August 16, 2001

The list of applications for hydroforming with end feeding is growing all the time. Maybe you should check into how this technology could benefit your operation.

Sections of tubular hydroformed components typically are developed to keep the section perimeter-the *length of line*—to within 2 and 5 percent of the tube's circumference in the central regions of the member.

Near the ends, the section perimeter can be increased by as much as 65 percent, depending on tube material, section shape, and type of lubricant used. This is done by *end feeding*, or pushing additional tubing into the tool ends. This is also called *hydro bulge forming*. This process increases the formability of the material by a considerable amount.

Hydro bulge forming applications are split into two categories— tubular expansion and multibranch components like T sections. During the bulge forming process, a considerable amount of the tube is pushed into the die cavity. Generally, this is done to achieve higher expansion ratios near the ends of long hydroformed members, as shown in **Figure 1**, draw out branches in T sections and Y joints, as shown in **Figure 2**, and to expand exhaust components and shafts with minimal reduction in material thickness, as shown in **Figure 3**. Components with multiple branches or bulged expanded areas require precise control of *axial feed*in relation to the end feed pressure inside the part.

The end feeding process increases the formability of the material considerably. The best way to understand the material behavior during the end feeding process is to plot the major versus minor strains on a forming limit diagram (FLD).

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The minor strain is imparted to the tube material along its length by the end force, while the major strain is induced in the circumferential direction by the internal pressure. The end feed and internal pressure are controlled in such a way as to stay on the constant thickness line represented on the FLD. How far along the constant thickness line the process can advance depends on the section shape and the amount of expansion. The changes in geometry caused by section expansion, and buildup, of frictional resistance oppose the compressive forces along the length until no more minor strain can occur.

During the hydroforming process, only a limited amount of material can be pushed into the die cavity. There is a point along the component at which the total resistance force is equal to the compressive or buckling limit of the blank. Beyond this point, no more material can be fed.

The following equations show the relationship between maximum compressive end force (Fe), the opposing frictional force (Ff), coefficient of friction (u) between the tube and die surface, and the length (L) along the tube.

Maximum compressive force (Fe) for tube diameter (D) and thickness (T) with material ultimate tensile strength (UTS):

- Fe = pi x (D-T) x T x UTS (1-1)

Frictional force (Ff) from internal feed pressure (Pa)

- Ff = pi x (D-2T) x L x u x Pa (1-2)

By equating these two equations, the value for tube length (L) beyond which material cannot be fed can be found:

- L = T x UTS x (1-T/D) / [(1-2T/D) x u x Pa] (1-3)

From the equation 1-3, it follows that the maximum value of L beyond which material cannot be fed to expand the section without thinning can be increased only by lowering the coefficient of friction (u) and by keeping the feed pressure (Pa) as low as possible to prevent material wrinkling and excessive thickening near the ends. During the axial feeding stage the feed pressure for round sections is approximated by the following equation:

- Pa = (2 x 0.85 UTS x T)/(D-2T) (1-4)

For large D/T ratios, (D-2T) approximates to D; (1-T/D)/(1-2T/D) approximates to 1; therefore, equations 1-3 and 1-4 can be simplified to the following approximate relationship:

- L = D/(u x 1.7) (1-5)

The maximum length to which material can be fed is approximately:

- L = 12 x D For coefficient of friction u = 0.05

- L = 6 x D For coefficient of friction u = 0.10

The amount of feed is approximated by equating the material volume of the hydroformed component to the material volume of the tubular blank. For simple component shapes, the volume can be approximated by hand calculations; for complex shapes, the component volume can be derived from a CAD model. In these calculations—if constant thickness profile is assumed—the calculated feed will be a little conservative but provides a good starting point number that can be optimized through detailed process simulation and at prototype tryout.

For tube blank diameter(D), thickness(T), and blank length(Bl), and for component material volume(Vc) and component length(Cl), the axial feed length(Fd) can be calculated as follows:

- pi x D x T x Bl = Vc (1-6)

- Blank length: Bl = Vc/(pi x D x T)

- Feed amount: Fd = Bl - Cl (1-7)

The following guidelines are for reference only. The actual dimensions that can be hydroformed depend on numerous variables related to material, tool, and process control. Better estimates can be achieved by conducting a finite element analysis (FEA) of the hydroforming process.

T or Y sections, as shown in Figure 2:

Maximum branch height: Hb = 1.0 x Dt

Branch diameter: Db = (0.75 to 1.0) x Dt

Axial symmetric expanded parts, as shown in Figure 3:

Maximum expanded diameter:

- De = 1.8 x Dt

For maximum expansion, unsupported length in tool:

- Lc = 2.5 x Dt

Expanded shape corner radius: Rc = 6.0 x T

The amount of feed for these components can be calculated using equations 1-6 and 1-7.

Currently, a lot of copper fittings such as T sections used for household plumbing, are made using this process. The technique also is being applied successfully to automotive exhaust components, such as catalytic converter casings, cones, and manifolds. Application of end feeding to automotive chassis and body structural members, in general, should lead to efficient material and packaging space utilization.

Improved material formability achieved by end feeding or hydro bulge forming can lead to greater component design flexibility; hence, the hydroforming process can be applied to a wider range of products than it is today.