Deep Drawn Cylinder Blank Diameter Reference

Choose a method from the part geometry

A cylindrical cup blank can be estimated by conserving the material in the finished part. The quick shop relationship uses a sharp corner and unchanged wall thickness. A more detailed estimate adds the bottom, rounded corner and cylindrical wall using dimensions measured at the mid-surface. If drawing reduces wall thickness by ironing, material volume is the appropriate starting point. These methods answer different geometry cases; using a formula outside its assumptions can shift the blank diameter enough to affect trim and material use.

For every estimate, define whether diameter, height and radius are inside, outside or mean dimensions. The mean surface is halfway through the sheet thickness. A drawing commonly gives outside dimensions, so using them without conversion can bias the result. Keep all lengths in one unit system and label the result as a preliminary mid-surface blank diameter until the tooling plan specifies the cut size.

Sharp-corner estimate

For a plain cylindrical cup with no flange and a sharp bottom corner, the classical first-pass equation is D = √(d² + 4dh), where d is the mean cup diameter and h is the mean cup height. It equates the flat circular blank area to the approximate bottom-plus-wall area. It assumes the wall retains its thickness and the corner radius is zero. The relationship is convenient for a quick check, but it can overestimate when a real cup has a generous corner radius.

Do not use the sharp-corner estimate as a forming-feasibility test. It does not calculate draw force, blank-holder load, wrinkling, tearing or the number of draws. Those depend on material formability, thickness, punch and die radii, lubrication and process control. If the calculated draw ratio looks high for the material, ask the forming supplier to review the process rather than simply increasing the blank.

Area method for a radiused cup

For a cup with a flat bottom and a bottom radius, the mid-surface area method breaks the formed surface into a bottom disc, a quarter-torus corner and a cylindrical wall. Add those areas to get A, then solve D = √(4A/π). Use the mean diameter, mean height and mean corner radius. A retained flange must also be included as an annular area. The result estimates the material area needed before earing and trimming allowances are added.

A published tooling-engineer example uses a cup with 50 mm outside diameter, 40 mm outside height, 5 mm outside bottom radius and 1 mm wall. Its corresponding mean dimensions are 49 mm, 39.5 mm and 4.5 mm. The guide reports 97.9 mm from the area method, compared with 100.7 mm from the sharp-corner method on the same mean dimensions. This comparison illustrates why the radius matters; it is not a universal correction factor.

Trimming and production validation

Rolled sheet can draw unevenly around the circumference, leaving an eared rim. A trim allowance makes room to remove that rim, but its value varies with stock, blank-holder control, geometry and the required edge. The cited guide describes a roughly 3–8% preliminary allowance. Apply it to the calculated estimate only as a planning input, then confirm the actual blank through draw trials and measurement.

The cut blank diameter can also differ from the mid-surface calculation depending on how the shop defines its drawing dimension and blank edge. Record that convention on the drawing. If the part is ironed, if the wall is relatively thick, or if volume changes through removed features, model the finished volume and sheet thickness instead of assuming area conservation. A formed part should be checked for wall thickness, rim condition and dimensional requirements.

Limits of the reference

This lookup covers simple cylindrical cups. It does not replace a finite-element forming model, a material-specific limiting draw ratio, a tool design review or a production tryout. The supplier’s worked example is a published engineering guide, not a universal standard. Use the actual alloy, temper, thickness tolerance and cup geometry, and record the source assumptions beside the estimate. A qualified forming engineer should approve the released blank size and any production change.

Source and scope

Source: Balford, How To Calculate Blank Size For A Deep Drawn Cup?. Use the source edition and conditions stated in the table.