A method for equivalent of billet size deviation in coreless rod swaging simulation

Abstract

This invention relates to an equivalent method for simulating billet dimensional deviations in mandrel-less rotary forging, belonging to the field of metal plastic forming technology. The method includes the following steps: determining whether the mesh of the finite element simulation for mandrel-less rotary forging can handle billet dimensional deviations; establishing the relationship between radial feed and equivalent strain in mandrel-less rotary forging; equating the billet dimensional deviations to the equivalent deformation of the first mandrel-less rotary forging; and performing conventional rotary forging simulation by equating the billet dimensional deviations to the material properties of the billet. This invention achieves accurate simulation of mandrel-less rotary forging considering billet dimensional deviations by establishing an equivalent relationship between dimensional deviations and equivalent strains, while maintaining the accuracy and efficiency of finite element simulation.

Description

Technical Field

[0001] This invention relates to the field of metal plastic forming technology, and in particular to an equivalent method for simulating billet dimensional deviations in mandrel-less rotary forging simulation. Background Technology

[0002] Rotary forging is an advanced near-net-shape manufacturing process that uses high-frequency radial reciprocating motion to strike the workpiece, causing it to rotate and move axially. Under the impact of the hammer, the workpiece undergoes radial compression and length extension deformation. Rotary forging can be divided into mandrel-less rotary forging and mandrel-containing rotary forging. Mandrel-less rotary forging has no internal support and can form complex irregular structures with varying cross-sections, wall thicknesses, and inner diameters through multiple radial feeds. Due to the natural flow of metal on the inner surface, and with strict control of radial feed parameters, compared to the radial feed parameters of several millimeters in mandrel-containing forging, the radial feed amount in each pass of mandrel-less rotary forging is only a few tenths of a millimeter to 0.1 mm. Furthermore, the entire mandrel-less rotary forging process, from initial forging to finish forging, is completed through multiple passes and coordinated circumferential feed. Therefore, the formulation of feed process parameters for mandrel-less rotary forging and the control of the dimensions, mechanical properties, and deviations of the billet are key technologies for mandrel-less rotary forging. Mandrel-less rotary forging technology and its finite element simulation have become the core technology and technical challenge of rotary forging manufacturing.

[0003] Finite element method (FEM) simulation is a numerical computation method that performs mechanical analysis on discretized continuous structures as finite elements. It is used to solve stress, deformation, and multiphysics coupling problems in complex engineering structures. The core workflow of FEM includes three stages: preprocessing, solution calculation, and post-processing. A computational model composed of nodes and elements is constructed through mesh generation, and linear / nonlinear problems are solved by computer using stiffness matrix integration and boundary condition handling. Mesh generation in FEM simulation, which divides the model into many small elements, is a crucial part of the preprocessing stage. The degree of matching between the mesh and the computational objective, and the quality of the mesh, determine the quality of the subsequent FEM calculations.

[0004] In finite element method (FEM) simulations, the number of mesh elements affects both accuracy and computational workload. While the mesh does become finer as the minimum mesh size decreases, the number of mesh elements increases rapidly. Although accuracy improves to some extent, this leads to a significant, even geometrically, increase in computational cost. Determining the minimum mesh size in FEM simulations is a balance between accuracy and efficiency; the coarsest possible mesh should be used while ensuring the accuracy of the results. In engineering applications, the overall dimensions can be used as a reference. For smooth regions without singularities, the element size can be taken as 1 / 10 to 1 / 20 of the overall feature size of the model as a starting point. For fillets and holes, at least 2-3 layers of mesh elements are required.

