Reachability calculation method for flexible stretch bending die of profile

By establishing a multi-objective constraint equation in the flexible bending mold of the profile, the accessibility of the mold is solved, and the problem of unclear profile molding range is achieved, and the accurate judgment of the profile molding is achieved.

CN119720571APending Publication Date: 2025-03-28AVIC XIAN AIRCRAFT IND GRP CO LTD
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Patent Information

Application Number
CN202411857726.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-17
Publication Date
2025-03-28

AI Technical Summary

Technical Problem

The flexible bending mold of the profile is not clear about the molding range of the profile due to the original mold configuration size and the flexible unit movement stroke.

Method used

A method for calculating the accessibility of a flexible bending mold of a profile is provided. By determining the minimum radius, envelope angle, number of flexible units and maximum stroke of the mold, as well as the radius and envelope angle of the profile parts, a multi-objective constraint equation is established to determine whether the profile can be molded based on the mold.

Benefits of technology

Through this calculation method, it is possible to determine the reachable range of the flexible bending mold of the profile, determine whether the profile can be formed, avoid errors in later engineering practice, and provide a positive approach to reachability judgment.

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Abstract

The invention discloses a reachability calculation method for a profile flexible stretch-bending die, which comprises the following steps of: 1, determining the minimum radius and the enveloping angle of the profile flexible stretch-bending die based on the structure of the profile flexible stretch-bending die; secondly, the number and the maximum stroke of flexible units of the profile flexible stretch-bending die are determined based on the structure of the profile flexible stretch-bending die; 3, according to the minimum radius, the enveloping angle, the number of flexible units and the maximum stroke of the profile flexible stretch-bending die and the radius and the enveloping angle of the profile part, a multi-target constraint equation of the profile flexible stretch-bending die is established; and 4, based on the established multi-target constraint equation of the profile flexible stretch-bending die, the accessibility of the profile flexible stretch-bending die is determined, and whether a profile part can be formed based on the profile flexible stretch-bending die or not is judged. According to the technical scheme, the problem that due to the fact that a profile flexible stretch-bending die is limited by the original die configuration size and the flexible unit movement stroke, the profile forming range of the profile flexible stretch-bending die is not clear is solved.
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Description

Technical Field

[0001] The present invention relates to but is not limited to the field of flexible drawing and bending dies for profiles, and in particular to a method for calculating the accessibility of flexible drawing and bending dies for profiles. Background Art

[0002] With the development of manufacturing industry, the curvature of profile structure is complex and the cross-section is changeable. Traditional rigid molds can no longer meet the diversified and personalized production needs of profiles. With its powerful cross-sectional shape and curvature adaptive capabilities, flexible bending molds for profiles can quickly reconstruct the mold surface, thereby processing a variety of cross-sectional profiles, effectively shortening mold design, debugging and production time, providing a flexible and efficient solution for the manufacture of complex structure profiles, and realizing the rapid and precise manufacture of three-dimensional bending of profiles. It is widely used in high-end manufacturing fields such as automobiles, high-speed railways and aircraft.

[0003] Profile flexible bending dies have shown great advantages in achieving complex shapes of profiles, reducing the number of dies, and improving production efficiency, but there are still certain problems in the forming range. Profile flexible bending dies are restricted by the original die configuration size and the flexible unit motion stroke, and it is impossible to apply to all bending shapes of profiles, which makes the profile flexible bending dies unclear about the forming range of profiles. Summary of the invention

[0004] Purpose of the present invention: In order to solve the above-mentioned technical problems, an embodiment of the present invention provides a method for calculating the accessibility of a flexible stretch-bending die for a profile, so as to solve the problem that the flexible stretch-bending die for the profile has unclear forming range of the profile due to the constraints of the original die configuration size and the movement stroke of the flexible unit.

