A press brake die set is a pair of tools: an upper punch that is driven into the sheet and a lower die that supports it through the bend. Nearly everything the machine does afterwards has already been decided by geometry that was fixed when the tool was made, namely the included angle of the punch, the radius at its tip, the width of the die opening and the radius on the die shoulders. Engineers who treat those figures as a drawing convention rather than as process variables usually meet their effect during tryout, at the point where a correction is most expensive.

Press brake V-die and punch set illustrating die geometry and forming methods fundamentals
Three forming methods use that same tooling in different ways, and each method asks something different of the geometry. The choice between them changes the force required, the inside radius produced and how much of the final angle has to be recovered from springback. The sections below work through the geometry, the forming methods and the forces behind them, and close with the inputs worth confirming before a tool is made.
Tooling is normally ordered against a drawing rather than a description, so it helps to see the finished shapes in a bending machine tooling range before the geometry is fixed.
Four figures carry most of the influence. The punch angle sets the shape of the nose that enters the material. The punch tip radius sets the smallest inside radius the tool can impose, and it also controls how concentrated the contact stress becomes at the point of contact. The die opening, usually called the V opening, sets the lever arm over which the material is bent and therefore how much force is needed. The shoulder radius on the die controls how the outer surface slides during the bend, which matters most on coated, polished or pre-painted material.
These four figures are not independent. Change the V opening and the inside radius changes with it, which changes the required penetration depth for a given angle, which changes the force. A drawing that lists a punch angle and a V opening without stating the intended thickness range and material is only half a specification. The missing half is normally agreed in a short technical exchange, and it is worth having that exchange before the tool is ground rather than after.
In air bending the punch does not press the material onto the die. The sheet rests on the two shoulders and is deflected between them, so the final angle depends on how far the punch travels rather than on the die angle. This is the most flexible method: a single tool can produce a range of angles and a range of radii, and it asks the least force of the three. Its cost is springback, which is why the machine has to over-bend slightly and why the angle has to be verified on the part.
In bottoming the punch presses the material until it contacts the die flanks, so the bend angle is more closely tied to the tool angle and less to the travel. The material is still not forced to fill the die, and the inner radius remains tied to the punch tip. Force rises well above air bending, and springback falls, which makes bottoming attractive when angle consistency along a long part matters more than flexibility.
Coining presses the punch into the material hard enough that the surface yields and the tool geometry is largely imposed on the part. The inside radius becomes close to the punch tip radius and springback is at its lowest, but the force required is an order higher again and the tooling is loaded accordingly. In practice most job shops run air bending as the default method and reserve the other two for parts where the angle tolerance or the radius cannot be held any other way.
The force needed to bend a given part rises with the tensile strength of the material, with the square of the thickness and with the length of the bend, and it falls as the die opening widens. That relationship explains why a job that runs comfortably in one thickness becomes marginal in the next size up: the thickness term is squared, so a modest change in gauge moves the load more than the same percentage change in length would.
Springback comes from the elastic part of the deformation. When the punch is withdrawn, the outer fibers that were stretched and the inner fibers that were compressed try to recover, and the bend opens slightly. The amount of recovery grows with the yield strength of the material and with the ratio of inside radius to thickness, so a high-strength sheet bent over a large radius springs back far more than the same sheet bent tightly. This is a property of the material and the geometry, not a defect of the tool, and it is the reason a compensated angle is normally designed into the punch rather than chased with machine settings.
In air bending the inside radius that forms is not the punch tip radius; it is determined mainly by the die opening, with a widely used working figure of roughly one sixth of the V opening for the natural radius. The punch tip only imposes a radius when it is larger than the natural radius the material would form on its own. This distinction matters during design: specifying a small tip radius on a wide die opening does not produce a small inside radius.
Two limits follow from the same relationship. The die opening cannot be made arbitrarily narrow, because the punch would be too slender for the load, and the flange being bent cannot be shorter than the distance the material needs to span the die shoulders. When a part drawing calls for a radius and a flange that the geometry cannot support together, the honest answer is to change one of them, and that answer is much cheaper to reach at the design stage than at the press.
Tool profiles are chosen for clearance rather than for appearance. A straight punch is the simplest and the stiffest. A gooseneck or offset punch exists so that a previously formed flange has somewhere to go while a new bend is made, which is what makes box and return-flange work possible. Acute punches allow angles below ninety degrees to be reached without the punch shoulders touching the material. Radius punches are used where the part drawing specifies a large inside radius that the natural radius of the material would not produce. On the die side, single V and multi V dies cover most work, while adjustable and rotating dies serve setups where the opening has to change frequently.
Segmentation is the other design decision that affects the tool. A long tool built from a center section, intermediate pieces and short ends can be assembled around an obstruction, can be used to bend a section of the part rather than its full length, and can have a worn or damaged section replaced on its own. The practical consequence for the design review is that the segment combination belongs in the request, because a tool quoted only as a total length may not assemble into the shape the part needs.
Most design-stage failures come from a missing input rather than a wrong calculation, and the missing input is usually cheap to supply. The list below is short enough to complete in one sitting with the part drawing and the machine documentation to hand.
1. Material grade and its tensile strength, not just its common name.
2. Thickness range the tool has to cover, including any future sizes.
3. The inside radius the drawing calls for, and whether the material can form it.
4. The shortest flange on the part, checked against the die opening.
5. The forming method that will be used, since air bending and bottoming load the tool very differently.
6. Machine shut height, tonnage available and the clamping system already in use.
7. Whether obstructions on the part require a gooseneck or an offset profile.
8. The segment combination needed for the longest and the shortest bend on the part.
Two of these are worth extra attention. The material grade and the forming method determine the force, and the force is what decides whether the tool is adequate or marginal. The shortest flange and the die opening determine feasibility, and no amount of adjustment on the machine recovers a bend that the geometry cannot make.
Press brake die design rewards a short conversation held early. When the material, thickness, radius, flange and forming method are settled before the tool is ordered, the geometry that follows is a calculation rather than a gamble, and the tryout stage confirms the design instead of correcting it. The tooling is a fixed cost; the cost of discovering a geometry problem at the press is not.
Describe the material, thickness, radius and flange on your part, and the describe your forming application in as much detail as the drawing allows.