## Conventional Rule-of-Thumb Calculations Lead to Inaccurate Press Tonnage Predictions

The rule of thumb estimates used in 1989 during my internship with an automotive stamping supplier were simple calculations for the peak load. Tonnage for trim and pierce operations depended on the length of line of trim, material thickness and the shear strength of the material. Tonnage for forming operations depended on the size of the form, material thickness and material tensile strength. These calculations typically over-predicted the tonnage requirement, but due to the relatively low strength compared to AHSS, the overall part size that dictated the required press size became the limiting factor rather than the tonnage requirement.

Applying these same rules of thumb to the advanced steels in use today will likely under-predict the tonnage requirements. To understand why, let us examine the guidelines I used over 30 years ago.

For piercing a hole:   Tonnage = d * t * 80                Equation 1

In this equation d is the punch diameter in inches, t is the material thickness in inches, and it calculates tonnage in tons. This was a simple and effective way to estimate the tonnage of all the holes pierced. Equation 1 is a simplification of the proper calculation being the length of line doing the work, in this case the circumference of a circle, multiplied by the sheet thickness and the material’s shear strength (ꚍ). The generic equation for any type of piercing or trimming is Tonnage = P * t * ꚍ where P is the perimeter or length of line of the trim, t is the sheet thickness and ꚍ is the shear strength of the material. A typical estimate for the shear strength (ꚍ) of mild steel is 60% of the tensile strength (T). Therefore, the equation development for a simple hole piercing looks like:

 Generic trim equation: Tonnage = P * t * ꚍ Equation 2 Specific for a round hole: Tonnage = πd * t * 0.6T Simplifying: Tonnage = d * t * 0.6Tπ Mild steel T = 300 MPa = 43.5 ksi: 0.6 * 43.5 * 3.14 = 82 Pierce a round hole: Tonnage = d * t * 80

Knowing how the rule of thumb was derived allows us to highlight some possible sources of error. First, the equation assumes trimming of the full thickness. In reality, a typical trim operation for steel consists of 20% to 50% trimming and the remainder is breakage. The press needs to apply load only for the trimming portion. Second, shear strength is not a fixed percentage of tensile strength. The actual shear strength should be measured for each specific grade as the microstructure differences of the AHSS will affect the material strength in shear. Lastly each of these errors are multiplied since today’s AHSS material has a tensile strength of three to five times that of mild steel. To see this, we can consider a simple example of piercing a 1-inch hole in 0.06 inch (1.5 mm) thick mild steel. Mild steel tensile strength typically ranges from 40 ksi to 55 ksi (280 MPa to 380 MPa). Looking at Equation 1 relative to Equation 2 with low- and high -end assumptions:

 Equation 1 estimate Tonnage = 1 * 0.06 * 80 = 4.8 tons Equation 2 minimum Tonnage = 3.14 * 0.06(20%) * 0.6(40) = 0.9 tons Equation 2 maximum Tonnage = 3.14 * 0.06(50%) * 0.6(55) = 3.1 tons

This simple example shows sources of error that could lead to an estimate ranging from 0.9 to 4.8 tons to pierce a single hole. A similar exercise could apply to a drawing operation. In this situation, most rules of thumb attempt to use the perimeter or surface area of the part, the material thickness and the material tensile strength to predict the tonnage needed. Sources for error in this type of calculation include: 1) Using the perimeter of the draw area, tending to under-predict; 2) Using the surface area of the part, tending to over-predict; and 3) Using the tensile strength of the material, also tending to over-predict as it assumes the material is stretched right to the level of splitting. Correction factors have been developed over time, but it is still easy to see there are many possible sources of error in these types of calculations.

## AHSS Magnifies Press Tonnage Prediction Challenges

A number of reasons explain why the inherent challenges with old-school rules of thumb are exaggerated with AHSS:

• Strength: The strength of today’s cold stamped steels is quite incredible. Where a mild steel may have a tensile strength of 280 MPa, it is now common to cold stamp dual phase (DP) steels and 3rd Generation steels with up to 1180 MPa. In addition, new materials having a tensile strength of 1500 MPa with enough elongation to allow for cold stamping are starting to enter the market. This five-fold increase in strength acts as a multiplying factor for any errors in traditional predictions.
• Formability: The formability of AHSS has also increased dramatically. Today a DP 590 steel and even a 980 3rd Generation steel can have nearly the same elongation as a high-strength low alloy (HSLA) steel of 30 years ago. This affords the part designers the ability to incorporate more complex forms into a part including using darts and beads to increase a part’s stiffness, tight radii and deeper draws. All of these add to the tonnage used and are generally not part of the old school rule of thumb calculations.
• Springback Corrections: Springback is linearly related to the yield strength of a material. Therefore, stamping AHSS grades require more features to be added to the die process to control springback. These may include draw beads (used to control material flow early in the press stroke), stake beads (used at the bottom of the stroke to minimize springback) and tighter radii (Figure 2). These features are typically off product, in the addendum, and are easily ignored by typical rule of thumb calculations.

Figure 2: Draw and Stake Bead PlacementA-6

• Hardening Curves: The complex microstructure of AHSS offers many advantages to increase formability. All AHSS grades produce microstructural phase transformations during the stamping process. This allows the lower yield strength in the as-rolled material, which aids in formability, to increase during the stamping operation. This yield strength increase can be as much as 100 MPa. Models that estimate these hardening curves of the material are ignored when doing hand calculations.
• Other Considerations: Lastly the typical rule of thumb calculations, as we have discussed, only consider the part characteristics. They generally do not include the other sources that consume energy during the stamping process including off-product feature (beads, pilot holes, etc.), spring stripper pressure, pad pressure from nitrogen springs or air cushions, driven cams and part lifters. Many of these could be ignored 30 years ago with mild steels, but they become more significant with the strength of today’s AHSS.

## Next Steps

Accurately predicting press requirements is a decades-long, industry-wide issue. Auto/Steel Partnership (A/SP), a partnership between automotive OEMs, steel mills and affiliate suppliers, teamed up with formability software suppliers to improve press tonnage prediction accuracy. A/SP’s efforts, including this project, looks to bridge the gap between research laboratories and the shop floor.

Stamping companies should keep press tonnage monitors in good working order, and upgrade to systems that can capture full through-stroke force curves. Engaging with organizations like A/SP, OEMs and steel mills, allows efficient information sharing and capturing best-practices. Get the steel mill involved early, even in the die design phase. All steel mills have teams of application engineers to help OEMs and their suppliers transition into using the newest grades of steel – they want stampers to succeed and have the tools and data to help.