[0005] The technical solution of the present invention: The embodiment of the present invention provides a method for calculating the accessibility of a profile flexible drawing and bending die, comprising the following steps:

[0006] Step 1: Based on the structure of the profile flexible drawing and bending die, determine the minimum radius and envelope angle of the profile flexible drawing and bending die;

[0007] Step 2: Based on the structure of the profile flexible drawing and bending die, determine the number of flexible units and the maximum stroke of the profile flexible drawing and bending die;

[0008] Step 3, according to the minimum radius, envelope angle, number of flexible units and maximum stroke of the profile flexible stretch-bending die, as well as the radius and envelope angle of the profile parts, a multi-objective constraint equation of the profile flexible stretch-bending die is established;

[0009] Step 4: Based on the established multi-objective constraint equation of the profile flexible stretch-bending die, determine the accessibility of the profile flexible stretch-bending die and judge whether the profile part can be formed based on the profile flexible stretch-bending die.

[0010] Optionally, in the above-mentioned accessibility calculation method of a flexible drawing and bending die for a profile, the overall structure of the flexible drawing and bending die for the profile is a fan-shaped ring structure, and a plurality of flexible units in a radial direction are evenly arranged along the circumference of the fan-shaped ring structure, and each flexible unit is used to move in the radial direction, and the step one includes:

[0011] The minimum radius of the fan-shaped ring structure of the profile flexible drawing and bending die is determined as the radius corresponding to the starting position of each flexible unit in the radial direction, and the angle between the flexible units on both sides is determined as the envelope angle.

[0012] Optionally, in the reachability calculation method of a profile flexible stretch-bending die as described above, the multi-objective constraint equation of the profile flexible stretch-bending die established in step three includes: a constraint equation based on the profile part size and a constraint equation based on the profile part process.

[0013] Optionally, in the above-mentioned method for calculating the accessibility of a profile flexible stretch-bending die, the step three comprises:

[0014] The intersection of the outer arc line of the profile flexible stretch-bending die in the fan-shaped ring structure and the central axis is taken as the origin of the coordinate system, the central axis is taken as the Y-axis, and the tangent at the intersection is taken as the X-axis. The Cartesian coordinate system of the profile flexible stretch-bending die is established, and the shape equation group of the profile flexible stretch-bending die is obtained in the Cartesian coordinate system, thereby establishing the multi-objective constraint equation of the profile flexible stretch-bending die.

[0015] Optionally, in the above-mentioned method for calculating the accessibility of a flexible bending die for a profile, the method of obtaining the shape equation group of the flexible bending die for the profile in a Cartesian coordinate system in step 3 includes:

[0016] The shape equations of the profile flexible bending die include:

[0017]

[0018] Among them, x1 and y1 are any points on the outer arc line of the profile flexible bending die fan ring structure, x2 and y2 are any points on the inner arc line of the profile flexible bending die fan ring structure, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die;

[0019] By substituting the radius and envelope angle of the profile part into the shape equation group of the flexible stretch-bending die of the profile, it is determined whether the profile part to be formed is constrained within the range of the profile that can be formed by the flexible stretch-bending die, which is limited by the minimum radius of the flexible stretch-bending die, the envelope angle and the maximum stroke of the flexible unit of the profile flexible stretch-bending die, and the constraint equations based on the size of the profile part and the constraint equations based on the process of the profile part are established.

[0020] Optionally, in the above-mentioned method for calculating the accessibility of a profile flexible stretch-bending die, the constraint equation based on the profile part size established in step 3 includes:

[0021] The upper limit equation of mold accessibility is:

[0022]

[0023] The lower limit equation of mold accessibility is:

[0024]

[0025] The left limit equation of mold accessibility is:

[0026]

[0027] The right limit equation of mold accessibility is:

[0028]

[0029] Among them, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die, α is the envelope angle of the profile flexible stretch-bending die, α0 is the envelope angle of the profile part, and R0 is the radius of the profile part.

[0030] Optionally, in the above-mentioned method for calculating the accessibility of a profile flexible stretch-bending die, in the step three,

[0031] The constraint equation established based on the profile part process is:

[0032]

[0033] Among them, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die, α is the envelope angle of the profile flexible stretch-bending die, α0 is the envelope angle of the profile part, and R0 is the radius of the profile part.

