Punching and Shearing Force
Calculate the required punching or shearing force for shear cutting (blanking, piercing) using F = l·s·τ_aB. Choose the cutting contour (round hole, rectangle or free perimeter length), enter sheet thickness and material - the calculator returns cut-line length, shear area, cutting force in kN and the cutting work, live with every input.
Calculation
Shear cutting per F = l·s·τ_aB with τ_aB ≈ 0.8·Rm (approximation from tensile strength, documented in the literature). The cutting work W = x·F·s uses the force-travel factor x as a literature guideline (0.4 … 0.7). Cutting clearance, bevel grind and tool wear change the real force. Add a safety margin when selecting the press.
Results
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Formulas and fundamentals
Cutting force
In shear cutting the punch separates the sheet along the cutting contour. The required cutting force follows from:
Here l is the cut-line length (the perimeter of the contour, for a round hole l = π·d, for a rectangle l = 2·(a+b)), s the sheet thickness and τ_aB the shear strength of the material. The product A_s = l·s is the shear area that is sheared through.
Shear strength
The shear strength is estimated from the tensile strength as an approximation:
This relation is documented in the manufacturing-technology literature (F = l·s·k_s with k_s ≈ 0.8·Rm). The actual force also depends on the cutting clearance and drops by up to about 14 percent for a larger clearance; a bevel ground into the cutting edge (rooftop grind) reduces the peak force further because not the whole contour cuts at once.
Cutting work
The cutting work describes the work done over the cutting travel (about the sheet thickness s):
The dimensionless force-travel factor x accounts for the fact that the force is not constant over the travel but equals the area under the force-travel curve. Its numerical value is a literature guideline (x ≈ 0.4 to 0.7, often 0.5) and is not tabulated with a fixed value in the reference books - thin, soft sheets are higher, thick, hard ones lower.
Worked example
A round hole with diameter d = 20 mm is to be punched into a steel sheet of thickness s = 3 mm with tensile strength Rm = 400 N/mm². The shear strength is τ_aB = 0.8·400 = 320 N/mm², the cut-line length l = π·20 = 62.83 mm.
This gives the cutting force F = l·s·τ_aB = 62.83 · 3 · 320 = 60,319 N, about 60.3 kN. The sheared shear area is A_s = l·s = 188.5 mm².
With the force-travel factor x = 0.5 the cutting work is W = x·F·s = 0.5 · 60,319 · 3 = 90,478 Nmm, about 90.5 J. A safety margin is customary when sizing the press, since wear of the cutting edges can raise the force by up to a factor of 1.6.
Frequently asked questions
How are shear strength τ_aB and tensile strength Rm related?
As an approximation τ_aB ≈ 0.8·Rm. This factor is documented in the literature and common for rough sizing. The exact value depends on material, heat treatment and cutting clearance; for hard or work-hardened sheets it can differ somewhat. The factor can be freely adjusted in the calculator.
What is the cut-line length l?
The length of the entire contour to be cut, i.e. its perimeter. For a round hole l = π·d, for a rectangle l = 2·(a+b). For arbitrary (free-form) contours you enter the perimeter length directly. The cutting force is proportional to this length.
Why does a bevel grind reduce the force?
With a flat grind the whole contour cuts simultaneously and the peak force is fully effective. A bevel grind (rooftop grind on the punch or die) makes the contour cut progressively - the force peak is spread over the travel and drops, while the cutting work stays about the same.
What is the minimum size of a punched hole?
As a rule of thumb the hole diameter should not be smaller than the sheet thickness (d ≥ s), otherwise the punch may fail by buckling. The calculator warns when d < s is chosen. Thin, hard sheets can require stricter limits.
Is the calculated force the rated press force?
No. The formula gives the theoretically required cutting force for a sharp, new cut. When selecting the press, add a safety margin and account for tool wear (factor up to about 1.6). Counter-pressure and stripper forces come on top depending on the tool.
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