A mathematical programming solution based on finite element method is used to analyze wall slip of viscoplastic lubrication in a metal-rolling inlet zone. Slip velocity can be directly obtained by parametric quadratic programming without an iterative process between the oil film pressure and the slip velocity. It is found that wall slip causes the oil film thickness to decrease dramatically. The initial limiting shear strength and proportional constant of the viscoplastic lubricant have a larger effect on the oil film pressure than the rolling speed. The nonsensitivity of oil film thickness to the rolling speed is a great particular advantage to metal-rolling processing.

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