[0034] Optionally, in the accessibility calculation method of a flexible stretch-bending die for a profile as described above, the accessibility of the flexible stretch-bending die for the profile in step four refers to: the parameter range of the profile part prepared using the flexible stretch-bending die for the profile, including: the radius range and envelope angle range of the profile part.

[0035] Optionally, in the above-mentioned method for calculating the accessibility of a profile flexible stretch-bending die, in the step 4,

[0036] Based on the given radius of the profile part, the envelope angle range of the profile part is obtained by using the multi-objective constraint equation of the profile flexible stretch-bending die; or,

[0037] Based on the given envelope angle of the profile part, the radius range of the profile part is obtained by using the multi-objective constraint equation of the profile flexible stretch-bending die.

[0038] Beneficial effects of the present invention: An embodiment of the present invention provides a method for calculating the accessibility of a flexible stretch-bending die for a profile. In view of the current unknown accessibility problem of the flexible stretch-bending die for a profile, the embodiment of the present invention first determines the minimum radius and envelope angle of the flexible stretch-bending die for the profile based on the structure of the flexible stretch-bending die for the profile, and determines the maximum stroke of the flexible unit of the flexible stretch-bending die for the profile; secondly, according to the determined minimum radius, envelope angle, number of flexible units and maximum stroke of the flexible stretch-bending die for the profile, as well as the radius and envelope angle of the profile parts, a multi-objective constraint equation for the flexible stretch-bending die for the profile is established; thereby determining the reachable range of the profile stretch-bending die through the multi-objective constraint equation, and judging whether the profile can be formed based on the flexible stretch-bending die for the profile. The technical solution provided by the embodiment of the present invention is a positive method for determining the accessibility of the flexible stretch-bending die for a profile, which avoids errors in later engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The accompanying drawings are used to provide a further understanding of the technical solution of the present invention and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present invention and do not constitute a limitation on the technical solution of the present invention.

[0040] Figure 1 A schematic flow chart of a method for calculating the accessibility of a profile flexible stretch-bending die provided in an embodiment of the present invention;

[0041] Figure 2 Schematic diagram of the structure and coordinate system of the flexible bending die for fan-shaped annular profiles in an embodiment of the present invention;

[0042] Figure 3 A diagram showing the change of the upper and lower limits of the profile flexible bending die along with the envelope angle of the profile part in an embodiment of the present invention;

[0043] Figure 4 It is a diagram showing the change of the left and right limits of the profile flexible bending die along with the envelope angle of the profile part in the embodiment of the present invention;

[0044] Figure 5 This is a diagram showing how the process limit of the profile flexible stretch-bending die changes with the envelope angle of the profile part in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the present invention more clear, the embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other arbitrarily without conflict.

[0046] The above background technology has already explained the advantages of the profile flexible bending die and its wide application scenarios in various manufacturing fields. However, the profile flexible bending die is subject to the original die configuration size and the flexible unit movement stroke, so it has the problem of unclear profile forming range.

[0047] Based on the above problems, the accessibility of the profile flexible drawing and bending die can be considered when designing the profile flexible drawing and bending die to ensure that the designed profile flexible drawing and bending die can meet the forming requirements of the profile. According to this design idea, the present invention proposes a method for calculating the accessibility of the profile flexible drawing and bending die.

[0048] The present invention provides the following specific embodiments which can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0049] Figure 1 A schematic diagram of a flow chart of a method for calculating the accessibility of a profile flexible bending die provided by an embodiment of the present invention, such as Figure 1 As shown, a method for calculating the accessibility of a profile flexible bending die provided by an embodiment of the present invention comprises the following steps:

[0050] Step 1: Based on the structure of the profile flexible drawing and bending die, determine the minimum radius and envelope angle of the profile flexible drawing and bending die;

[0051] Step 2: Based on the structure of the profile flexible drawing and bending die, determine the maximum stroke of the flexible unit of the profile flexible drawing and bending die;

[0052] Step 3, according to the minimum radius, envelope angle, number of flexible units and maximum stroke of the profile flexible stretch-bending die, as well as the radius and envelope angle of the profile parts, a multi-objective constraint equation of the profile flexible stretch-bending die is established;

[0053] Step 4: Based on the established multi-objective constraint equation of the profile flexible stretch-bending die, determine the accessibility of the profile flexible stretch-bending die and judge whether the profile part can be formed based on the profile flexible stretch-bending die.