[0005] Mandrel-less rotary forging falls within a relatively flat region lacking singularities. The radial feed parameters for mandrel-less rotary forging are typically from a few tenths of a millimeter to 0.1 mm, while the structural dimensions of the forged billet range from tens to hundreds of millimeters. In contrast, the minimum dimensional deviation of seamless steel pipe billets, according to standards, can be ±0.5 mm, ±0.3 mm, or ±0.1 mm, resulting in a post-forging dimensional accuracy of ±0.02 mm. Therefore, the minimum mesh size, radial feed rate, billet size, and billet dimensional deviation during mandrel-less rotary forging can vary by 2-3 orders of magnitude. Current finite element simulations cannot adequately handle these differences through mesh refinement alone; simplification is necessary to eliminate these magnitude differences, such as by disregarding structural dimensional deviations. Summary of the Invention

[0006] To address the technical problem that existing finite element simulations of mandrel-less rotary forging suffer from significant differences in the minimum mesh size, radial feed process parameters, and billet size deviation, making direct coordination difficult, this invention aims to provide a method that equates billet size deviation to changes in material mechanical properties. By establishing an equivalent relationship between size deviation and equivalent strain, accurate simulation of mandrel-less rotary forging considering billet size deviation can be achieved while maintaining the accuracy and efficiency of finite element simulation.

[0007] To achieve the above objectives, the technical solution of the present invention provides an equivalent method for billet size deviation in mandrel-less rotary forging simulation, which includes the following steps: determining whether the mesh of the finite element simulation of mandrel-less rotary forging can handle billet size deviation; establishing the relationship between radial feed and equivalent strain in mandrel-less rotary forging; equating the billet size deviation to the equivalent deformation of the first rotary forging in mandrel-less rotary forging; and performing conventional rotary forging simulation by equating the billet size deviation to the material properties of the billet.

[0008] Preferably, determining whether the mesh of the finite element simulation for mandrel-less rotary forging can handle the billet size deviation specifically includes: determining the minimum mesh size of the finite element simulation based on the billet structure shape and size, the accuracy and efficiency of the finite element simulation; comparing the minimum mesh size with the billet size deviation; if the billet size deviation is greater than the minimum mesh size, then the size deviation is directly handled by the minimum finite element mesh size; otherwise, it is determined that the billet size deviation cannot be directly handled by the minimum finite element mesh size, and equivalent processing is required.

[0009] Preferably, the relationship between radial feed and equivalent strain in mandrel-less rotary forging is established, specifically including: establishing a functional relationship between the equivalent strain of the i-th radial feed and the radial feed amount and equivalent radius based on the principal stress method. The equivalent strain is related to the billet wall thickness before the i-th rotary forging, the radial feed amount of the i-th rotary forging, the outer radius of the billet before the i-th rotary forging, and the outer radius of the billet after the i-th rotary forging.

[0010] Preferably, the dimensional deviation of the billet is equivalent to the equivalent deformation of the first mandrel-less rotary forging, specifically including: converting the dimensional deviation of the billet into the additional equivalent deformation of the first mandrel-less rotary forging; wherein, positive deviation is equivalent to increasing the radial feed of the first pass, negative deviation is equivalent to decreasing the radial feed of the first pass, and the equivalent deformation of subsequent rotary forging passes remains unchanged.

[0011] Preferably, the billet size deviation is equivalent to the material properties of the billet in the conventional rotary forging simulation, specifically including: according to the hardening function relationship of the material, the additional equivalent strain caused by the billet size deviation is equivalent to the pre-strain of the material; by adjusting the stress-strain function relationship, the size deviation is equivalent to the range of mechanical property changes of the billet, wherein positive deviation is equivalent to additional hardening of the material and negative deviation is equivalent to additional weakening of the material.

[0012] Preferably, the equivalent strain of the i-th radial feed is calculated using the following formula (1).

[0013] (1) Where, ε i b is the equivalent strain of the radial feed of the i-th mandrel-less rotary forging pass; i-1 t is the wall thickness of the billet before the i-th mandrel-less rotary forging pass; i r is the radial feed rate for the i-th mandrel-less rotary forging pass; i-1 r is the outer radius of the billet before the i-th mandrel-less rotary forging pass; i Let be the outer radius of the billet after the i-th mandrel-less rotary forging.

