Press Tools, Punches, Dies and Sheet-Metal Forming: Approximate Tensile Strengths for Punching Calculations

Approximate Tensile Strengths for Punching Calculations

The Practical Shortcut Formulas

For circular holes in steel:

$$F_{tons} = D \times T \times 80$$

Where $D$ = hole diameter (inches), $T$ = stock thickness (inches), and 80 is the factor for steel. The result is force in tons.

Example: Punch a 2-inch diameter hole through ¼-inch steel:

$$F = 2 \times 0.25 \times 80 = 40 \text{ tons}$$

For non-circular holes in steel:

Replace the hole diameter with one-third of the perimeter of the hole.

Example: Punch a 1-inch square hole in ¼-inch steel. The perimeter is 4 inches, so one-third is 1⅓ inches:

$$F = 1.333 \times 0.25 \times 80 = 26.67 \text{ tons}$$

For brass: Replace the factor 80 with 65.

Example: Punch a 1 × 2-inch rectangular hole in ¼-inch brass. The perimeter is 6 inches, so one-third is 2 inches:

$$F = 2 \times 0.25 \times 65 = 32.5 \text{ tons}$$

Quick-Reference Punching Force Factors

Shut Height of Press — The Setup Specification That Prevents Disasters

The term "shut height" describes the die space when the slide is at the bottom of its stroke and the slide connection has been adjusted upward as far as possible.

The ambiguity problem: Shut height can be measured two ways:

1. From the lower face of the slide to the top of the bed
2. From the lower face of the slide to the top of the bolster plate

Best practice: Define shut height as the distance from the top of the bolster to the bottom of the slide, with the stroke down and the adjustment up. Most dies are mounted on bolster plates of standard thickness, and a misunderstanding that results in too much die space is less serious than having insufficient die space.

The shut height of a die is the distance from the bottom of the lower section to the top of the upper section (or punch), excluding the shank, measured when the punch is in the lowest working position.

Diameters of Shell Blanks — The Mathematics of Drawn Shells

This is where the real engineering begins. Calculating blank diameters for drawn cylindrical shells is the gateway skill that separates competent toolmakers from guesswork operators.

Formula 1: Sharp-Cornered Shells (Thin Stock)

$$D = \sqrt{d^2 + 4dh}$$

Where:

• $D$ = diameter of flat blank
• $d$ = diameter of finished shell
• $h$ = height of finished shell

Example: A shell with diameter 1.5 inches and height 2 inches:

$$D = \sqrt{1.5^2 + (4 \times 1.5 \times 2)} = \sqrt{2.25 + 12} = \sqrt{14.25} = 3.78 \text{ inches}$$

Formula 2: Round-Cornered Cups

$$D = \sqrt{d^2 + 4dh} - r$$

Where $r$ = the radius of the corner. This formula gives fairly accurate results provided the radius does not exceed approximately ¼ of the shell height.

Formula 3: When Stock Thickness Reduces During Drawing

When heavy stock is drawn and the shell becomes thinner than the original stock, Formulas 1 and 2 produce blanks that are too large. First, calculate the mean height:

$$M = \frac{h \times t}{T}$$

Where:

• $M$ = approximate mean height of drawn shell
• $h$ = height of drawn shell
• $t$ = thickness of shell after drawing
• $T$ = thickness of metal before drawing

Then use $M$ instead of $h$ in the blank diameter lookup.

Example: A shell 2 inches in diameter, 3¾ inches high, original stock thickness 0.050 inch, drawn shell thickness 0.040 inch:

$$M = \frac{3.75 \times 0.040}{0.050} = 3.0 \text{ inches}$$

The blank diameter for a 2-inch diameter shell at 3-inch mean height is 5.29 inches. If the shell has a ¼-inch corner radius, subtract: 5.29 − 0.25 = 5.04 inches.

Important: Formula 3 is accurate unless the thickness reduction exceeds about one-fifth of the original thickness. Greater reductions produce a shell that's too long — but this error is acceptable because drawn shell edges are ordinarily trimmed.

Formula 4: Volume-Based Blank Diameter (Heavy Reduction)

$$D = \sqrt{a^2 + \frac{(a^2 - b^2) \times h}{t}}$$

Where:

• $a$ = outside diameter of shell
• $b$ = inside diameter of shell
• $t$ = thickness of shell at bottom
• $h$ = depth of shell

Formula 5: Irregular Cross-Section Shells (Weight-Based)

$$D = \sqrt{\frac{1.1284 \times W}{w \times t}}$$

Where:

• $W$ = weight of shell
• $w$ = weight of metal per cubic inch
• $t$ = thickness of the shell

Blank Diameters for Drawn Cylindrical Shells — Reference Table

This table provides blank diameters for sharp-cornered shells across a wide range of shell diameters and heights. Values are in inches.

