubic spline function method fits the double-formula method to obtain a smoother thickness prediction curve, but all of these are based on the assumption of a straight fiber bundle, which differs from the actual area covered by the fiber bundle during winding. In recent years, Northwestern Polytechnical University has proposed a geodesic offset winding method for predicting the thickness of fiber-wound composite pressure vessels. This method calculates the fiber bundle edge line of the end cap segment by dividing a series of discrete reference lines in a polar coordinate system and using linear interpolation to calculate the intersection points with the boundary, obtaining various thickness curves. The average of these curves is then used to predict the end cap thickness. This method takes the actual winding profile into account, predicting the winding thickness of the end cap segment more closely to reality. However, the use of discrete data acquisition methods cannot accurately represent the thickness at any point on the end cap. Furthermore, all the above methods predict a single value at the radius of the parallel circle. In reality, wound products often exhibit some unevenness at the same parallel circle radius, and the thickness is not uniform. This is not conducive to establishing a model that more closely approximates the actual wound product.

[0004] In summary, while methods such as the single-formula method, the double-formula method, and the cubic spline function method can predict the thickness of the end cap section, they are based on the theory of the straight fiber bundle assumption, which differs from the actual winding pattern. Northwestern Polytechnical University considers the thickness prediction method based on the actual winding trajectory, but uses a discrete method to characterize the thickness of the end cap, which cannot accurately represent the thickness at any point on the end cap. Summary of the Invention

[0005] To fully understand the thickness variation at every point of the fiber-wound pressure vessel head, this invention characterizes and calculates the design path of the fiber bundle on the head, comprehensively obtains the head thickness value in the theoretical linear design, and realizes all-round thickness prediction of the head. The purpose of this invention is to provide a method that can continuously and comprehensively predict the thickness value of the fiber-wound pressure vessel head.

[0006] The present invention adopts the following technical solution.

[0007] A method for continuously and comprehensively predicting the thickness of fiber-wound pressure vessel heads, comprising the following steps:

[0008] Step 1: Obtain the fiber bundle distribution area of ​​the pressure vessel head and characterize it as a planar region.

[0009] Step 2: Detect the overlap of the obtained fiber bundle distribution areas to obtain the final layer distribution of the fiber bundles in the pressure vessel head;

[0010] Step 3: Based on the distribution of fiber bundle layers, obtain the number of layers at any location in the fiber bundle distribution area;

[0011] Step 4: Remap the surface region of the pressure vessel head to three-dimensional space, and calculate the thickness at the corresponding location using layer numerical calculations.

[0012] Furthermore, step 1 specifically includes:

[0013] Step 11: Based on the fiber winding model, obtain the discrete points of the fiber winding trajectory centerline and the fiber winding angle and rotation angle at each discrete point;

[0014] Step 12: Calculate the offset angle corresponding to the discrete point according to equation (Ⅰ);

[0015]

[0016] In the formula, d represents the fiber bundle bandwidth, α0 represents the winding angle at a point on the pressure vessel cylinder, Lc represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel cylinder, R represents the radius of the pressure vessel cylinder, and θ p This indicates the offset angle of a point on the cylinder.

[0017] Let i represent a point on the end cap, and αi R represents the winding angle at that point on the pressure vessel head, Le represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel head, and R represents the fiber bundle width. i θ represents the radius of that point on the pressure vessel head. i θ represents the rotation angle corresponding to that point on the pressure vessel head. ip This indicates the offset angle of that point on the end cap;

[0018] Step 13: Based on the obtained offset angle, offset left and right from the original rotation angle at that point to obtain the boundary point of the fiber bundle; specifically:

[0019] Combination Figure 4 As shown, at a point i on the end cap, the rotation angle is θ. i Shift it left and right by θ ip The angles at the two boundary points of the fiber bundle can be obtained by taking two angles, i.e., θ. i ±θ ip / 2, since the end cap radius remains constant here, and the coordinates of a certain point i are known, the spatial position (spatial coordinates) of the fiber bundle boundary point can be obtained by combining these angles, thus obtaining the boundary point of the fiber bundle; it should be noted that as it approaches the pole hole, the winding angle gradually approaches 90°. When calculating using the above method, it is found that θ at a certain point ip If the value is too large, the portion from that point to the polar aperture will be processed using geodesic offset to obtain the boundary point.

[0020] Step 14: Project the pressure vessel head from the side end face, so that the obtained fiber bundle boundary points and the arc surface of the transition part between the pressure vessel head and the cylinder are projected onto the spatial plane, and then connect the projection points into a line to obtain the fiber bundle surface region of the pressure vessel head.

[0021] Furthermore, step 2 specifically includes:

[0022] Step 21: Perform preliminary processing on the fiber bundle region of each complete cycle:

[0023] (a) When the fiber bundle region of a single complete cycle has at most two overlapping structures, the intersection of the fiber bundles is taken as the overlapping area, and the difference of the union sets is used to obtain a single-layer region. The overlapping areas with different numbers of layers in the obtained single complete cycle are collectively recorded as a layered region.

