January 10, 2002
The bending characteristics of a tube depend on the material it is made of. Exceeding the allowable limits of this deformation results in unusable parts. The author relates his company's examination and comparison of the bending of two different seamless, extruded tubes: aluminum alloy and steel.
Aluminum-alloy and steel tubes were compared.
Bending tube is an integral first step in many hydroforming applications. The outcome of this preparatory step is critical to the final results.
The bending process causes elastic and plastic deformation. During initial bend unloading, the inherent elasticity of the material can result in bend springback. Other bend effects, such as the ovality of the cross section or the wall thickness variance around the tube circumference, are consequences of plastic deformation. Exceeding the allowable limits of this deformation results in unusable parts.
All of these effects depend on the mechanical properties of the tube material and the process parameters, such as bend procedure, speed, and lubricant.
Experimental Setup and Execution
To determine the material's influence on the bending characteristics of tubes, this author's company examined and compared the bending of two different seamless extruded tubes: one aluminum alloy and one steel (see Figure 1).
Researchers performed all the bending operations on a rotary draw bender without a mandrel under the same bending conditions (see Figure 2). The bender's bending rate was 18 degrees per second, and it was electrohydraulically driven with digital adjustment of the desired bending angle, a2.
This schematic depicts all the bending equipment and the measurement system.
The bend die had a centerline radius of Rk= 50 millimeters. During the bending process, all the bend-reaction forces were measured online.
Two load cells, located separately on the pressure die, measured the normal forces, FN1and FN2, between the pressure and friction dies. A third load cell, located on the end of the friction die, measured a normal reactive force equivalent to the friction force, FR, between the slide and friction dies. A potentiometer at the bending axis was used to record bend angle, a, during the bending operation.
These measured values were used to calculate the applied bending moment, Mb, as a function of the bend angle:
The lengths L1and L2were constant, whereas L3varied with the bend radius. These bend parameters were measured online with a personal computer using measurement software. Researchers reported results based on an average of three tests repeated under the same bend conditions.
Results of all the bending tests showed that the bending moment curve peaked at a maximum and then dropped slightly to a plateau. This slight drop was due to unloading in the bend area caused by cross-section flattening, or ovality.
Maximum ovality was about 2.5 percent higher for the aluminum tube.
The measured bending moments of the steel tubes were about 2.5 times higher than those of the aluminum tubes. After removing the tubes from the bending equipment, researchers measured the formed tubes for ovality, springback, and thickness distribution.
Ovality develops as a result of the radial components of the bend reaction forces in the bend zone of the tube. Ovality, U, is expressed as the percentage of cross-sectional deviation of a bent tube from its original circularity:1
where: Da = initial tube diameter.
Dq(a) = diameter perpendicular to the bend plane
Dr(a) = diameter on the bend plane
a = bend angle
The aluminum tubes had about 80 degrees more springback than the steel, with the same geometry and radius.
Sample tubes of both AlMgSi0.5 aluminum and A573-81 65 steel were bent 90 degrees and measured for ovality in 5-degree increments around the bend arc. First, researchers determined the apex (a = 45 degrees) of the bent tube using a template. Subsequently, they measured the diameters (Dqand Dr) at increments of 5 degrees toward both straight ends of the tube using a digital micrometer with an accuracy of 1/100 mm. These measured values were used to determine ovality according to Equation 2.
Figure 3 shows tube ovality versus bend angle, a, for AlMgSi0.5 aluminum tube and A573-81 65 steel tube. Maximum ovality was about 10 percent for steel tubes and 12.5 percent for aluminum tubes. This showed an influence of tube material on the ovality.
Ovality was almost constant through the middle area of the bend and extended into the straight areas immediately preceding and following the bend area. Extrapolation indicated that ovality would extend farthest into the straight section of the aluminum tube.
The right side (at a = 90 degrees) of the curves began with lower ovality values than the left side (at a = 0 degrees), because the right side of the tubes was totally constrained by the bend and clamp dies, while the left side was only partially constrained (no wiper die).