The Trial Method for Irregular Shells

For shells of irregular cross-section, the most reliable method is empirical:

1. Make the drawing tool first.
2. Cut a trial blank as close to estimated size as possible.
3. Scribe the outline of this blank on a flat sheet.
4. Draw the blank. If the finished shell shows the blank is wrong, cut a new trial blank either larger or smaller, using the scribed line as a guide.

Alternative method (when a model shell exists): Cut a blank somewhat large from the same material used for the model, then reduce the size until its weight equals the model's weight.

Depth and Diameter Reductions of Drawn Cylindrical Shells

Picture this scenario: an illustrative engineering practitioner designs a four-stage progressive die for a cylindrical housing. He sizes the reductions evenly — 25% per draw. By the third draw, shells are cracking at the base. His mistake? He didn't account for work hardening between draws, and his reductions exceeded what the material could tolerate without annealing.

The Fundamental Rules

Rule 1: The depth or length of the first draw should never be greater than the diameter of the shell.

Rule 2: If the shell has a flange at the top, you may not be able to draw as deeply as Rule 1 allows, because the larger blank needed for the flange subjects the stock to higher tensile stress.

Rule 3: The depth given the shell on the first draw should equal approximately one-third the diameter of the blank.

Rule 4: Ordinarily, sheet steel of any thickness up to ¼ inch can be drawn so that the diameter of the first shell equals about six-tenths (60%) of the blank diameter.

Diameter Reduction Limits in the supplied reference figures assume the shell is annealed after the first draw and at least between every two following operations

Example: A shell made of 1/16-inch stock is 3 inches in diameter after the first draw. It can be reduced 20% on the next draw (to 2.4 inches), then 20% again (to 1.92 inches), and so on until the required diameter is obtained.

Double-Action Press Advantage

In double-action presses, where the inside of the cup is supported by a bushing during drawing, the possible reductions increase significantly to approximately 30%, 24%, 18%, 15%, and 12% respectively. These same increased figures also apply to brass in single-action presses.

Ironing Limits

The extent to which a shell can be ironed (thinned) in one drawing operation:

Critical Warning: Reduction in gauge means greater force against the bottom of the shell. When significant ironing is needed, the diameter reduction per draw must be smaller to prevent bottom fractures.

Special Considerations

• Taper shells require smaller reductions than cylindrical shells because the metal tends to wrinkle if the shell is much larger than the punch.
• Necking operations (drawing a short portion of the lower part into a long neck) may be performed without the frequent annealing required for diameter reductions.
• When a hole must be pierced at the bottom of a cup before further drawing, always pierce from the opposite direction to the drawing direction. Machine the metal around the pierced hole to prevent crack initiation in subsequent draws.

Annealing Drawn Shells — The Work-Hardening Reset

Annealing Requirements by Material

Drawing Brass — Special Techniques

When drawing brass shells or cup-shaped articles, the depth of the first draw can equal the diameter of the shell. By heating brass to a temperature just below a dull red (visible in a dark room), difficult shapes — otherwise nearly impossible — can be drawn, including shapes with square corners.

Drawing Rectangular Shapes — Corner Radius Rules

When drawing square or rectangular shapes, maximize corner radii. Defects occur primarily in corners, and smaller radii limit achievable depth.

These figures come from actual production experience and can be exceeded slightly with material prepared specifically for the process. If the box needs to be deep and the radius is small, multiple drawing operations are required.

Bending Sheet Metal — Formulas, Tables, and Precision Methods

Consider a fabrication shop that produces HVAC ductwork, electrical enclosures, and architectural panels. Every single part requires accurate bending calculations. The question is always the same: How long must the straight stock be before bending, so that the finished part hits the target dimensions?

The answer depends on three variables: material type, material thickness, and bend radius.

The Three Core Bending Formulas

Where $L$ = length (inches) of straight stock required for a 90° bend, $T$ = thickness (inches), and $R$ = inside radius of bend (inches):

Formula 1 — Soft Brass and Soft Copper:

$$L = (0.55 \times T) + (1.57 \times R)$$

Formula 2 — Half-Hard Copper and Brass, Soft Steel, and Aluminum:

$$L = (0.64 \times T) + (1.57 \times R)$$

Formula 3 — Bronze, Hard Copper, Cold-Rolled Steel, and Spring Steel:

$$L = (0.71 \times T) + (1.57 \times R)$$

These formulas are based on extensive experiments by the an electrical manufacturer and apply to parts bent with simple tools or on the bench, where limits of ±1/64 inch are specified.