[0014] Preferably, when the billet size deviation is δ, it can be equivalent to the first equivalent strain of mandrel-less rotary forging, as shown in Equation (2). The equivalent strain of subsequent mandrel-less rotary forging is still calculated according to Equation (1).

[0015] (2) in, δ represents the equivalent strain of the radial feed in the first pass of mandrel-less rotary forging; b0 is the wall thickness of the mandrel-less rotary forging billet; t1 is the radial feed amount in the first pass of mandrel-less rotary forging; r0 is the outer radius of the billet in the mandrel-less rotary forging billet; r1 is the outer radius of the billet after the first pass of mandrel-less rotary forging; δ is the dimensional deviation of the billet, with positive deviations being positive and negative deviations being negative.

[0016] Preferably, the hardening function relationship of 25CrMo4 material is shown in equation (3). (3) In the formula: This represents the actual stress. To respond to real situations; This represents the pre-strain value.

[0017] Preferably, the stress-strain function relationship after considering the equivalent of the billet size deviation is as shown in equation (4). (4) Where σ is the actual stress of rotary forging; ε is the actual strain of rotary forging; ε0 is the pre-strain value; Δ is the equivalent material pre-strain caused by the billet size deviation; and ε1 is the first equivalent strain without considering the billet size deviation.

[0018] Preferably, the billet is a seamless steel pipe made of 25CrMo4, with a nominal outer diameter of 37mm. The mandrel-less rotary forging employs a multi-pass radial feed, including 3 passes of 0.5mm feed, 8 passes of 0.3mm feed, 8 passes of 0.2mm feed, and 2 passes of 0.1mm feed, to form complex shaft structures with variable cross-section, variable wall thickness, and variable inner diameter.

[0019] Compared with the prior art, the present invention has the following beneficial technical effects: This invention establishes an equivalent relationship between the billet size deviation and the material mechanical properties in mandrel-less rotary forging, which can solve the problem of magnitude differences between the minimum mesh size, feed process parameters, structural dimensions and their deviations in mandrel-less rotary forging simulation. It also provides a technical basis for handling the magnitude differences between structural dimensions, dimensional tolerances and minimum mesh size in finite element simulation.

[0020] This invention, combined with the manufacturing process of mandrel-less rotary forging, proposes an equivalent method for simulating billet size deviation in mandrel-less rotary forging by exploring the relationship between mandrel-less rotary forging deformation, radial feed parameters, billet size, and mechanical properties. This method can solve problems such as the order-of-magnitude differences between minimum mesh size, structural dimensions, and size deviations in mandrel-less rotary forging simulation. It provides a basis for the coordinated matching of mandrel-less rotary forging dimensions, mechanical properties, and their value ranges, and also provides a theoretical basis and technical reference for structural size deviations in other finite element simulations. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the dimensions and tolerances of the rotary forging billet in the equivalent method for simulating the dimensional deviation of the billet in the mandrel-less rotary forging simulation of the present invention; Figure 2 This is a schematic diagram of the nominal dimensions of the rotary forging product structure in the equivalent method for billet size deviation simulation of mandrel-less rotary forging according to the present invention; Figure 3 This is a flowchart of an equivalent method for simulating billet size deviation in mandrel-less rotary forging according to the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments 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.

[0023] This invention discloses an equivalent method for simulating billet size deviation in mandrel-less rotary forging.

[0024] A finite element simulation example of a rotary forging shaft with variable cross-section and wall thickness is provided. The material is 25CrMo4, and the forging billet is a seamless steel pipe. The yield strength of the billet material is less than 390 MPa, and the surface hardness is less than 190 HV. The structure and dimensions of the billet and the product are as follows: Figure 1 and Figure 2 As shown. The blank outer diameter tolerance of the rotary forging shaft is ±0.5mm, and the outer diameter tolerance of the product after rotary forging can reach ±0.02mm. The rotary forging process of this shaft includes mandrel-less rotary forging shaft section I, shaft section III, and mandrel-containing rotary forging shaft section II. This example focuses on the finite element simulation of mandrel-less rotary forging shaft section III. The mandrel-less rotary forging uses multi-pass radial feed of 0.5mm (3 feeds), 0.3mm (8 feeds), 0.2mm (8 feeds), and 0.1mm (2 feeds).

