Method for verifying accuracy of structural analysis of plastic working

Abstract

The present invention provides a method for verifying the accuracy of structural analysis of plastic working, the method involving using a plate-like workpiece as an analytical model for the finite element method using shell elements, performing computer-based structural analysis of plastic working, and acquiring analytical shape data after plastic working of the analytical model. The workpiece is subjected to a plastic working step in which the same shape as a target shape of the plastic working of the analytical model is set as the target shape, and shape data for the front and back sides of a plastic-worked article is acquired. The shape data for the front and back sides is used as a basis for calculating evaluation surface shape data corresponding to an evaluation surface generated between the surface on the front side and the surface on the back side of the plastic-worked article. The evaluation surface shape data obtained as a result of the plastic working of the plastic-worked article is used to make a comparison between the evaluation surface shape data and the analytical shape data.

Description

Accuracy verification method for structural analysis of plastic processing

[0001] The present invention relates to a method for verifying the accuracy of structural analysis of plastic working.

[0002] Patent Document 1 discloses generating an expected springback shape of a press forming die by performing a plastic working simulation using the finite element method.

[0003] JP 2011-164709 A

[0004] In plastic processing simulations using the finite element method, structural analysis of an analytical model is sometimes performed using shell elements. To verify the accuracy of the structural analysis, the shape match rate is sometimes evaluated based on the analytical shape data and the shape data of a plastically processed product that has been subjected to a test in which the plastic processing is performed to produce a shape identical to the target shape of the plastic processing applied in the structural analysis. However, in cases such as dieless forming, where the thickness of the workpiece varies significantly depending on the plastic processing angle, partial differences may occur between the analytical shape data and the shape data corresponding to the shape surface of the plastically processed product, making it difficult to properly evaluate the shape match rate.

[0005] An object of the present invention is to provide a verification method that can appropriately verify the accuracy of structural analysis of plastic working.

[0006] A method for verifying the accuracy of structural analysis of plastic working according to one aspect of the present invention uses a plate-shaped workpiece as an analytical model of the finite element method using shell elements, performs structural analysis of the plastic working of the analytical model using a computer, and obtains analytical shape data of the analytical model after plastic working. The workpiece is subjected to a plastic working process with a target shape identical to the target shape of the plastic working of the analytical model, and surface shapes of the front and back sides of the plastic worked product are measured to obtain shape data of the front and back sides. Based on the shape data of the front and back sides, evaluation surface shape data generated between the front and back surfaces of the plastic worked product is calculated. Using the evaluation surface shape data as a result of plastic working of the plastic worked product, the evaluation surface shape data is compared with the analytical shape data.

[0007] According to the method for verifying accuracy of structural analysis of plastic working according to one aspect of the present invention, the accuracy of structural analysis of plastic working can be properly verified.

[0008] FIG. 1 is an explanatory diagram showing an overview of an accuracy verification method according to an embodiment. FIG. 2 is an explanatory diagram showing a reduction in plate thickness in dieless forming according to an embodiment. FIG. 3 is an explanatory diagram showing a reduction in plate thickness in dieless forming according to an embodiment. FIG. 4A is an explanatory diagram showing a calculation method for an evaluation surface according to an embodiment. FIG. 4B is an explanatory diagram showing a calculation method for an evaluation surface according to an embodiment. FIG. 5 is a flowchart in which processing steps executed by an accuracy verification method according to an embodiment are arranged in chronological order.

[0009] Hereinafter, a method for verifying the accuracy of structural analysis of plastic working according to an embodiment will be described with reference to the drawings. In each figure, L indicates the normal line of each intersecting plane. Furthermore, components having the same functions as those already described will be assigned the same reference numerals and will not be described again.

[0010] First, an outline of a method for verifying the accuracy of structural analysis of plastic working according to an embodiment will be described (see FIG. 1 ). In structural analysis of plastic working, a finite element method using shell elements is used to perform numerical analysis using a computer 1 (see FIG. 1 ). As a result of the numerical analysis, analytical shape data 5 after plastic working is performed using a plate-shaped workpiece W as an analytical model is obtained (see FIG. 1 ). Here, in plastic working, after the workpiece W is formed into a target shape, a shape change may occur in the direction in which the formed portion returns to the shape before forming, which is generally called springback. The analytical shape data 5 is the shape after the shape change due to springback occurs.