[0024] (b) When the fiber bundle region of a single complete cycle exceeds two overlapping structures, define n (n>2 and take integer) regions and assign an index to each region from 1 to n. Assuming that the overlapping area to be obtained is m (m>2 and take integer), then adopt the combination method to select m data from n data C(n,m)=n! / (m!*(nm)!). The selected value corresponds to the index of the region. Then, the regions in each combination are intersected, and the union of the obtained intersection is obtained. Finally, the difference set is obtained with the region with a higher number of overlapping layers to obtain the region with the current number of overlapping layers. The overlapping regions with different numbers of layers in a single complete cycle are collectively recorded as a layered region.

[0025] Step 22: Calculate the overlapping region after processing in step 21.

[0026] The subscript in layer_i represents the number of overlapping layers at the region. For example, layer_1 is a region covered by 1 fiber bundle, layer_2 is a region covered by 2 fiber bundles, and so on.

[0027] The calculation is performed between the two overlapping regions, and the process is repeated. During the calculation, the overlapping areas after the calculation need to be removed. After the calculation is completed, the union of the previously remaining area and the newly calculated area is the new overlapping region. The calculation between the new overlapping regions is repeated until the final solution is obtained, which is the final layer distribution at the pressure vessel head.

[0028] Furthermore, step 3 specifically includes:

[0029] Method 1: Obtain the number of layers at a certain point in the fiber bundle distribution area along the radial direction: continuously detect the area where the measured point is located along the radial direction to obtain the number of layers at the measured point;

[0030] or,

[0031] Method 2: Obtain the number of layers at a point in the fiber bundle distribution area along the circumferential direction: Starting from the starting point, until the entire circular motion is completed, detect the surface area to which the measured point belongs and obtain the number of layers at the measured point;

[0032] or,

[0033] Method 3: Use a custom curve to obtain the number of layers at a certain point in the fiber bundle distribution area, continuously detect the area to which the measured point belongs, and obtain the number of layers at the measured point.

[0034] Furthermore, step 4 specifically includes:

[0035] Step 41: Remap the surface region of the pressure vessel head to three-dimensional space. Based on the two-dimensional coordinates of the measured points and the surface equation of the head, obtain the three-dimensional coordinates.

[0036] Step 42: Based on the surface equation of the pressure vessel head, obtain the unit normal vector (n) of a point (x0, y0, z0) on the surface of the pressure vessel head. x ,n y ,n z The length is set to the product of the number of layers and the fiber bundle thickness at that point, defined as l. Then, the position (x) of the wound fiber bundle is obtained according to the point-direction equation of the straight line. n0 ,y n0 ,z n0 );

[0037] Step 43: Output the fiber bundle thickness position and radius of the measured point, and obtain the thickness prediction profile of the measured point of the pressure vessel head.

[0038] A system employing the aforementioned method includes a computer device, the computer device including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to perform the following steps:

[0039] S1, Read the fiber winding model data of the pressure vessel, and obtain the discrete points of the center line of the fiber winding trajectory in the model, as well as the fiber winding angle and rotation angle at each discrete point;

[0040] S2, calculate the offset angle corresponding to the discrete point according to equation (Ⅰ);

[0041]

[0042] In the formula, d represents the fiber bundle bandwidth, α0 represents the winding angle at a point on the pressure vessel cylinder, Lc represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel cylinder, R represents the radius of the pressure vessel cylinder, and θ p This indicates the offset angle of a point on the cylinder.

[0043] Let i represent a point on the end cap, and α i Let Le represent the winding angle at a point on the pressure vessel head, and let R represent the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel head. i θ represents the radius of that point on the pressure vessel head. i θ represents the rotation angle corresponding to that point on the pressure vessel head. ip This indicates the offset angle of that point on the end cap;

[0044] S3, based on the obtained offset angle, offset left and right from the original rotation angle at that point to obtain the boundary point of the fiber bundle; specifically:

[0045] Combination Figure 4 As shown, at a point i on the end cap, the rotation angle is θ. i Shift it left and right by θ ipThe angles at the two boundary points of the fiber bundle can be obtained by taking two angles, i.e., θ. i ±θ ip / 2, since the end cap radius remains constant here, and the coordinates of a certain point i are known, the spatial position (spatial coordinates) of the fiber bundle boundary point can be obtained by combining these angles, thus obtaining the boundary point of the fiber bundle; it should be noted that as it approaches the pole hole, the winding angle gradually approaches 90°. When calculating using the above method, it is found that θ at a certain point ip If the value is too large, the portion from that point to the polar aperture will be processed using geodesic offset to obtain the boundary point.

[0046] S4. Project the pressure vessel head from the side end face, so that the obtained fiber bundle boundary points and the arc surface of the transition part between the pressure vessel head and the cylinder are projected onto the spatial plane. Then connect the projection points into a line to obtain the fiber bundle surface area of ​​the pressure vessel head.

[0047] S5, performs preliminary processing on the fiber bundle region of each complete cycle:

[0048] (a) When the fiber bundle region of a single complete cycle has at most two overlapping structures, the intersection of all fiber bundles is taken as the overlapping region, and the difference of the union sets is used to obtain a single-layer region. The overlapping regions with different numbers of layers in the single complete cycle are collectively recorded as a layered region.

