JP2005131696A - Method for calculating coefficient of friction in non-ferrous metallic sheet, and forming simulation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for highly precisely and efficiently calculating a coefficient of friction, that varies during forming, in carrying out a forming simulation of a non-ferrous metallic sheet material, and also to provide a forming simulation method improved in analytical precision. <P>SOLUTION: The coefficient of friction μ is expressed in equation (1): μ=a0+a1P<SB>N</SB>+a2P<SB>N</SB><SP>2</SP>+a3P<SB>N</SB><SP>3</SP>+a4P<SB>N</SB><SP>4</SP>where [Pa] is parameter, with constants a<SB>0</SB>, a<SB>1</SB>, a<SB>2</SB>, a<SB>3</SB>and a<SB>4</SB>determined by measuring change in the surface pressure and the coefficient of friction, fitting the data obtained and calculating through the method of least squares for example. Then, equation (1) is applied to a finite element method simulation in which a nonlinear frictional model is taken into consideration. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a friction coefficient calculation method and a finite element method for predicting a press failure by a finite element method simulation with high accuracy and efficiency when designing a die for press forming a non-ferrous metal plate, particularly an aluminum plate or an aluminum alloy plate. The present invention relates to a molding simulation method based on the above.

  When press-molding non-ferrous metal plates, especially aluminum plates and aluminum alloy plates, using mechanical presses, hydraulic presses, transfer presses, AC servo control presses, etc., before using the finite element method forming simulation to manufacture press dies Whether the molding is possible or not is fed back to the mold design to shorten the work period and reduce the cost. Improving the accuracy of molding simulation using the finite element method is indispensable for shortening the work period and cost reduction in the design of this mold.

  Forming simulation by the finite element method inputs the mechanical properties of the material as a material constitutive equation and solves the contact problem with the tool by a balance equation of the deformation state of the material with the friction coefficient as a parameter (static implicit method or static method). This is a method of outputting stress distribution and strain distribution by solving dynamic equation) or solving equations of motion (dynamic explicit method).

Nakamachi et al., “Derivation of Experimental Formula for Friction Properties of Surface-treated Plates and Formability Evaluation by Finite Element Method” 1992 Plastic Working Spring Lecture Meeting Proceedings I (May 24, 25 am), Nippon Plastics Processing Society, May 6, 1992, p355 Hashimoto et al., “Change in frictional force due to sliding distance of plated steel sheet and its effect on deep drawing”, plasticity and processing, vol. 44, no. 504, Japan Society for Technology of Plasticity, published on January 25, 2003, p35 Kuwahara et al., “Bead drawing characteristics and bead tension calculation model of aluminum alloy plate A5182-O”, plasticity and processing, vol. 36, no. 413, The Japan Society for Technology of Plasticity, published on June 20, 1995

  However, conventional molding simulation programs using the finite element method use the Coulomb friction law that treats the friction coefficient as a constant, and do not accurately reflect changes in the friction coefficient during molding. The distribution could not be output, and the accuracy of predicting molding was not sufficient.

  In response to such problems, workpieces caused by changes in friction coefficient due to machining conditions such as molding speed and changes in wrinkle pressure, and increased sliding distance between the workpiece and the mold There has been proposed a method of incorporating a change in friction coefficient associated with a change in the surface topology of the material into a forming simulation by a finite element method.

  As an example in which the friction coefficient is treated as a state function and a nonlinear friction model is incorporated into a forming simulation by the finite element method, a state function (for example, a non-linear function) that uses a sliding distance and a strain applied to a non-processed material as parameters is used. Patent Document 1), an example of a state function (for example, Non-Patent Document 2) obtained by polynomial approximation using two parameters of surface pressure and friction work is reported. As for the friction coefficient of an aluminum plate, a method for obtaining the friction coefficient as a state function obtained by approximating a polynomial up to the third order of the surface pressure has been reported (for example, Non-Patent Document 3).

  However, even if these methods are used, the accuracy of evaluation of the friction coefficient in the molding simulation by the finite element method is insufficient, and the prediction accuracy of the molding possibility is not satisfactory.

  The present invention has been made in view of the above points, and in carrying out a forming simulation of a plate-shaped non-ferrous metal material typified by an aluminum plate or an aluminum alloy plate, a friction coefficient that changes during forming is determined. It is an object of the present invention to provide a friction coefficient calculation method for efficiently calculating with high accuracy and a forming simulation method with improved analysis accuracy.