[0011] Next, a plastic working test is performed on the workpiece W (see FIG. 1). The target shape of the workpiece W after plastic working in this test is set to the same shape as the target shape in plastic working of the analytical model applied in the structural analysis. Therefore, by comparing the degree of agreement between the shape data calculated from the shape of the plastically worked product 10 obtained by performing the plastic working test on the workpiece W and the analytical shape data 5, the accuracy of the structural analysis relative to the results of the plastic working test can be verified.

[0012] Next, the shape of the plastically processed product 10, which is the workpiece W subjected to the plastic processing test, is measured, and evaluation surface shape data 13A corresponding to the evaluation surface 13 described below is calculated (see FIG. 1). The shape of the plastically processed product 10 subjected to the plastic processing test is the shape after the shape change due to springback occurs. Then, the analysis shape data 5 is compared with the evaluation surface shape data 13A. If the shape match rate between the analysis shape data 5 and the evaluation surface shape data 13A is equal to or greater than a predetermined threshold, this indicates that the results of the structural analysis of the plastic processing match the actual test results of the plastic processing within a certain range. Therefore, in this case, this indicates that the accuracy of the structural analysis of the plastic processing falls within a certain range with respect to the actual test results of the plastic processing. In other words, the greater the shape match rate between the analysis shape data 5 and the evaluation surface shape data 13A, the higher the accuracy of the structural analysis. Furthermore, if the shape match rate between the analysis shape data 5 and the evaluation surface shape data 13A is less than a predetermined threshold, the structural analysis conditions may have been set inappropriately. In such a case, the structural analysis is repeated by changing parameters or the like so that the shape matching rate based on the shape comparison becomes equal to or exceeds a predetermined threshold value (see FIG. 1).

[0013] Here, in order to properly verify the accuracy of the structural analysis of plastic working, it is necessary to properly calculate the evaluation surface shape data 13A to be compared with the analysis shape data 5. In other words, if the evaluation surface 13 of the plastic worked product 10 is not properly set and the evaluation surface shape data 13A is not properly calculated, it may not be possible to properly verify the accuracy of the structural analysis of plastic working. This is because the accuracy of the structural analysis of plastic working is verified based on the evaluation surface shape data 13A.

[0014] When the shape coincidence rate is equal to or greater than a predetermined threshold, the accuracy of the structural analysis of the plastic working falls within a certain range under predetermined conditions relative to the test results of the actual plastic working. Therefore, for example, by performing structural analysis of the plastic working, it is possible to predict the shape of the plastic working product 10 after a shape change due to springback within a certain accuracy, without actually conducting a plastic working test. Furthermore, by performing structural analysis of the plastic working, it is also possible to generate expected springback shape data that is offset in the opposite direction to the shape change due to springback, anticipating the shape change due to springback. Furthermore, a fitting process may be required in which the expected springback shape data, which is the formed shape, is corrected based on the difference between the plastic working product 10 after a shape change due to springback and the target shape. In such cases, by performing structural analysis of the plastic working, it is possible to predict the shape of the plastic working product 10 after a shape change due to springback within a certain accuracy, thereby reducing the number of plastic working tests and improving the efficiency of the fitting process.

[0015] Next, structural analysis of plastic processing according to the embodiment will be described. The finite element method (FEM) is used as the structural analysis method. In structural analysis using the FEM, an analytical model is divided into elements, and numerical analysis is performed assuming that each divided element deforms according to predetermined material properties. When the plate-shaped workpiece W according to the embodiment is used as the analytical model, plate-shaped shell elements are used to reduce the computational load, and structural analysis is performed using mid-plane shell elements. Analysis is performed on the analytical model based on predetermined analysis conditions, and shape data corresponding to the mid-plane, which is the analysis result, can be calculated (see FIG. 1 ). The computer 1 that performs the numerical analysis is a general-purpose computer including, for example, a volatile memory, a non-volatile memory, a hardware processor such as a CPU (Central Processing Unit), and the like. The computer 1 also includes, for example, an input / output control unit, a memory unit that stores shape data, an analysis unit that performs numerical analysis, and a calculation unit that calculates shape data and performs shape comparison. The computer 1 can execute a predetermined program to verify the accuracy of the structural analysis of plastic processing according to the embodiment.

