A parameter design method for a round section wire ring under a target minimum clearance constraint based on a law plane section method

Abstract

A kind of target minimum gap constraint under the parameter design method of round section steel ring based on law plane section method, it relates to a kind of round section steel ring parameter design method.The present application is to solve the problems of existing technology, such as large calculation deviation, more variables to be solved, large amount of calculation and difficult to directly integrate with engineering parameter back analysis closed loop.The steps of the present application include input parameter-establish center line-construct law plane-establish one equation-solve root and screening-take global minimum center line distance in cycle-calculate minimum gap of adjacent steel wire in the same layer g i -feasibility repair-threshold approximation iteration-output parameter;Through the closed loop optimization relationship of "calculation-determination-adjustment-re-calculation" realized by loop structure, the output parameter meets the minimum gap of adjacent steel wire not less than target threshold, and is as close as possible to target threshold in engineering feasible region, so as to realize the accurate calculation of minimum gap of adjacent steel wire of round section steel ring and parameter design under target gap constraint.The present application belongs to the technical field of wire processing.

Description

Technical Field

[0001] This invention relates to a method for designing parameters of a circular cross-section steel wire ring, and more particularly to a method for designing parameters of a circular cross-section steel wire ring under the target minimum clearance constraint based on the normal plane section method, belonging to the field of metal wire processing technology. Background Technology

[0002] The tire bead is a critical load-bearing and positioning component of a tire. It works in conjunction with the rim to achieve tire assembly, positioning, and sealing, and transmits driving force, braking force, steering force, and impact loads. Its structural reliability has a significant impact on tire safety. Existing tire bead structures exist in various cross-sectional shapes and arrangements, including circular, hexagonal, and approximately rectangular shapes. Compared to other forms, circular cross-section beads, due to their geometric characteristics, typically offer more uniform stress distribution, a more compact structure, and better impact resistance, making them suitable for applications with high safety and load-bearing capacity requirements.

[0003] Circular cross-section wire coils typically consist of two parts: an inner core wire ring and an outer spiral winding layer of wires forming a spiral around the core's outer surface. During service, wire coils are subjected to complex alternating loads and have high safety requirements. Therefore, engineering design often requires accurately controlling the minimum gap between adjacent winding wires in the same layer while meeting manufacturing and structural constraints, in order to balance load-bearing capacity, structural stability, and manufacturability. The key fundamental question arising from this is: how to accurately calculate the minimum gap between adjacent winding wires in the same layer, and based on this, to achieve parameter design and selection oriented towards the target minimum gap.

[0004] Currently, the parameter design methods for circular cross-section wire coils are still imperfect. In particular, there is a lack of an integrated method that can accurately calculate the true minimum gap between adjacent wound wires in the same layer without relying on the approximation of the cross-section projection profile, and thereby realize parameter inverse calculation, feasible parameter optimization, and target threshold approximation parameter design.

[0005] In existing technologies, to facilitate calculation and engineering design, the projected profile of the winding wire centerline in the normal plane of the coil centerline is typically geometrically simplified or empirically approximated (e.g., approximated as a circle or ellipse). Based on this approximate model, the gap between adjacent wires in the same layer is estimated, and parameter selection and layout design are carried out. However, in actual spatial winding structures, the winding wire centerline is a three-dimensional spatial curve. Its true projected profile in the normal plane is often coupled with factors such as winding angle and curvature, exhibiting irregular closed curve characteristics, which are difficult to accurately represent with a single regular profile. Therefore, the gap estimation method based on the projection profile assumption is essentially an approximate solution, which cannot accurately reflect the true geometric correspondence between adjacent wires in the same layer, easily introducing systematic calculation errors, thereby reducing the reliability of parameter design and selection. On the other hand, there are also schemes that transform the solution for the minimum spacing between adjacent wires in the same layer into a numerical optimization problem of the minimum distance between two adjacent centerlines, and use swarm intelligence algorithms such as particle swarm optimization to search for the closest point pairs between the two spatial curves. Such methods typically require searching for the nearest point pair on two curves simultaneously, with the variables to be determined being the parameters of the two curves (at least two). The computational load is large, and the convergence and stability are significantly affected by the algorithm parameter settings. At the same time, the solution process lacks clear judgment conditions for the geometric positional relationship of the nearest point pair, making it difficult to form a closed-loop mechanism of "calculation-judgment-adjustment-recalculation" that can be directly embedded into the engineering design process. This is not conducive to carrying out feasibility repair and iterative parameter design that can be repeatedly executed.

