| Abstrakt: |
The collapse of tubes in a cold-drawing process using a V-grooved tubespin block machine is analyzed for the first time in this paper. A collapsed shape is assumed for the analysis based on the observation of the actual collapsed shape of the tube cross section. The draw pull force is converted into the load acting on the cross-sectional plane. Since the tube is very long compared with its cross-sectional dimensions, a ring of unit length under plane-strain deformation is considered. The effects of plastic strain hardening rate, semi-groove angle, friction, and the thickness and diameter of the tube on the collapse, are studied in detail and the results are presented graphically. A special case, the crushing of a tube between two parallel rigid plates, is considered and the results are compared with the existing analytical and experimental results found in the literature. The close agreement of the analytical predictions with the experimental data verifies the validity of the model and analysis presented in this paper. NOMENCLATURE A cross-sectional area of the tube C tracer coefficient in equation (29) c total circumference of the ring cross section c 1 , c 2 arc lengths of arcs having radii r 1 and r 2 d 0 initial outside diameter of tube E modulus of elasticity E p plastic strain-hardening modulus F circumferential force at the centerline (see Fig. 2) F eff total load on the ring per unit length F r reaction force of the tube on the die block I area moment of inertia of initial tube cross section about its centroidal axis L length of tube cross section in contact with one side of the V-block M circumferential bending moment M e value of M at yield M i M 1 or M 2 M 1 , M 2 M in the respective elastic and plastic regions M 0 value of M at the centerline (see Fig. 2) P d draw pull force p effective pressure on the tube cross section, due to axial draw pull force p eff intensity of load due to F eff p r intensity of load due to F r R m mean radius of the tubespin block R 1 , R 2 axial and circumferential radii r instantaneous radius r 0 initial mean radius of the tube r 1 , r 2 minimum and maximum deformed radii (see Fig. 1) r y radius corresponding to yield s arc length on the ring s 1 , s 2 arc lengths of arcs I and II t tube wall thickness U c complementary energy x distance along straight (flat) portion of circumference α E E p β semi-groove angle of the die block (see Fig. 1) θ angular position along arc κ circumferential curvature κ e value of κ at yield κ 1 , κ 2 κ in the respective elastic and plastic regions μ coefficient of friction σ a axial stress on the tube σ y modified yield stress ( 2 3 of uniaxial yield) σ 1 , σ 2 axial and circumferential stresses |
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