[0054] In one implementation of the embodiment of the present invention, the overall structure of the profile flexible drawing and bending die is set to be a fan-shaped ring structure, and a plurality of flexible units in the radial direction are evenly arranged along the circumference of the fan-shaped ring structure, and each flexible unit is used to move in the radial direction. The implementation method of the above step one specifically includes:

[0055] The minimum radius of the fan-shaped ring structure of the profile flexible drawing and bending die is determined as the radius corresponding to the starting position of each flexible unit in the radial direction, and the angle between the flexible units on both sides is determined as the envelope angle.

[0056] In this implementation, based on the overall structure of the profile flexible drawing and bending die being a fan-shaped structure, in step three, the specific method of establishing the multi-objective constraint equation of the profile flexible drawing and bending die including the constraint equation based on the profile part size and the constraint equation based on the profile part process is as follows:

[0057] The intersection of the outer arc line of the profile flexible stretch-bending die in the fan-shaped ring structure and the central axis is taken as the origin of the coordinate system, the central axis is taken as the Y-axis, and the tangent at the intersection is taken as the X-axis. The Cartesian coordinate system of the profile flexible stretch-bending die is established, and the shape equation group of the profile flexible stretch-bending die is obtained in the Cartesian coordinate system, thereby establishing the multi-objective constraint equation of the profile flexible stretch-bending die.

[0058] In a specific implementation, the method of obtaining the shape equation group of the profile flexible bending die in the Cartesian coordinate system in step 3 includes:

[0059] The shape equations of the profile flexible bending die include:

[0060]

[0061] Among them, x1 and y1 are any points on the outer arc line of the profile flexible bending die fan ring structure, x2 and y2 are any points on the inner arc line of the profile flexible bending die fan ring structure, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die;

[0062] By substituting the radius and envelope angle of the profile part into the shape equation group of the flexible stretch-bending die of the profile, it is determined whether the profile part to be formed is constrained within the range of the profile that can be formed by the flexible stretch-bending die, which is limited by the minimum radius of the flexible stretch-bending die, the envelope angle and the maximum stroke of the flexible unit of the profile flexible stretch-bending die, and the constraint equations based on the size of the profile part and the constraint equations based on the process of the profile part are established.

[0063] In the specific implementation, the constraint equation based on the profile part size established in step 3 includes:

[0064] The upper limit equation of mold accessibility is:

[0065]

[0066] The lower limit equation of mold accessibility is:

[0067]

[0068] The left limit equation of mold accessibility is:

[0069]

[0070] The right limit equation of mold accessibility is:

[0071]

[0072] Among them, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die, α is the envelope angle of the profile flexible stretch-bending die, α0 is the envelope angle of the profile part, and R0 is the radius of the profile part.

[0073] In addition, the constraint equation based on the profile part process established in step 3 is:

[0074]

[0075] Among them, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die, α is the envelope angle of the profile flexible stretch-bending die, α0 is the envelope angle of the profile part, and R0 is the radius of the profile part.

[0076] In one implementation of the embodiment of the present invention, the accessibility of the profile flexible drawing and bending die in the above step four refers to: the parameter range of the profile part prepared by the profile flexible drawing and bending die, including: the radius range and envelope angle range of the profile part.

[0077] In step 4 of this implementation method,

[0078] Based on the given radius of the profile part, the envelope angle range of the profile part is obtained by using the multi-objective constraint equation of the profile flexible stretch-bending die; or,

[0079] Based on the given envelope angle of the profile part, the radius range of the profile part is obtained by using the multi-objective constraint equation of the profile flexible stretch-bending die.