[0049] (b) When the fiber bundle region of a single complete cycle exceeds two overlapping structures, define n (n>2 and take integer) regions and assign an index to each region from 1 to n. Assuming that the overlapping area to be obtained is m (m>2 and take integer), then adopt the combination method to select m data from n data C(n,m)=n! / (m!*(nm)!). The selected value corresponds to the index of the region. Then, the regions in each combination are intersected, and the union of the obtained intersection is obtained. Finally, the difference set is obtained with the region with a higher number of overlapping layers to obtain the region with the current number of overlapping layers. The overlapping regions with different numbers of layers in a single complete cycle are collectively recorded as a layered region.

[0050] S6, calculate the overlapping area after step 5.

[0051] The subscript in layer_i represents the number of overlapping layers at the region. For example, layer_1 is a region covered by 1 fiber bundle, layer_2 is a region covered by 2 fiber bundles, and so on.

[0052] The calculation is performed between the two overlapping regions, and the process is repeated. During the calculation, the overlapping areas after the calculation need to be removed. After the calculation is completed, the union of the previously remaining area and the newly calculated area is the new overlapping region. The calculation between the new overlapping regions is repeated until the final solution is obtained, which is the final layer distribution at the pressure vessel head.

[0053] S7. Obtain the number of layers at any location in the fiber bundle distribution region using one of the following methods:

[0054] Method 1: Obtain the number of layers at a certain point in the fiber bundle distribution area along the radial direction: continuously detect the area where the measured point is located along the radial direction to obtain the number of layers at the measured point;

[0055] Method 2: Obtain the number of layers at a point in the fiber bundle distribution area along the circumferential direction: Starting from the starting point, until the entire circular motion is completed, detect the surface area to which the measured point belongs and obtain the number of layers at the measured point;

[0056] Method 3: Use a custom curve to obtain the number of layers at a certain point in the fiber bundle distribution area, continuously detect the area to which the measured point belongs, and obtain the number of layers at the measured point.

[0057] S8 remaps the surface region of the pressure vessel head to three-dimensional space. Based on the two-dimensional coordinates of the measured point and the equation of the head surface, the three-dimensional coordinates are obtained.

[0058] S9, Based on the head surface equation, obtain the unit normal vector (n) of a point (x0, y0, z0) on the pressure vessel head surface. x ,n y ,n z The length is set to the product of the number of layers and the fiber bundle thickness at that point, defined as l. Then, the position (x) of the wound fiber bundle is obtained according to the point-direction equation of the straight line. n0 ,y n0 ,z n0 );

[0059] S10 outputs the fiber bundle thickness position and radius of the measured point, obtains the thickness prediction profile of the measured point of the pressure vessel head, and outputs the result data.

[0060] The ingenious concept of this invention lies in the following: Based on the relationship between the fiber bundle winding angle and bandwidth, this invention uses a rotation angle offset method to obtain the boundary curve of the fiber bundle on the end cap. Simultaneously, when the winding angle is large, a geodesic offset method is used to obtain the boundary points. The combination of rotation angle offset and geodesic offset methods can directly and completely separate the cylinder section data from the end cap data. The calculation process is simple, eliminating the complex calculations of geodesic offset in the transition section between the cylinder and the end cap. Furthermore, a projection method simplifies the calculation process, projecting the area of ​​each fiber bundle at the end cap onto a two-dimensional plane. A plane is denoted as a surface region. Then, by calculating the overlap of different planar surface regions within a loop, different overlapping areas within a complete loop are obtained and denoted as a layered surface region. The layered surface regions are traversed and iterated to obtain the final layered surface region, which yields the number of projected layers in the two-dimensional surface region. Then, through the end cap surface equation, the two-dimensional surface region is mapped to three-dimensional space, thus obtaining the number of layers at any point on the end cap surface. Finally, the number of fiber layers is combined with the fiber bundle thickness, and a specified length is taken along the normal vector of the end cap surface to obtain the final fiber winding layer thickness representation surface.

[0061] Beneficial Effects: The fiber-wound pressure vessel head thickness prediction method proposed in this invention takes into account the theoretically designed surface area covered by each cycle in the entire fiber winding process. By detecting the overlap between surface areas, the overall thickness distribution at the head of the fiber-wound pressure vessel is obtained, providing comprehensive and continuous thickness data for fiber-wound composite pressure vessels, which is beneficial to improving the design optimization efficiency of fiber-wound composite pressure vessels. This invention uses a combination of rotation angle offset and geodesic offset to obtain the theoretically designed fiber bundle coverage area, directly separating the cylinder section data from the head data. The calculation process is simple, eliminating the complex calculation of geodesic offset in the cylinder-head transition section. By representing the overlap of a complete cycle through the layered surface area, and by detecting the overlap between different layered surface areas in the entire winding design, comprehensive data on the number of fiber bundle coverage layers at the head is obtained, which can be used to establish a fiber winding finite element analysis model that is closer to the actual winding condition. This invention realizes the detection at any point at the head of the fiber-wound pressure vessel, and the obtained value is a comprehensive and continuous thickness change value. It is an effective method for comprehensively detecting and predicting the head thickness, not limited to calculations for a certain angle or a certain area. Theoretically, the thickness calculation of various rotary pressure vessels can be performed using the solution of this invention, which has good universality. At the same time, the completeness of the obtained head thickness data provides better assurance for the optimization of pressure vessel structural design. Attached Figure Description

[0062] Figure 1 , Figure 2 This is a schematic diagram of the single fiber bundle winding structure on the pressure vessel in the embodiment;

[0063] Figure 3 This is a schematic diagram of the centerline of a single fiber bundle on the pressure vessel head in the embodiment.

