THE ANALISYS OF A FORMULS FOR A SPREAD CALCULATION IN THE ELONGATION PASSES

VLADINIR S. SOLOD, VICTOR G. STRELNICKOV

At the calibration of any section one of the most important questions is a spread, on which depends the infilling of a caliber by metal and, accordingly, reception of a sections and sizes depends.

It is necessary to note, that, despite of significant number of explorations, the question on spread of metal in calibers is still unsufficiently investigated, that in a maximum degree complicates all accounts on calibration connected to infilling of calibers.

The majority of the known formulas for spread calculation are intended for spread calculation at rolling of strips, and the recommendations given by some authors for spread calculation at rolling in calibers are frequently not clear.

However, as show the further explorations, potential of the classical formulas for spread calculation is still farly from being depleted.

For spread calculation at rolling of metal in calibers most often methods of the "respective" and "given" strip are used.

In the given job the formulas of V.K. Smirnov(1), Z.Vusatovskogo (2), Z.Vusatovskogo with the amendments Suppo-Izzo (3), V.I.Zuzina (4), S.I. Gubkina (5), A.P. Chekmareva without the account of friction - (6), in view of friction - (9), B.P. Bahtinova (7), A.I. Celikova(8). A numbers of the formulas in the tables 1 and 2 are shown in brackets .

The comparative assaying of spread calculations under the known formulas in systems of calibers is executed: ov - square, rhombus - square, ov - circle, rhombus - rhombus. Pair of calibers understand a combination of the molding box of a strip plate and caliber, in which it rolling. System of calibers understand set of pairs calibers allowing to receive a final section of small section from stock material.

At the assaying of the formulas, the experimental data of G. Couhar's job on a forming were used at rolling in breakdown passes. The data were taken on photos темплетов, selected from the first series rolling for each type breakdown passes of calibers as the data on the sizes темплетов of other series in G. Couhar's job are not given. Rolled samples were fabricated of steel Mst3b.

Factor of friction calculated under the formula S. Ekelunda and other authors with the B.P. Bahtinov's and M.M. Dhternov's amendments. The sizes of metal up to rolling and after rolling recalculated on given on a known method of the given strip.

For of each passing of all rolling series under all specified formulas calculates a spread of metal. Then for all received data, expected a root-mean-square error, which is given by each of the formulas at the spread calculation in breakdown passes or systems.

For the account of the molding box of caliber and strip plate at calculates a spread correction factor, on sense equal to factor of restriction spread is entered .

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Factor of spread restriction for pairs and systems of calibers calculated with use of a method of linear programming realized as algorithm « Search of the decision » in environment MS Excel, selecting it so that the total root-mean-square error of account on all same pairs calibers or systems was minimal. The errors of spread calculation on each of the formulas for all pairs and systems of calibers are given in the Table 1. The correction factors of restriction уширения for all pairs and systems of calibers on each of the formulas are given in the Table 2.

Root-mean-square error of spread calculation under the formulas

Table 1

Correction factors for systems and pairs of calibers

Table 2

The carried out(spent) explorations have shown, that is most expedient at spread calculation in breakdown passe to apply the A.P. Chekmarev's formula with a considering of friction. Taking into account friction with factor Shown below

This formula provides the minimal average error equal 9,5 %, average factor of spread restriction is approximately identical to all pairs and systems of calibers and can be accepted equal 0,86.