[0080] The present invention provides a method for calculating the accessibility of a flexible stretch-bending die for a profile. The embodiment of the present invention aims at the unknown accessibility problem of the current flexible stretch-bending die for a profile. First, based on the structure of the flexible stretch-bending die for the profile, the minimum radius and envelope angle of the flexible stretch-bending die for the profile are determined, as well as the maximum stroke of the flexible unit of the flexible stretch-bending die for the profile; secondly, according to the determined minimum radius, envelope angle, number of flexible units and maximum stroke of the flexible stretch-bending die for the profile, as well as the radius and envelope angle of the profile parts, a multi-objective constraint equation for the flexible stretch-bending die for the profile is established; thereby, the reachable range of the profile stretch-bending die is determined through the multi-objective constraint equation, and it is judged whether the profile can be formed based on the flexible stretch-bending die for the profile. The technical solution provided by the embodiment of the present invention is a positive method for determining the accessibility of the flexible stretch-bending die for a profile, which avoids errors in later engineering practice.

[0081] Application Examples

[0082] Figure 2 Schematic diagram of the flexible bending die structure and coordinate system of the fan-shaped ring profile in the embodiment of the present invention. In an application example of the embodiment of the present invention, Figure 2 The profile flexible bending die shown in the figure has a minimum radius R of the profile flexible bending die determined based on its fan-shaped ring structure. min The envelope angle α is 3700 mm, the flexible unit movement stroke l is 300 mm, and the profile radius R0 is 1500 mm. Based on the given radius of the profile part, the multi-objective constraint equation of the profile flexible bending die is used to obtain the envelope angle range of the profile part.

[0083] The upper limit equation of mold accessibility is:

[0084]

[0085] The lower limit equation of mold accessibility is:

[0086]

[0087] Figure 3 : is a graph showing the upper and lower limits of the profile flexible bending die according to the profile part envelope angle in the embodiment of the present invention. Figure 3 As shown, it can be seen that when the radius of the profile part is 1500mm, the envelope angle range of the profile part limited by the upper and lower limits of the profile flexible stretch-bending die is 10-90°.

[0088] The left limit equation of mold accessibility is:

[0089]

[0090] The right limit equation of mold accessibility is:

[0091]

[0092] Figure 4 : is a graph showing the change of the left and right limits of the profile flexible bending die with the envelope angle of the profile part in the embodiment of the present invention; Figure 4 As shown, it can be seen that when the radius of the profile part is 1500mm, the left and right limits of the profile flexible stretch-bending die do not impose any restrictions on the angle range of the profile part.

[0093] The constraint equation based on the profile part process is:

[0094]

[0095] Figure 5 : is a diagram showing the variation of the process limit of the profile flexible bending die with the envelope angle of the profile part in the embodiment of the present invention; Figure 5 As shown, it can be seen that when the radius of the profile part is 1500mm, the angle range of the profile part limited by the process limit of the profile flexible stretch-bending die is 10-110°.

[0096] Taking into account the upper, lower, left, right and process limits of the flexible stretch-bending die for profiles, when the radius of the profile part is 1500mm, the accessibility of the flexible stretch-bending die is that the envelope angle of the profile part is 10 to 90°.

[0097] Although the embodiments disclosed in the present invention are as above, the contents are only embodiments adopted to facilitate understanding of the present invention and are not intended to limit the present invention. Any technician in the field to which the present invention belongs can make any modifications and changes in the form and details of implementation without departing from the spirit and scope disclosed in the present invention, but the patent protection scope of the present invention shall still be subject to the scope defined in the attached claims.

Claims

1. A method for calculating the accessibility of a flexible bending die for a profile, characterized in that: include; Step 1: Based on the structure of the profile flexible drawing and bending die, determine the minimum radius and envelope angle of the profile flexible drawing and bending die; Step 2: Based on the structure of the profile flexible drawing and bending die, determine the maximum stroke of the flexible unit of the profile flexible drawing and bending die; Step 3, according to the minimum radius, envelope angle, number of flexible units and maximum stroke of the profile flexible stretch-bending die, as well as the radius and envelope angle of the profile parts, a multi-objective constraint equation of the profile flexible stretch-bending die is established; Step 4: Based on the established multi-objective constraint equation of the profile flexible stretch-bending die, determine the accessibility of the profile flexible stretch-bending die and judge whether the profile part can be formed based on the profile flexible stretch-bending die.

