Sheet metal drawing — estimate the blank size for a cylindrical cup A cylindrical cup of diameter 25 mm and height 15 mm is to be made by deep drawing. Neglecting thinning and trimming, the approximate diameter of the round blank should be chosen as (closest value).

Introduction / Context:In deep drawing design, an early sizing task is to estimate the flat blank diameter that supplies sufficient material for both the side wall and the base of a cylindrical cup. A quick, conservative estimate helps select tooling and evaluate draw ratio before detailed process planning and allowances for trimming, ironing, or corner radii are added.

Given Data / Assumptions:

• Cup outside diameter, d = 25 mm.
• Cup height, h = 15 mm.
• Neglect thinning, corner radii, draw beads, and trimming allowances.
• Constant thickness assumption (area conservation).

Concept / Approach:For a cylindrical cup without a flange, equate the blank area to the area of the cup's base plus the area of its side wall (developed). Using plain-text formulas: blank area = (pi/4)Db^2, side area = pidh, base area = (pi/4)d^2. Solving for blank diameter Db gives Db = sqrt(d^2 + 4dh). This provides an approximate value prior to checking draw ratio limits and adding practical margins for trimming.

Step-by-Step Solution:

Verification / Alternative check:Check limiting draw ratio LDR. Blank diameter about 46 mm gives initial draw ratio Db/d ≈ 46/25 ≈ 1.84, typically within feasible limits for many draw-quality steels with appropriate lubrication and corner radii, though process design may still require redrawing or ironing depending on grade.

Why Other Options Are Wrong:

• 42 mm, 44 mm: underestimates area; inadequate material for side wall.
• 48 mm, 50 mm: overly conservative; adds excess material and trimming waste.

Common Pitfalls:Forgetting to include the base area; confusing inner and outer diameters; ignoring allowances for trimming when moving from estimate to die design.

Final Answer: