The technique for determination of critical compressing stresses and shape parameter during elastic-plastic loss of strip longitudinal stability in thin sheet rolling is presented in the paper. It was established that critical stresses and shape parameter can be located both in elastic and plastic areas for dimension range of strips processed on hot rolling and cold rolling mills. Consequently, it requires development of calculation technique for shape parameter, taking into account elastic-plastic bending by metal thickness for corrugated strip part. Pilot rolling of 12Kh18N10T stainless steel strips of austenite type at 4-high reversing rolling mill 1700 located at “Mechel” metallurgical works has displayed that corrugating amplitude in increasing respectively since 6th till 9th pass from 10 to 20 mm, while wave period length decreases from 1200 mm to 1000 mm. and a/L shape parameter rises from 0.008 to 0.02. Comparison of actual and calculated shape parameters has shown that deviation doesn't exceed 15.7–16.6%, it allows to improve precision of calculation of critical stresses and flatness parameters. The new technique can be used in development of reduction procedures and for estimation of operating efficiency of the systems for adjusting geometrical shape and cross section.

1. Timoshenko S. P. Ustoychivost’ sterzhney, plastin i obolochek (The stability of rods, plates and shells). Moscow: Nauka, 1971. 807p.
2. Grigoryan G. G., Zheleznov Yu. D., Chernyy V. A. et al. Nastroyka stabilizatsiya i kontrol’ protsessa tonkolistovoy prokatki (Setting up, stabilization and control of the process sheet rolling). Moscow: Metallurgiya, 1975. 368 p.
3. Tselikov A. I., Nikitin G. S., Rokotyan S. E. Teoriya prodol’noy prokatki (The theory of longitudinal rolling). Moscow: Metallurgiya, 1980. 345 p.
4. Barkaya V. F., Rokotyan S. E., Ruzanov F. I. Formoizmenenie listovogo metalla (Forming of sheet metal). Moscow: Metallurgiya, 1976. 264 p.
5. Maksimov E. A., Shatalov R. L., Boskhamdzhiev N. Sh. Proizvodstvo planshetnykh polos pri prokatke (Production of strips with high flatness). Moscow: Teplotekhnik, 2008. 336 p.

6. Tomlenov A. D. Mekhanizm teorii obrabotki metallov davleniem (The mechanism of the theory of metal forming). Moscow: Mashinostroenie, 1971. 253 p.
7. Kachanov L. M. Osnovy teorii plastichnosti (Fundamentals of plasticity theory). Moscow: Gostekhizdat, 1956. 325 p.
8. Tret’yakov A. V., Kondashevskiy I. M. Rezul’taty analiticheskikh i eksperimental’nykh issledovaniy neploskostnosti tonkolistovoy prokatki (The results of analytical and experimental studies of non-flatness sheet). Coll. of Sc. Papers No. 51. (VNIImetmash). Moscow: Mashinostroenie, 1977. pp. 60–63.