2. The method for calculating the accessibility of a profile flexible bending die according to claim 1, characterized in that: The overall structure of the profile flexible drawing and bending die is a fan-shaped ring structure, and a plurality of flexible units in the radial direction are evenly arranged along the circumference of the fan-shaped ring structure, and each flexible unit is used to move in the radial direction. The step one includes: The minimum radius of the fan-shaped ring structure of the profile flexible drawing and bending die is determined as the radius corresponding to the starting position of each flexible unit in the radial direction, and the angle between the flexible units on both sides is determined as the envelope angle.

3. The method for calculating the accessibility of a flexible bending die for a profile according to claim 2, characterized in that: The multi-objective constraint equation of the profile flexible stretch-bending die established in the step three includes: a constraint equation based on the profile part size and a constraint equation based on the profile part process.

4. The method for calculating the accessibility of a profile flexible bending die according to claim 3, characterized in that: The step three comprises: The intersection of the outer arc line of the profile flexible stretch-bending die in the fan-shaped ring structure and the central axis is taken as the origin of the coordinate system, the central axis is taken as the Y-axis, and the tangent at the intersection is taken as the X-axis. The Cartesian coordinate system of the profile flexible stretch-bending die is established, and the shape equation group of the profile flexible stretch-bending die is obtained in the Cartesian coordinate system, thereby establishing the multi-objective constraint equation of the profile flexible stretch-bending die.

5. The method for calculating the accessibility of a profile flexible bending die according to claim 4, characterized in that: The method of obtaining the shape equation group of the profile flexible bending die in the Cartesian coordinate system in step 3 includes: The shape equations of the profile flexible bending die include: Among them, x1 and y1 are any points on the outer arc line of the profile flexible bending die fan ring structure, x2 and y2 are any points on the inner arc line of the profile flexible bending die fan ring structure, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die; By substituting the radius and envelope angle of the profile part into the shape equation group of the flexible stretch-bending die of the profile, it is determined whether the profile part to be formed is constrained within the range of the profile that can be formed by the flexible stretch-bending die, which is limited by the minimum radius of the flexible stretch-bending die, the envelope angle and the maximum stroke of the flexible unit of the profile flexible stretch-bending die, and the constraint equations based on the size of the profile part and the constraint equations based on the process of the profile part are established.

6. The method for calculating the accessibility of a profile flexible bending die according to claim 4, characterized in that: The constraint equation based on the profile part size established in step 3 includes: The upper limit equation of mold accessibility is: The lower limit equation of mold accessibility is: The left limit equation of mold accessibility is: The right limit equation of mold accessibility is: Among them, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die, α is the envelope angle of the profile flexible stretch-bending die, α0 is the envelope angle of the profile part, and R0 is the radius of the profile part.

7. The method for calculating the accessibility of a profile flexible bending die according to claim 4, characterized in that: The constraint equation based on the profile part process established in step 3 is: Among them, R min is the minimum radius of the profile flexible stretch-bending die, l is the movement stroke of the flexible unit in the profile flexible stretch-bending die, α is the envelope angle of the profile flexible stretch-bending die, α0 is the envelope angle of the profile part, and R0 is the radius of the profile part.

8. A method for calculating the accessibility of a profile flexible drawing and bending die according to any one of claims 1 to 7, characterized in that: The accessibility of the profile flexible drawing and bending die in step 4 refers to: the parameter range of the profile part prepared by the profile flexible drawing and bending die, including: the radius range and envelope angle range of the profile part.

9. A method for calculating the accessibility of a profile flexible drawing and bending die according to any one of claims 1 to 7, characterized in that: In the step 4, Based on the given radius of the profile part, the envelope angle range of the profile part is obtained by using the multi-objective constraint equation of the profile flexible stretch-bending die; or, Based on the given envelope angle of the profile part, the radius range of the profile part is obtained by using the multi-objective constraint equation of the profile flexible stretch-bending die.