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| Pernis R. |
| DRAW DIE WITH TRACTRIX CURVE |
Abstract
The technology of deep drawing begins with the operation of cupping, where from a cut-out roundel, a cup is drawn out by a punch and a draw die. Theoretical calculations and practical experience confirmed that the optimal shape of the draw die is given by the tractrix curve. The tractrix curve is defined as an evolvent of common catenary curve. There are general mathematical conditions for the calculation of equidistance. On the curve k, to point M is allocated an equidistant point Me. Its allocation was accomplished by a vertical at the point M. This allocation is expressed by equations (3) or (4) . These equations require the angle ? to be known, and due to that equations were derived, which define the sinus and cosines of angle. By the application of tractrix curve equation into equations, were gained final equations for the calculation of co-ordinates for the equidistance of tractrix curve. The production of draw die with a tractrix shape on NC machines requires a mathematical description of equidistance of the tractrix curve. In the carried out analysis of the tractrix curve were derived simple mathematical relationships which define the equidistance from which are calculated cutting trajectories for the contours of the tractrix curve. Based on the knowledge about the tractrix curve was constructed a sequence for preparation of NC-program. In reality in NC-program is the equidistance of tractrix curve approximated by cusped line. At a practical process of planar curves in NC-program, a method of determining the number of segments, based on the angle difference of two consecutive abscises, was attested. In this case a condition - for the angle ? between the two neighbouring segments to be in maximum one degree - was selected. Worked out NC-program on NC machines enabled to decrease the need for spare material for finishing operations and polishing of the draw die. The production of draw dies with draw curve tractrix and their use in the cupping technology has enabled to increase the efficiency of this production technology.
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| Keywords: deep drawing|draw die|draw curve|tractrix|equidistance equation|equidistance tractrix| |
| No 1 (2006), p. 33-41 |
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