Method for acquiring the relationship between bending radius and different offset distances of free bending forming of a catheter

Abstract

This invention discloses a method for fitting the bending radius relationship under different eccentricities during free bending of a catheter, relating to the field of three-dimensional free bending technology for catheters. The method includes obtaining the fitting relationship between different eccentricities (U) and bending radii (R) in a single direction, a U-R bending test fitting method in the positive Y-axis direction of the bending mold, and fitting methods in different directions. The U-R relationship data in the positive Y-axis direction is obtained through experiments, and a precise U-R relationship is obtained through function curve fitting. Several sets of bending tests are performed in the x-y plane to obtain the influence coefficient k due to catheter material parameters and mold parameters. By curve fitting of k values ​​in different directions, a fitting function for the influence coefficient k in the x-y plane is obtained. The U-R relationship function provided by the method of this invention can reduce the deviation of the bending component in different directions and improve the efficiency of three-dimensional free bending forming.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional free bending technology for pipes, specifically a method for fitting the relationship between bending radii under different offsets in the free bending of conduits. Background Technology

[0002] With the rapid technological advancements in aerospace, nuclear engineering, and automotive fields, lightweight design of equipment structures has become a key development direction. Spatially complex curved components are widely used in high-tech industries such as aviation, aerospace, and automotive for crucial applications including heat transfer, media transport, structural load-bearing, and mechanism separation. The required high-performance spatially complex curved components typically possess significant geometric features such as complex three-dimensional axes, continuously variable curvature radii, or multiple curvature radii, leading to increased manufacturing challenges. Conventional manufacturing techniques struggle to achieve precise one-time forming of these spatially complex curved components, often requiring segmented approximate forming followed by welding. This results in low axial and cross-sectional accuracy, diverse defect types, and difficulty in simultaneously meeting the comprehensive requirements of precise overall forming of three-dimensional continuously variable curvature components, minimal cross-sectional distortion, and low wall thickness reduction rates. Furthermore, the inherent limitations of conventional manufacturing techniques lead to excessive redundancy in equipment piping structure design, making it difficult to guarantee crucial indicators such as development cycle, space utilization, system functionality, and service life, and increasing equipment safety risks. These problems severely restrict the research, development, and engineering application of critical equipment across various industries. Therefore, there is an urgent need to study the overall precision forming technology of three-dimensional complex curved components with strong adaptability to spatial shape and high manufacturing precision.

[0003] Three-dimensional free bending forming technology combines multi-axis servo linkage control technology with plastic forming technology in free bending equipment. It achieves flexible bending forming of pipes by dynamically adjusting the spatial posture of the forming mechanism and simultaneously combining it with the axial feed of the tube blank. However, different pipe materials exhibit significant differences in mechanical properties and anisotropy. Furthermore, due to the low precision of the equipment molds and the influence of gravity on the pipe material, the bending radius corresponding to the same eccentricity varies in different directions during bending experiments. Therefore, obtaining an accurate UR relationship is crucial for the overall forming and accuracy of the pipe. Summary of the Invention

[0004] The purpose of this invention is to provide a method for fitting the relationship between bending radii under different offsets in the free bending and forming of a catheter, so as to solve the problems in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for fitting the bending radius relationship under different offsets in the free bending and forming of the conduit includes function fitting of the UR relationship in a single direction and fitting function of the scaling factor k in each direction on the XY plane;

[0007] The UR relationship is the relationship between the bending die eccentricity U and the pipe bending radius R, as shown in the following equation: ;

[0008] The expression for the bending radius of pipes can be represented by an exponential function model, an inverse proportional function model, and a binary exponential function model. Where a, b, c, and d are function coefficients; through free bending forming experiments, the bending radius of the pipe corresponding to different bending die eccentricities is obtained, and the function in the formula is used to fit the data to obtain the value of the function coefficients.

[0009] Based on the above technical solutions, the present invention also provides the following optional technical solutions:

[0010] In the optional scheme: the scaling factor k in each direction on the XY plane is the ratio to the bending die eccentricity U corresponding to the bending radius R of the same pipe;

[0011] The expression for the scaling factor k is: ,in, The bending die eccentricity in one direction. The eccentricity of the bending die under the same pipe bending radius. It ranges from 0 to 360°.

[0012] In the alternative scheme: the fitting function for the scaling factor k is: The scaling factor fitting function is expressed as a third-order polynomial function model and an Ellipse model: Where a, b, c, and d are function coefficients, which can be obtained through curve fitting;

[0013] By conducting free bending forming experiments in different directions, the ratio of bending die eccentricity U corresponding to the bending radius R of the same pipe is obtained. The data is then fitted using the function in the formula to obtain the value of the function coefficient.

[0014] In the alternative: the modified UR relation expression is: .

[0015] In the optional solution: pipe bending radius fitting function This includes multivariate exponential functions and multivariate power functions.

[0016] Among the alternatives: scaling factor fitting function This includes functions of circles and functions of multi-order polynomials.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] 1. This invention addresses existing problems by providing a UR relationship function that can reduce the deviation of bending components in different directions and improve the efficiency of three-dimensional free bending forming. Attached Figure Description

[0019] Figure 1 For the present invention Fitting diagram;

[0020] Figure 2 For the present invention The fitting diagram shows the value of k projected onto the y-axis of the plane, and kx is the value of k projected onto the x-axis of the plane. For ease of fitting, k is divided into projections along the x and y directions. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0022] The purpose of this invention is to provide a precise fitting method for obtaining the relationship between the bending radius and the three-dimensional free bending forming of a conduit under different offsets. This method can obtain an accurate UR relationship, which can improve efficiency and save costs in optimizing the process of different bending components.

