Springback compensation in busbar bending

Ask a shop why a 90° busbar bend measured 88.4° and you will usually be told "springback". That names the effect. It does not tell you whether to change the tool, the programme or the material, and those are the only three things you can do about it.

Springback is arithmetic before it is anything else. The governing relationship has been in the forming literature for decades, the material constants are published, and the residual scatter around the prediction is precisely what a compensation table exists to absorb. What follows works the problem through in the order you meet it on the shop floor: what recovers and why, which material numbers control it, how to get a first estimate, where that estimate stops being trustworthy, and how a CNC bender turns the whole thing into a lookup an operator never has to think about.

What recovers, and why

Bend a bar and the outer fibres go into tension, the inner fibres into compression. Between them is a core where the stress never reached yield. Every fibre in the section, including the ones that yielded, still carries an elastic component of strain. Release the punch and that elastic component is recovered. The bar unbends until the internal moment returns to zero.

Springback is the elastic part of the deformation you deliberately imposed, coming back out. The plastic part stays. The ratio between the two sets the angle you lose. It is not a material defect and not a machine fault, though it gets reported as both.

That framing pays off immediately. Anything that increases the fraction of the section driven past yield reduces springback. Anything that increases the elastic strain stored at a given curvature increases it. Both levers appear explicitly in the equation.

The ratios that move it

Two ratios govern, and a third variable follows from the second.

Yield strength over elastic modulus (σy/E). A material stores elastic strain up to σy/E before it yields at all. Raise the yield strength and you raise the recoverable strain everywhere in the section. Raise the modulus and you lower it, because a stiffer material reaches the same stress at less strain. Copper's modulus sits at around 120 kN/mm² whatever you do to it, so σy/E is a temper variable in practice. Hard copper springs back roughly four times as much as soft copper at the same geometry.

Inside radius over thickness (R/t). At large R/t the bend is gentle, the plastic zone is a thin skin at each surface, and the elastic core dominates. At small R/t the plastic zone reaches almost to the neutral axis and there is very little elastic material left to pull the bar back. Springback rises monotonically with R/t, and it rises fast. Going from R/t = 2 to R/t = 8 roughly quadruples the angular loss.

Thickness enters through that second ratio rather than on its own. For a fixed former radius, a thicker bar has a smaller R/t and therefore springs back less. That trips people up. Operators who assume thick bar is harder to hold on angle are conflating force with springback: a 16 mm bar over a 20 mm former is more dimensionally obedient than a 6 mm bar over the same former, even though it needs three times the tonnage. For the tonnage itself, the busbar bending force calculator sizes it from bar section and die opening.

The springback equation

The standard closed-form relation, in the form given by Kalpakjian and Schmid and reproduced across the forming literature, is:

Ri / Rf = 4 (Ri·σy / E·t)³ − 3 (Ri·σy / E·t) + 1

where Ri is the inside radius under load, Rf is the inside radius after release, σy is the 0.2% proof strength, E is the elastic modulus and t is bar thickness.

The bracketed group carries the whole result. Call it x:

x = (Ri/t) × (σy/E)

so the relation collapses to K = 4x³ − 3x + 1, where K is the springback factor. Two sanity checks before you use it. First, K must come out slightly below 1, because springback always opens the radius, never closes it. Second, for copper x is of order 10⁻³, so the cubic term is six orders of magnitude smaller than the linear one and contributes nothing you can measure. In practice K ≈ 1 − 3x. Several published versions of this formula have the signs transposed and will hand you K > 1. If that happens, the formula is wrong, not the material.

The same factor converts angles. The neutral-axis arc length is conserved through the elastic recovery, so Riθi = Rfθf, which gives K = θf/θi. One number does both jobs. To land on a target angle θf, form to:

θi = θf / K

Which numbers go in

The modulus. The Copper Development Association's busbar guidance gives an elastic modulus of 116 to 130 kN/mm² for high-conductivity copper, and uses 124 × 10³ N/mm² in its own beam-deflection worked examples. That spread is not sloppiness. Copper is elastically anisotropic at the crystal level, and cold rolling develops a texture, so the in-plane modulus of a rolled copper sheet varies with direction by around 7% depending on how heavily it was worked. Measurements by Bunge on cold-rolled copper sheet put the angular variation at about that figure, with the sheet normal as the symmetry axis.

For springback arithmetic the practical consequence is modest. Recomputing the worked example below at 116 and at 130 kN/mm² shifts the required overbend from 0.85° to 0.75°, a spread of about 12% on a number that is itself under a degree. Use 124 kN/mm² and let the compensation table absorb the difference.