[0016] Next, the plastic working process according to the embodiment will be described. In the plastic working process, incremental forming using dieless forming is performed. Plastic working that involves sequential shaping is generally referred to as incremental forming. Furthermore, a technique for performing plastic working by moving a tool against a workpiece without using a die is also referred to as dieless forming. In dieless forming, a jig is used to hold the lower surface (the backside) of a positioned workpiece W1, and a rod-shaped tool 2 is pressed against the upper surface (the frontside) (see Figure 2). At this time, the thickness of the workpiece decreases depending on the plastic working angle α relative to the horizontal direction. It is generally known that the thickness T1 of the inclined portion of the workpiece W2 that has undergone dieless forming has a relationship with the thickness T0 of the horizontal portion, as shown in Equation (1) below (see Figure 2). Therefore, the larger the plastic working angle α, the thinner the thickness T1 of the processed portion becomes. For example, when the plastic working angle α is 60°, the thickness T1 of the processed portion is half the thickness T0 of the horizontal portion.

[0017]

[0018] Next, the shape measurement of the plastically worked product 10 according to the embodiment will be described. First, the shape of the front surface 11 of the plastically worked product 10, which has been subjected to a plastic working process on a workpiece W, is measured to obtain front-side shape data 11A. The front side of the plastically worked product 10 is the processed surface against which the tool 2 is pressed (see FIG. 2). Next, the shape of the back surface 12 of the plastically worked product 10 is measured to obtain back-side shape data 12A. In this case, the plastically worked product 10 may be turned upside down, and shape measurement may be performed with the back surface 12 of the plastically worked product 10 facing upward. The acquired data may then be converted to the back-side shape data 12A by inverting it upside down. The back side of the plastically worked product 10 is the processed surface held down by a jig (see FIG. 2). The shape data is obtained, for example, using a three-dimensional shape measuring device. The three-dimensional shape measuring device is capable of obtaining the three-dimensional coordinates of each point within the measurement surface. The three-dimensional shape measurement method may be, but is not limited to, a contact type or a non-contact type.

[0019] Next, we will explain how to calculate the evaluation surface shape data 13A corresponding to the evaluation surface 13. The evaluation surface 13 is a virtual surface generated between the front surface 11 and the back surface 12 of the plastically worked product 10 (see FIG. 3). The evaluation surface shape data 13A corresponding to the evaluation surface 13 is calculated based on the front side shape data 11A and the back side shape data 12A.

[0020] The following describes an example of calculating evaluation surface shape data 13A using back-side shape data 12A as reference data (see FIG. 4A ). First, consider a plane 12A1 formed by three data points 12a1, 12a2, and 12a3 included in the back-side shape data 12A. A normal line L extending from point 12a4 within plane 12A1 is calculated. Point 12a4 is, for example, a virtual point located equidistant from data points 12a1, 12a2, and 12a3 within plane 12A1. Next, point 11a4 is calculated, which is the intersection of normal line L and plane 11A1 formed by data points 11a1, 11a2, and 11a3 included in front-side shape data 11A. Point 11a4 is a virtual point located within plane 11A1 and can be calculated from data points 11a1, 11a2, and 11a3 and the normal line L. Next, the length of the normal line L from point 12a4 in plane 12A1 to point 11a4 in plane 11A1 is calculated. Then, point 13a4, which is the midpoint on the normal line L between point 12a4 in plane 12A1 and point 11a4 in plane 11A1, is calculated. Furthermore, plane 12A1 is moved along the normal line L to point 13a4, and the moved plane is designated as plane 13A1 (see FIG. 4A). The shape data 12A includes multiple planes 12A1, 12A2, ..., 12An formed by each data point. By repeating this operation for all data points, evaluation surface shape data 13A can be calculated by moving the back-side shape data 12A. The length of the normal line L corresponds to the distance in the normal direction to the front surface 11 and the back surface 12. That is, the length of the normal line L corresponds to the plate thicknesses T0 and T1 of each portion of the plastically worked product 10. Therefore, the evaluation surface 13 corresponds to a midplane generated at a position half the distance to the other surface in the normal direction of the front or back surface. Point 12a4 in plane 12A1, point 11a4 in plane 11A1, and point 13a4 on normal line L are virtual points that can be calculated based on three-dimensional coordinates, but may also be data points included in shape data 11A, 12A, and 13A. Note that the evaluation surface shape data 13A may be calculated using the front-side shape data 11A as reference data.