[0064] Figure 4 This is a schematic diagram showing the fiber bundle boundary point obtained by the offset of a single fiber bundle on the pressure vessel head in the embodiment.

[0065] Figure 5 This is a schematic diagram of the projection of a complete loop of fiber bundle in the embodiment.

[0066] Figure 6 This is a schematic diagram of a stacked surface region in steps 21 and 22 of the embodiment;

[0067] Figure 7 This is a schematic diagram of the calculation principle of step 22 in the embodiment;

[0068] Figure 8 This is a two-dimensional projection effect of the overlapping (multiple fiber bundle surface regions) in the embodiment;

[0069] Figure 9 This is a diagram illustrating the effect of layer calculation in the embodiment;

[0070] Figure 10 This is a diagram showing the thickness prediction effect in the embodiment;

[0071] Figure 11 This is a schematic diagram of the path for obtaining the fiber bundle distribution area in the embodiment. Detailed Implementation

[0072] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] Example 1

[0074] Combination Figures 1 to 11 As shown, a method for continuously and comprehensively predicting the thickness value of fiber-wound pressure vessel heads includes the following steps:

[0075] Step 1: Obtain the fiber bundle distribution area of ​​the pressure vessel head and characterize it as a planar region; specifically:

[0076] Step 11: Based on the fiber winding model, obtain the discrete points of the fiber winding trajectory centerline and the fiber winding angle and rotation angle at each discrete point;

[0077] Step 12: Calculate the offset angle corresponding to the discrete point according to equation (Ⅰ);

[0078]

[0079] In the formula, d represents the fiber bundle bandwidth, α0 represents the winding angle at a point on the pressure vessel cylinder, Lc represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel cylinder, R represents the radius of the pressure vessel cylinder, and θ p This indicates the offset angle of a point on the cylinder.

[0080] Let i represent a point on the end cap, and α i Let Le represent the winding angle at a point on the pressure vessel head, and let R represent the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel head. i θ represents the radius of that point on the pressure vessel head. i θ represents the rotation angle corresponding to that point on the pressure vessel head. ip This indicates the offset angle of that point on the end cap;

[0081] Step 13: Based on the obtained offset angle, offset left and right from the original rotation angle at that point to obtain the boundary point of the fiber bundle; specifically:

[0082] Combination Figure 4 As shown, at a point i on the end cap, the rotation angle is θ. i Shift it left and right by θ ip The angles at the two boundary points of the fiber bundle can be obtained by taking two angles, i.e., θ. i ±θ ip / 2, since the end cap radius remains constant here, and the coordinates of a certain point i are known, the spatial position (spatial coordinates) of the fiber bundle boundary point can be obtained by combining these angles, thus obtaining the boundary point of the fiber bundle; it should be noted that as it approaches the pole hole, the winding angle gradually approaches 90°. When calculating using the above method, it is found that θ at a certain point ip If the value is too large, the portion from that point to the polar aperture will be processed using geodesic offset to obtain the boundary point.

[0083] Step 14: Project the pressure vessel head from its side end face, projecting the resulting fiber bundle boundary points and the arc surface of the transition area between the pressure vessel head and the cylinder onto a spatial plane. Then connect these projection points with a line to obtain the fiber bundle surface region of the pressure vessel head, as shown below. Figure 5 The diagram shows a complete loop of fiber bundle region.

[0084] Step 2: Detect the overlap of the obtained fiber bundle distribution areas to obtain the final layer distribution of the fiber bundles in the pressure vessel head.

[0085] The fiber bundle overlap of the entire end cap is obtained through the following processing method, which can be programmed and calculated using languages ​​such as C++ and Python. Specifically:

[0086] Step 21: Perform preliminary processing on the fiber bundle region of each complete cycle:

[0087] (a) Under normal circumstances, during the winding process of fiber-wound composite pressure vessel, when the fiber bundle region of a single complete cycle is at most two overlapping structures, the intersection of all fiber bundles is taken as the overlapping area, and the difference of the union sets is used to obtain a single-layer region. The overlapping areas with different numbers of layers in a single complete cycle are collectively recorded as a layered region.

[0088] (b) When the fiber bundle region of a single complete cycle exceeds two overlapping structures, define n (n>2 and take integer) regions and assign an index to each region from 1 to n. Assuming that the overlapping area to be obtained is m (m>2 and take integer), then adopt the combination method to select m data from n data C(n,m)=n! / (m!*(nm)!). The selected value corresponds to the index of the region. Then, the regions in each combination are intersected, and the union of the obtained intersection is obtained. Finally, the difference set is obtained with the region with a higher number of overlapping layers to obtain the region with the current number of overlapping layers. The overlapping regions with different numbers of layers in a single complete cycle are collectively recorded as a layered region.

[0089] Step 22: Calculate the stacked surface region processed in Step 21, and combine... Figure 6 , Figure 7 As shown, the subscript i in layer_i represents the number of overlapping layers at the surface region. For example, layer_1 is a surface region covered by 1 fiber bundle, layer_2 is a surface region covered by 2 fiber bundles (i.e., two overlapping layers), and so on. Figure 7 In this context, k represents k layers of overlap, i+k represents i+k layers of overlap, and i+2 represents i+2 layers of overlap.