The strength. This is where most estimates go wrong. The equation wants proof strength, not tensile strength, and EN 13601 designates tempers by tensile strength. R220 covers 220 to 260 N/mm², R240 covers 240 to 300 N/mm², R290 covers 290 to 360 N/mm². Feed any of those into the springback equation and you will overpredict by a factor of two or more.

The proof strengths that mill datasheets publish alongside those tempers for Cu-ETP are broadly: R220 with Rp0.2 capped at 140 N/mm², R240 at 180 N/mm² minimum, R290 at 250 N/mm² minimum. The CDA figures for busbar-section copper are lower still at the soft end, 50 to 55 N/mm² for fully annealed material and 170 to 200 N/mm² for half-hard.

The R220 case deserves a flag of its own. The specification sets a ceiling on proof strength, not a floor. A properly soft-annealed bar can sit at 55 N/mm² while another bar sold against the same designation sits near 140. That is a factor of 2.5 in springback between two deliveries that both conform. It is the single most common reason a soft-copper offset table that worked last quarter drifts this quarter, and no amount of machine calibration will fix it. Ask for measured proof strength on the mill certificate, or characterise each coil on a first article.

A worked case

Take an 80 × 10 mm Cu-ETP bar in R240 half-hard, bent 90° flatwise over a 20 mm punch radius, so R/t = 2.

x  = (Ri/t) × (σy/E) = 2 × (180 / 124 000) = 0.00290
K  = 4(0.00290)³ − 3(0.00290) + 1 = 0.9913
Rf = 20 / 0.9913 = 20.18 mm
θi = 90 / 0.9913 = 90.79°

Form to 90.8° to land on 90°, and expect the inside radius to open from 20 mm to about 20.18 mm. That radius change is small but it is not nothing: it shifts the developed length, so a bend allowance computed from the tool radius will run a few tenths of a millimetre short over a multi-bend part.

Typical overbend by temper

The table below runs the same calculation across the temper and R/t combinations that turn up in panel work. Overbend is the additional angle to command on a nominal 90° bend, computed at E = 124 kN/mm² and at proof strengths of 60, 180 and 250 N/mm² for R220, R240 and R290 respectively.

These are first-article starting points, not production settings. Four qualifications apply, and every one of them is larger than the precision implied by two decimal places.

The R220 column assumes a fully soft bar at 60 N/mm². Recompute at the 140 N/mm² specification ceiling and the R/t = 2 figure rises from 0.26° to 0.61°. Buy R220 without a proof-strength requirement and you have bought that whole range.

The model treats copper as elastic and perfectly plastic. Copper work-hardens through the bend, so material in the plastic zone finishes stronger than it started and stores more elastic strain than the model allows. The prediction is a floor.

The model assumes the formed radius is the tool radius. That holds for bottoming and coining. It does not hold for air bending, and the difference is large enough to deserve its own section.

Bar sourced from slit plate, rather than rolled or drawn to section, can carry a different texture and different in-plane properties along its length. Treat it as a separate material in the offset table.

Why air bending springs back more

Air bending forms the bar over a die opening with the punch never bottoming out. The bar contacts the punch nose and the two die shoulders and nothing else, so the radius it takes during the stroke is set by the die opening, not by the punch. That formed radius is typically several times the punch nose radius, which means the effective R/t during forming is several times higher than the R/t you assumed from tooling. Push R/t from 2 to 8 in the table above and half-hard copper goes from 0.79° to 3.25°. That is the whole explanation for why air-bent copper misbehaves relative to the calculation.

Bottoming closes the punch into the die so the bar is forced to take the tool geometry. The formed radius is then the punch radius, the model applies, and springback drops to something close to the table. The cost is force: bottoming is commonly quoted at five to six times the air-bending tonnage for the same section.

Coining drives the punch nose into the material so the whole bend zone, elastic core included, is taken past yield. With no elastic core left there is almost nothing to recover and springback approaches zero. Tonnage rises well beyond bottoming, which on busbar sections of 10 to 20 mm thickness quickly exceeds what a benchtop machine can deliver.

Most CNC busbar bending heads work closer to bottoming than to free air bending, because busbar formers are matched sets rather than universal vee dies. That is why busbar springback generally lands in the one to three degree band rather than the five to fifteen degrees quoted for thin sheet, and why a well-built offset table stays valid for a long time.

