Analysis of asymmetrical rolling of strip considering percentages of three regions in deformation zone
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ORIGINAL ARTICLE
Analysis of asymmetrical rolling of strip considering percentages of three regions in deformation zone Xiangkun Sun 1 & Xianghua Liu 1,2 & Ji Wang 1 & Junlong Qi 1 Received: 15 January 2020 / Accepted: 22 June 2020 / Published online: 16 August 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract An analytical model based on slab method considering the percentages of three regions in deformation zone is proposed for analyzing asymmetrical rolling of strip and used to calculate the percentages of three regions, the roll force, and roll torque. The asymmetrical rolling is more effective in reduction than the symmetrical rolling due to the existence of cross-shear zone. The percentage of cross-shear zone increases with the increasing of speed ratio and friction coefficient and decreasing of back and the front tensions, thickness of the strip, and roll force. With increasing of the percentage of cross-shear zone, the contribution ratio of reduction increases. The proposed model has good accuracy for the analysis results are in good agreement with the results measured in experiments. Keywords Asymmetrical rolling . Percentage of cross-shear zone . Slab method . Rolling pressure distribution
Symbol list H, h Thicknesses at the entrance and exit of the roll gap, respectively hb, hf Thicknesses at the lower and the upper neutral point, respectively hx Variable strip thickness at the roll gap Δh Reduction of thickness vf, vs Peripheral speeds of the upper and the lower roll, respectively l Length of contact lb, lc, lf Lengths of the backward-slip zone, the cross-shear zone and the forward-slip zone, respectively Qb, Qc, Qf Percentages of the backward-slip zone, the cross-shear zone and the forward-slip zone, respectively i Speed ratio αf, αs Neutral angles of the upper and the lower roll, respectively αl Contact angle of the roll gap α Variable angle of contact at the roll gap * Xianghua Liu [email protected] 1
State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China
2
Key Laboratory of Lightweight Structural Materials, Shenyang 110819, Liaoning, People’s Republic of China
σx, px Horizontal and vertical stresses at the roll gap, respectively σb, σf Back and front tensions, respectively τf1, τf2 Surface shear stresses of the upper and the lower roll, respectively K Plane deformation resistance f1, f2 Friction coefficients of the upper and the lower roll, respectively p xb, p xc , p xf Rolling pressures per unit width in the backward-slip zone, the cross-shear zone and the forwardslip zone, respectively P Roll force per unit width R Radius of the work roll D Diameter of the work roll x Horizontal distance from the exit point in the roll gap C1, C2, C3 Constants Shf, SHf Forward-slip and backward-slip coefficients of the upper roll, respectively Shs, SHs Forward-slip and backward-slip coefficients of the lower roll, respectively η Contribution ratio of reduction Tf, Ts Roll torque of the upper and the lower roll
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