The inventor pays attention to the friction coefficient that changes during the molding process due to various press working conditions, analyzes the relationship between the friction coefficient and the surface pressure in detail, and calculates the friction coefficient μ as the surface pressure P _N [Pa] only. It has been found that the calculation can be performed with the highest accuracy and efficiency by using a fourth-order polynomial approximation. This invention is made | formed based on such knowledge, The summary is as follows.
(1). A friction coefficient calculation method for a non-ferrous metal plate, wherein the friction coefficient is calculated by polynomial approximation of the fourth or higher order of only the surface pressure.
(2). (1) A forming simulation method of a non-ferrous metal plate, wherein forming simulation by a finite element method is performed using the friction coefficient described in (1).
(3). A procedure for measuring changes in the friction coefficient and surface pressure of a non-ferrous metal plate;
State function μ = a ₀ + a _{1 PN} + a _{2 PN} ² + a _{3 PN} ³ + a _{4 PN} ⁴
The constants a ₀ , a ₁ , a ₂ , a ₃ , a ₄ are determined using the above measurement results;
A non-ferrous metal sheet forming simulation method comprising a step of performing a forming simulation by a finite element method using a state function in which the constants a ₀ , a ₁ , a ₂ , a ₃ , and a ₄ are determined .

  In the present invention, the non-ferrous metal plate refers to a non-ferrous metal material such as plate-shaped aluminum, aluminum alloy, titanium, titanium alloy, magnesium and magnesium alloy used for press forming.

  According to the present invention, it becomes possible to perform a press molding simulation of a non-ferrous metal plate, in particular, an aluminum plate or an aluminum alloy plate by a finite element method with high accuracy and high efficiency. The industrial contribution is extremely remarkable, such as shortening

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. Factors affecting the coefficient of friction can be broadly classified into those caused by molding conditions and those caused by changes in the material during the molding process. Factors resulting from the molding conditions include the molding speed S when a metal plate is molded using a mechanical press, hydraulic press, transfer press, AC servo control press, etc., and on the die face, die shoulder and bead. Such as the difference in local surface pressure P _N received by the material, the change in wrinkle holding pressure due to variable wrinkle holding pressure control, etc. The hardness difference ΔH from the material, the roughness Ra, and the like are typical factors that affect the friction coefficient.

In addition, factors resulting from changes in the material during the molding process include changes in the surface topology of the workpiece as the sliding distance between the workpiece and the mold increases, as well as processing heat generation and sliding. It is known that the thermal effect due to dynamic heat generation, the plastic strain ε _P generated while the workpiece is subjected to plastic deformation, and the like affect the friction coefficient.

Among these factors, the surface pressure P _N in a sample of the same surface topology state, a significant impact on the coefficient of friction, has been reported in Non-Patent Document 3 or the like, the surface pressure P _N is the coefficient of friction conditions It is extremely important as a parameter for function notation. The inventor paid attention to the friction coefficient between the mold and the aluminum plate that changes during the molding process under various press working conditions, and intensively studied the influence of the surface pressure that affects the change.

As schematically shown in FIG. 1, the friction coefficient is determined by inserting the plate material 2 between the flat plate molds 1a and 1b, pulling out the plate material 2 while pressing the flat plate molds 1a and 1b, and pressing the flat plate molds 1a and 1b ( Specifically, it was measured by a flat plate pull-out test for measuring a force (referred to as a pulling force) required for pulling out the plate member 2 with respect to a pressing load. Flat pull-test apparatus is a flat die 1a, mechanism for pressing the sheet material 2 to retain 1b and tensile tester installed a pressing device provided with a measuring mechanism of the surface pressure P _N, pullout force P _S by a cross head Can be loaded. The surface pressure _PN is obtained by dividing the force for pressing the flat plate molds 1a, 1b against the test piece (referred to as pressing force) by the area of the portion where the flat plate molds 1a, 1b are in contact with the plate material 2. The plate material 2 has a width of 10 to 20 mm and a length of 250 to 400 mm, and the flat plate molds 1a and 1b installed in the pressing device have a height of 5 to 10 mm and a width of 25 mm.

  The upper end of the plate material 2 was fixed to the cross head of the flat plate pull-out test apparatus using a jig, and the lower portion of the plate material 2 was sandwiched between flat plate molds 1a and 1b installed in the pressing device. A relationship between the pulling force and the displacement was measured while pulling out the plate member 2 by moving the cross head by applying a constant surface pressure by the pressing device. The average value of the maximum value and the minimum value of the pulling force (referred to as the average pulling force) was determined at a portion where the change in the pulling force with respect to the displacement of the crosshead was almost constant. The surface pressure was changed in the range of 0 to 150 MPa, the surface pressure was plotted on the horizontal axis, the average pulling force was plotted on the vertical axis, and the slope of the graph was determined as the friction coefficient. The coefficient of friction was measured by changing the sliding distance, lubricant, and number of sliding of the plate material.

