## 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.

 Thanks are given to Michael Davenport, Executive Director, Auto/Steel Partnership, who contributed this article.

## Press Tonnage Predictions

For a stamping operation, knowing the press tonnage required to produce a part is essential. Running a part in a press without enough capacity can cause press fatigue, damage and significant downtime. Also, an operation that must run a part in a much larger press than anticipated in order to get enough tonnage will see decreases in throughput and efficiency, resulting in increased cost. Therefore, it is critical to be able to predict a part’s stamping tonnage requirements early in the design phase of the component and the stamping process. This is even more important with the continual developments in Advanced High-Strength Steels (AHSS) that the steel industry has made. These steels offer similar formability of traditional high-strength steels with twice the strength or more, as shown in Figure 1. In this article, I will explain why typical rules of thumb that appeared to work in the past are no longer applicable and touch on how the automotive and steel industries are addressing the changes.

Figure 1: AHSS add to the spectrum of options available for automotive body construction.A-69

## Tonnage Requirements and Press Capacity

When discussing the press capacity requirements, it is typical to mainly refer to ‘tonnage’ as the measurable needed. Tonnage is the peak load required during a stamping operation. The tonnage rating for a press refers to the peak load that the press can safely deliver without causing damage to the press frame, ram, bushings, etc. For a mechanical press, the peak tonnage is only available at the bottom of the stroke.

Besides peak load requirements, it is also important to understand the total energy required to form a part. It is typical for the force available from a mechanical press just a few inches off bottom to be 50% of the press tonnage rating. For drawing operations that may start several inches off bottom, it is important to predict the part tonnage requirements through the entire stroke and to compare that with the force curve from the press manufacturer. Integrating this press force curve over the entire stroke is a measure of the total energy capacity of the press. Many times, when a press stalls at bottom dead center, the issue may not be that the peak load of the press was exceeded, rather the full amount of energy that was stored in the flywheel had been expended. More information about press force and press energy are found on our page highlighting Press Requirements.

A few years ago, I saw an example of energy vs. tonnage requirements. The part was a relatively thick gage AHSS frame bracket. The design was a simple flanged hat section. In plan view, the part was only about 6-inch x 6-inch with the depth of the hat being about 4-inch. Based on the tonnage require to flange, trim and pierce a hole, the part should have easily been able to fit in a small 600-ton press. However, in order to have enough energy to produce the part, this small die was placed in the center of the 180-inch bed of a 1200-ton press. Not only was it ergonomically difficult for the operator, but the large press burden rate was much higher, and the speed was much slower than that of the smaller press, causing a significant cost increase.

Furthermore, it is good to know how off-center the load required to form a part is. Obviously, the die setter will center the die under the ram. However, most parts are not symmetric, causing the load going into the ram, bushings and press frame to be biased to one side or the other. This becomes more exaggerated in a large transfer press that may have a major draw operation at the entry end and a minor trim operation at the exit end.

Putting this all together, having the ability to predict not only the peak load required to form a part, but also the total energy through the stroke and the off-center bias gives us the ability to design a stamping process that is safe and efficient. Also, in lean manufacturing terms, a predicted through-stoke force curve provides a good baseline defining the basic condition of the die. Comparing this to actual force curves and evaluating any changes over time will help to develop preventive maintenance schedules and will offer many new capabilities with servo presses as they become more prevalent.

## Conventional Rule-of-Thumb Calculations Lead to Inaccurate Press Tonnage Predictions, Especially in AHSS

In 1989, I worked for an automotive stamping supplier as a college intern. One of my tasks was to do basic calculations of part size and tonnage requirements that were used by the process engineers to design the die process and quote the manufacturing and die costs to produce the part. The rule of thumb estimates used at that time were simple calculations for the peak load. Tonnage for trim and pierce operations were dependent on the length of line of trim, material thickness and the shear strength of the material. Tonnage for forming operations were dependent on the size of the form, material thickness and material tensile strength. These calculations typically over-predicted the tonnage requirement, but because of the relative low strength steels used, as compared to today’s AHSS, most times, the limiting factor was the overall part size that dictated the size of the press to be used rather than the tonnage requirement.

So why do we hear today that these same rules of thumb do not work, or worse, that they now under predict the tonnage requirements? To understand this, let us look at a few 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 gives the tonnage in tons. This was a very simple and effective way to estimate the tonnage of all the holes pierced. Let us look at how this rule of thumb was derived. The equation is a simplification of the fact that the actual calculation is the length of line doing the work, in this case the circumference of a circle, multiplied by the material 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 material thickness and is the shear strength of the material. A typical estimate for the shear strength () is 60% of the tensile strength (T) for the material. 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

Now that we know how the rule of thumb was derived, we can point out some possible sources of error. First, the equation uses the full thickness of the material. In reality, a typical trim operation for steel consists of 20% to 50% trimming and the remainder is breakage. The press only needs to produce load for the trimming portion. Second, the shear strength of the material is not a fixed percentage of the 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 any of these errors are multiplied since today’s AHSS material has an overall tensile strength of three, four or even five times that of mild steel – taking any error in this estimate and magnifying it. To see this, we can take a look at a simple example of piercing a 1-inch hole in 1.5 mm thick mild steel. The steel tensile strength has a range of 40 ksi to 55 ksi (280 MPa to 380 MPa). If we look at Equation 1 with the high- and low-end assumptions, we see:

 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

In this very simple example, we see sources of error that could lead to an estimate of 0.9 to 4.8 tons to pierce a single hole. A similar exercise could be taken on 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 overpredict; 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 overtime, 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

We can see that there are inherent challenges with the old school rules of thumb, but why are they so exaggerated with today’s AHSS? There are a number of reasons.

• 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.

## Accurate Tonnage Predictions Require Accurate and Complete Inputs

The answer in recent years is to rely more on simulations using finite element analysis (FEA) software. Care must be taken when using these sophisticated software packages. Many times, the software is blamed when inaccurate press tonnage predictions are given. However, we know that if any of the characteristics mentioned above are ignored, the user will develop a very precise but very inaccurate tonnage prediction.

## Next Steps

The issue with accurately predicting press requirements is industry-wide and has been around for decades. The recent advances in AHSS have multiplied the sources of errors that exist in the past rules of thumb and from the incorrect usage of advanced software packages. Many people within the steel and automotive industries are working on improving the reliability of these predictions including the Auto/Steel Partnership (A/SP). A/SP, founded in 1987, is a partnership between automotive OEMs, steel mills and affiliate suppliers. A/SP has teamed up with formability software suppliers to collaborate on this subject. A/SP’s project will work to measure sources of error and develop guidelines to address these in the areas of material characterization, modeling techniques and numerical analysis techniques. A/SP’s efforts, including this project, looks to bridge the gap between research laboratories and the shop floor.

What can stamping manufacturers do? First, prepare for the digital manufacturing era (often call the 4th Industrial Revolution) by keeping press tonnage monitors in good working order. Also, consider upgrading to systems that can capture full through-stroke force curves. Secondly, do not go it alone. Engage with organizations like A/SP, OEMs and steel mills. When evaluating new parts using AHSS, 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 to transition into using the newest grades of steel – they want stampers to succeed and have the tools and data to help.

 Thanks are given to Michael Davenport, Executive Director, Auto/Steel Partnership, who contributed this article.

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