ABSTRACT
Standard terms that are commonly used in theories of flat rolling are summarized in Table 10.1. Equations for standard terms used in theories of flat rolling. https://www.niso.org/standards/z39-96/ns/oasis-exchange/table"> Parameter Equations for Reduction In Thickness Equations for Reduction In Width Arithmetic average thickness and width https://www.w3.org/1998/Math/MathML"> h a = h 1 + h 2 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> w a = w 1 + w 2 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0002.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Parabolic mean thickness and width https://www.w3.org/1998/Math/MathML"> h p = h 1 + 2 h 2 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0003.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> w p = w 1 + 2 w 2 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0004.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Geometric mean thickness and width https://www.w3.org/1998/Math/MathML"> h g = h 1 h 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0005.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> w g = w 1 w 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0006.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Draft https://www.w3.org/1998/Math/MathML"> Δ = h 1 − h 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0007.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> Δ w = w 1 − w 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0008.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Relative reduction https://www.w3.org/1998/Math/MathML"> r = Δ h 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0009.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> r w = Δ w w 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0010.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Elongation https://www.w3.org/1998/Math/MathML"> e = h 1 h 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0011.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> e w = w 1 w 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0012.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Roll bite angle https://www.w3.org/1998/Math/MathML"> α = arccos 1 − Δ 2 R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0013.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> α w = arccos 1 − Δ e 2 R e https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0014.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Roll contact length https://www.w3.org/1998/Math/MathML"> L = R Δ − Δ 2 / 4 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0015.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> L w = R w Δ w − Δ e 2 / 4 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0016.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Arithmetic average aspect ratio of deformation zone https://www.w3.org/1998/Math/MathML"> z a = L h a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0017.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> z aw = L e w a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0018.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Parabolic mean aspect ratio of deformation zone https://www.w3.org/1998/Math/MathML"> z p = L h p https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0019.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> z p w = L c w p https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0020.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Geometric mean aspect ratio deformation zone https://www.w3.org/1998/Math/MathML"> z g = L h g https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0021.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> z g w = L e w g https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367800611/83d6caa5-86bf-42a2-99fd-8ab886d55ae4/content/ieq0022.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> 262where
R, R e = radii of work rolls for reduction in thickness and width respectively
h1, w1 = entry thickness and width respectively
h 2 , w 2 = exit thickness and width respectively.
