Deep Drawing Clearance, Radii and Force
A drawn shell is made or lost on three numbers. The clearance between punch and die, the radius at the die opening, and the amount of metal the blank carries. This page collects the source tables for those numbers, the blank diameter formulas, and the force and reduction limits that decide how many draws a shell needs.
| Blank thickness, in. (mm) | First draws | Redraws | Sizing draw |
|---|---|---|---|
| Up to .015 (0.38) | 1.07t to 1.09t | 1.08t to 1.1t | 1.04t to 1.05t |
| .016 to .050 (0.41 to 1.27) | 1.08t to 1.1t | 1.09t to 1.12t | 1.05t to 1.06t |
| .051 to .125 (1.30 to 3.18) | 1.1t to 1.12t | 1.12t to 1.14t | 1.07t to 1.09t |
| .136 (3.45) and up | 1.12t to 1.14t | 1.15t to 1.2t | 1.08t to 1.1t |
Source: Fundamentals of Tool Design, 6th edition (Society of Manufacturing Engineers, 2010), Chapter 8, Table 8-3. The values are the punch to die space expressed in multiples of t, the thickness of the original blank.
- In the source example a blank of .125 in. (3.18 mm) takes a draw clearance of .138 to .140 in. (3.50 to 3.56 mm), which is the 1.1t to 1.12t row read against the working thickness.
- The sizing draw column is used for straight sided shells where the diameter or the wall thickness matters, or where the surface finish has to improve enough to cut the finishing cost.
| Thickness of stock, in. (mm) | Drawing radius, in. (mm) |
|---|---|
| 1/64 (0.4) | 1/16 (1.6) |
| 1/32 (0.8) | 1/8 (3.2) |
| 3/64 (1.2) | 3/16 (4.8) |
| 1/16 (1.6) | 1/4 (6.4) |
| 5/64 (2.0) | 3/8 (9.5) |
| 3/32 (2.4) | 7/16 (11.1) |
| 1/8 (3.2) | 9/16 (14.3) |
Source: Fundamentals of Tool Design, 6th edition (Society of Manufacturing Engineers, 2010), Chapter 8, Table 8-2. The values are built on a radius of roughly four times the stock thickness, and the source allows four to six times in practice.
The two failure modes that sit on either side
Too large a radius lets the blank holder release the metal before the draw is complete, and the wall wrinkles. For a straight walled shell drawn without a flange, a large radius can fold the metal as blank holder control is lost. Beyond six times the stock thickness there is little further reduction in drawing force, and approaching ten times the thickness invites puckering as the metal flows over the radius.
Too small a radius ruptures the material as it crosses the radius or bears against the punch face. A tight radius also strains the metal harder, which increases work hardening, which in turn asks for more force on the next pass.
| Shell geometry | Formula for the blank diameter |
|---|---|
| d/r of 20 or more | D = √(d² + 4dh) |
| d/r between 15 and 20 | D = √(d² + 4dh − 0.5r) |
| d/r between 10 and 15 | D = √(d² + 4dh − r) |
| d/r below 10 | D = √((d − 2r)² + 4d(h − r) + 2πr(d − 0.7r)) |
| Wall ironed thinner than the bottom | D = √(d² + 4dh × t / T) |
- D is the blank diameter, d the shell diameter, h the shell height, r the corner radius, t the wall thickness and T the bottom thickness.
- The formulas assume that the surface area of the blank equals the surface area of the finished shell. Where the wall is ironed thinner than the bottom, the volume of metal has to match instead, and a shell such as a brass case is developed by trial.
- In the source example a 2.75 in. (69.9 mm) shell 1.5 in. (38.1 mm) high with a d/r ratio above 20 draws from a 4.9 in. (124.5 mm) blank, and the ratio of blank area to punch nose area of about 4 to 1 keeps it inside a single draw.
| Limit | What the source gives |
|---|---|
| First draw, blank area against punch area | The area of the blank should not be more than 3.5 to 4 times the cross-sectional area of the punch. The greater the difference between blank and shell diameter, the more metal has to flow in one operation and the higher the stress required to move it. |
| Thickness ratio t/D | As the ratio falls, the tendency to wrinkle rises and more blank holder pressure is needed to control the flow and keep wrinkles from starting. |
| Single action first draw | A top limit of about 48 percent reduction, taken from practice. |
| Double action redraw | A limit of 30 percent, modified by the corner radii, friction and the angle of the blank holding faces against the shell wall. |
| Third and later draws | Not more than 20 percent reduction without an annealing operation, because of the strain hardening already in the metal. |
Where the limits come from
The area of metal held between the blank holding faces has to stay reasonably proportional to the area the punch is pressing, because there is a limit to how much metal can be made to flow in one operation. Steel that work hardens between passes has to be softened before the next one, and the schedules for that are on the annealing and normalizing chart.
| Quantity | Formula | Working notes |
|---|---|---|
| Drawing force | P = π d t s (D / d − C) | s is the yield strength of the metal, and C a constant of 0.6 to 0.7 that covers friction and bending. The whole load passes through the punch to the bottom of the cup. |
| Blank holder force | A few pounds up to one third of the drawing force | Determined largely by trial and error. Enough pressure to prevent wrinkles without retarding the flow of metal into the die. |
The worked example
In the source example the drawing force works out to 20 tons (178 kN) for the shell described above, and a blank holder force around 6 tons (53 kN) is quoted as more than adequate. A standard 30 ton (267 kN) open backed inclinable press carries the job.
