Application of numerical simulation in forging

I. Introduction

Forging is one of the important processing methods in modern manufacturing. Forged parts have good mechanical properties that are difficult to achieve with other processing methods. With the development of science and technology, the forging process is facing enormous challenges. The requirements for the quality and precision of forgings are getting higher and higher in various industries, and the production cost requirements are getting lower and lower. This requires the designer to design a viable process solution and mold structure in the shortest possible time. However, most of the current forging process and mold design still use the traditional method of experiment and analogy, which is not only time-consuming but also difficult to improve the quality and precision of forgings. With the maturity of finite element theory and the rapid development of computer technology, the finite element method numerical simulation is used for forging forming analysis, and the metal flow law, stress field and strain field in forming are obtained with little or no physical experiment. Such information, and the design of processes and molds, has become an effective means.

Most of the forging shapes belong to three-dimensional unsteady plastic forming, and generally cannot be simplified to simple problems such as plane or axis symmetry to approximate processing. In the forming process, there are both material nonlinearity and geometric nonlinearity. At the same time, there are nonlinear boundary conditions, the deformation mechanism is very complicated, and the contact boundary and friction boundary are also difficult to describe. The application of the rigid (viscous) plastic finite element method for numerical simulation of three-dimensional elements is one of the best internationally recognized methods for solving such problems.

Second, rigid (viscous) plastic finite element method

The rigid (viscous) plastic finite element method neglects the elastic effect in metal deformation. According to the basic equation of plastic mechanics that should be satisfied when the material is plastically deformed, the velocity field is used as the basic quantity to form the finite element formula. Although this method cannot consider elastic deformation problems and residual stress problems, it can greatly simplify the calculation procedure. When the elastic deformation is small or even negligible, this method can achieve higher calculation efficiency.

The theoretical basis of the rigid plastic finite element method is the Markov variational principle. According to the different processing methods of volume invariant conditions (such as Lagrange multiplier method, penalty function method and volume compressible method), different finite element formulas can be obtained, and the penalty function method is widely used. According to the Markov variational principle, using the penalty function method and discretizing with eight-node hexahedral elements, the total functional corresponding to the real velocity field in the permissible velocity field satisfying the boundary condition, coordination equation and volume invariant condition is:

∏≈∑π(m)=∏(1,2,...,m)(1)

For the change of the functional function in the above formula, we obtain:

∑=0(2)

Linearize the equation (2) by perturbation:

=+Δun(3)

Substituting equation (3) into equation (2), and considering the contribution of external force and friction force to the overall stiffness matrix and load array in the local coordinate system, the velocity field of the deformed material can be solved by an iterative method.

Third, the key technology in the simulation

The application of finite element method numerical simulation in forging shape is the first two-dimensional simulation analysis. The development of 2D simulation analysis technology is relatively mature. After appropriate simplification, it can simulate simple problems such as ordinary plane strain, stress and axisymmetric forming. However, in production, most of the parts are more complex in shape and have many influencing factors. If they are still treated as plane or axisymmetric problems, the results will be quite different from the actual ones. Performing 3D finite element simulation is an effective way to solve such problems. Therefore, since the 1980s, a lot of work has been done on 3D finite element simulation at home and abroad, and the key control techniques and corresponding solutions have been clarified, mainly in the following aspects:

3.1 Mathematical description of the mold structure The plastic deformation of the material depends on the contact with the mold surface. Therefore, accurately and completely describing the cavity information of the mold is the basis for obtaining the ideal simulation results. Due to the complicated structure of the complex forgings, it is difficult to describe. At present, commonly used description methods include analytical method, approximate description method of finite element mesh, parametric surface method and CAD solid model description method combined with parameter surface.

The approximate description method is to perform finite element meshing on the mold cavity, divide the continuous cavity structure into a finite number of tiny unit bodies, and use the combination of these units to approximate the cavity information of the mold. This method uses the finite element mesh to express the structural information, which is convenient for mathematical processing and facilitates the simplified processing of dynamic boundary conditions in the simulation. However, due to its low precision and high precision requirements, more cells need to be divided, which reduces the search efficiency of the intersection in dynamic contact.

Combining the parametric surface method, the Bezier surface is still used in the description of the cavity surface of the mold, and the solid modeling is adopted for the whole module, so that the geometric characteristics of the mold are accurately and effectively described. Many commercial CAD software now use this modeling method, so the software can easily establish the geometric characteristics of the mold, and the exchange of data is also very convenient.

Among these methods, the analytical method is the most limited in practical applications, and its application is rare. The approximate description method of finite element mesh becomes the current mainstream method because of the convenience of its data exchange with the finite element solver; With the wide application of 3D solid modeling software, CAD solid modeling description method will be more and more widely used in numerical simulation due to its own advantages.

3.2 Friction boundary conditions The contact friction between the forging and the mold cavity during the forging process is unavoidable, and the contact area, pressure distribution and friction state of the two contacts vary with the loading time, ie contact and friction. It is a complex problem with highly nonlinear boundary conditions. The theory used in the finite element simulation of the friction problem was originally the classical dry friction law. Later on it, the friction theory with tangential relative slip as a function and the friction theory similar to the elastoplastic theory form were developed.