  FIG. 2 shows changes in the friction coefficient of a 1 mm-thick 5000 series aluminum alloy plate due to surface pressure. From FIG. 2, a new finding was found that the coefficient of friction decreased once with increasing surface pressure, but then increased again. Therefore, as proposed in Non-Patent Document 3, if the coefficient of friction is calculated as a cubic expression of the surface pressure, an increase in high surface pressure cannot be taken into account, so the error increases, and the finite element method press In molding simulation, accuracy decreases.

  The present inventor further conducted detailed examinations such as reviewing various parameters with respect to the approximate expression for accurately calculating the upward tendency at high surface pressure. As a result, it has been found that if the friction coefficient is a fourth or higher order polynomial of the surface pressure, the change of the friction coefficient due to the surface pressure can be calculated with high accuracy. Further, if the friction coefficient is a polynomial of 5th order or higher of the surface pressure, the accuracy is further improved than that of the 4th order polynomial, but the calculation takes time. Therefore, the 4th order polynomial may be optimal in practice. all right.

That is, the equation that can calculate the friction coefficient μ with the highest accuracy and efficiency is the following equation (1) using the surface pressure P _N [Pa] as a parameter.
μ = a ₀ + a ₁ P _N + a ₂ P _N ² + a ₃ P _N ³ + a ₄ P _N ⁴ (1)

In the above equation (1), a ₀ , a ₁ , a ₂ , a ₃ , and a ₄ are constants, and the changes in the surface pressure and the friction coefficient are measured. Each parameter is determined by the calculation of, and a state function of the friction coefficient expressed by a fourth-order polynomial approximation can be obtained. In order to measure the change of the friction coefficient due to the surface pressure, the friction coefficient may be obtained by changing the surface pressure. As a test method for measuring the friction coefficient, in addition to the above-described flat plate pull-out test method, edited by the Japan Society for Technology of Plasticity, “Plastics Technology Series 3 Process Tribology-Lubrication of Plasticity”, Corona, March 25, 1993 Issue, p. A general friction coefficient test method such as the Bowden test method described in 66, 67 can be employed. Further, using the continuous sliding tester described in Non-Patent Document 2, the friction coefficient may be measured by changing the surface pressure _PN and sliding the same portion a plurality of times.

  This knowledge is the same for aluminum plates other than aluminum plates such as aluminum plates, 5000 series, and 6000 series, and can be applied to non-ferrous metal plates such as titanium plates, titanium alloy plates, magnesium plates, and magnesium alloy plates. In addition, although the reason which cannot apply to a steel material is not clear, it is mentioned that a nonferrous metal material is inferior to press formability than a steel material.

  In addition, the new finding that the coefficient of friction decreases and then increases with increasing surface pressure in non-ferrous metal materials is due to the fact that non-ferrous metal materials are softer than molds made of hard steel materials. There is a possibility. That is, as the surface pressure increases, first, when the surface comes into contact with the mold, the convex portion is crushed by plastic deformation, the lubricating oil is discharged from the concave portion to form an oil film, the lubrication becomes good, and the friction coefficient Decreases. Thereafter, the plastic deformation further proceeds, and it is considered that the friction coefficient increases again as the contact area increases.

  Next, Equation (1) was applied to a finite element method simulation considering a nonlinear friction model. This is because the material parameters and press molding conditions of the work material are parameterized and input, and the friction coefficient μ is applied to the existing finite element method molding simulation program that outputs the stress distribution and strain distribution according to the molding. A subroutine program for calculating a pressure-only fourth-order or higher-order polynomial (1) as a state function is incorporated.

  Also, as existing molding simulation programs, known dynamic explicit FEM (Pam-stamp, LS-DYNA, etc.), static explicit FEM (ITAS-3D, etc.), static implicit FEM (ABAQUS, AUTOFORM, etc.) Can be used.

(Example)
Hereinafter, the details of the molding simulation method by the finite element method considering the friction coefficient change during the molding process according to the present invention will be described by way of examples. A change in friction coefficient due to surface pressure of a 6000 series aluminum alloy having a thickness of 1 mm was obtained using a continuous sliding tester, and constants a ₀ , a ₁ , a ₂ , a ₃ , and a ₄ of Equation (1) were determined. .
μ = a ₀ + a ₁ P _N + a ₂ P _N ² + a ₃ P _N ³ + a ₄ P _N ⁴ (1)
However, a ₀ = 0.124, a ₁ = 0.0056, a ₂ = −0.0003,
a ₃ = 6 × 10 ⁻⁶ , a ₄ = −4 × 10 ⁻⁸
It is.