[0021] Furthermore, the evaluation surface shape data 13A corresponding to the evaluation surface 13 according to the embodiment may be calculated as follows. First, in a plane 12A1 formed by three data points 12a1, 12a2, and 12a3 included in the back-side shape data 12A, a normal line L extending from a point 12a4 within the plane 12A1 is calculated. Point 12a4 is, for example, a virtual point located equidistant from the data points 12a1, 12a2, and 12a3 within the plane 12A1. Next, the angle between the normal line L and the horizontal direction M is calculated. When the plastic processing angle is α, this angle is expressed as (90 - α). Next, the plate thicknesses T0 and T1 are calculated based on the above-described formula (1). Then, a point 13a4 is calculated, which is located along the normal line L a distance half the plate thickness T0 and T1 from point 12a4 within the plane 12A1. Point 13a4 is a virtual point and can be calculated from data points 12a1, 12a2, and 12a3, normal line L, and plate thicknesses T0 and T1. Furthermore, plane 12A1 is moved along normal line L to point 13a4, and the moved plane is designated plane 13A1 (see FIG. 4B ). Shape data 12A includes multiple planes 12A1, 12A2, ..., 12An formed by each data point. By repeating this operation for all data points, evaluation surface shape data 13A can be calculated by moving back-side shape data 12A. The length of the normal line L corresponds to half the plate thicknesses T0 and T1 at each portion of plastically worked product 10. Therefore, evaluation surface 13 is a surface generated by offsetting a position half the plate thickness T0 and T1 in the normal direction of the front or back surface. That is, the evaluation surface shape data 13A corresponds to the evaluation surface 13 calculated by calculating the reduction in the plate thickness T0, T1 according to the plastic processing angle α and offsetting from the front surface 11 or the back surface 12 of the plastically processed product 10 in the normal direction to the front surface 11 or the back surface 12. Note that the evaluation surface shape data 13A may be calculated by calculating the reduction in the plate thickness T0, T1 according to the plastic processing angle α based on the front side shape data 11A.

[0022] Next, the process steps S1 to S6 executed by the method for verifying accuracy of structural analysis of plastic working according to the embodiment will be described (see FIG. 5). The computer 1 can execute a predetermined program that sequentially executes the process steps S1 to S6.

[0023] First, step S1 will be described. In step S1, a computer 1 performs a structural analysis of the plastic processing of the analytical model using a finite element method that uses shell elements and a plate-shaped workpiece W as an analytical model. In step S2, analytical shape data 5 is calculated and acquired, and stored in a memory unit. This makes it possible to acquire analytical shape data 5, which is the shape of the analytical model after plastic processing. By comparing this analytical shape data 5 with the shape data of the plastic processing test results, it is possible to verify the accuracy of the analysis and confirm the validity of the analysis.

[0024] In step S3, a plastic processing test is performed on a plate-shaped workpiece W, with the target shape being the same as the target shape in the plastic processing of the analytical model. Specifically, plastic processing is performed on the plate-shaped workpiece W by incremental forming using dieless forming. Then, the shapes of the front surface 11 and the back surface 12 of the plastically processed plastically processed product 10 are measured. In step S4, the front and back surface shape data 11A, 12A are acquired using the above-described method. In step S5, evaluation surface shape data 13A corresponding to the evaluation surface 13 generated between the front surface 11 and the back surface 12 of the plastically processed product 10 is calculated based on the front and back surface shape data 11A, 12A. The calculation method is as described above. In step S6, the evaluation surface shape data 13A is used as the result of plastic processing of the plastically processed product 10, and the evaluation surface shape data 13A is compared with the analysis shape data 5. If the shape matching rate is equal to or greater than a predetermined threshold, it is suggested that the accuracy of the structural analysis of the plastic processing is within a certain range, as described above.