[0006] A patent application (CN119870337A, filed March 3, 2025) discloses a design method for densely arranged circular cross-section steel wire coils and a circular cross-section steel wire coil itself. This design method can quickly calculate the maximum number of steel wires that can be arranged in each layer, as well as the wire spacing for various wire arrangement schemes. It can rapidly determine design schemes for densely arranged steel wires of different diameters, improving the overall performance of the circular cross-section steel wire coil and the tire. While this patented technology can achieve rapid estimation of dense arrangement parameters to a certain extent, its core relies on the geometric approximation that the "cross-sectional projection profile is a regular curve (such as a standard ellipse)." In actual winding structures, the centerline of the wound steel wire is a three-dimensional spatial curve. Influenced by factors such as spatial torsion, circumferential curvature, and phase, its actual projected profile in the cross-sectional plane may not satisfy the assumption of a regular ellipse. Especially when the winding angle is large or the curvature effect is significant, this geometric approximation may introduce non-negligible errors, causing the estimated gap to deviate from the actual minimum gap. This affects the consistency and reliability of the parameter design and parameter selection results, making it difficult to meet the requirements for high-precision gap calculation and controllable design of the target gap. Summary of the Invention

[0007] To address the problems of large calculation deviations, numerous variables to be determined, large computational load, and difficulty in directly integrating with engineering parameters to obtain closed-loop calculations, this invention proposes a parameter design method for circular cross-section steel wire rings with adjustable minimum gap between adjacent steel wires based on the normal plane section method.

[0008] The technical solution adopted by the present invention to solve the above problems is as follows: The steps of the present invention include: Step 1: Input design parameters to obtain the parameter set of the circular cross-section steel wire ring and the target minimum intermittent threshold; Step 2: Establish the parametric equations for the centerline of the wound steel wire; Step 3: Calculate the tangent vector and construct the normal plane; Step 4: Find the intersection of the normal plane with the adjacent rings on the same level, substitute the adjacent center lines, and establish a univariate equation about the difference in rotation angle; Step 5: Numerically solve for the angle difference, select valid intersection points, and calculate the minimum distance of the cross section; Step 6: Sample and calculate the global minimum centerline distance within one cycle; Step 7: Calculate the minimum gap and determine its feasibility and make repairs; Step 8: When the minimum gap equals the target minimum gap threshold, directly output the design parameters; under the premise that the minimum gap is greater than the target minimum gap threshold, continue to iterate the parameters to make the obtained minimum gap as close as possible to the target minimum gap threshold, and output the design parameters of the circular cross-section wire ring.

[0009] Furthermore, in step 3, the tangent vector is obtained by differentiating the centerline, and then the normal plane is constructed using the tangent vector as the normal vector.

[0010] Furthermore, in step 4, the points on the trajectory equations of the center lines of adjacent circles in the same layer are substituted into the equations of the normal plane and rearranged to obtain a univariate equation for the difference in rotation angle.

[0011] Furthermore, in step 5, the fixed turning angle is solved within a preset interval to obtain a solution set. For each root, candidate intersection points are constructed, candidate distances are calculated, and the smallest one is taken as the minimum cross-sectional distance under the normal plane.

[0012] Furthermore, in step 6, the corner is sampled within one cycle, and steps 3 to 5 are repeated to obtain the minimum distance between the center lines of adjacent steel wires in the same layer.