Bends at Angles Other Than 90 Degrees

For any angle other than 90°, calculate $L$ using the formulas above, then multiply:

$$L_{actual} = L \times \frac{\text{Angle of Bend}}{90}$$

Critical Distinction: The "angle of bend" is the angle through which the material has actually been bent — not necessarily the angle shown on the drawing.

Examples of angle interpretation:

• Drawing shows 60° → Actual bend angle = 180° − 60° = 120°
• Drawing shows 60° (direct angle) → Actual bend angle = 60°
• Drawing shows 30° from vertical → Actual bend angle = 90° − 30° = 60°

Worked Example: Multi-Bend Part in Soft Steel

Problem: Find the length before bending for a part with a 180° bend (R = 0.375 in.) and a 60° bend (R = 0.625 in.) in soft steel, material thickness 0.125 in. Straight section = 3.5 inches.

For the 180° bend (using Formula 2):

$$L = [(0.64 \times 0.125) + (1.57 \times 0.375)] \times \frac{180}{90} = 1.338 \text{ inches}$$

For the 60° bend (using Formula 2):

$$L = [(0.64 \times 0.125) + (1.57 \times 0.625)] \times \frac{60}{90} = 0.707 \text{ inches}$$

Total length before bending:

$$3.5 + 1.338 + 0.707 = 5.545 \text{ inches}$$

Lengths of Straight Stock Required for 90° Bends — Reference Tables

Table 2: Half-Hard Brass, Sheet Copper, Soft Steel, and Aluminum

Table 3: Hard Copper, Bronze, Cold-Rolled Steel, and Spring Steel

Other Bending Allowance Methods

Quick rule for sheet steel and brass: Add ⅓ to ½ of the stock thickness for each bend to the sum of the inside dimensions. Use ⅓ for soft stock and ½ for hard material.

V-Die Deduction Formula:

$$X = 1.67 \times B \times G$$

Where:

• $X$ = amount to deduct from the sum of outside bend dimensions
• $B$ = number of bends
• $G$ = decimal equivalent of the gauge

Draw-Bench Deduction Formula:

$$X = 1.33 \times B \times G$$

Fine Blanking — Precision Flat Components from Sheet Metal

an illustrative engineering practitioner was outsourcing precision flat components — small spur gears, lock plates, and ratchet teeth — to a wire EDM subcontractor. The cost per part was staggering, and lead times stretched to weeks. When she discovered fine blanking, those same parts could be produced at stamping speeds with tolerances that rivaled wire-cut parts. Edge finishes as smooth as 80 µin. Ra. Perpendicularity within 0.004 inch on 0.2-inch-thick material.

Fine blanking changed her business. Here's how it works and when to use it.

How Fine Blanking Differs from Conventional Stamping

Fine blanking uses special presses and tooling with three separate and distinct movements:

1. Clamping the work material
2. Blanking the part
3. Ejecting the finished part

Forces required are 1.5 to 2.5 times those used in conventional stamping, so machines and tools must be designed and constructed accordingly.

Press Types for Fine Blanking

All fine-blanking press types are also suited to embossing, coining, and impact extrusion work.

Tooling Materials and Clearances

Compare this to conventional blanking clearances of 0.005–0.015 inch per side for typical stock thicknesses. Fine blanking operates at an order of magnitude tighter clearance.

The V-Projection System — The Secret Behind Fine-Blanking Quality

The clamping elements are sharp projections of 90-degree V-section that follow the outline of the workpiece. They are incorporated into each tool as part of the stripper plate (for thin material) and also as part of the die plate (for material thicker than 0.15 inch).

How it works:

1. Pressure is applied to the V-projection elements before the blanking operation begins.
2. The sharp edges penetrate the material surface, preventing sideways movement of the blank.
3. The penetrating pressure squeezes the material, causing it to flow toward the cutting edges.
4. This flow reduces the usual rounding effect at the cut edge.

When small details like gear teeth must be produced, V-projections are used on both sides of the work, even with thin materials, to enhance the flow effect.

V-Projection Positioning Rules

• A small V-projection close to the line of cut has about the same effect as a large V-projection spaced away from the cut.
• If the V-projection is too close to the cut, it may move out of the material at the start of cutting, reducing its effectiveness.
• Positioning farther away increases both material consumption and blanking force requirements.
• V-projection location also affects tool life.