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0024] Example 1

[0025] The first step is to select a stainless steel pipe with an outer diameter of 6mm and conduct a single-bend test of the conduit plane under different bending eccentricities in the positive Y-axis direction. The maximum eccentricity Umax is set to D / 2mm, the minimum eccentricity Umin is set to 1mm, the test interval is set to 0.2-2mm, and the number of test groups is not less than 10 groups.

[0026] The second step, after completing the bending test, involves measuring the bending radius R at three points on the stable forming section and taking the average value. The corresponding UR data are as follows: U=1mm, R=1704mm; U=2mm, R=853mm; U=3mm, R=569mm; U=4mm, R=427mm; U=5mm, R=342mm; U=6mm, R=286mm; U=7mm, R=245mm; U=8mm, R=215mm; U=9mm, R=191mm; U=10mm, R=172mm; U=11mm, R=157mm; U=12mm, R=144mm.

[0027] The third step is to use the formula. By fitting the bending eccentricity U and bending radius R data, and selecting a function with a fitting accuracy ≥99.8%, the UR relationship in the positive Y-axis direction is obtained, as shown below. Figure 1 The figure shows the relationship between eccentricity U and 1 / R. We obtain...

[0028] Fourth, conduct bending tests in various directions of the XY plane, and calculate the scaling factor k according to formula (3): For ease of fitting, the projections of the scaling factor k at each angle onto the x and y axes are kx and ky, respectively.

[0029] according to By fitting the data, the scaling factor fitting function is obtained. Expressions. For example... Figure 2 As shown, we obtain

[0030] Fifth step, according to The UR relationship in the positive Y-axis direction is fitted with the scaling factor function. The product yields the exact UR relationship:

[0031]

[0032] Example 2

[0033] The first step is to select a welded pipe with an outer diameter of 30mm, place the weld in the positive Y-axis direction, and conduct a single-bend test of the conduit plane under different bending eccentricities in the positive Y-axis direction. The maximum eccentricity Umax is set to D / 2mm, and the minimum eccentricity Umin is set to 1mm.

[0034] The second step, after completing the bending test, involves measuring the bending radius R at three points on the stable forming section and taking the average value. The corresponding UR data are as follows: U=1mm, R=2754mm; U=2mm, R=1001mm; U=3mm, R=763mm; U=4mm, R=647mm; U=5mm, R=542mm; U=6mm, R=346mm; U=7mm, R=285mm; U=8mm, R=235mm; U=9mm, R=201mm; U=10mm, R=172mm; U=11mm, R=157mm; U=12mm, R=154mm.

[0035] The third step is to use the formula. The bending eccentricity U and bending radius R data are fitted, and a function with a fitting accuracy ≥99.8% is selected to obtain the UR relationship in the positive Y-axis direction. See step 3 of the embodiment.

[0036] The fourth step is to conduct bending tests in various directions of the XY plane, according to formula (3). Calculate the scaling factor k:

[0037] .

[0038] Based on the third-order polynomial function model and the Ellipse model By fitting the data, the scaling factor fitting function is obtained. Expression. As in the calculation method of step four in Example 1.

[0039] Fifth step, according to The UR relationship in the positive Y-axis direction is fitted with the scaling factor function. The product is used to obtain the accurate UR relationship. This is the calculation method in step five of Example 1.

[0040] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for fitting the relationship between bending radii under different offsets during free bending of a conduit, characterized in that, This includes function fitting of the UR relationship in a single direction and function fitting of the scaling factor k in each direction on the XY plane; The UR relationship is the relationship between the bending die eccentricity U and the pipe bending radius R, as shown in the following equation: ; The expression for the bending radius of pipes can be represented by an exponential function model, an inverse proportional function model, and a binary exponential function model. Where a, b, c, and d are function coefficients; through free bending forming experiments, the corresponding pipe bending radii under different bending die eccentricities are obtained, and the function in the formula is used to fit the data to obtain the values ​​of the function coefficients; The scaling factor k in each direction on the XY plane is the ratio of the bending die eccentricity U corresponding to the bending radius R of the same pipe. The expression for the scaling factor k is: ,in, The bending die eccentricity in one direction. The eccentricity of the bending die under the same pipe bending radius. 0-360°; The fitting function for the scaling factor k is: The scaling factor fitting function is expressed as a third-order polynomial function model and an Ellipse model: Where a, b, c, and d are function coefficients; By conducting free bending forming experiments in different directions, the ratio of bending die eccentricity U corresponding to the bending radius R of the same pipe was obtained. The data was fitted using the function in the formula to obtain the value of the function coefficient. The revised UR relation expression is as follows: .

2. The method for fitting the relationship between bending radii under different offsets during free bending of a conduit, as described in claim 1, is characterized in that... Pipe bending radius fitting function This includes multivariate exponential functions and multivariate power functions.

3. The method for fitting the relationship between bending radii under different offsets during free bending of a conduit, as described in claim 1, is characterized in that... Scale factor fitting function This includes functions of circles and functions of multi-order polynomials.

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