[0013] Furthermore, in step 7, the minimum gap between adjacent steel wires in the same layer is calculated. If the minimum gap between adjacent steel wires in the same layer is greater than or equal to the threshold of the minimum gap between adjacent targets in the same layer, then proceed to step 8; if the minimum gap between adjacent steel wires in the same layer is less than the threshold of the minimum gap between adjacent targets in the same layer, then parameter repair is performed, prioritizing the reduction of the lead number by step size, and steps 2 to 7 are repeated to recalculate the minimum gap between adjacent steel wires in the same layer.

[0014] Furthermore, in step 7, the first... Layer lead number lower limit As a constraint; when It has dropped to There is still a minimum gap between adjacent steel wires in the same layer. Minimum gap threshold between adjacent targets in the same layer When, decrease the first Number of winding turns And repeat the calculation until you get... Or reach the preset minimum limit.

[0015] The beneficial effects of this invention are: 1. This invention starts from the geometrically necessary condition for the existence of minimum distance point pairs, and utilizes constraints such as "the line connecting the closest point pairs is orthogonal to the tangent vectors of the two curves" to reduce the dimensionality of solving for the minimum distance between two curves in three dimensions to a univariate solution: In the curves r i,j Take a point P on the curve, construct a normal plane with the tangent vector at that point as the normal vector, and then connect the adjacent curves. r i , j+1 Substituting into the plane equation, we obtain a result containing only the angle difference Δ. φ The univariate equation is used to obtain candidate intersection points by numerical root finding, and then the distance between point pairs is calculated and the minimum value is taken to obtain the minimum distance of the centerline, which is used for parameter design under the target minimum gap threshold constraint.

[0016] 2. This invention transforms the two-parameter search problem into a univariate solution and selection by introducing a plane cross-section dimensionality reduction solution. Furthermore, it forms a closed loop with parameter determination, parameter adjustment, and threshold approximation iteration, which is more conducive to improving computational efficiency, stability, and engineering design applicability. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention; Figure 2 yes The influence curve on the minimum distance between the centerlines of adjacent steel wires is shown in the figure. , ; Figure 3 Is the number of leads and number of steel wires The impact on the minimum distance between the centerlines of adjacent steel wires. Detailed Implementation

