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TECHNICAL PAPERS

# Evaluation of Estimates of Roll Separating Force in Bar Rolling

[+] Author and Article Information
A. R. Ragab

Department of Mechanical Design and Production Faculty of Engineering, Cairo University, Giza 12613, Egypta.r.ragab@link.net

S. N. Samy

Department of Industrial Engineering, Faculty of Engineering, Cairo University, Fayoum, 63111, Egyptnsameh2002@yahoo.com

J. Manuf. Sci. Eng 128(1), 34-45 (Jun 18, 2005) (12 pages) doi:10.1115/1.2120779 History: Received December 27, 2004; Revised June 18, 2005

## Abstract

A systematic approach is presented to estimate the roll separating force in bar rolling. This force is the product of the contact area between the rolled material and the roll pass, the mean unit pressure on the roll and the average flow stress within the roll gap. The contact area is determined by a computerized scheme based on a descriptive geometry approach. Also an approximate model to determine the average strain, hence the strain rate and the rolling temperature within the roll gap is proposed to estimate the flow stress from available material characterizations. The mean unit pressure on the rolls uses models existing in the literature pertinent to three-dimensional analysis of bar rolling. These models are slightly modified to encompass the unifying $Δ$ parameter expressing the geometry of the deformation zones, namely the ratio between the mean cross-sectional area and the contact area. The present approach is applied for a variety of common types of passes employed in bar rolling. Validation of the approach is realized through comparisons of predictions with a set of about 100 experimental and industrial data points for bar rolling in various passes. A fair agreement between the predictions and the measured data points is found. Reasons for the discrepancies are discussed. Furthermore a simplified analytical model to estimate the roll separating force which includes the least of adjusting empirical factors is suggested.

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## Figures

Figure 1

Graphical determination of the contact areas Ax and Ay for a typical oval-round pass

Figure 2

A model for the determination of vertical and lateral strain components for an ingoing oval of h0∕b0=2 and outgoing round of h1∕h0=b1∕h0=0.5

Figure 3

(a) Definition of the average bite and average die angles. (b) A scheme to estimate the average bite and average die angles represented on a 3D model for an O-R pass.

Figure 4

Schematic representation of the contact area and strain distributions for various types of passes: (a) D-D, (b) O-DS, (c) R-O, (d) S-O, (e) DS-O, (f) Bx-Bx. Data of passes are given in Table 3.

Figure 5

Estimates of contact areas for various pass geometries according to the present method. Data of passes are extracted from Ref. 1 as well as those given in Table 3. (a) Comparison of estimates with those obtained from different empirical formulas. (b) Comparison of estimates with those obtained from semi-analytical formulas.

Figure 6

Flow stress as determined by three empirical expressions for typical ranges of strain and strain rates encountered in bar rolling

Figure 7

Comparison of the mean unit pressure as determined by various rolling models for sticking friction. Data of passes are given in Table 3 and Ref. 1.

Figure 8

The average separating force for different pass geometries as predicted by various rolling models. Data of passes are given in Table 3 and Ref. 1.

Figure 9

Full comparison of the experimental forces and the predicted ones according to the models of simple compression, Orowan-Pascoe (2), Yanagimoto and Aoki (3), and Shinokoua and Takai (4). The contact areas are according to each rolling model for the rolling data of Table 3.

Figure 10

(a) and (b) Comparison of force predictions by Orowan-Pascoe model (2) versus experiments. The contact areas are according to the present estimation for the rolling data of Table 3

Figure 11

(a) and (b) Comparison of the forces predicted by Orowan-Pascoe model (2) and measured data according to Table 3 and data from Ref. 1.

## Errata

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