Abstract:
The stamping of a metal sheet within a stamping die is simulated. The die includes a drawbead running perpendicular to a draw direction. A plurality of successive states are generated for iteratively representing the metal sheet from a blank shape to a final stamped shape. The drawbead is represented as a two-dimensional flat band within a model of the stamping die. Forces acting on the metal sheet are calculated at each successive state to define a next successive state. The calculating step includes a restraining force of the drawbead acting on the metal sheet calculated in response to a predetermined function of a length of the metal sheet engaged in the flat band in respective states. The particular width and location of the flat band achieve improved accuracy of estimating the restraining force.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    Not Applicable. 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
       [0002]    Not Applicable. 
       BACKGROUND OF THE INVENTION 
       [0003]    The present invention relates in general to simulating a metal stamping process, and, more specifically, to providing a two-dimensional modeling of the restraining forces created by a drawbead that is accurate and computationally efficient. 
         [0004]    The purpose of a drawbead in a typical stamping process is to provide a restraining force that helps control material flow when a metal sheet or blank is deformed into the shape of the die. There are two stages in a typical draw (i.e., stamping) process: binderset and die closure. In binderset, upper and lower blankholders close up against the blank to initiate the restraining force. In die closure, the blank is drawn or punched into the die cavity and deformed into the shape of the die. A drawbead consists of a male and a female side that is mounted separately to upper and lower holders. When the two holders move to a closed position in the binderset phase, the two sides of the drawbead engage the blank and then deform the metal sheet into the bead. The drawbead then remains fully engaged during the die closure phase. As the blank is forced into the die cavity, the metal flows through the drawbead. The sheet metal undergoes stretching and bending deformations, moving against friction to create a restraining force acting on the metal flow. 
         [0005]    The restraining force generated by a drawbead changes throughout the entire binderset process. It reaches its maximum as the drawbead becomes fully engaged with sheet metal all around. Thus, the restraining force ramps up to a maximum value at the end of the binderset phase, and it keeps this value throughout the die closure phase until the blank edge (i.e., outline) moves into the drawbead. At that point, the force decreases according to the portion of the metal sheet still engaging the drawbead. Because of the desire to keep material utilization high and minimize scrap, stamping processes are often designed so that the blank outline partially or completely flows into and through the drawbead. 
         [0006]    When developing a stamping process and the tooling and the metal blanks to be used, various computer aided engineering (CAE) tools are often used to analyze candidate designs and to optimize them. One particular example of a method and apparatus for analyzing a stamping process is shown in U.S. Pat. No. 5,379,227, entitled “Method for Aiding Sheet Metal Forming Tooling Design,” which is incorporated herein by reference in its entirety. It is imperative for CAE engineers to accurately simulate the forces acting during the stamping process in order to properly choose an initial blank design that results in a desired final stamped shape while minimizing the outline of the blank. In conventional models, a line bead has been used to simulate a real drawbead due to its computational efficiency over a full three-dimensional model. In the line bead model, a drawbead centerline and its strength have been used to define a real drawbead&#39;s location and its maximum restraining force. This model remained fixed during a complete simulation. The prior models fail to simulate the force changes either during initial drawbead engagement or during movement of a blank edge into the drawbead. It would be desirable to simulate these force changes while remaining computationally efficient. 
       SUMMARY OF THE INVENTION 
       [0007]    In one aspect of the invention, a method is provided for simulating the stamping of a metal sheet within a stamping die including a drawbead having a gap G, a height H, and a centerline C 1  substantially perpendicular to a draw direction in which the metal sheet flows through the drawbead. A plurality of successive states are generated for iteratively representing the metal sheet from a blank shape to a final stamped shape. The drawbead is represented as a two-dimensional flat band with a width W and a centerline C 2 . The three-dimensional drawbead defines a curve at the intersection of the drawbead with a plane perpendicular to centerline C 1 , wherein width W is equal to the length of the curve. Centerline C 2  is parallel with centerline C 1  and is offset from centerline C 1  by a distance d substantially equal to (W−G)/2. Forces acting on the metal sheet are calculated at each successive state to define a next successive state. The calculating step includes a restraining force of the drawbead acting on the metal sheet calculated in response to a predetermined function of a length of the metal sheet engaged in the flat band in respective states. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]      FIG. 1  is a block diagram showing prior art apparatus for simulating a stamping process. 
           [0009]      FIG. 2  is a cross-sectional view of a stamping process at the beginning of the binderset phase. 
