ISBN-10: 087170644X

ISBN-13: 9780871706447

Offers a complete creation to the explosion of data that has develop into to be had within the box of aluminum extrusion know-how over the last fifteen or two decades. DLC: Aluminum--Extrusion.

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Extra resources for Aluminum extrusion technology

Sample text

The average values of the flow stress and thermal properties are assumed. The expressions to calculate strain, strain rate, and the flow stress of the billet material were shown by Saha (Ref 14). Figure 3 shows the gridded meridian plane of the billet for numerical computation of the temperature distribution during extrusion. Finite Difference Approximation. The expressions can be written in the finite difference form as per the scheme shown in Fig. 4(a) and (b) for equal and unequal spacing as: ∂ T = Tm, j +1 + Tm, j −1 − 2Tm, j ∂r 2 (Δr )2 2 (Eq 2) 34 / Aluminum Extrusion Technology 2 ∂ T = Tm+1, j + Tm−1, j − 2Tm, j ∂z 2 (ΔZ )2 (Eq 3) 2 ∂ T = 2Tm+1, j + 2φTm−1, j − 2(1 + φ )Tm, j ∂z 2 (ΔZ )2 (φ +φ2) (Eq 4) ∂T = Tm, j +1 − Tm, j −1 2Δr ∂r (Eq 5) ∂T = Tm+1, j − Tm−1, j 2ΔZ ∂Z (Eq 6) ∂T = Tm+1, j − φ Tm−1, j − (1 − φ )Tm, j ∂Z ΔZ (φ + φ2) 2 2 (Eq 7) where φ = ΔZ′/ΔZ.

Altan et al. (Ref 17) have performed a slab method analysis to determine the extrusion pressure. The following considerations were used in making the analysis: • • • • Extrusion using a cylindrical billet through a flat die Extrusion shape equivalent to a rod of diameter DE Frictional shear stress at the dead-metal/flowing metal interface Frictional shear stress at the billet-container interface Consider the static equilibrium of the forces acting on the shaded element within the dead-metal zone area as shown in Fig.

A) Freebody diagram of element inside the container wall. (b) Freebody diagram of element under the dead-metal zone. (c) Geometric relationship among dz, dD, and ds Fundamentals of Extrusion / 21 Substituting the boundary conditions at D = DE, pz = 0, C will be determined by: C= 1 (Eq 29) 2 DE where DE, the equivalent diameter of extruded rod, could be calculated by using Eq 8. Substituting the value of constant, C, in Eq 28 and simplifying, the average extrusion pressure is given by: – (1 + cot α ) ln DC pave, z=0 = 2σ DE 3 (Eq 30) where DC is the equivalent diameter of the billet (container bore diameter) filled in the container after upsetting.