[0025] 1. Determine whether the mesh used in the finite element simulation of mandrel-less rotary forging can handle billet dimensional deviations. Based on the shape and size of the billet structure, and the accuracy and efficiency of finite element simulation, determine the minimum mesh size for finite element simulation. Compare the minimum mesh size with the billet size deviation. If the billet size deviation is much larger than the minimum mesh size (2-3 times), the size deviation can be directly handled by the minimum finite element mesh size; otherwise, the billet size deviation cannot be directly handled by the minimum finite element mesh size.

[0026] In this example, the nominal size of the billet is 37mm, with a dimensional deviation of 0.5mm. The minimum mesh size that the finite element simulation of mandrel-less rotary forging can handle is between 0.2-0.7mm. This minimum mesh size is almost identical to the dimensional deviation of the rotary forging billet and is significantly larger than the minimum radial feed of 0.1mm and the product dimensional tolerance of ±0.02mm in mandrel-less rotary forging. Therefore, the dimensional deviation cannot be directly handled by the finite element mesh size in this example; an equivalent treatment of the billet's dimensional deviation is required.

[0027] 2. Establish the relationship between radial feed and equivalent strain in mandrel-less rotary forging. In the radial feed process of mandrel-less rotary forging, the equivalent strain of rotary forging generated by each radial feed can be solved by the principal stress method. For the mandrel-less rotary forging process, the functional relationship between the equivalent strain of the i-th radial feed and the radial feed amount and the equivalent radius is shown in Equation (1). (1) Where: ε i b is the equivalent strain of the radial feed of the i-th mandrel-less rotary forging pass; i-1 t is the wall thickness of the billet before the i-th mandrel-less rotary forging pass; i r is the radial feed rate for the i-th mandrel-less rotary forging pass; i-1 r is the outer radius of the billet before the i-th mandrel-less rotary forging pass; i Let be the outer radius of the billet after the i-th mandrel-less rotary forging.

[0028] 3. Equivalently represent the dimensional deviations of the billet to the equivalent deformation of the first rotary forging without a mandrel. In mandrel-free rotary forging, the die completes the radial feed motion according to its geometric position. From the perspective of the billet's geometric position, the billet's dimensional deviation changes the initial radial feed amount in mandrel-free rotary forging; positive deviation increases the feed, and negative deviation decreases the feed. Moreover, the billet's dimensional deviation does not affect subsequent mandrel-free rotary forging. From the perspective of the billet's mechanical properties, the deviation is equivalent to additional hardening of the material during rotary forging; positive deviation increases the billet's mechanical properties, and negative deviation decreases them. Based on the hardening characteristics of mandrel-free rotary forging, the billet's dimensional deviation can be translated into changes in the billet's mechanical properties, and the dimensional deviation can be distributed according to the range of values ​​for the billet's mechanical properties.

[0029] In this example, when the billet size deviation is δ, it can be equivalent to the first equivalent strain of mandrel-less rotary forging, as shown in Equation (2). The equivalent strain of subsequent mandrel-less rotary forging is still calculated according to Equation (1).

[0030] (2) In the formula: δ represents the equivalent strain of the radial feed in the first pass of mandrel-less rotary forging; b0 is the wall thickness of the mandrel-less rotary forging billet; t1 is the radial feed amount in the first pass of mandrel-less rotary forging; r0 is the outer radius of the billet in the mandrel-less rotary forging billet; r1 is the outer radius of the billet after the first pass of mandrel-less rotary forging; δ is the dimensional deviation of the billet, with positive deviations being positive and negative deviations being negative.