The force is limited by the tensile failure of the sidewall, so it depends on the cross sectional area of the wall and on the yield strength of the metal as it is worked. Where the force is limited by the press rather than the die, the answers are the same as in cutting. Spread the work over the stroke, and keep the peak away from the bottom of the press stroke.
| Root cause | What it looks like |
|---|---|
| Drawability of the stock too low | The wall necks or thins near the punch radius before the depth is reached. |
| Blank holder force too high | Metal cannot flow into the cavity and the wall stretches until it tears. |
| Scoring or galling on the die surfaces | Drag rises along the draw radius and the wall picks up damage. |
| Blank holder geometry and draw radius | The metal is not allowed to thicken and flow smoothly into the die cavity. |
| Incorrect or insufficient lubricant | Friction and force rise together, and the surface finish suffers. |
| Depth of draw or percentage reduction too great | The sidewall fails before the full depth is reached. |
| One more draw needed | The shell calls for a redraw, with an anneal between passes where the steel work hardens quickly. |
Catch the neck before it breaks
A necking failure is preceded by local thinning that is usually invisible on the finished part. The thinning can be tracked with an ultrasonic thickness gage before the wall breaks, and the areas that need watching are the ones where the part is drawn or formed hardest. The onset of trouble shows up first as a quickening trend in the measurements.
Where the damage is scoring or galling on the die face, the relevant wear mode and the tool steels chosen against it are collected on the adhesive wear resistant tool steels page.
| Operation class | Typical lubricants |
|---|---|
| Mild operations | Mineral oil of medium heavy to heavy viscosity, soap solutions of 0.03 to 2 percent high titer soap, or fat and fatty oil emulsions in soap base. |
| Medium operations | Fat or oil in soap base emulsions carrying finely divided fillers such as whiting or lithopone, sulfurized oils, dissimilar metals deposited on steel, rust or phosphate deposits, or a dried soap film. |
| Severe operations | Dried soap or wax film with light rust or phosphate coatings, sulfide or phosphate coatings with filled emulsions, sulfur bearing combinations, or sulfurized oil base blends with fillers. |
The draw ring is a tool steel part
The die of a draw die is often the draw ring itself, made of tool steel with the cavity edge forming a spherical zone over which the metal is drawn. Large drawing dies usually carry a replaceable inserted draw ring in tool steel, so the working edge can be renewed without scrapping the block behind it.
Material moves up with the run length
The source scales the die material with the number of parts. Below a hundred parts a plastic or zinc alloy form is satisfactory, a few hundred parts run in a plain cast iron ring, and the cast irons can be flame hardened or hard chrome plated and ion nitrided for longer runs. Tool steel enters for long runs in small dies, where the choice follows wear, strength and hardness, and carbide inserts take the very long runs on abrasive stock.
The grade question for a draw die
Which tool steel carries a deep drawing die follows the same logic as the rest of the cold work family. The shortlist used on this site, with the reasons for each grade, is on the deep drawing die selection page, and a longer discussion of the trade behind it sits in the deep drawing tool steel article.
Blocks arrive annealed
A draw die is machined in the soft state and hardened afterwards, so the block is ordered in the annealed condition with enough stock for movement during heat treatment. What that condition means for machining and for the hardening step is set out on the annealed condition page, and the forming and drawing family as a whole is collected under forming, drawing and bending dies.
Confirm before quoting
These figures are for general reference only. Draw clearance and radii move with the material, the lubricant, the blank holder and the press. Confirm against your own trial or contact Aobo Steel.
Related reference pages
Cold work tool steels · Die clearance and cutting force · Springback and bend allowance · Forming and drawing selection · Surface roughness chart · Tool steel supply
Sources: Fundamentals of Tool Design, Sixth Edition (Society of Manufacturing Engineers, 2010), Chapter 8, the draw die design, reduction factors, force, failure cause and lubrication sections, with Tables 8-2 and 8-3 and Equations 8-17 to 8-22. Reference data for comparison only. Confirm the draw schedule, the die material and the press capacity with your die shop before production. Aobo Steel supplies tool steel in the annealed condition.