(8) 017 У У θβ1.771...... ю E-mal: avk7777@mal.ru....... Р х х.. 93 % 6 % 166 %. М х х хх. : х х. ю. ю ( ). ю ю. ю. ю ю. - ю ю. ю [1 8] ю. [9 11] ю. [1]. 58

(8) 017 У ю μ (У) юю (. 1). u u+1 ЭС - ЭС (+1)- M ω S M+1 ω+1 S+1 υ0 h0 N0 σ0β - υ h N σ (+1)- υ+1 h+1 N+1 σ+1 u u +1 - (+1)- ; ω ω +1 - (+1)- ; М М +1 - (+1)- ; υ 0 ; h 0 ; υ υ +1 - (+1)- ; h h +1 - (+1)- ; N 0 N N +1 ; P P +1 - (+1)- ; g g +1 - (+1)- ; σ 0β ; σ σ +1 - (+1)- ; S S +1 - (+1)- 1 С ю У. μ ю ю. ю ю ю У. P g P+1 g+1 У - У (+1)- ю. -С Д13Ж У. ю ю. У. 1 ю. ю -. - Д14 17]. (. β) μ 1) x 1 ; β) x μ х х 3 ; γ) x 4. h 1 x ω A A R α/ υ 1 N h N x1 x x3 x4 x β С. lc l c y B B C C υ Δh/ h 59

(8) 017 У μ l c = x 1 +x +x 4. ю μ 1 1 х 4 8 R ; R ; ;. ю μ х 1 х R h x4 Δh ю. σ μ B1 B1 A 1 0 B 1 1 σ 0β ; A B ; ε -1 ε ю. У μ Р l b c b. ю (. 1) М - μ М М М М М. М ; М. ; М ; М ю. ю μ М N N ; ω. μ М R. P R P ю ю ; ρ. μ М Р d Р ю ; d Р. ю μ N N- 1 М R N -1 N. (+1)-ю (υ ) - ю ω S : ( 1 S ) R. μ h S 1 h 1 tg h. p ю 60

(8) 017 У ю ююю (. γ). 1 3 5 7 9 6 4 8 10 1 11 13 15 14 16 1 ; β ; γ ; 4 ; η θ ; 7 8 «-»; λ 10 ; 11 1β ; 1γ ; 14 ; 1η 1θ γ. Д18 1λЖ. 1700. 4. 4. ю μ d M M J M ; M ю; ω ; J. μ d1 M M 1 J1 ; d M M J ; 1 M / 1 c1 1 3 1 3 / ; M 0 / 1 1 3 М 1 ; 1 ё ё ; φ 1 φ ω 1 ω J 1 J ; Δφ 3. ю μ d u e R L ; M C M ; E Cω ω u ; e (ЭС) ; ; ; R ; L ; ω ю ЭС;. 61

(8) 017 У Дβ0Ж. 1. У ю ю μ ds V dp Q S r P E S ; S ; V ; E ; Р ; r. β. У ю μ d S ds P S P m b m ю ; b ю У. γ. У μ dq Т Q k u k P Т ; u ; k ; k -. -Сμ P h g K K. О MATLAB/Smulnk. η- 1700.. η (. 1) β.. η. 1. 0λ 107η η- 1700 «С». υ / h 1 N h % -1 N 1 77 30 606 111 39 1058 16 71 39 71 3 144 16 1 573 71 6 4 184 1 094 198 6 186 5 19 094 09 395 186 44. -. Р ) 10 9 8 0 Р 00 400 600 800 1000 t 10 ) 9 8 0 00 400 600 800 1000 ; η. ю. β. θ. β.. С ΔP max % 166 ΔP mn % 0 Δ P % 186 D P 415 С S P 04 % t 6