[0031] 4. Simulate conventional rotary forging by equating the billet dimensional deviations to the billet's material properties. By combining the material hardening relationship and the equivalent strain of dimensional deviations in mandrel-less rotary forging billets, and through the equivalent strain of the initial radial feed of the mandrel-less forging billet, the dimensional deviations of the billet can be equated to the range of changes in the billet's mechanical properties, allowing for conventional mesh generation and finite element simulation. Since the mechanical properties of the billet are independent of the mesh, the equivalence of the mechanical properties of the billet deviations resolves the order-of-magnitude scale problem between dimensional deviations and structural dimensions, and minimum mesh size, in finite element simulation. In the equivalence process of billet deviations, positive deviations are taken as positive, equivalent to additional hardening of the billet material properties; negative deviations are taken as negative, equivalent to additional weakening of the billet material.

[0032] For this example, the hardening function relationship of 25CrMo4 material is shown in equation (3).

[0033] (3) In the formula: This represents the actual stress. To respond to real situations; This represents the pre-strain value.

[0034] The stress-strain function relationship after considering the equivalent deviation of the billet size is shown in equation (4).

[0035] (4) In the formula: σ is the actual stress of rotary forging; ε is the actual strain of rotary forging; ε0 is the pre-strain value; Δ is the equivalent material pre-strain caused by the billet size deviation; ε1 is the first equivalent strain without considering the billet size deviation.

[0036] In this example, if the billet outer diameter deviation reaches a maximum of 0.5 mm, under the same feed parameters, it is equivalent to an additional 0.25 mm of radial feed and a 4.39% increase in necking. In this case, this is equivalent to an additional micro-strain of 150 mm. The dimensional deviation is equivalent to an increase in hardness of approximately 5 HV and an increase in strength of approximately 30 MPa. By using the stress-strain relationship after hardening for finite element simulation, the billet dimensional deviation can be equated to the billet's mechanical properties, thus resolving the billet dimensional deviation effect in the finite element simulation.

[0037] By applying the billet size deviation to calculate the equivalent feed and equivalent additional strain in mandrel-less rotary forging, the billet size deviation can be equated to the equivalent stress-strain function of the billet material. This achieves the equivalent mechanical properties of the billet size deviation in mandrel-less rotary forging simulation. A flowchart of the billet size deviation equivalence method for mandrel-less rotary forging simulation according to this invention is shown below. Figure 3 As shown.

[0038] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for simulating billet dimensional deviations in mandrel-less rotary forging simulation, characterized in that, The steps include: determining whether the mesh of the finite element simulation of mandrel-less rotary forging can handle the billet size deviation; establishing the relationship between radial feed and equivalent strain in mandrel-less rotary forging; and equating the billet size deviation to the equivalent deformation of the first rotary forging of the mandrel. The dimensional deviation of the billet is equivalent to the material properties of the billet for conventional rotary forging simulation.

2. The equivalent method for billet size deviation simulation of mandrel-less rotary forging according to claim 1, characterized in that, Determining whether the mesh of the finite element simulation for mandrel-less rotary forging can handle the billet size deviation includes: determining the minimum mesh size of the finite element simulation based on the billet structure shape and size, and the accuracy and efficiency of the finite element simulation; comparing the minimum mesh size with the billet size deviation; if the billet size deviation is greater than the minimum mesh size, then the size deviation is directly handled by the minimum finite element mesh size; otherwise, it is determined that the billet size deviation cannot be directly handled by the minimum finite element mesh size, and equivalent processing is required.

3. The method for simulating billet dimensional deviations in mandrel-less rotary forging according to claim 2, characterized in that, Establish the relationship between radial feed and equivalent strain in mandrel-less rotary forging. Specifically, this includes: establishing a functional relationship between the equivalent strain of the i-th radial feed and the radial feed amount and equivalent radius based on the principal stress method. The equivalent strain is related to the billet wall thickness before the i-th rotary forging pass, the radial feed amount of the i-th rotary forging pass, the outer radius of the billet before the i-th rotary forging pass, and the outer radius of the billet after the i-th rotary forging pass.

