Machinery's Handbook, 31st Edition
Drawing Sheet Metal 1429 Force for the First Drawing Operation: The calculation of the punch force for the first drawing operation (neglecting friction) is given by the following formula: (44) where d m 1 = mean diameter of shell after the first operation, (inch or mm) T = material thickness, (inch or mm) UTS = ultimate tensile strength of the material, (lb/in 2 or N/mm 2 ) Force for Subsequent Drawing Operations: Subsequent drawing operations are differ ent from the first operation: as in the deep-drawing process, the flange diameter decreases but the zone of the plastic deformation does not change. The punch force for the next draw ing operation can be calculated by the approximate empirical formula as follows: (45) where d p = punch diameter (inch or mm) D = blank diameter (inch or mm) T = material thickness (inch or mm) UTS = ultimate tensile strength of the material (lb/in 2 or MPa) Shapes of Blanks for Rectangular Shells: There is no formula for determining the shape of the blank for rectangular drawing that will produce the part as drawn to print. All corner contours must be developed. However, the following conservative procedure will get the die in the final design ballpark with a minimum of trials. When laying out a blank by this method, first draw a plan view of the finished shell or lines representing the shape of the part at the bottom, the corners being given the required radius, as shown in Fig. 20. Next, insert the sides and ends, making the length L and the width W equal to the length and width of the drawn part minus twice the radius r at the corners. To provide just the right amount of material for the corners, the first step is to find what blank diameter will be required to draw a cylindrical shell having a radius r . This diameter can be calculated by the formula for the blank diameter ( D ) of the cylindrical shell: (46) where D = blank diameter (inch or mm) d = diameter of drawn shell (inch or mm) h = height of shell (inch or mm) After determining the diameter D , scribe arcs at each corner having radius R equal to one-half of diameter D . The outline of the blank for the rectangular part is then obtained by drawing curved lines between the ends and the sides, as shown in Fig. 20. These curves should touch the arcs R . L F d T UTS m 1 1 π = ^ h . F d T UTS d D 07 i p p r = − ^ c h m D d dh 4 2 = −
h
D
W
r
Fig. 20. Layout Design for Deep Drawn Rectangular Shell
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