[0018] Specific implementation method one: as follows Figure 1 The steps of the method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method include: Step 1: Input design parameters; Obtain the parameter set of the circular cross-section steel wire ring. and the target minimum gap threshold ,in, This represents the radius of curvature of the coil core. Indicates the radius of the core wire. Indicates the first The radius of the layered steel wire, Indicates the first Number of winding turns, Indicates the first Number of layer leads, Indicates the first Layer winding angle, Indicates the winding layer number, and , Indicates the first The number of the winding loops of the layer, and , Indicates the first Layer The initial phase of the loop has the following values: (1); Step 2, establish the first Layer Equation of parameters for the centerline of the coiled steel wire; definition: , in, Indicates the first i The centerline of the layered wound steel wire at the parameter angle φ The radial distance relative to the center line of the ring core, This represents the radius of curvature of the coil core. Indicates the first The helical radius from the center line of the layer winding to the center line of the ring core. This represents the cross-sectional parameter angle, used to determine the position of the centerline in the cross-sectional direction (i.e., the angle through which the winding wire rotates around the core). Indicates the first i The phase growth factor of the layer (i.e., unit) φ (Rate of circumferential phase change caused by change) Indicates the first i Layer j Circumferential phase angle of the circle's centerline; The centerline is then represented as: (2), In formula (2), Represents the coordinate vector of the centerline in three-dimensional space; Step 3: Calculate the tangent vector and construct the normal plane; right Differentiation yields the tangent vector: (3), by The normal vector passes through the point. Construction plane Its equation is: (4), In formula (4), For any point in space; Step 4: Find the intersection of the normal plane with the adjacent rings on the same level and establish the angle difference. The one-variable equation of Adjacent circles on the same layer (the first) i Layer j The point on (+1 lap) is written as: ,in Let the angle difference be the unknown (the only unknown quantity); let the initial phase difference be... And define the angular parameter difference: (5), In formula (5), Indicates the first i The initial phase difference between the center lines of two adjacent rings in the same layer Indicates the angle of the cross-section parameter; Will Substituting the equations into the plane equations and rearranging them, we obtain the following about The one-variable equation of: (6); Step 5: Numerical Solution Select the intersection points and calculate the minimum distance between the cross sections; For fixed Solve within the preset interval The solution set is obtained. For each root, construct candidate intersection points: (7), In formula (7), Indicates the first s One candidate intersection point Indicates the first i Layer j +1 turn of the center line coordinate vector of the wound steel wire Describe the first variable in a univariate equation s One valid root; Calculate candidate distances: (8), The minimum value is taken as the minimum cross-sectional distance under the plane of this method: (9); Step 6: Find the global minimum within the periodic domain to obtain the minimum distance to the centerline; because Follow It changes periodically, within one cycle Internal Sampling, repeating steps 3 through 5, yields: (10); Step 7: Calculate the minimum clearance and determine its feasibility and adjust parameters accordingly. , Indicates the minimum gap between adjacent steel wires in the same layer. This represents the minimum gap threshold between adjacent targets in the same layer; calculate: (11), like Proceed to step 8; if Then perform parameter repair: prioritize decreasing by step size. (Updated simultaneously according to closed relationships) Repeat steps 2 through 7 to recalculate. ; To avoid entanglement that does not meet process requirements, the first step is to set... Lower limit of layer lead number As a constraint (the lower bound expression obtained from the non-empty condition, and used for judgment; if there are other specific requirements, values ​​can be set by oneself); when It has dropped to Still When, decrease And repeat the calculation until you get... Or reach the preset minimum limit; Step 8: Threshold approximation iteration, when the following conditions are met... As close as possible under the premise ; When a feasible solution is obtained Then, save the current parameters and perform threshold approximation iteration: 1) Candidate to increase the number of steel wires in the same layer: Let Repeat steps 2 through 7 to calculate the new... If still satisfied If yes, accept and update the parameters; otherwise, cancel the update. 2) Increase the number of candidate leads: Let (and update according to closed relationships) Repeat steps 2 through 7. If the condition is still met... If yes, accept and update the parameters; otherwise, cancel and end the iteration. The final output parameter design result should meet the following requirements. And as close as possible during the iteration process. This enables the output of parameter design results that approximate the threshold.

[0019] like Figure 2 As shown, under the premise of meeting design requirements, in order to reduce the gap between adjacent steel wires, priority should be given to selecting Smaller options, namely R θ Under the premise of a fixed value, use small-diameter outer layer winding steel wire as much as possible to make the gap between steel wires as uniform as possible, and avoid large gap fluctuations that lead to sparse winding steel wires.

[0020] Given a set of structural parameters, the method of this invention is first used to calculate... And obtained g i The parameters are then adjusted according to the following rules to achieve the target minimum gap threshold design: (1) If g = g If the value is 0, the design parameters will be output directly.

[0021] (2) If g i > g 0, prioritize increasing the number of circles on the same level. m i To reduce the minimum distance between adjacent steel wires, the original m i Change to m i +1, recalculate g i until g i < g If 0, then take the previous value. g i > g 0 o'clock m i The value is used as the critical number of winding turns. Then, N i Change to N i +1, recalculate g i until g i < g If 0, then take the previous value. g i > g 0 o'clock N iThe value is used as the critical lead number.

[0022] (3) If g i < g 0. Adjust parameters according to the following priority (recalculate after each adjustment). g i And determine): Calculate the lower limit of the number of leads that are not suspended in this layer: (12) when N i > N i,min season N i = N i -1, recalculate g i If iterates to N i = N i,min Still g i < g 0, then it is determined that in m i The bottom line is only based on adjustment N i Unable to eliminate interference, making m i = m i -1 (Synchronous Reset) N i To satisfy the initial value of the constraint, repeat the above calculation until the constraint is satisfied. g i ≥ g 0, if g i > g If the value is 0, then continue to optimize according to case (2).