4. The equivalent method for billet size deviation simulation of mandrel-less rotary forging according to claim 3, characterized in that, The dimensional deviation of the billet is equivalent to the equivalent deformation of the first mandrel-less rotary forging. Specifically, the dimensional deviation of the billet is converted into the additional equivalent deformation of the first mandrel-less rotary forging. Positive deviation is equivalent to increasing the radial feed of the first pass, negative deviation is equivalent to decreasing the radial feed of the first pass, and the equivalent deformation of subsequent rotary forging passes remains unchanged.

5. The equivalent method for billet size deviation simulation of mandrel-less rotary forging according to claim 4, characterized in that, The blank size deviation is equivalent to the material properties of the blank for conventional rotary forging simulation. Specifically, this includes: based on the material hardening function relationship, the additional equivalent strain caused by the blank size deviation is equivalent to the material pre-strain; by adjusting the stress-strain function relationship, the size deviation is equivalent to the range of mechanical property changes of the blank, where positive deviation is equivalent to additional material hardening and negative deviation is equivalent to additional material weakening.

6. The method for simulating billet dimensional deviations in mandrel-less rotary forging according to claim 5, characterized in that, The equivalent strain of the i-th radial feed is calculated by the following equation (1). （1） Where, ε i b is the equivalent strain of the radial feed of the i-th mandrel-less rotary forging pass; i-1 t is the wall thickness of the billet before the i-th mandrel-less rotary forging pass; i r is the radial feed rate for the i-th mandrel-less rotary forging pass; i-1 r is the outer radius of the billet before the i-th mandrel-less rotary forging pass; i Let be the outer radius of the billet after the i-th mandrel-less rotary forging.

7. The equivalent method for billet size deviation simulation of mandrel-less rotary forging according to claim 6, characterized in that, When the billet size deviation is δ, it can be equivalent to the first equivalent strain of mandrel-less rotary forging, as shown in Equation (2). The equivalent strain of subsequent mandrel-less rotary forging is still calculated according to Equation (1). （2） in, δ represents the equivalent strain of the radial feed in the first pass of mandrel-less rotary forging; b0 is the wall thickness of the mandrel-less rotary forging billet; t1 is the radial feed amount in the first pass of mandrel-less rotary forging; r0 is the outer radius of the billet in the mandrel-less rotary forging billet; r1 is the outer radius of the billet after the first pass of mandrel-less rotary forging; δ is the dimensional deviation of the billet, with positive deviations being positive and negative deviations being negative.

8. The method for simulating billet dimensional deviations in mandrel-less rotary forging according to claim 7, characterized in that, The hardening function relationship of 25CrMo4 material is shown in equation (3). （3） In the formula: This represents the actual stress. To respond to real situations; This represents the pre-strain value.

9. The equivalent method for billet size deviation simulation of mandrel-less rotary forging according to claim 8, characterized in that, The stress-strain function relationship after considering the equivalent of the billet size deviation is shown in equation (4). （4） Where σ is the actual stress of rotary forging; ε is the actual strain of rotary forging; ε0 is the pre-strain value; Δ is the equivalent material pre-strain caused by the billet size deviation; and ε1 is the first equivalent strain without considering the billet size deviation.

10. The equivalent method for billet size deviation simulation of mandrel-less rotary forging according to any one of claims 1-9, characterized in that, The billet is a seamless steel pipe made of 25CrMo4. The nominal outer diameter of the billet is 37mm. The mandrel-less rotary forging adopts a multi-pass radial feed, including 3 passes of 0.5mm feed, 8 passes of 0.3mm feed, 8 passes of 0.2mm feed, and 2 passes of 0.1mm feed, in order to form a complex shaft structure with variable cross-section, variable wall thickness, and variable inner diameter.

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