           [0010]      FIG. 3  is a cross-sectional view of stamping dies and a metal sheet at the beginning of a die closure phase. 
           [0011]      FIG. 4  is a cross-sectional view later during the die closure phase. 
           [0012]      FIG. 5  is a perspective view showing a flat blank placed on a stamping die prior to stamping. 
           [0013]      FIG. 6  is a perspective view of the stamped part with a final stamped shape. 
           [0014]      FIG. 7  is a cross-section showing progression into a drawbead during binderset. 
           [0015]      FIG. 8  is a graph showing the relationship between restraining force and the penetration into the drawbead during binderset. 
           [0016]      FIG. 9  is a cross-section showing flowing of the metal sheet through the drawbead during die closure, with the sheet edge or outline moving through the drawbead. 
           [0017]      FIG. 10  is a graph showing a relationship between restraining force and the proportion of the drawbead engaging the metal sheet during die closure. 
           [0018]      FIG. 11  is a diagram for defining a two-dimensional representation of the drawbead. 
           [0019]      FIG. 12  shows a curve useful in deriving a flat band representing the drawbead. 
           [0020]      FIGS. 13A and 13B  represent a planned view of a three-dimensional drawbead and a two-dimensional flat band in a die surface model, respectively. 
           [0021]      FIG. 14  is a flowchart showing one preferred method of the present invention. 
           [0022]      FIG. 15  is a block diagram showing a simulator in one preferred embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0023]    Referring now to  FIG. 1 , computer apparatus for performing a conventional stamping simulation includes a processing unit  10  and a display  11 . The processing unit implements finite element models  12  to represent the tooling structures and the sheet metal component during various stages of the stamping process. Processor  10  also implements a force and displacement calculator  13  for interacting with finite element models  12  to iteratively determine the changing shape of the metal sheet during the complete stamping process according to the response of the metal sheet to the forces being applied to it. The changing shape and other details of the simulation are shown to a user on display  11 . 
         [0024]    A typical stamping process is shown in greater detail in  FIGS. 2-4 . An upper die  15  has a punch portion  16  and upper drawbead portions  17  and  18  for drawbeads on opposite sides of the tool. Drawbead portions  17  and  18  protrude from upper die  15  in the direction of drawbead cavities  20  and  21  in lower blankholders  22  and  23 , respectively. A lower die  24  includes a die cavity  25  complementary with punch  16 . A metal sheet or blank  26  is loaded between upper and lower dies  15  and  24  and has an outline with opposite edges  27  and  28 .  FIG. 2  shows the initially loaded position of blank  26 , and  FIG. 3  depicts the completion of the binderset stage when the drawbeads are fully engaged. 
         [0025]    As shown in  FIG. 4 , lower die  24  continues to approach upper die  15  during the die closure phase, resulting in ends  27  and  28  approaching the respective drawbeads as blank  26  is drawn into the shape of the die surfaces. 
         [0026]      FIGS. 5 and 6  further illustrate the stamping process with the upper die removed for clarity. A metal blank  30  is formed into a desired shape by stamping in a stamping die  31  having drawbeads  32  and  33  on opposite sides of a die cavity  34 . Blank  30  has outlines  35  and  36  that flow at least partially through drawbeads  32  and  33  during stamping as shown in  FIG. 6 . Outlines  35  and  36  may have a wavy shape as shown in order to reduce the amount of blank material required, since the edges are typically removed as scrap after stamping. 
         [0027]    Modeling of the stamping process takes into account drawbead penetration height during the binderset phase as shown in  FIG. 7 . As upper die  15  progressively moves into positions  40 ,  41 , and  42 , die protrusion  17  has a penetration height h into drawbead cavity  20 . Height h goes from zero up to a maximum penetration height H determined by the geometry of protrusion  17  and cavity  20 . As shown in  FIG. 8 , during closing in the binderset phase an increasing restraining force is created as penetration height h increases. A maximum force F max  is obtained at the maximum penetration height H. The actual force depends upon the material properties of the metal sheet and the stamping die, the frictional condition between the metal sheet and the stamping die, and the geometry of the drawbead. Using known techniques, the relationship in  FIG. 8  is obtained in a conventional manner. 
         [0028]    During the subsequent die closure phase, the restraining force begins at maximum F max  and remains at maximum until a blank edge moves into the drawbead as shown in  FIG. 9 . As metal sheet  26  flows through the drawbead, edge  28  passes through so that a length L measured from edge  28  to the inside edge of the drawbead is decreasing. As shown in  FIG. 10 , restraining force F falls from maximum force F max  at a full engagement length L to a zero restraining force when engaged length L falls to zero. Once again, the actual force depends upon the material properties of the metal sheet and the stamping die, the frictional condition between the metal sheet and the stamping die, and the geometry of the drawbead. Using known techniques, the relationship in  FIG. 10  is obtained in a conventional manner. 