Calculating Fine-Blanking Forces

Cutting Force (lb):

$$F_{cut} = 0.9 \times L_{cut} \times T \times \sigma_{tensile}$$

Where:

• $L_{cut}$ = length of cut (inches)
• $T$ = material thickness (inches)
• $\sigma_{tensile}$ = tensile strength (lbf/in²)

Clamping Force (V-projection pressure) in lb:

$$F_{clamp} = L_{Vproj} \times h \times \sigma_{tensile} \times f$$

Where:

• $L_{Vproj}$ = length of V-projection (inches)
• $h$ = V-projection height (inches)
• $f$ = empirical factor (2.4 – 4.4 for tensile strengths of 28,000 – 113,000 lbf/in²)

Shortcut: Clamping pressure is approximately 30% of the cutting force.

Fine-Blanking Quality Achievable

Design Considerations for Fine-Blanked Parts

• Flatness is better than conventional methods, but distortion may occur with thin materials due to release of internal stresses.
• Strip width must be 2–3 times the thickness, plus the width of the part measured transverse to the feed direction.
• Additional operations such as countersinking, coining, and bending up to 60° can be incorporated in fine-blanking tooling.

Steel Rule Dies — The Cost-Effective Alternative

Remember the gear manufacturer the practitioner? Her colleague the practitioner faced a different challenge. He needed to produce 500 prototype gaskets and 2,000 aluminum shields — volumes too small to justify conventional blanking dies. At 25–35% of the cost and a fraction of the lead time, steel rule dies were the perfect solution.

What Steel Rule Dies Are

Steel rule dies (also called knife dies), patented by the practitioner in 1879, use cutting edges made from steel strips of approximately the same proportions as steel measuring rules. Originally used in printing and shoemaking for cutting paper, cardboard, leather, rubber, cork, and felt, they've since been adopted for:

• Automotive upholstery material
• Simple to intricate shapes in sheet metal (copper, brass, aluminum)
• Multi-operation tools (blanking + piercing + forming in one press stroke)

Cost advantage: Steel rule dies generally cost 25–35% of the cost of conventional blanking dies and can be produced in much less time.

Die Block Materials

Steel Rule Cutting Edge Profiles

The cutting edges can be shaped to suit the material and operation:

Die Construction Details

• Slot cutting: Saw blade must be maintained vertical; carbide or carbide-tipped blades recommended. Trial cuts on scrap die block material verify tight fit for the rule thickness.
• Islands (center of circles, etc.): Slots are cut to less than full depth at intervals (¼ to ½ inch long, 5/8 to ¾ inch high) to create bridges that hold island pieces in position. Corresponding slots in the steel rules accommodate these bridges.
• Rule bending: Purpose-built bending machines with tooling that can produce small radii through a peening/hammering action. Complex forms may be made in two or more pieces, then joined by welding or brazing with mitered joints.

Heat Treatment of Steel Rules

Punch Specifications in Steel Rule Dies

Punches incorporated into steel rule dies for piercing holes, cutting slots, or forming ribs:

• Material: High-carbon, high-vanadium alloy steel
• Cutting end hardness: Rc 61 – 63
• Head end hardness: Rc 45 – 50

Clearance for Steel Rule Dies

Clearances are approximately half those used in conventional blanking dies. After the tool is loaded in the press, the sharp die is used to shear the sides of the counter-pad to match the die contours exactly, ensuring a close fit. Adjustments are made by grinding either the die steel or the punch. After adjustment, the sharp edges are ground flat to produce a land of about 1/64 inch for the working edges.

Decision Framework: Choosing the Right Press Work Method

Here's the synthesis — the decision tool that ties everything together:

Your Next Step

You now possess the engineering reference data that covers the entire spectrum of punch, die, and press work operations — from basic clearance calculations through advanced fine-blanking V-projection sizing.

Here's what to do with it:

1. Audit your current clearance specifications. Are they defined as per-side or total? If the documentation is ambiguous, clarify it today — before the next production run.
2. Review your lubricant strategy. If you're running stainless steel or deep draws with generic oil, you're leaving die life and surface quality on the table.
3. Calculate your next blank diameter using the formulas above — don't rely on trial-and-error alone. The mathematics exist to get you within tolerance on the first attempt.
4. Evaluate whether fine blanking or steel rule dies could reduce your costs for current production parts that are being produced with conventional tooling at unjustified expense.

The question that separates great toolmakers from average ones: Are your press work decisions driven by data and calculation — or by habit and "the way we've always done it"?

The formulas, tables, and specifications in this guide have been validated across decades of industrial production. They work. The only question is whether you'll apply them.

What's the most expensive press work mistake you've encountered — and which of the specifications above could have prevented it? That answer is your first action item.