The classical dry friction law was proposed by Coulomb in 1781. He believes that when the tangential force is less than the critical value, it is in a purely stuck state, and the relative slip of the contact surface is zero. Modern research shows that any friction below the critical value produces a small displacement. Therefore, the classical friction law is inaccurate in solving the friction problem during plastic deformation.

Based on the classical friction theory, Oden and Pires proposed the friction theory as a function of relative slip. It can reflect the nonlinear and non-local features of the friction problem, and the theory is relatively complete, but the parameters involved are not easy to determine, so the application in numerical analysis is limited.

Frericksson, Curnier et al. proposed a friction theory similar to the elastoplastic theory form, which can reflect the microscopic displacement of the contact point before the macroscopic slip, thus overcoming the defects of the classical friction law to some extent. Based on this theory, Kobayasgu proposed a modified Coulomb friction model and applied the model to the finite element simulation. The methods used to solve the boundary friction include the Lagrange multiplier method and the penalty function method. Since the penalty function method does not increase the degree of freedom of the structure, the solution is convenient and more applicable.

3.3 Dynamic contact boundary treatment The metal plastic forming process in forging is an unsteady large deformation process. In the finite element simulation process, the shape of the deformed body changes continuously, and its contact state with the mold is also constantly changing: some boundary nodes in the free state may contact the surface of the mold cavity; the original contact with the surface of the mold cavity The nodes may slip along the surface of the mold cavity as the deformation process progresses, or may become free nodes away from the surface. These changes constitute the dynamic contact surface between the workpiece dies. Correctly determining the contact surface is the basis for determining the boundary element body node load column for finite element analysis. Therefore, after each load step converges in the finite element simulation, the boundary conditions of these nodes need to be modified accordingly, that is, the dynamic boundary condition processing is performed. The commonly used method is divided into three steps: the judgment and processing of the free node sticking; the correction of the position of the touch node; the judgment and processing of the demolding of the touch node.

The free node model is judged by the method of intersecting the relative velocity vector direction of the boundary free node with the mold, obtaining the intersection point and obtaining the time required for the node to contact the mold, and judging whether the mold is applied according to the time. The determination of the demolding of the contact node is based on whether the boundary node of the contacted mold is separated from the mold and according to the force state of the contact node. If the joint force (or stress) of the contact node is less than zero in the normal direction of the mold surface (Pressure) means that the node is still in contact with the mold in the next step; otherwise, the node leaves the mold. For a node that leaves the mold, its boundary speed constraint should be removed to make it a free node.

The position correction of the contact nodes uses the shortest distance method, that is, the contact nodes are pulled back to the mold surface along the shortest distance from the mold surface. When you use this method to make corrections, you will often get a "deadlock". After studying the phenomenon of "deadlock", Zhan Mei et al. analyzed the reason that the "deadlock" was caused by the discontinuity of the discrete die mesh normal vector; and when the shortest distance method was used to correct the position of the contact node, the mold was The direction of the perpendicular line of each grid unit of the cavity changes continuously with the normal vector of each grid unit. In order to overcome the "deadlock" problem caused by the continuous change of the vertical line in the shortest distance method, they proposed a method of initial correction to correct the position of the contact node, avoiding the occurrence of "deadlock" in the finite element simulation. .

In addition, they also used the grid redraw method proposed by themselves to re-distort the distorted grid, and carried out three-dimensional finite element simulation on the blade forging process. The analysis of the simulation results shows that the method of correcting the position of the contact nodes by the initial vector correction method is effective for avoiding "deadlock" caused by the discrete mold mesh.

3.4 Meshing and re-division processing The unit discretization of the structure is very important in the finite element simulation. The quality of the divided unit body directly affects the calculation result, and even determines whether the calculation can proceed normally. The units used to deal with the forging problem are mostly three-dimensional unit bodies. The tetrahedral unit has simple results and is easy to generate, but the unit mass is not high, and the accuracy of the calculation results is low, which is difficult to meet the needs of simulation analysis; and the hexahedral unit division The unit mass is relatively good, but the effective partitioning method is still under further exploration. At present, the eight-node hexahedral element is divided into four methods: finite octree method, regular grid method, super-cell mapping method, module method and tetrahedral transformation method.

When the finite element simulation is carried out to a certain extent, the mesh will be interrupted due to severe distortion, so the corresponding processing must be performed. That is, the new mesh suitable for the calculation is re-divided, and the information required for the simulation is uploaded from the old mesh to the new mesh, so that the calculation can be continued. The re-division of a mesh generally has three steps: the judgment of the mesh distortion, the new mesh generation, and the data conversion.

Zuo Xu, Wei Yuanping, Chen Jun et al. studied the method of dividing the eight-node hexahedral mesh and the re-division technique of the grid, and developed the simulation software to form the single-step cross of the fly-free bridge. The process was analyzed.

