Sizing press force for busbar punching

Punching force is one of the few things in busbar fabrication that can be calculated exactly, from first principles, in about thirty seconds. It is also one of the things most often specified by copying whatever the previous machine had. Those two facts sit uncomfortably together, because the calculation is not difficult and the cost of getting it wrong runs in both directions: an undersized press stalls on the one job that matters, and an oversized one is capital you did not need to spend.

The formula

Punching shears a cylinder of material out of the bar. The area being sheared is the perimeter of the hole multiplied by the thickness, and the force is that area multiplied by the shear strength of the material:

F = perimeter × t × τ

For a round hole the perimeter is π × d, giving the form most people memorise:

F = π × d × t × τ

with d and t in millimetres and τ in N/mm², producing force in newtons. Divide by 1000 for kN, by 9807 for metric tonnes.

For a shaped hole (a slot, a rectangle, an obround, a busduct louvre) the perimeter is the developed cut length, not a nominal size. A 20 × 40 mm rectangular slot with 5 mm corner radii has a perimeter of about 2 × (20 + 40) − 8 × 5 + 2π × 5, which comes to roughly 111 mm rather than the 120 mm you get from ignoring the corners. On a single hole that difference is noise. Across a gang of eight it is not.

Shear strength values that are worth using

Shear strength is the variable that decides the answer, and it is the one people guess at. The figures below are from published tooling supplier data for the alloys and tempers that actually turn up as busbar. They are typical values for sizing, not certified minima, and a mill certificate always beats a chart.

Two corrections to the numbers that circulate informally. First, copper is often quoted at 200-230 N/mm², which is high; those figures are tensile strengths that have been used as though they were shear strengths. Under EN 13601, Cu-ETP bar is specified at 220-260 N/mm² tensile for R220 soft, 240-300 for R240 half-hard and 300-360 for R290 hard. The measured shear values above are roughly 0.65-0.70 of the corresponding tensile figure, not the 0.8 that the common rule of thumb suggests. Where you have nothing better than a tensile figure, 0.8 × tensile is a conservative fallback and it will overestimate copper by 15-20%.

Second, "aluminium is about 80 N/mm²" is only true for the soft 1xxx conductor grades. 6101-T6, which is the standard alloy for extruded busbar wherever mechanical strength and creep resistance matter, is roughly double that. A press sized on 80 N/mm² and then fed 6101-T6 bar will be short of force, and the failure mode is not a clean stall but a half-punched hole with the punch stuck in it.

A worked example

Take a common case: an M12 clearance hole, 13 mm diameter, in 10 mm half-hard copper.

F = π × 13 × 10 × 179
  = 40.84 × 10 × 179
  = 73 100 N
  ≈ 73 kN  (7.5 tonnes)

Now the same hole in the same bar at 6101-T6 aluminium, τ ≈ 150:

F = π × 13 × 10 × 150 = 61 300 N ≈ 61 kN

And the largest hole a mid-range machine is usually asked for, 32 mm in 16 mm hard copper:

F = π × 32 × 16 × 193 = 310 400 N ≈ 310 kN  (31.7 tonnes)

That last one is the number that decides which machine you buy, and it came from one line of arithmetic. The same calculation for any hole and material combination runs in the busbar punching force calculator.

Stripping force, and why it belongs in the total

After the slug separates, the bar springs back onto the punch flank and grips it. Pulling the punch out takes real force, supplied by the stripper, and it is reacted through the machine.

Published rules of thumb put stripping force at 5-20% of the punching force, with MetalForming's die-design guidance quoting 10-30% and noting that softer materials and tighter clearances need more. Copper is soft and tends toward the upper part of that range. For sizing purposes on copper busbar, 15% of punch force is a defensible working figure, and 20% if you are running clearance at the tight end of the band.

On the 310 kN example that adds roughly 45-60 kN. It does not occur simultaneously with peak punching force, so it does not simply add to the tonnage requirement, but it does load the stripper, the tool holder and the frame, and it is the reason a machine that is nominally adequate can chatter or drift on hole position. If your stripping force is running high, the cause is usually clearance rather than the press, which is dealt with in the article on punch-to-die clearance.

Size for the worst case, not the average

The average hole in a switchgear job is an M10 or M12 clearance hole in 6-10 mm copper, which needs 40-75 kN. Sizing a machine on that number guarantees you cannot do the job.

The worst case is the combination of:

• the largest hole in the drawing set, including slots and cutouts, measured by developed perimeter rather than nominal size
• the thickest bar you will process, which is often not the bar that carries the largest hole
• the hardest temper you will accept. Hard-drawn bar is roughly 8% stronger in shear than half-hard and 27% stronger than annealed, and procurement will substitute temper when supply is tight
• the largest gang, if you punch multiple holes on one stroke

These do not have to occur together on a real part for the machine to need to survive them. They have to be possible. A tender specification that says "copper up to 12 mm" and a drawing set with a 32 mm hole means you must assume a 32 mm hole in 12 mm hard copper, which is 233 kN, whether or not that part exists yet.