Three mechanisms sold as springback compensation

Machine literature conflates them constantly. They differ in what they measure and when.

Offset tables keyed by material, thickness, temper and tool

The baseline. The control holds a lookup indexed on the four variables that the physics says matter: alloy and temper, thickness, tool set, and target angle. The operator, or a teach cycle, bends a sample, measures it, and the control stores the difference between commanded and achieved angle. Next time that combination is called, the control adds the stored offset before it moves.

This is open loop. It carries no knowledge of the bar in front of it, only of the bar that was in front of it last time. Most production runs on it, because within one coil of one temper the bar-to-bar variation is small. It fails when the material changes underneath the table, which is the R220 problem described above.

The key discipline is table hygiene. An offset stored against "copper 10 mm" is worthless. An offset stored against "Cu-ETP R240, 10 mm, former R20, 90°, coil batch 4471" is a usable engineering record. Machines that read the geometry directly from a 3D or 2D file, as the EMAC-BB-H12 does, can carry that key through from the design system, which removes the transcription step where most table corruption happens.

First-article measurement

The bridge between open and closed loop. The first part of a batch is bent to the table value, measured off the machine with a protractor or a CMM, and the offset is corrected before the batch runs. Cheap, universally applicable, and it catches the material-to-material drift a static table cannot.

It costs one part and one measurement cycle per batch. Automate the record-keeping rather than the measurement. On short runs with many part numbers that cycle dominates the time budget, and that is where in-process measurement earns its price.

Closed-loop angle measurement during the stroke

The control measures the flange angle while the bar is still in the tool. On press brakes this is done optically, with a laser line projected onto the flange and read by a camera; published accuracies for these systems are in the region of 0.1° to 0.15°. The sequence is: approach the target under load, relieve the ram just enough to unload the bend, measure the relaxed angle, compute the springback for this specific bar, then descend again past the original depth by the measured amount.

This is closed loop in the strict sense. It compensates for thickness variation, temper variation and rolling-direction effects on the individual workpiece, with no prior knowledge required. It is also the most expensive option, adds a measure-and-return cycle to every bend, and needs line of sight to the flange, which a busbar former does not always leave you.

For busbar the practical hybrid is a maintained offset table plus disciplined first-article verification, with in-process measurement kept for high-mix work or for materials whose certificates you do not trust.

Where the machine specification fits

Two numbers on a bending machine datasheet bear on springback and they are not the same thing.

Repeatability is how closely the machine reproduces its own result. The EMAC-BB-S12 pure-servo head and its hybrid-hydraulic sibling are both specified at ±0.1° bending accuracy over a 200 × 16 mm capacity. That figure says the ram position, the encoder and the frame stiffness are consistent enough that the same command produces the same angle. It says nothing about whether that angle is the one you wanted.

Springback compensation closes the gap between the commanded angle and the wanted one. Electronic springback compensation on these heads is the offset-table mechanism: the control stores a correction per material and tool combination and applies it automatically. Together the two figures mean something. Compensation puts you on the target angle; ±0.1° repeatability keeps you there for the rest of the batch.

A machine with excellent repeatability and no compensation will make five hundred identical wrong parts. A machine with compensation and poor repeatability will centre on the target and scatter around it. You need both. When you compare machines, ask which of the two a quoted "accuracy" refers to, because vendors are inconsistent about it.

Building an offset table that survives

A few habits separate tables that hold for a year from tables that need rebuilding every month.

Record material against the mill certificate rather than the stock description. The certificate carries the temper designation and, if you asked for it, measured proof strength. Bend behaviour tracks the certificate.

Store one offset per angle rather than one per tool. Springback in degrees is not constant across bend angles for the same tooling, because the arc over which recovery accumulates changes. A table holding 1.2° for a 90° bend and applying it to a 30° bend will be wrong on the 30°.

Re-verify when the coil changes, when the supplier changes and when the tool is reground. A reground former has a larger nose radius than it started with, which raises R/t and raises springback.

Keep flatwise and edgewise offsets separate. Different plastic zones, different constraint, and the numbers do not transfer, as edgewise versus flatwise busbar bending sets out.

Treat springback and minimum radius as one decision. Temper drives both, and it drives them the same way: the temper that springs back least is the temper that cracks least, which is why so many bending problems resolve into purchasing problems. The relationship between copper temper and minimum bend radius sets the floor on R/t; this article sets the compensation for whatever R/t you end up with. Both read off the same line of the mill certificate, and both sit inside the same busbar bending process decision.