3.5 Visualization of calculation results A large amount of data obtained after simulation by the finite element method must be described by the image and become information that the researcher can easily accept. For example, when forging, the flow of metal during the actual deformation of the metal, the temperature field change during deformation, and the like are visually displayed. The development of such visualization processing is generally performed on general-purpose CAD software, such as AUTOCAD, UG, SOLID WORKS, and the like. At present, the more mature commercial finite element simulation software itself has developed such a post-processing module, and its processing power has become one of the standards for measuring the pros and cons of simulation software.

Fourth, the implementation of the simulation

4.1 Develop a targeted finite element analysis program to simulate the application of the above-mentioned related technologies, and write special program processing related problems for different research objects using programming tools such as VC++. Therefore, the calculation efficiency is high and the solution is accurate. For example, Li Jun developed a general finite element simulation system for forging process based on his own key technology to solve the simulation problem, and used this system to complete the deformation analysis and mold optimization design of the engine valve forging process; Yan Shuqing et al. Applying the numerical solution of the boundary friction problem proposed by the author to prepare the relevant program, the three-dimensional large deformation elasto-plastic finite element numerical simulation analysis of the deformation process of the spur gear with closed tubular upset forging; Cai Zhongyi and others apply their friction The finite element analysis software was developed for the interface numerical simulation method. The frictional contact problem of the rubber plate in the wedge groove and the ring compression was analyzed, and the numerical simulation of the cylindrical surface of the plate was carried out. Zuo Xu, Wei Yuanping, Chen Jun et al. developed simulation software to analyze the forming process of the single-step cross shaft without the fly-bridge and the multi-station die forging process of the automobile cross shaft.

The solution to this problem is targeted, and the most effective processing method can be used to obtain better simulation results according to actual needs. However, the limitations are limited to fixed issues set in the program. In addition, programming is difficult and the application is not flexible.

4.2 Application of commercial finite element simulation software to simulate commercial 3D finite element simulation software (Deform3d, Surper Form, etc.) has good versatility, and contains relatively complete pre- and post-processing programs, which are relatively powerful and can simulate well. Some problems in volume forming. To apply them, firstly perform solid modeling in CAD software (such as Pro/e, ug, etc.), establish the physical information of the mold and blank and convert it into the corresponding data format; then set the corresponding environment of the deformation process in the software. Information, meshing; then numerical simulation calculations on the application software; finally, the calculation results are output as needed in the post-processing unit. Zhai Fubao et al. used MSC/MARC to carry out three-dimensional elastoplastic finite element simulation, studied the deformation mechanism of the cylindrical part by the distance spinning, and used Deform3d to simulate the temperature extrusion flow law of the material during the radial temperature extrusion process.

Because commercial simulation software has good versatility and good human-computer interaction environment, it is easy to operate, and the problems that can be solved are limited. Therefore, it has been more and more applied to the simulation of various forming processes, and gradually become The main means of numerical simulation.

V. Application status of numerical simulation in forging

In the forging shape, most of the deformation process can not be simplified into a two-dimensional deformation process, so the application of finite element method numerical simulation in forging shape is mainly based on three-dimensional simulation analysis. Since the 1980s, scholars at home and abroad have applied it to the forging shape and have done a lot of work.

Representatives in China are: Jiang Xiongxin et al. carried out three-dimensional rigid-plastic finite element simulation and experimental research on the precision forging forming process of hollow spur gears, and obtained the metal flow law and deformation mechanics of the precision forging process of spur gears. The characteristics reveal the deformation mechanism of the precision forging process of spur gears; Xiao Hongsheng and Wu Xilin et al. explored the method and implementation of numerical simulation of warm forging precision forming, and analyzed the warm forging forming steps of the pawl parts by using three-dimensional finite element analysis. And using the simulation results to guide the forming process and mold design of the part; Chen Zezhong carried out the spur-cylinder gear squeezing precision forging simulation;

The foreign AGMamalis used the implicit finite element software MARC and the explicit finite element software DYNA3D to calculate the precision forging process of a three-dimensional helical gear, and gave the comparison results. Volker Szentmihali and K.Lange used FORGE3 to three-dimensional helical gears. The forging process was simulated; Thieery Coupez used FORGE3 to simulate the three-dimensional forging process of the trigeminal shaft.

It can be seen from the application examples in recent years that the application of numerical simulation in forging is getting more and more in-depth, and the simulation work gradually shifts from simulating simple parts to simulating complex parts, from analog single-step forming to analog multi-step forming, from simple The metal flow simulates a multi-faceted composite simulation of the steering temperature field. The problems solved by the simulation are no longer simply academic, but more combined with reality and applied to production.

Sixth, the development trend of numerical simulation in forging

Although the application of numerical simulation in forging is deeper and more extensive, it is mainly to simulate the forming process in which some parts are not too complicated in shape, the mold structure has no flash, and only one step is required for processing. With the further development of some key technologies in the simulation and the improvement of computer hardware level, the application of numerical simulation in forging will have the following trends: 1 simulate the forming process of complex forgings with flash; 2 simulate multi-station forging Forming process; 3 simulate the force of the workpiece in forging while considering the influence of temperature factors, and obtain more accurate results through thermal coupling; 4 research work will deepen the combination with actual production, and more solve practical problems.

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