[0090] The calculation is performed between the two overlapping regions, and the process is repeated. During the calculation, the overlapping areas after the calculation need to be removed. After the calculation is completed, the union of the previously remaining area and the newly calculated area is the new overlapping region. The calculation between the new overlapping regions is repeated until the final solution is obtained, which is the final layer distribution at the pressure vessel head.

[0091] It is important to note that in the calculation of two overlapping regions, the maximum possible number of layers is the sum of the maximum number of layers of both layers. Therefore, it is necessary to reserve space in advance. This reserved number of layers will not be less than the maximum number of layers, but the reserved space layer number is not necessarily the maximum number of layers. The final calculated overlapping effect is as follows. Figure 8 As shown.

[0092] Step 3: Based on the distribution of fiber bundle layers, obtain the number of layers at any location in the fiber bundle distribution area;

[0093] The number of layers at any location in the fiber bundle distribution region can be obtained using one of the following methods:

[0094] Method 1: Obtain the number of layers at a specific point in the fiber bundle distribution area along the radial direction: combined with... Figure 11 As shown, starting from the center of the circle along the radial direction at a certain angle (such as angle β), the area where the measured point is located is continuously detected to obtain the number of layers of the measured point; the center of the circle refers to the intersection of the radial section where the measured point is located and the axis of the pressure vessel, and the radius refers to the radius of the radial section where the measured point is located;

[0095] Method 2: Obtain the number of layers at a specific point in the fiber bundle distribution area along the circumferential direction: e.g. Figure 11 As shown, based on the selected radius, starting from any point on the circumference, the motion continues until the entire circle is completed, detecting the surface region to which the measured point belongs and obtaining the number of layers of the measured point; the radius refers to the radius of the radial section where the measured point is located.

[0096] Method 3: Use a custom curve to obtain the number of layers at a certain point in the fiber bundle distribution area, continuously detect the area to which the measured point belongs, and obtain the number of layers at the measured point.

[0097] Step 4: Remap the surface region of the pressure vessel head to three-dimensional space, and calculate the thickness at the corresponding location using layer numerical calculations. Specifically:

[0098] Step 41: Remap the surface region of the pressure vessel head to three-dimensional space. Based on the two-dimensional coordinates of the measured points and the surface equation of the head, obtain the three-dimensional coordinates.

[0099] Step 42: Based on the surface equation of the pressure vessel head, obtain the unit normal vector (n) of a point (x0, y0, z0) on the surface of the pressure vessel head. x ,n y ,n z The length is set to the product of the number of layers and the fiber bundle thickness at that point, defined as l. Then, the position (x) of the wound fiber bundle is obtained according to the point-direction equation of the straight line. n0 ,y n0 ,z n0 );

[0100] Step 43: Output the fiber bundle thickness position and radius of the measured point, and obtain the thickness prediction profile of the measured point of the pressure vessel head.

[0101] Based on the scheme in Example 1, the thickness of an ellipsoidal head pressure vessel with a cylinder radius of 110 mm, a cylinder length of 600 mm, an aperture radius of 25 mm, a head height of 50 mm, a fiber bundle thickness of 0.4 mm, a fiber bundle width of 10 mm, and a cylinder section winding angle of 10.26° was predicted. The results are shown in […]. Figure 9 and Figure 10 . Figure 9This indicates that, at a certain radial angle, the number of fiber layers in the fiber bundle at the end cap varies with the end cap height. Figure 10 The thickness prediction curve at the end cap is obtained by moving the product of the number of fiber bundle layers and the thickness of a single fiber bundle at the selected point along the normal vector direction at that point.

[0102] Example 2

[0103] This embodiment provides a system using the aforementioned method for predicting the thickness value of a fiber-wound pressure vessel head. The system primarily relies on a computer system to implement the entire process, including a computer device. The computer device comprises a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it performs the following steps:

[0104] S1, Read the fiber winding model data of the pressure vessel, and obtain the discrete points of the center line of the fiber winding trajectory in the model, as well as the fiber winding angle and rotation angle at each discrete point;

[0105] S2, calculate the offset angle corresponding to the discrete point according to equation (Ⅰ);

[0106]

[0107] In the formula, d represents the fiber bundle bandwidth, α0 represents the winding angle at a point on the pressure vessel cylinder, Lc represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel cylinder, R represents the radius of the pressure vessel cylinder, and θ p This indicates the offset angle of a point on the cylinder.

[0108] Let i represent a point on the end cap, and α i Let Le represent the winding angle at a point on the pressure vessel head, and let R represent the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel head. i θ represents the radius of that point on the pressure vessel head. i θ represents the rotation angle corresponding to that point on the pressure vessel head. ip This indicates the offset angle of that point on the end cap;

[0109] S3, based on the obtained offset angle, offset left and right from the original rotation angle at that point to obtain the boundary point of the fiber bundle; specifically:

[0110] Combination Figure 4 As shown, at a point i on the end cap, the rotation angle is θ. i Shift it left and right by θ ip The angles at the two boundary points of the fiber bundle can be obtained by taking two angles, i.e., θ. i ±θ ip / 2, since the end cap radius remains constant here, and the coordinates of a certain point i are known, the spatial position (spatial coordinates) of the fiber bundle boundary point can be obtained by combining these angles, thus obtaining the boundary point of the fiber bundle; it should be noted that as it approaches the pole hole, the winding angle gradually approaches 90°. When calculating using the above method, it is found that θ at a certain point ip If the value is too large, the portion from that point to the polar aperture will be processed using geodesic offset to obtain the boundary point.