  Next, a disk-shaped test piece having a plate thickness of 1 mm and a diameter of 190 mm was prepared from the same material, the punch diameter was 100 mm, the punch shoulder R was 10 mm, the die diameter was 105 mm, and the die shoulder R was 10 mm. A drawing test was conducted. The mold is made of SKD11.

  The lubricating oil used in the test was the same as that used in the measurement of the friction coefficient, and the oil was applied to the test piece. A deep drawing test was conducted with a wrinkle pressing force of 4 t, and the breaking height was obtained. Further, the thickness of the portion 2 mm away from the rupture portion of the test piece after rupture (referred to as rupture plate thickness) was measured with a micrometer.

In the molding simulation calculation, the friction coefficient μ is calculated by the equation (1) (referred to as an example of the present invention), and the friction coefficient μ is set to a constant value regardless of the surface pressure P _N , specifically 0.15 ( The calculation was performed on both of them. The molding height by calculation was evaluated as the molding height when the fractured plate thickness of the test piece subjected to the actual press test was equal to the plate thickness obtained by the calculation of the molding simulation. In FIG. 3, the molding height at the time of the fracture | rupture by molding simulation is shown with measured data. FIG. 3 shows that the example of the present invention using the subroutine for calculating the friction coefficient as a fourth-order polynomial of the surface pressure has higher accuracy than the conventional example.

  FIG. 4 is a diagram illustrating an example of a hardware configuration of a computer capable of executing a molding simulation by the finite element method. As shown in the figure, a CPU 651, a ROM 652, a RAM 653, a keyboard controller (KBC) 655 of a keyboard (KB) 659, a display controller (CRTC) 656 of a display (CRT) 660 as a display unit, a hard disk ( An HD) 661 and a flexible disk (FD) 662 disk controller (DKC) 657 and a network interface controller (NIC) 658 for connection to the network 670 are connected to each other via a system bus 654. Configured.

  The CPU 651 comprehensively controls each component connected to the system bus 654 by executing software stored in the ROM 652 or the hard disk 661 or software supplied from the FD 662. In other words, the CPU 651 performs a control for realizing the operation of the present embodiment by reading a processing program according to a predetermined processing sequence from the ROM 652, the hard disk 661, or the flexible disk 662 and executing it. The RAM 653 functions as a main memory or work area for the CPU 651.

  The keyboard controller KBC655 controls an instruction input from a keyboard KB659 or a pointing device (not shown). The display controller 656 controls display on the display 660. The disk controller 657 controls access to the hard disk 661 and the flexible disk 662 that store a boot program, various applications, edit files, user files, a network management program, a predetermined processing program in the present embodiment, and the like.

  The network interface controller 658 exchanges data bidirectionally with devices or systems on the network 670.

  It should be noted that the shapes and structures of the respective parts shown in the above embodiments are merely examples of implementation in carrying out the present invention, and these limit the technical scope of the present invention. It should not be interpreted. That is, the present invention can be implemented in various forms without departing from the spirit or the main features thereof.

It is a schematic diagram of the flat plate pull-out test which is an example of a friction coefficient test method. It is a figure which shows the change by the surface pressure of a friction coefficient. It is a figure which shows the comparison with the measured value of the fracture | rupture shaping | molding height by shaping | molding simulation. It is a figure which shows an example of the hardware constitutions of the computer which can perform the shaping | molding simulation by a finite element method.

Explanation of symbols

1a, 1b Flat plate mold 2 Plate material _PN surface pressure (pressing force)
P _S pull-out force

Claims (3)

  A method for calculating a friction coefficient of a non-ferrous metal plate, comprising a step of calculating the friction coefficient of the non-ferrous metal plate by a fourth-order or higher polynomial approximation of only the surface pressure.   A forming simulation method for a non-ferrous metal plate, wherein a forming simulation by a finite element method is performed using the friction coefficient calculated by the friction coefficient calculating method for a non-ferrous metal plate according to claim 1. A procedure for measuring changes in the friction coefficient and surface pressure of a non-ferrous metal plate;
State function μ = a ₀ + a _{1 PN} + a _{2 PN} ² + a _{3 PN} ³ + a _{4 PN} ⁴
The constants a ₀ , a ₁ , a ₂ , a ₃ , a ₄ are determined using the above measurement results;
A non-ferrous metal sheet forming simulation method comprising a step of performing a forming simulation by a finite element method using a state function in which the constants a ₀ , a ₁ , a ₂ , a ₃ , and a ₄ are determined .

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