[0023] Working principle This invention uses the actual three-dimensional spatial trajectory of the center line of the wound steel wire as the calculation object, and does not make geometric approximations such as circles or ellipses on the cross-sectional projection contour.

[0024] For the centerlines of two adjacent wound steel wires in the same layer, when their closest point pair appears, the direction of the line connecting the two curves at the corresponding point is perpendicular to the tangential direction of the two curves. This condition is a geometrically necessary condition for the minimum distance point pair. Based on this geometric condition, the present invention selects a point on a centerline. P Construct a normal plane using the tangent vector at that point as the normal vector, and substitute the adjacent centerlines into the equation of the normal plane to form a plane containing only the angle difference. The intersection point of the univariate equation is obtained through numerical solution. Q By combining candidate distance calculation and screening, the "three-dimensional minimum distance problem between two curves" is transformed into "one-dimensional solution and screening".

[0025] Furthermore, the present invention provides a parameter period for... Sampling was performed to calculate the minimum distance between adjacent centerlines on the same floor. And based on this, the minimum gap between adjacent steel wire entities in the same layer is obtained. .

[0026] During the design phase, a target minimum gap threshold is introduced. (Used to meet manufacturing tolerances, assembly clearance allowables, and other process requirements, this part is not discussed in this patent), constructing a parameter iteration process of "calculation—judgment—adjustment—recalculation": first perform feasibility optimization to make... Then perform threshold approximation iterations to ensure the design results meet the requirements. As close as possible under the premise This enables the output of parameters for the target minimum gap threshold.

[0027] Effect verification To verify the effectiveness of the proposed method for designing adjustable minimum gaps between adjacent wires in a circular cross-section wire coil based on the normal plane section method, a set of existing circular cross-section wire coil structural parameters were selected as the initial scheme, and a three-dimensional geometric model was built using Siemens NX (UG) for comparative verification. The verification approach is as follows: given a target minimum gap threshold... g Under the condition of 0=0, the structural parameters are designed using the method of this invention to obtain the desired result. g i ≥ g 0 and as close as possible to the threshold g The parameter combination is 0; then an interference check is performed in the UG model to verify the consistency between the "calculation judgment result" and the "3D geometric verification result".

[0028] The verification steps are as follows: (1) Set the minimum gap threshold for the target g 0=0, with "non-interference" as the feasibility boundary, parameter design is performed under this threshold constraint, and the output satisfies g i ≥ g 0 and as close as possible g 0 structural parameters; (2) Based on the output parameters of step (1), a three-dimensional model is established in UG, and the interference check function of UG is used to determine the interference of adjacent steel wires in the same layer to verify that they meet the non-interference requirement; (3) Based on the above scheme, the number of leads in each layer is increased.N i Add 1 to each parameter (keeping other parameters unchanged), rebuild the UG 3D model and perform an interference check; (4) Compare the minimum gap calculated by the present invention. g i The interference check results from UG confirm that the parameter scheme is near the non-interference boundary and is the optimal scheme. Further reducing the gap will lead to interference.

[0029] The inner diameter of the wire coil in the verification model is 267 mm. The initial structural parameters and the calculated minimum gap between layers are shown in Table 1. Table 1 shows the minimum gap between each layer. g i All values ​​are greater than 0, indicating that there may be room for further approximation of the target threshold under the premise of non-interference. Therefore, in g Under the 0=0 constraint, the parameters of the three-layer winding were optimized using the iterative method of this invention. The optimized structural parameters and UG interference check results are shown in Table 2. Table 2 shows that the minimum gap between each layer is significantly reduced after optimization, and the UG verification results are all "non-interference," indicating that the method of this invention can satisfy the following conditions. g i ≥ g Under the condition of 0, the design parameters are iterated until they approach the non-interference boundary.