         [0029]    Rather than constructing a three-dimensional computationally intensive model, the present invention uses a two-dimensional representation of the drawbead derived according to the relationships shown in  FIG. 11 . An actual drawbead  45  being modeled is located between an upper die  46  and a lower holder  47  and has a centerline C 1 . Centerline C 1  is perpendicular to the draw direction in which the metal sheet flows through drawbead  45  and is midway between opposite ends of drawbead  45 . A plane  48  is taken perpendicular to centerline C 1  at a point where it intersects drawbead  45 . The intersection of drawbead  45  and plane  48  defines a curve  50  as shown in  FIG. 12 . Curve  50  spans a gap G of drawbead  45 . Curve  50  has a length as would be measured after stretching into a straight line that corresponds to a maximum potential engagement surface with the metal sheet as it flows through drawbead  45 . The full engagement length of curve  50  provides a width W for a two-dimensional flat band representing the drawbead as described below. 
         [0030]      FIG. 13A  shows an actual surface  55  of a die being modeled which includes an actual drawbead  56  having centerline C 1 .  FIG. 13B  shows a corresponding modeled surface  57  of the die which includes a flat band  58  to represent the drawbead, wherein flat band  58  has a width W corresponding to the length of curve  50  as determined in accordance with  FIGS. 11 and 12 . Flat band  58  has a centerline C 2  which is parallel with centerline C 1 . Flat band  58  is located in the surface model at a position such that its centerline C 2  is offset from centerline C 1  (as projected into the two-dimensional surface model) by a distance d, wherein d is substantially equal to (W−G)/2. For portions of the metal sheet located within flat band  58  during a simulation, a force determination can be performed according to the relationships shown in  FIGS. 8 and 10 . Those relationships together with the particular placement of flat band  58  provide both an accurate estimate of the forces and computational efficiency. 
         [0031]    A preferred method of the invention is shown in  FIG. 14 . In step  60 , the metal sheet is initially represented as a flat blank. In the binderset phase, the holder dies are moved until they achieve full engagement (and the main punching surfaces do not engage and there is no significant flow of the metal sheet. A binder position of the holder dies is incremented in step  61 . Based on the amount of movement, all forces acting on the metal sheet are calculated in step  62  including the calculation of a drawbead restraining force that is based on penetration height h. Displacements occurring as a result of the forces are calculated in step  63  and the state (i.e., shape) of the metal sheet is updated. A check is made in step  64  to determine whether the binderset phase has completed. If not, then a return is made to step  61  for determining the result of the next incremental movement of the binder. 
         [0032]    Upon completion of the binderset phase, the die closure phase begins at step  65  wherein the punch die position is incremented by a predetermined step size. The resulting forces acting on the metal sheet are calculated in step  66 , including a drawbead restraining force determined in response to a length L the engages the flat band (i.e., the effective zone). In step  67 , displacements of respective points on the metal sheet are calculated and the resulting state or shape of the metal sheet is updated. A check is made in step  68  to determine whether die closure has completed. If not, then a return is made to step  65  for the next increment. Otherwise, results of the simulation are displayed to a user in step  69 . 
         [0033]      FIG. 15  shows a simulator system  70  in accordance with one embodiment of the present invention. A sheet representation module  71  includes a memory for storing representations of a plurality of successive states of the metal sheet. A configuration module  72  includes a conventional surface model  73  representing surfaces of the tooling dies along with information relating to their movements during a stamping cycle. Configuration module  72  further includes a drawbead representation  74  for storing a representation of the drawbead as a two-dimensional flat band as described above. 
         [0034]    A calculation module  75  is coupled to sheet representation module  71  for receiving a current state of the metal sheet and is coupled to configuration module  72  for determining the interaction of a current state with the tooling surfaces and with the flat band representation of the drawbead. For calculating the restraining force of the drawbead acting on the metal sheet, calculation module  75  includes function/look-up tables (LUT)  76  and  77 . Function/LUT  76  stores the relationship between penetration height and restraining force during the binderset phase as shown in  FIG. 8 . Function/LUT  77  stores the restraining force relationship used during the die closure phase as shown in  FIG. 10 . Either a mathematical representation of the functions or pre-calculated look-up tables can be employed.