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RESEARCH PAPERS

# Viscoplastic Lubrication Analysis in a Metal-Rolling Inlet Zone Using Parametric Quadratic Programming

[+] Author and Article Information
C. W. Wu

State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,  Dalian University of Technology, Dalian 116024, People’s Republic of Chinacwwu@dlut.edu.cn

G. J. Ma

State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,  Dalian University of Technology, Dalian 116024, People’s Republic of China

H. S. Sun

Department of Science and Technology,  Dalian University of Technology, Dalian 116024, People’s Republic of China

J. Tribol 127(3), 605-610 (Mar 16, 2005) (6 pages) doi:10.1115/1.1924576 History: Received September 23, 2004; Revised March 16, 2005

## Abstract

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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## Figures

Figure 1

Schematic of lubrication model

Figure 2

Schematic of the inlet zone lubrication in a metal-rolling process

Figure 3

Effects of the rolling speed on the wall slips in an inlet zone (τ0=0.2MPa,k=0.007,h0=20μm): (a) film pressure; (b) wall slip velocity and (c) surface shear stresses. 1. U=0.3m∕s; 2. U=0.5m∕s, 3. U=1m∕s.

Figure 4

Effects of the initial limiting shear stress on the wall slips in an inlet zone (k=0.007,h0=20μm,U=0.3m∕s): (a) film pressure; (b) wall slip velocity and (c) surface shear stresses. 1. τ0=0.2MPa; 2. τ0=0.8MPa; 3. τ0=2MPa.

Figure 5

Effects of the proportional constant on the wall slips in an inlet zone (h0=20μm,U=0.3m∕s,τ0=0.2MPa): (a) film pressure; (b) wall slip velocity and (c) surface shear stresses. 1. k=0.007; 2. k=0.02; 3. k=0.03.

Figure 6

Comparison between the experimental observations and those predicted by Wilson and Huang (2) (solid lines) and present work (dashed lines, ▴ and 엯). Experimental (2): ●. U=0.24m∕s and U=0.37m∕s. Theoretical predictions by Wilson and Huang: 1. U=0.24m∕s and 2. U=0.37m∕s and by the present paper: ▴. U=0.24m∕s and 엯. U=0.37m∕s employing the limiting shear stress parameters of the lubricant τ0=0.2MPa, k=0.0069 and workpiece yield stress Eq. 12; 3. U=0.24m∕s and 4. U=0.37m∕s employing τ0=0.16MPa, k=0.007, and Eq. 13.

## Errata

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