[0025] (1) In the method for verifying the accuracy of structural analysis of plastic working according to the embodiment, a plate-shaped workpiece W is used as an analytical model of the finite element method using shell elements, and a computer 1 is used to perform structural analysis of the plastic working of the analytical model, thereby obtaining analytical shape data 5 after plastic working of the analytical model. The workpiece W is subjected to a plastic working process in which the target shape is the same as the target shape of the plastic working of the analytical model. Surface shapes of the front and back sides of a plastically worked product 10 are measured, and front and back side shape data 11A, 12A are obtained. Based on the front and back side shape data 11A, 12A, evaluation surface shape data 13A corresponding to an evaluation surface 13 generated between the front surface 11 and the back surface 12 of the plastically worked product 10 is calculated. Using the evaluation surface shape data 13A as the result of plastic working of the plastically worked product 10, the evaluation surface shape data 13A is compared with the analytical shape data 5.

[0026] By calculating the evaluation surface shape data 13A based on the front and back side shape data 11A, 12A, it is possible to suppress errors that may be included when using the shape data 11A, 12A as the result of plastic working of the plastic worked product 10. Therefore, in comparing the analysis shape data 5 with the shape data resulting from the plastic working of the plastic worked product 10, it is possible to verify the accuracy of the structural analysis of the plastic working more appropriately than when using the shape data 11A, 12A. This makes it possible to generate expected springback shape data based on springback prediction, reduce plastic working tests, and improve the efficiency of the fitting process.

[0027] (2) Furthermore, according to the embodiment, the evaluation surface shape data 13A is calculated corresponding to the evaluation surface 13, which is a neutral surface based on the distance in the normal direction to the front surface 11 and the back surface 12 of the plastically worked product 10. The evaluation surface shape data 13A calculated as described above enables more accurate verification to be performed when comparing the shape data of the plastically worked product 10 with the analysis shape data 5.

[0028] (3) Furthermore, according to an embodiment, the evaluation surface shape data 13A may be calculated by calculating the reduction in the plate thickness T0 according to the plastic processing angle α, corresponding to the evaluation surface 13, which is a surface offset from the front surface 11 or the back surface 12 of the plastically processed product 10 in the normal direction relative to the front surface 11 or the back surface 12. The evaluation surface shape data 13A calculated as described above enables more accurate verification to be performed when comparing the shape data of the plastically processed product 10 with the analysis shape data 5.

[0029] (4) According to the embodiment, the method of the plastic processing step performed on the workpiece W is incremental forming using dieless forming. With the above configuration, it is possible to perform highly accurate verification in the concept analysis of incremental forming, which is significantly affected by the reduction in the plate thickness T0 according to the plastic processing angle α.

[0030] (5) Furthermore, the calculation method according to the embodiment calculates evaluation surface shape data 13A based on the front and back side shape data 11A, 12A in the method for verifying accuracy of structural analysis of plastic working. The evaluation surface shape data 13A calculated as described above can reduce errors that may be included in the shape data to be compared with the analysis shape data 5.

[0031] (6) In addition, the program according to the embodiment uses a plate-shaped workpiece W as an analytical model for the finite element method using shell elements, performs structural analysis of the plastic processing of the analytical model using a computer 1, and obtains analytical shape data 5 after the plastic processing of the analytical model. The program measures the surface shapes of the front and back sides of a plastically processed product 10 that has been subjected to a plastic processing process on the workpiece W, with the target shape being the same as the target shape in the plastic processing of the analytical model, and obtains shape data 11A and 12A for the front and back sides. Based on the shape data 11A and 12A for the front and back sides, evaluation surface shape data 13A corresponding to an evaluation surface 13 generated between the front surface 11 and the back surface 12 of the plastically processed product 10 is calculated, and the evaluation surface shape data 13A is used as the result of the plastic processing of the plastically processed product 10 to compare the evaluation surface shape data 13A with the analytical shape data 5.