[0030] Table 1 Initial parameters and calculation results of minimum gap in the same layer for circular cross-section steel wire rings.

[0031] Table 2. Structural parameters, minimum gap between adjacent steel wires in the same layer, and UG interference results after optimization by the method of the present invention.

[0032] Furthermore, the number of leads for each layer in Table 2... N i Each parameter was increased by 1 to obtain the boundary check parameters, which were then verified. The results are shown in Table 3. Table 3 shows that the minimum gap calculated by this invention at this point... g i When the value becomes negative, the UG interference check also shows "interference", indicating that the test parameter has crossed the non-interference boundary.

[0033] Table 3 Validation of the optimized structural parameters of this invention

[0034] The comparison results in Tables 1-3 show that the minimum gap calculation and parameter iterative design of the present invention can be consistent with the verification results of the three-dimensional geometric model, and can stably push the parameters close to the boundary position under the target threshold constraint, thus providing a reliable basis for the parameter design and feasibility judgment of the circular cross-section steel wire ring.

[0035] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention, and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for designing parameters of a circular cross-section wire ring under the constraint of minimum clearance based on the normal plane section method, characterized in that, The specific steps include: Step 1: Input design parameters to obtain the parameter set of the circular cross-section wire ring and the target minimum gap threshold; Step 2: Establish the parametric equations for the centerline of the wound steel wire; Step 3: Calculate the tangent vector and construct the normal plane; Step 4: Find the intersection of the normal plane with the adjacent steel wires in the same layer, substitute the adjacent center lines, and establish a univariate equation about the angle difference; Step 5: Numerically solve for the angle difference, select valid intersection points, and calculate the minimum distance of the cross section; Step 6: Sample and calculate the global minimum centerline distance within one cycle; Step 7: Calculate the minimum wire gap and determine its feasibility and make necessary repairs; Step 8: Under the premise that the minimum gap is not less than the target minimum gap threshold, continue to iterate the parameters to make the obtained minimum gap as close as possible to the target minimum gap threshold, and output the design parameters of the circular cross-section wire ring.

2. The method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method according to claim 1, characterized in that, In step 3, the tangent vector is obtained by taking the derivative with respect to the centerline, and then the normal plane is constructed using the tangent vector as the normal vector.

3. The method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method according to claim 1, characterized in that, In step 4, the points on the trajectory equations of the center lines of adjacent circles in the same layer are substituted into the plane equation and rearranged to obtain a univariate equation for the difference in rotation angle.

4. The method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method according to claim 1, characterized in that, In step 5, the fixed turning angle is solved within a preset interval to obtain a solution set. For each root, candidate intersection points are constructed, candidate distances are calculated, and the smallest one is taken as the minimum cross-sectional distance under the normal plane.

5. The method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method according to claim 1, characterized in that, In step 6, the corner is sampled within one cycle, and steps 3 to 5 are repeated to obtain the minimum distance between the center lines of adjacent steel wires in the same layer.

6. The method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method according to claim 1, characterized in that, In step 7, the minimum gap between adjacent steel wires in the same layer is calculated. If the minimum gap between adjacent steel wires in the same layer is greater than or equal to the threshold of the minimum gap between adjacent targets in the same layer, then proceed to step 8. If the minimum gap between adjacent steel wires in the same layer is less than the threshold of the minimum gap between adjacent targets in the same layer, then parameter repair is performed. The number of leads is reduced by step size first, and steps 2 to 7 are repeated to recalculate the minimum gap between adjacent steel wires in the same layer.

7. The method for designing parameters of a circular cross-section wire ring under the target minimum clearance constraint based on the normal plane section method according to claim 6, characterized in that, In step 7, set the first Layer lead number lower limit As a non-empty constraint; when It has dropped to There is still a minimum gap between adjacent steel wires in the same layer. Minimum gap threshold between adjacent targets in the same layer When, decrease the first Number of winding turns And repeat the calculation until you get... Or reach the preset minimum limit.

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