[0111] S4. Project the pressure vessel head from the side end face, so that the obtained fiber bundle boundary points and the arc surface of the transition part between the pressure vessel head and the cylinder are projected onto the spatial plane. Then connect the projection points into a line to obtain the fiber bundle surface area of ​​the pressure vessel head.

[0112] S5, performs preliminary processing on the fiber bundle region of each complete cycle:

[0113] (a) When the fiber bundle region of a single complete cycle has at most two overlapping structures, the intersection of all fiber bundles is taken as the overlapping region, and the difference of the union sets is used to obtain a single-layer region. The overlapping regions with different numbers of layers in the single complete cycle are collectively recorded as a layered region.

[0114] (b) When the fiber bundle region of a single complete cycle exceeds two overlapping structures, define n (n>2 and take integer) regions and assign an index to each region from 1 to n. Assuming that the overlapping area to be obtained is m (m>2 and take integer), then adopt the combination method to select m data from n data C(n,m)=n! / (m!*(nm)!). The selected value corresponds to the index of the region. Then, the regions in each combination are intersected, and the union of the obtained intersection is obtained. Finally, the difference set is obtained with the region with a higher number of overlapping layers to obtain the region with the current number of overlapping layers. The overlapping regions with different numbers of layers in a single complete cycle are collectively recorded as a layered region.

[0115] S6, calculate the overlapping area after step 5.

[0116] The subscript in layer_i represents the number of overlapping layers at the region. For example, layer_1 is a region covered by 1 fiber bundle, layer_2 is a region covered by 2 fiber bundles, and so on.

[0117] The calculation is performed between the two overlapping regions, and the process is repeated. During the calculation, the overlapping areas after the calculation need to be removed. After the calculation is completed, the union of the previously remaining area and the newly calculated area is the new overlapping region. The calculation between the new overlapping regions is repeated until the final solution is obtained, which is the final layer distribution at the pressure vessel head.

[0118] S7. Obtain the number of layers at any location in the fiber bundle distribution region using one of the following methods:

[0119] Method 1: Obtain the number of layers at a point in the fiber bundle distribution area along the radial direction: Starting from the center of the circle along the radial direction, continuously detect the area where the measured point is located to obtain the number of layers at the measured point;

[0120] Method 2: Obtain the number of layers at a point in the fiber bundle distribution area along the circumferential direction: Combine the selected radius, start from the starting point and move until the entire circumference is completed, detect the surface area to which the measured point belongs, and obtain the number of layers at the measured point;

[0121] Method 3: Use a custom curve to obtain the number of layers at a certain point in the fiber bundle distribution area, continuously detect the area to which the measured point belongs, and obtain the number of layers at the measured point.

[0122] S8 remaps the surface region of the pressure vessel head to three-dimensional space, and obtains the three-dimensional coordinates based on the two-dimensional coordinates of the measured points and the surface equation of the head.

[0123] S9, Based on the head surface equation, obtain the unit normal vector (n) of a point (x0, y0, z0) on the pressure vessel head surface. x ,n y ,n z The length is set to the product of the number of layers and the fiber bundle thickness at that point, defined as l. Then, the position (x) of the wound fiber bundle is obtained according to the point-direction equation of the straight line. n0 ,y n0 ,z n0 );

[0124] S10 outputs the fiber bundle thickness position and radius of the measured point, obtains the thickness value of the measured point on the pressure vessel head, and outputs the result data.

[0125] The fiber-wound pressure vessel head thickness prediction method proposed in this invention utilizes the relationship between the fiber bundle winding angle and bandwidth. It employs a rotation angle offset to obtain the boundary curve of the fiber bundle on the head. Simultaneously, when the winding angle is large, a geodesic offset is used to obtain the boundary points. The combination of rotation angle offset and geodesic offset directly and completely separates the cylinder section data from the head data, obtaining the fiber bundle boundary line on the head. Combined with the circumferential curve at the transition between the cylinder section and the head section, a theoretical design surface region is formed. By detecting the overlap between surface regions, the overall thickness distribution at the fiber-wound pressure vessel head is obtained, providing more accurate thickness data for fiber-wound composite pressure vessels and improving the design optimization efficiency. This invention considers all theoretically designed winding regions, completes the overlap detection between different layered surface regions, obtains the number of fiber bundle layers at any position on the head, and obtains comprehensive data on the number of fiber bundle coverage layers at the head. This data can be used to establish a fiber-wound finite element analysis model that more closely approximates the actual winding condition. This invention enables the detection of any point on the end cap of a fiber-wound pressure vessel, obtaining comprehensive and continuous thickness variation values. It is an effective method for comprehensively detecting and predicting end cap thickness, not limited to calculations at a specific angle or region. Theoretically, this invention can be used to perform comprehensive thickness calculations on various rotary pressure vessels, demonstrating good universality. Furthermore, the completeness of the obtained end cap thickness data provides better assurance for optimizing the structural design of pressure vessels.