[0032] By using the above program to calculate the evaluation surface shape data 13A based on the front and back side shape data 11A, 12A, it is possible to suppress errors that may be included when using the shape data 11A, 12A as the result of plastic working of the plastic worked product 10. Therefore, in comparing the analysis shape data 5 with the shape data resulting from the plastic working of the plastic worked product 10, it is possible to verify the accuracy of the structural analysis of the plastic working more appropriately than when using the shape data 11A, 12A. This makes it possible to generate expected springback shape data based on springback prediction, reduce plastic working tests, and improve the efficiency of the fitting process.

[0033] The above-described embodiments are merely examples described to facilitate understanding of the invention. The technical scope of the invention is not limited to the specific technical matters disclosed in the above-described embodiments, but also includes various modifications, changes, alternative technologies, etc. that can be easily derived therefrom.

[0034] In the above embodiment, the plastic processing step is described using an example of a configuration in which incremental forming using dieless forming is performed, but other plastic processing may be performed. Also, although springback has been used as an example of shape change after forming, this is similarly applicable to shape changes due to spring back, etc. Furthermore, the workpiece W according to the embodiment can be applied to, for example, steel plates used for automobile parts and components.

[0035] REFERENCE SIGNS LIST 1 Computer 5 Analysis shape data 10 Plastically processed product 11 Front surface 11A Front shape data 12 Back surface 12A Back shape data 13 Evaluation surface 13A Evaluation surface shape data L Normal line T0, T1 Plate thickness W Workpiece α Plastic processing angle

Claims

1. A plate-shaped workpiece is used as an analysis model for the finite element method using shell elements, and the structural analysis of the plastic deformation of the analysis model is performed by computer to obtain the analysis shape data of the analysis model after plastic deformation. A plastic deformation process is performed on the workpiece to achieve the same shape as the target shape in the structural analysis of the plastic deformation of the analysis model, and shape data of the front and back surfaces of the plastically deformed product is obtained by measuring the surface shapes of the front and back surfaces. Based on the shape data of the front and back sides, evaluation surface shape data corresponding to the evaluation surface generated between the front surface and the back surface of the plastically deformed product is calculated. A method for verifying the accuracy of structural analysis of plastic deformation, comprising comparing the evaluation surface shape data with the analysis shape data, using the evaluation surface shape data as the result of plastic deformation of the plastically deformed product.

2. The method for verifying the accuracy of structural analysis of plastic deformation according to claim 1, wherein the evaluation surface shape data is calculated in relation to a neutral plane based on the distance in the normal direction to the front surface and the back surface of the plastically deformed product.

3. The method for verifying the accuracy of structural analysis of plastic deformation according to claim 1, wherein the evaluation surface shape data is calculated by calculating the reduction in plate thickness according to the plastic deformation angle, and corresponds to a surface offset in the direction normal to the front surface or the back surface of the plastic deformation product.

4. The method for verifying the accuracy of structural analysis of plastic deformation according to any one of claims 1 to 3, wherein the plastic deformation process performed on the workpiece is incremental forming using die-less forming.

5. A calculation method for calculating evaluation surface shape data based on the shape data of the front and back sides in the accuracy verification method for structural analysis of plastic deformation according to any one of claims 1 to 3.

6. A plate-shaped workpiece is used as an analysis model for the finite element method using shell elements, and the structural analysis of the plastic deformation of the analysis model is performed by computer to obtain the analysis shape data of the analysis model after plastic deformation. A plastic deformation process is performed on the workpiece to achieve the same shape as the target shape in the structural analysis of the plastic deformation of the analysis model, and shape data of the front and back surfaces of the plastically deformed product is obtained by measuring the surface shapes of the front and back surfaces. Based on the shape data of the front and back sides, the evaluation surface shape data generated between the front surface and the back surface of the plastically deformed product is calculated. A program that uses the evaluation surface shape data as the result of plastic deformation of the plastically deformed product to compare the evaluation surface shape data with the analysis shape data.