R&D Update: Press brake bending, Part II

During air bending a sheet is placed on the die, and bends the sheet into a V shape (see Figure 1a ). The process is common because dies don’t need to be changed to achieve different bending angles. For a given die opening, the bend angle is determined by the punch stroke.

What is Bend Allowance?

Various air bending parameters-stress, strain, bending moment, bent force, spingback, and bend allowance-can affect the process. During bending the outer fiber of sheet material, indicated by radius R0 is in tension while the inner fiber, indicted by Ri, is in compression (see Figure 1b ). The length of the fibers in tension increases while the length of those in compression decreases.

Between Ro and Ri , is the neutral axis. Fibers along the axis are under neither tension nor compression; their length does not change. In the unbent sheet, the neutral axis coincides with the sheet’s centerline. However, as the sheet undergoes bending, the neutral axis shifts toward the inner radius, Ri ,(see in Figure 1b).

During air bending a sheet’s thickness decreases and its length increases. Thus, if a sheet of length L is bent to an angle and its length along centerline XOY is measured, L is less than length (XOY) (see Figure 2 ). Because the length changes during bending, it is necessary to calculate the being allowance or bend deduction. These parameters are important when close tolerances have to be met because the part will be used in an assembly.

Bend allowance and bend deduction are interchangeable terms and depend on how a sheet’s bend length is measured (see Figure 2). Most stampers use bend deduction to determine length because it is easy to calculate.

The ERC/NSM developed a mathematical mode for air bending sheet and plate. BEND, a computational program, was developed based on this model. Details of this model and the BEND program were published earlier in the September/October 2003 issue of STAMPING Journal , page 58.

How to Calculate Bend Allowance

The mechanics of bending are complex even though bending is a simple process. To calculate the bend allowance, determine the bent sheet’s centerline (C.L.) length (see Figure 3 ). To calculate the C.L., it’s essential to know the bent sheet’s profile.

The profile of a bent sheet changes along the length, depending on the type of deformation. Based on the type of deformation, the bent sheet can be divvied into four zones: plastic zone, elastoploplastic zone, elastic zone, and riding zone (see Figure 3)

The rigid zone (region B-C) does not undergo any deformation. The material in region E-B undergoes elastic deformation and regains its original shape after unloading. These zones don’t elongate and are not considered when calculating bend allowance.

In the elastoplatic zone (region A-E), part of the sheet undergoes elastic deformation and the other part undergoes plastic deformation. Only the profile of the plastically deformed sheet must be calculated. Wang’s model, developed by the ERC/NSM, calculates the profile of the sheet along line OAE, based on the fundamentals of bending mechanics. According to this model (see Figure 4a, 4b ), the radius of the neutral axis is a function of:

• Sheet width (w) and thickness (t)

• Bend arc length (S)

• Contact angles (θ_c)

• Half bend angle (θ₁)

• Punch radius (R_p) and the die radius (Rd)

• Half die opening (L_d)

Material properties: yield stress, strain hardening coefficient (n), strength coefficient (K), Young’s modulus (E), Poisson’s ratio (ν), and anisotropy (R)

The elongation of the bent sheet is calculated by using a numerical method. The curve AE is divided into small segments. Each segment is assumed to be circular with a different bending radius. Calculations can be carried out with a short computer program.

The plastic zone (region O-A) is the region of the bent sheet in contact with the punch and undergoing plastic deformation. The deformed sheet’s profile remains unaltered after unloading. Because this region is circular (and has the shape of the punch nose), sheet length can be found based on the shift of the neural axis, reduced thickness, and sheet/punch contact angle.

Case Study Example

The bend allowances were calculated for various bending operations. One set of the parameters is shown in Figure 5 . It shows bending parameters and compares the bend allowance with experimental data. Results indicate that the predicated and measured bend allowance values vary 2 percent. The current calculation method offers reliable bend allowance predictions.