After each bending test, researchers removed the tube from the bending equipment and measured the angle after unloading, a1, with a universal bevel protractor. They calculated the springback, Da, as the difference between the measured angle and the prescribed bend angle, a2:
Figure 4 shows the springback angles for both aluminum and steel tubes with identical geometry (20 by 1.5 mm) and bend radius (50 mm), averaged over three test repetitions. The springback of the tested tubes had an approximately linear characteristic.
Figure 4 shows that the springback in the aluminum tubes was about 80 percent higher than that in the steel tubes, a result of aluminum's lower Young's modulus, E.
This graph shows the thickness change in the two metals around the tube circumference after bending to a radius of 50 mm. The initial wall thickness of tubes of both metals was 1.5 mm.
To measure changes in wall thickness, Dt, researchers sliced the tubes across the cross section at a = 45 degrees and measured the exposed cross section to obtain wall thicknesses at 10-degree increments around the circumference of the tube. A reference angle, q, was introduced, with q = 0 degrees corresponding to the point on the outermost radius of the bent tube. They measured wall thickness, t(q), with a micrometer with precision of 0.01 mm and calculated wall thickness change as a percentage using the following equation:
where: t0= initial tube wall thickness
t(q)= measured thickness around the circumference of bent tubes in appropriate positions of angle q
Figure 5 graphically shows the percentage of wall thickness changes in the steel and aluminum tubes, both having an initial wall thickness of t0= 1.5 mm.
In comparison to the steel tube, the wall thickness change of the aluminum tube was about 30 percent smaller in the inner bend radius (positive Dt) and 70 percent larger in the outer bend radius (negative Dt). The intersections of the curves (particularly for aluminum) with the initial neutral axis (X axis at Dt= 0 percent) were at q >90 degrees and q < 270 degrees.
At these angle positions, the wall thickness did not change as a result of bending. These intersections determine the position of a new axis, which has the same length as the neutral axis of tube before bending. As bending takes place, the neutral axis shifts inward at the same time and rate as the bend radius increases after unloading the tube.2To compensate for this effect, the radius of the bend die must be made smaller than the desired centerline radius.
The tube elongation is equal to the neutral axis displacement multiplied by the bend angle (in radians). The larger the displacement, the greater the elongation of the tube.
These investigations showed, then, that with identical tube geometry and bend radii, the ovality resulting from bending the steel tubes was approximately 20 percent lower than that of aluminum tubes in the grades measured. Also, springback and changes in wall thickness were higher for aluminum tubes than for steel tubes having the same initial geometry and bend conditions.
Finally, the displacement of the nonelongated axis was significantly higher for the aluminum tubes, indicating greater tube elongation because of the bending.
When using prebent tubes for hydroforming, the following two points should be considered:
1. For manufacturing identical parts using the same prebent tube hydroforming die, it is necessary to use different bend dies for aluminum and steel tubes because the two metals have different spingbacks and ovalities. Using different bend dies prevents problems with fitting the prebent tubes into the hydroforming die.
2. The prebend operation uses a greater portion of the allowable formability of aluminum tube compared to steel tube. That is, a higher wall thickness decrease occurs in the outside radius of aluminum tubes. Therefore, the formability of prebent aluminum tubes for hydroforming is relatively lower than that for steel tubes.
Ghafoor Khodayari, Ph.D., M.E., is senior project leader, metal forming, with Industrial Research & Development Institute, 649 Prospect Blvd., P.O. Box 518, Midland, ON L4R 4L3, phone 705-526-2163, ext. 208, fax 705-526-2701, e-mail firstname.lastname@example.org, Web site www.irdi.com. The Industrial Research & Development Institute is a contract research and development organization with capabilities in free-expansion and corner-fill tube hydroforming tests; stamping and formability analysis; and lubricant evaluations.
1. W.D. Franz, Maschinelles Rohrbiegen (Düsseldorf: VDI Verlag), 1989.
2. G. Khodayari, Untersuchungen zum elastisch-plastischen Biegen von Stahlrohrprofielen, Dissertation, Uni-GH-Siegen, December 1993.
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