(8) 017 У.. ю 5000 0000 15000 10000 5000 θ. 1θθ Σ. λγ1 Σ θ Σ; βγ Σ 10 Σ. ю. 0 10 8 6 4 0 4 6 8 10 1 14 16 ΔР % ю ю ю.. ( 11.γλ4γ.β017/). 1. FХОМФ σ.a. JШСЧМШЧ K.L. TШаКrНЬ ЧОа theory of cold rollng thn fol. // Internatonal Journal of Mechancal Scences N 9 1987. p. 507 54.. Lee W.H. Mathematcal model for cold rollng and temper rollng process of thn steel strp. // Journal of Mechancal Scence and Technology N 16(10) 00. p. 196 130. 3. Jortner D. Osterle J.F. Zorowsk C.F. An analyss of cold strp rollng. // Internatonal Journal of Mechancal Scences N (3) 1960. p. 179 194. 4. Roberts W.L. Cold rollng of steel. New York: Marcell Dekker Inc. 1978. 5. Lu Y. Lee W.H. Mathematcal model for the thn strp cold rollng and temper rollng process wth the nfluence functon method. // ISIJ Internatonal N 45(8) 005. p. 1173 1178. 6. Freshwater I.J. Smplfed theores of flat rollng I. The calculaton of roll pressure roll force and roll torque. // Internatonal Journal of Mechancal Scences N 38(6)1996. p. 633 648. 7.....μ 1λλη. γθ8. 8... μ С.....: 198. 360. 9. Alves P.G. Morera L.P. de Castro J.A. Dynamc smulator for control of tandem cold metal rollng. // ABCM Symposum Seres n Mechatroncs N 5 01. p. 39 48. 10. Lee W.H. Lee S.R. Computer smulaton of dynamc characterstcs of tandem cold rollng process. // KSME Internatonal Journal N 13(8) 1999. p. 616 64. 11. Pttner J. Samaras N.S. Smaan M.A. A smple rollng mll model wth lnear quadratc optmal controller. // 37th IEEE Industry Applcatons Socety Annual Meetng N 1 00. p. 14 149. 1. Meshcheryakov V.N. Tolcheev V.M. Development of a method for reducng the dynamc loads of the electrc drve of the roll stand of the cold rollng mll. // Electrotechncal systems and complexes N 8(3) 015. p. 14 19. 1γ.......... γ..μ 1λ88. θ80. 14.... μ У У β010. β7η. 15. Э..... μ У;.μ β01γ. γ0η. 16. Garber E.A. Shadrunova I.A. Trano 63

(8) 017 У AI Yusupov VS. Analyss of a deformaton zone and the refned calculaton of the forces for cold rollng of strps thnner than 0.5 mm n a contnuous mll. // Russan Metallurgy N 4 00. p. 300 315. 17. Garber E.A. Nktn D.I. Shadrunova I.A. Trano A.I. Calculaton of the cold-rollng power wth allowance for the varable work of frcton along a deformaton zone. // Russan Metallurgy N 4 003. p. 340 346. 18... Э..μ 1λ7β. η1β. 1λ.....μ 1967. βηλ. β0... ю..... У. С «Э». Сμ 1λ88.. 40 51........ Р х х.. 93 % 6 % 166 %. М х х хх. : х х. Key words: Cold rollng non-steady process stochastcty of parameters deformaton zone electromechancal system. Kozhevnkov A.V. Kozhevnkova I.A. Bolobanova N.L. Mathematcal modelng of cold rollng process n conons of nonstatonarty and stochastcty of technologcal parameters. A dynamc model of the cold rollng process at the contnuous rollng mll that combnes the model of the electromechancal system the model of the deformaton zone and the model of the hydraulc clampng devce has been developed. The paper presents the results of the statstcal evaluaton of the accuracy of the model for uncertanty calculaton of rollng force. The results showed that more than 93% of the cases the calculaton error does not exceed 6 % the maxmum error of 16.6 %. The mathematcal model ensures hgh accuracy of predctng the magntude and nature of the change of rollng force wth the consderaton of non-statonarty and stochastcty of technologcal parameters. Ths research was fnancally supported by the Mnstry of Educaton and Scence of Russan Federaton wthn the framework of the project part of state task of CСОrОpovОts StКtО UЧТvОrsТtв ( 11.3943.017/). 1..017 Р - х... 64