Claims

1. A method for continuously and comprehensively predicting the thickness value of fiber-wound pressure vessel heads, characterized in that the steps include... include: Step 1: Obtain the fiber bundle distribution area of ​​the pressure vessel head and characterize it as a planar region. Step 2: Detect the overlap of the obtained fiber bundle distribution areas to obtain the final layer distribution of the fiber bundles in the pressure vessel head; Step 3: Based on the distribution of fiber bundle layers, obtain the number of layers at any location in the fiber bundle distribution area; Step 4: Remap the surface region of the pressure vessel head to three-dimensional space, and calculate the thickness at the corresponding location using layer numerical calculations.

2. The method according to claim 1, characterized in that, Step 1 specifically includes: Step 11: Based on the fiber winding model, obtain the discrete points of the fiber winding trajectory centerline and the fiber winding angle and rotation angle at each discrete point; Step 12: Calculate the offset angle corresponding to the discrete point according to equation (Ⅰ); ， In the formula, d Indicates the fiber bundle bandwidth. This indicates the winding angle at a point on the cylinder of a pressure vessel. Lc This represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel cylinder. R Indicates the radius of the pressure vessel cylinder. This indicates the offset angle of a point on the cylinder. A point on the end cap is represented by the letter i. This indicates the winding angle at that point on the pressure vessel head. Le This represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel head. This indicates the radius of that point on the pressure vessel head. This indicates the rotation angle corresponding to that point on the pressure vessel head. This indicates the offset angle of that point on the end cap; Step 13: Based on the obtained offset angle, offset left and right from the original rotation angle at that point to obtain the boundary point of the fiber bundle; specifically: At a point i on the head, the rotation angle is... Shift it left and right The angles of the two boundary points on both sides of the fiber bundle can be obtained by taking two angles, that is... Since the end cap radius remains constant at this point, and the coordinates of point i are known, the spatial location of the fiber bundle boundary point can be obtained by combining these angles, thus obtaining the fiber bundle boundary point. It should be noted that as the polar aperture approaches, the winding angle gradually approaches 90°. When calculating using the above method, it was found that at a certain point... If the value is too large, the portion from that point to the polar hole will be processed using geodesic offset to obtain the boundary point; Step 14: Project the pressure vessel head from the side end face, so that the obtained fiber bundle boundary points and the arc surface of the transition part between the pressure vessel head and the cylinder are projected onto the spatial plane, and then connect the projection points into a line to obtain the fiber bundle surface region of the pressure vessel head.

3. The method according to claim 1, characterized in that, Step 2 specifically includes: Step 21: Perform preliminary processing on the fiber bundle region of each complete cycle: (a) When the fiber bundle region of a single complete cycle has at most two overlapping structures, the intersection of all fiber bundles is taken as the overlapping region, and the difference of the union sets is used to obtain a single-layer region. The overlapping regions with different numbers of layers in the single complete cycle are collectively recorded as a layered region. (b) When the fiber bundle region of a single complete cycle exceeds two overlapping structures, define n A region, n＞ 2. Assign an index to each region, from 1 to n, and round to the nearest integer. Assume the overlapping region to be calculated is... m , m＞ If 2 is an integer, then the combination method is used, from... n Select from data m Data The selected value corresponds to the index of the region. Then, the regions within each combination are intersected, and the union of the resulting intersection is calculated. Finally, the difference between the intersection and the region with the higher number of overlapping layers is calculated to obtain the region with the current number of overlapping layers. The overlapping regions with different numbers of layers in a single complete loop are collectively recorded as a layered region. Step 22: Calculate the overlapping region after processing in step 21. The subscript in layer_i represents the number of overlapping layers at the region. For example, layer_1 is a region covered by 1 fiber bundle, layer_2 is a region covered by 2 fiber bundles, and so on. The calculation is performed between the two overlapping regions, and the process is repeated. During the calculation, the overlapping areas after the calculation need to be removed. After the calculation is completed, the union of the previously remaining area and the newly calculated area is the new overlapping region. The calculation between the new overlapping regions is repeated until the final solution is obtained, which is the final layer distribution at the pressure vessel head.

4. The method according to claim 1, characterized in that, Step 3 specifically includes: Method 1: Obtain the number of layers at a certain point in the fiber bundle distribution area along the radial direction: continuously detect the area where the measured point is located along the radial direction to obtain the number of layers at the measured point; or, Method 2: Obtain the number of layers at a point in the fiber bundle distribution area along the circumferential direction: Starting from the starting point, until the entire circular motion is completed, detect the surface area to which the measured point belongs and obtain the number of layers at the measured point; or, Method 3: Use a custom curve to obtain the number of layers at a certain point in the fiber bundle distribution area, continuously detect the area to which the measured point belongs, and obtain the number of layers at the measured point.

5. The method according to claim 1, characterized in that, Step 4 specifically includes: Step 41: Remap the surface region of the pressure vessel head to three-dimensional space. Based on the two-dimensional coordinates of the measured points and the surface equation of the head, obtain the three-dimensional coordinates. Step 42, based on the head surface equation, obtain the value of a point on the pressure vessel head surface ( x 0 , y 0 , z 0 The unit normal vector of ) n x , n y , n z The length is set as the product of the number of layers at that point and the fiber bundle thickness, defined as... l Then, the position of the wound fiber bundle is obtained according to the point-direction equation of the straight line. x n0 , y n0 , z n0 ); Step 43: Output the fiber bundle thickness position and radius of the measured point, and obtain the thickness prediction profile of the measured point of the pressure vessel head.

