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## Application of the Universal Mathematical Model of the Free Profile Forming to Determine the Contact Form and Area in the Grooves

V. S. Solod, Candidate of Engineering Science, Assistant Professor, Head of Department,
R. Y. Kulagin, Junior Research Assistant,
A. G. Benetskiy, Research Assistant (RPC «Donix»)

Magazine «Metall i Lit'ye Ukrainy» № 7-8 2006

It is known  that the errors of the calculation of the energy-power parameters of pass rolling in the grooves by the method of the reduced or corresponding strip make up to 45 - 60%. Most errors are due to inaccurate determination of the projection of the metal-roll contact surface. To improve the calculation accuracy the paper  presents empirical dependencies that, according to the authors, work only for the conditions under which they were obtained.

G. Tsoukhar  also presents engineering formulas to calculate the area of the projection of the strip-roll contact surface (contact surface), based on an approximate description of the form of the deformation zone by rectangles and trapeziums, but they also work only for the studied systems.

To improve the accuracy of the calculation of the strip-roll contact form and area we present a universal mathematical model of metal forming in the grooves. The mathematical model is based on two local rules of profile transformation, namely: the rule of transverse «stickiness» and the rule of spread distribution along the height, the mathematical model is described in detail in Ref. . Using the said mathematical model we can build the profiles of the deformation zone step by step taking into account the rules of the metal spread development on the free profile, based on the developed rules, as well as the dependence which defines the spread profile equation as (1)

b0 и b are the initial and the final strip width, respectively; Ld is the length of the deformation zone.

To prove the validity of the present mathematical model for the description of the form and calculation of the area of the horizontal projection of the strip-roll contact line we used experimental data obtained by G. Tsoukhar, , for pass sequences «oval-square», «oval-round», «diamond-square», «diamond-diamond».

Modeling of the metal forming in the passes showed that the above equation of the spread profile is to be corrected due to different conditions of the spread development along the length of the deformation zone for the passes with grooves of different forms. The parameters conventional signs and the form of the passes used for modeling are shown in Fig. 1 and their geometry - in Table 1-4,

Thus, it is suggested to use the equation of the spread profile along the horizontal plane of the stock symmetry in the following form (2)

n is the exponent, characterizing the groove form (n=1...2) tha depends on the mean integral characteristic tgqср of the pass wall slope to the horizontal line qср on the strip-pass contact area , (3)

n is determined by the formula n = 3 - 2tgqср when tgqср<1 , and when tgqср≥1 it is taken equal to 1.

It is to be mentioned that such a correction scarcely influences the stock cross-section form and area at the exit from the rolls. Fig. 2 shows the stock cross sections calculated by the present model taking into account the groove form coefficient n.

The contact surface form and sizes calculated by the model, taking into account the groove form coefficient n are shown in Fig. 3 and in Table 1-4. The shaded area in the figure corresponds to the strip-roll contact area, the thick line - to the profile of the maximum width (spread) of the stock.

The contact surface and cross-section forms of the stock obtained by means of the present model visually are in good agreement with the experimental results (see Ref. ).

The obtained results prove that the developed method of the stock free profile description can be used for the development of computer modeling algorithms for the bar rolling in the grooves.

References

1.       Smirnov V.K., Shilov V.A., Inatovich Y.V. Roll Pass Design. - M.: Metallurgiya, 1987. - 368 p.

2.       Tsoukhar G. Power Influences for Pass Rolling, translated from German by V.G. Drozd, edited by Y.S. Rokotyan. M.: Metallurgiya, 1963. - 103 p.

3.       Solod V.S., Kulagin R.Y., Beygelzimer Y.Y. Universal Mathematical Model of the Metal Forming in the Grooves // Stal'. - 2006. - № 8.

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