Straining to understand bending?

Regression analysis predicts springback's magnitude, variation


April 10, 2007

By: ,

Before you can hydroform tube, you bend it. Then it springs back. You can compensate by overbending it, but first you have to predict the amount of springback.

Editor's Note: This article was adapted from the paper "Springback Characteristics of Bent Tubes for Hydroforming Applications," which was presented at the 4th Annual North American Hydroforming Conference & Exhibition, Sept. 25-27, 2006 London, Ontario, Canada.

The use of hydroforming technology continues to grow even though initial investment for a hydroforming line is high and production rates are low, when compared with conventional stamping. Its growth continues because, for many applications, the benefits outweigh the drawbacks. Advantages include assembly simplification because several components can be consolidated into a single part; improved vehicle safety because hydroformed components often are stronger than components made with other methods; better fuel efficiency because hydroformed components often weigh less than other components; and better part quality because hydroforming offers accurate geometric dimensions and excellent consistency.

To become a hydroformed component, a straight tubular blank with predetermined requirements such as diameter, wall thickness, and material composition is bent to desired angles so the tube resembles the finished component. The tube then is transferred to a preforming tool to deform it to a near-net-shaped component. The preformed tube then is hydroformed to the desired geometric shape using controlled internal pressure and axial feeding simultaneously.

Strains in Tube Production, Fabrication

As the original hot-rolled or cold-rolled sheet goes through the forming steps of tube-making, bending, preforming, and hydroforming, it is deformed along a

complicated strain path that introduces strain hardening and therefore increases the material's strength. Typical strain values for aluminum-killed draw-quality (AKDQ) steel for each step are as follows: 5 percent to 15 percent for tube-making; 20 percent to 30 percent for tube bending; and 5 percent to 15 percent for hydroforming. 1 The data implies that relatively high plastic strains occur during bending.

Springback, which is the material's elastic recovery after bending, is defined as Dq = qt - qm, where qt is the target angle and qm is the measured angle. Springback equalizes stresses—it allows the stress field in the tube to return to a state of static equilibrium after the forces are removed. Proper correction for springback is required for two reasons: to allow the tube to fit into the hydroforming die cavity and to prevent pinching the tube when the upper hydroforming die closes. Therefore, accurate springback prediction is necessary to produce quality parts. Without proper compensation, springback can result in severe surface scratching or part failure.

The Study and Results

It is understood that for a given tube size and radius, as the target angle increases, the formation region becomes larger and therefore incurs more strain. The elastic recovery energy in the material after unloading increases as the size of the formation region increases. A tube bending study examined tube characteristics and process parameters to derive a mathematical formula for predicting the amount of springback.

The tube specimens are made from a hot-rolled steel alloy, POS-HF370, which was developed specifically for hydroforming. The tube made from this alloy is formed using electric resistance welding (ERW). Its characteristics are shown in Figure 1.

The test specimens are 1,000-millimeter-long tubes bent to 90 degrees on a CNC rotary draw bender and then measured using a 3-D scanner with a touch probe, which has an accuracy of ± 0.02 degree, according to the manufacturer.

The Variables. This study investigates two diameters and several variable process parameters to determine how much each variable influences the amount of springback.

Figure 2 shows the tube dimensions for the experiments and the D of bend, which is the bend radius divided by the tube diameter. Figure 3 lists the bending process parameters and how they varied in this study.

Figure 4 shows how springback varies as the target angle varies for Tube 1, which has a D of bend of 1.89. The amount of springback increases linearly as the target angle increases. For a 90-degree target angle, the amount of springback varies between 1.46 degrees and 1.80 degrees, depending on the amount of boosting force. Increasing the amount of boost reduces the amount of springback.

For 4.8 to 6.0 tons of boost, which is the normal range for hydroforming, springback for a 90-degree angle increases by approximately 0.7 degree as compared with the amount of springback for a 22.5-degree bend angle.

Linear regression predicts the amount of overbending needed to compensate for springback:

Dq = 0.815 + 0.012qB - 0.05BF ,

where qB is the target angle in degrees and BF is the amount of boost force in tons. The square of the correlation coefficient (R2) is 0.95, indicating that the correlation between the measured and predicted values is very good. For tube with a D of bend of 1.89, this equation predicts a springback to an accuracy of ± 0.3 degree.

For Tube 2, which has a D of bend of 1.47, the equation predicts springback to be linear (as it was for Tube 1) but greater. This is because the bending radius is tighter and the bending stress is greater, so the tube releases more elastic energy after unloading. With normal boosting, the springback varies from 3.2 degrees to 5.2 degrees, depending on the target angle (see Figure 5).

For a D of bend of 1.47, linear regression predicts that the amount of overbending needed to compensate for springback is:

Dq = 0.84 + 0.025qB + 0.164BF

The square of the correlation coefficient (R2) is 0.97, so this correlation between the measured and predicted values is better than it was for the other equation. For tube with D of bend that equals 1.47, this equation predicts a springback to an accuracy of ± 0.3 degree.

In addition to the target angle and boost force, this study investigated two other bending parameters: mandrel position and bending speed. Analysis of the data revealed that changing these parameters had little effect on springback. Adjusting them through their full ranges as specified for this study resulted in less than 0.1 degree of springback variation.

Based on these results, the conclusion is that the target angle and boosting are critical factors that affect springback, and that their effects are predictable using regression analysis.

Ho-Kook Lee is assistant manager of the EVI Team, Automotive Flat Products Sales Dept., POSCO, South Korea, 82-2-3457-0570,

Chester J. Van Tyne is professor of the Department of Metallurgical and Materials Engineering, Colorado School of Mines, 1500 Illinois St., Golden, CO 80401, 303-273-3793,


1. Harry Singh, "Tubular hydroforming process and tool design optimization using computer simulation," in proceedings from the Automotive Tube Fabricating Conference: Focus on Hydroforming, Detroit, Mich., April 26-27, 1999.

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