Machinery's Handbook, 31st Edition
1428 Drawing Sheet Metal where M = approximate mean height of drawn shell (inch or mm); h = height of drawn shell (inch or mm); t = thickness of shell (inch or mm); and T = thickness of metal (inch or mm) before drawing. After determining the mean height, the blank diameter for the required shell diameter is obtained from Table 16, the mean height being used instead of the actual height. Example 2 : Suppose a shell 2 inches (mm) in diameter and 3 3 ∕ 4 inches (mm) high is to be drawn, and that the original thickness of the stock is 0.050 inch (mm) and the thickness of the drawn shell, 0.040 inch (mm). To what diameter should the blank be cut? Obtain the mean height from Formula (41): . . . M T ht 0050 375 0040 3inches (mm) # = = = According to Table 16, the blank diameter for a shell 2 inches (mm) in diameter and 3 inches (mm) high is 5.29 inches (mm). Formula (41) is accurate enough for all practical purposes, unless the reduction in the thickness of the metal is greater than about one-fifth of the original thickness. When there is considerable reduction, a blank calculated by this formula produces a shell that is too long. However, the error is in the right direction, as the edges of drawn shells are ordinarily trimmed. If the shell has a rounded corner, the radius of the corner should be deducted from the figures given in the table. For example, if the shell referred to in Example 2 had a corner of 1 ∕ 4 -inch (mm) radius, the blank diameter would equal 5.29 − 0.25 = 5.04 inches (mm). Another formula sometimes used for obtaining blank diameters for shells, when there is a reduction in the thickness of the stock, is as follows: (42) where D = blank diameter (inch or mm); a = outside diameter (inch or mm); b = inside diameter (inch or mm); t = thickness of shell at bottom (inch or mm); and, h = depth of shell (inch or mm). Equation (42) is based on the volume of metal in the drawn shell. It is assumed that the shells are cylindrical, and no allowance is made for a rounded corner at the bottom, or for trimming the shell after drawing. To allow for trimming, add required amount to depth h . When a shell is of irregular cross section, if its weight is known, the blank diameter ( D ) can be determined by the following formula: (43) where D = blank diameter, inches (mm) W = weight of shell, lbs (kg) In the construction of dies for producing shells, especially of irregular form, a common method to be used is to make the drawing tool first. The required blank diameter then can be determined by trial. One method is to cut a trial blank as near to size and shape as can be estimated. The outline of this blank is then scribed on a flat sheet, after which the blank is drawn. If the finished shell shows that the blank is not of the right diameter or shape, a new trial blank is cut either larger or smaller than the size indicated by the line previously scribed, this line acting as a guide. If a model shell is available, the blank diameter can also be determined as follows: First, cut a blank somewhat large and from the same material used for making the model; then, reduce the size of the blank until its weight equals the weight of the model. Forces: The punch force for drawing a cylindrical shell needs to supply the various types of work required in deep drawing, such as the work of deformation, redundant work, fric tion work, and the work required for ironing (if required). w = weight of metal, lb/in 3 (kg/mm 3 ) t = thickness of the shell, inch (mm) D a a b t h 2 2 2 = + − ^ h . D wt W = 11284
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