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A typical set of nonmandrel tooling will consist of a bend die, clamp die, and a pressure die.
The clamp die will remain unchanged from a round set of tools; that means that it will have a properly-sized round tube groove transversing the entire length. Also note that the tube groove will be less than the tube radius, to allow for gripping the tube.
Corresponding to the clamp die is the grip, or straight portion, of the bend die. The grip also has a properly-sized round tube groove. Generally, depth of the round groove is half the tube diameter, which allows for maximum support and control of the tube.
The changes in tooling begin to become more obvious at or near the tangent point of the CLR. At this point, there is a transition from the round groove to the shaped groove.
In most cases, the shaped tube groove will exist throughout the remaining tube groove portion of the bend die itself. There are applications in which the shaped groove exists only in the bend portion, and then makes a transition back to the round to satisfy the demands of a particular application.
The bend die is also the piece of tooling for which a series of controlled wrinkles would be employed in extreme allowable instances.
The pressure die is primarily of a traveling nature. Its length will correspond to the desired degree of bend, and will have a shaped tube groove along its entire length.
Note that the pressure die's shaped groove is generally the same shape and depth as the bend die's shaped groove. This is a departure from normal operation of round groove tooling, which has a shallow groove in the pressure die to maintain pressure throughout the bend.
Also note that the shaped tube groove in both the bend die and the pressure die are more shallow that the radius of the tube being bent.