Temper substitution deserves particular attention because it is invisible. The bar looks identical. The first symptom is usually burr height and hole position drift on a machine that was fine last month.

Gang and multi-hole punching

Punching several holes on one stroke multiplies the force by the number of holes, exactly. Four M12 holes in 10 mm half-hard copper on a single stroke is 4 × 73 = 292 kN, and it will not fit on a 300 kN machine once stripping and frame deflection are accounted for.

There are two ways to make gangs affordable. Stagger the punch lengths so that they engage sequentially rather than simultaneously, which spreads the force over the stroke at the cost of a longer stroke and higher side loads. Or punch sequentially at high hit rate, which is what a CNC busbar machine is built to do. At 150-200 hits per minute the time penalty for punching four holes individually rather than as a gang is under two seconds, and it removes the tonnage problem entirely. On most switchgear work that trade is worth taking.

Shear-ground punch faces

A flat punch face cuts the whole perimeter at once, so peak force equals the calculated force and the snap-through unloading is abrupt. Grinding shear onto the punch face staggers the cut and lowers the peak.

The gain depends on shear depth relative to material thickness, and on thick busbar it is smaller than the marketing suggests. Roper Whitney's published guidance is that shear can reduce punching force by as much as 50%, with the qualification that it is most effective on 14 gauge and lighter. H. Weiss's shear-factor chart is more useful for our thicknesses: at 1/4 in (6.35 mm) stock a 1/16 in (1.6 mm) shear depth gives a factor of 0.90, a 3/32 in (2.4 mm) depth gives 0.85, and a 3/16 in (4.8 mm) depth gives 0.65.

The practical reading for busbar is that a modest shear depth buys 10-15% on 6 mm copper and proportionally less on 12 mm, because the shear depth would have to grow with the thickness to keep the same ratio. Do not size a machine on the assumption that shear will rescue you. Treat it as insurance against snap-through shock and as a slug-control aid, and calculate tonnage from the flat-punch figure.

Use rooftop shear rather than single-angle shear on anything but the smallest holes. A single angle produces an unbalanced side force that deflects the punch and loads the guide.

The margin rule

Take the worst-case punching force, then apply margin for the things the formula does not model:

• Tool condition: a worn punch requires materially more force than a sharp one, because the edge radius grows and more of the cut becomes deformation. This is the largest single unmodelled term.
• Temper and thickness tolerance: bar arrives at the top of its thickness tolerance and the top of its strength range often enough to matter.
• Frame deflection and hydraulic derating: rated force is at the ram, at rated pressure, at temperature.
• Future work: the machine will be in the shop for fifteen years and the job mix will change.

A working rule is to size so that the worst-case calculated force is no more than about 60-70% of the machine's rated force. That is not a standard, it is accumulated practice, but it is consistent with where the published machine limits actually sit. On the 800 kN machines below, the largest published hole in the thickest published bar works out at roughly 485 kN in hard copper, which is about 61% of rating. That is not an accident.

Mapping onto a real machine ladder

Running the worst-case arithmetic against the published capacity of each frame size gives a straightforward selection table. All figures below use hard copper at 193 N/mm², which is the pessimistic case.

The rows marked "published max" are the manufacturer's stated maximum hole diameter at the stated maximum thickness. The two "derived" rows are the largest hole that arithmetic allows at roughly two thirds of rated force, since those machines do not publish a maximum hole diameter.

Read that table as a sizing guide rather than a price list. The 300 kN class covers panel work in 160 × 15 mm bar with M12 and M16 hole patterns and nothing exotic. The 400 kN EMAC-BP-40 covers most switchgear in 12 mm bar at 150 hits per minute. The step to 600 kN buys 16 mm capacity, not just more force, and the step to 800 kN buys 20 mm and 40 mm holes.

If the job includes large cutouts, busduct louvres or anything where developed perimeter runs past 100 mm, go up a class regardless of what the round-hole arithmetic says. Perimeter is the term that grows fastest.

The 800 kN class also matters for a reason that is nothing to do with holes. On a combined punch and shear machine the shearing station has to crop the full bar section, and on 300 × 20 mm copper that is a 6000 mm² cut face. Force required for shearing is governed by the blade geometry and rake angle rather than the simple perimeter formula, but the frame has to carry it, and it is frequently the shear rather than the punch that sets the frame size on wide heavy bar.

Two things the formula does not tell you

Force is not the same as capability. A press with adequate tonnage and inadequate positional accuracy produces holes in the wrong place, which on a bolted joint pattern to DIN 43673-1 is a scrapped bar. Hole pitch accuracy, repeatability and the stiffness of the bar feed are separate specifications and they deserve separate scrutiny.

Force also says nothing about hit rate, and hit rate is what determines whether the machine pays. A 400 kN machine at 150 hits per minute and an 800 kN machine at 200 hits per minute are different production propositions, and on a job dominated by M10 and M12 clearance holes, where neither machine is anywhere near its force limit, the hit rate is the only number that matters. The relationship between hit rate, tool life and the real cost of a hole is covered in tool life and cost per hole, and the mechanics of the cut itself in the punching process overview.