6. A system for predicting the thickness value of a fiber-wound pressure vessel head as described in any one of claims 1-5, comprising a computer device, the computer device including a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it performs the following steps: S1, Read the fiber winding model data of the pressure vessel, and obtain the discrete points of the center line of the fiber winding trajectory in the model, as well as the fiber winding angle and rotation angle at each discrete point; S2, calculate the offset angle corresponding to the discrete point according to equation (Ⅰ); ， In the formula, d Indicates the fiber bundle bandwidth. This indicates the winding angle at a point on the cylinder of a pressure vessel. Lc This represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel cylinder. R Indicates the radius of the pressure vessel cylinder. This indicates the offset angle of a point on the cylinder. A point on the end cap i To indicate, This indicates the winding angle at a point on the pressure vessel head. Le This represents the projected length of the fiber bundle bandwidth on the cross-section of the pressure vessel head. This indicates the radius of that point on the pressure vessel head. This indicates the rotation angle corresponding to that point on the pressure vessel head. This indicates the offset angle of that point on the end cap; S3, based on the obtained offset angle, offset left and right from the original rotation angle at that point to obtain the boundary point of the fiber bundle; specifically: At a point i on the head, the rotation angle is... Shift it left and right The angles of the two boundary points on both sides of the fiber bundle can be obtained by taking two angles, that is... Since the end cap radius remains constant at this point, and the coordinates of point i are known, the spatial location of the fiber bundle boundary point can be obtained by combining these angles, thus yielding the fiber bundle boundary point. It should be noted that as the polar aperture approaches, the winding angle gradually approaches 90°. When calculating using the above method, it was found that at a certain point... If the value is too large, the portion from that point to the polar hole will be processed using geodesic offset to obtain the boundary point; S4. Project the pressure vessel head from the side end face, so that the obtained fiber bundle boundary points and the arc surface of the transition part between the pressure vessel head and the cylinder are projected onto the spatial plane. Then connect the projection points into a line to obtain the fiber bundle surface area of ​​the pressure vessel head. S5, performs preliminary processing on the fiber bundle region of each complete cycle: (a) When the fiber bundle region of a single complete cycle has at most two overlapping structures, the intersection of all fiber bundles is taken as the overlapping region, and the difference of the union sets is used to obtain a single-layer region. The overlapping regions with different numbers of layers in the single complete cycle are collectively recorded as a layered region. (b) When the fiber bundle region of a single complete cycle exceeds two overlapping structures, define n A region, n＞ 2. Assign an index to each region, from 1 to n, and round to the nearest integer. Assume the overlapping region to be calculated is... m , m＞ If 2 is an integer, then the combination method is used, from... n Select from data m Data The selected value corresponds to the index of the region. Then, the regions within each combination are intersected, and the union of the resulting intersection is calculated. Finally, the difference between the intersection and the region with the higher number of overlapping layers is calculated to obtain the region with the current number of overlapping layers. The overlapping regions with different numbers of layers in a single complete loop are collectively recorded as a layered region. S6, calculate the overlapping area after step 5. The subscript in layer_i represents the number of overlapping layers at the region. For example, layer_1 is a region covered by 1 fiber bundle, layer_2 is a region covered by 2 fiber bundles, and so on. The calculation is performed between the two overlapping regions, and the process is repeated. During the calculation, the overlapping areas after the calculation need to be removed. After the calculation is completed, the union of the previously remaining area and the newly calculated area is the new overlapping region. The calculation between the new overlapping regions is repeated until the final solution is obtained, which is the final layer distribution at the pressure vessel head. S7. Obtain the number of layers at any location in the fiber bundle distribution region using one of the following methods: Method 1: Obtain the number of layers at a certain point in the fiber bundle distribution area along the radial direction: continuously detect the area where the measured point is located along the radial direction to obtain the number of layers at the measured point; Method 2: Obtain the number of layers at a point in the fiber bundle distribution area along the circumferential direction: Starting from the starting point, until the entire circular motion is completed, detect the surface area to which the measured point belongs and obtain the number of layers at the measured point; Method 3: Use a custom curve to obtain the number of layers at a certain point in the fiber bundle distribution area, continuously detect the area to which the measured point belongs, and obtain the number of layers at the measured point. S8 remaps the surface region of the pressure vessel head to three-dimensional space, and obtains the three-dimensional coordinates based on the two-dimensional coordinates of the measured points and the surface equation of the head. S9, based on the head surface equation, obtain a point on the pressure vessel head surface ( x 0 , y 0 , z 0 The unit normal vector of ) n x , n y , n z The length is set as the product of the number of layers at that point and the fiber bundle thickness, defined as... l Then, the position of the wound fiber bundle is obtained according to the point-direction equation of the straight line. x n0 , y n0 , z n0 ); S10 outputs the fiber bundle thickness position and radius of the measured point, obtains the thickness prediction profile of the measured point of the pressure vessel head, and outputs the result data.

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