# What is the K and Y factor in sheet metal?

K-factor and Y-factor in sheet metal both look at how bending affects the material and how much bending the metal will allow. When sheets of metal bend, the top surface compresses and the bottom expands. The boundary inside the metal between these two is the neutral radius. In flat metal, this boundary evenly bisects the material's thickness, but it shifts when you bend the metal.

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The K-factor comes from the ratio of the neutral radius divided by the thickness of the material on prepared charts and has a value between 0.3 and 0.5. The Y-factor looks at a similar value, but it takes the stresses inherent in the material into consideration, making it more accurate than the K-factor.

Y factor and K factor represent part constants used in formulas to calculate the developed length of flat sheet metal required to make a bend of a specific radius and angle in a design. Y factor and K factor are defined by the location of the sheet metal material's neutral bend line with respect to the thickness. The neutral bend line's position varies according to the type of sheet metal material used in part. The numeric references range from 0 to 1. The numeric references for Y factor and K factor can be negative, with the lower numbers representing softer material. The length of the neutral bend line is equal to the developed length.

K factor is a ratio between the distance from the neutral bend line to the inside bend radius and the material thickness. K factor uses the formula K factor = δ/T. Y factor uses the formula Y factor = K factor * (Π/2). The default value for the Y-factor is 0.50.

## What is K-Factor?

In sheet metal, the K-factor is the ratio of the neutral axis to the material thickness. When a piece of metal is being formed, the inner portion of the bend compresses while the outer portion expands (see Figure 1). The neutral axis is the area of transition between compression and expansion, where no change in the material occurs—except that it moves from its original location at 50 per cent of the material thickness toward the inside surface of the bend. The neutral axis does not change its length but instead relocates; this causes elongation to occur during bending. How far the neutral axis shifts depends on a given material's physical properties, its thickness, inside bend radius, and the method of forming.

Take the customary default K-factor value of 0.446, multiply it by the material thickness, and you know where the neutral axis will relocate. What we are doing, in essence, is forcing the measured length from a larger radius (that is, the length of the neutral axis at 50 per cent of the material thickness) onto a smaller radius. The same total measured length spread over the smaller radius means we have excess material or elongation.

Consider 0.060-in.-thick material. We multiply that by a K-factor of 0.446 to get 0.0268 in. The axis has shifted from 0.030 in. (at half the material thickness) to 0.0268 in., as measured from the bend inside the surface. Put another way, and the axis has moved 0.0032 in. inward. From there, we can find the answers we need for our bend calculations.

Note that the material type, method of forming, and the relationship of bend radius to material thickness all give us different K-factors. These, in turn, affect the total amount of elongation that occurs and the bend deductions we need to use.

## What is Y-Factor?

The Y-Factor is simply a variable based on the more commonly used K-Factor. It is derived by taking half of the K-Factor multiplied by pi.

Y={\dfrac{K \cdot \pi}{2}}

The Y-Factor is used, as far as I know, solely by PTC's Pro-Engineer, now known as Creo Elements/Pro. From and is defaulted at .5, leading to a K-Factor of approximately .318, which is not a terrible starting place for sheet metal design. The Y and K-Factors affect how the part stretches when transitioning from a flat pattern to a finished piece, so it is important to understand their values. However, to achieve truly accurate parts and designs, you are almost always going to have to edit the Y-Factor. To do so, there are a few basic methods.

The first method I would recommend is to edit the 'Material' file. You can do this by simply using the PTC_INITIAL_BEND_Y_FACTOR parameter when in the Material Definition screen. This will allow you to set specific Y-Factors to your materials. To my best understanding, you cannot set specific values to individual gauges, but this is a common limitation with design software. Being able to set a specific factor for each material should get you very close to perfect when designing parts. If, after setting the material, you unassign your material from the part the K-Factor will remain whatever it was set to last. This should be taken into account when switching materials.

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The second method for editing the Y-Factor is to use the 'Set Up' command. This will allow you to initialize the Y-Factor creating a new default. New parts created after the set up will have your new Y-Factor as their default. This may not be the best method as different materials will exhibit the need for different Y-Factors. Again you can reference our posting on the K-Factor, complete with charts and explanations.

The third option is to edit your configuration file and permanently set the Y-Factor for all new parts. This is practically speaking the same as using the 'Set Up' command and is like this not recommended if you're working with a variety of materials, or trying to get very accurate parts.

To add an extra level of accuracy to your parts, the Y-Factor can be edited for individual features. This can be beneficial towards the extreme ends of the Bend Angles or radii where the neutral axis becomes less and less aligned to the proper Bend Allowances.

If you wish to avoid using the Y-Factor Pro-Sheet Metal, as well as most design programs, will allow you to substitute a bend table in place of its own calculations. These tables are typically based off of the Machinist's Handbook, and a must-have for all manufacturing engineers. These tables were in turn based on experimentation. As far as I know, there is no absolute or all encompassing formula for deducting a flat pattern.

## What are the types of metal bending?

Bending and bend formation are important factors when it comes to calculating bend deduction, which is the total elongation for a particular type of bend. The methods used will affect the mathematical values chosen for the calculation.

Sheet metal bending is a forming operation. Where sheets are deformed plastically to change its shape. During bending, the material is stressed beyond its yield strength but below the ultimate tensile strength.

After bending, the total length of sheet metal is more than flat length. This change in length can be represented as a bend deduction or bend allowance.

**METAL BENDING TYPES**

When it comes to bending metal, you must consider four types of bends: minimum radius, perfect, radius and sharp. The minimum radius bend moves the metal until its radius is the smallest possible without creating a crease in the material. This value will help you identify perfect, radius and sharp bends.

Perfect bends have values between the minimum radius to 125% of the metal's thickness. When you surpass 125% of the metal's thickness, you'll create a radius bend.

On the other end of the spectrum are sharp bends. These happen when you bend the metal past the minimum radius to form a sharp crease.

First, let's step back and talk about the types of bends you can make in sheet metal. Have no fear; I will bring the K-factor into the discussion soon. Until then, bear with me.

There are four types of bends: minimum-radius, sharp, perfect, and radius. A minimum-radius bend has a radius that's equal to the smallest inside radius that can be produced without creasing the material. Try forming a radius smaller than the minimum, and you crease the centre of the radius, giving you a sharp bend.

The perfect bend has a radius that's equal or close to the material thickness. Specifically, the ideal bend's radius ranges from the minimum radius value up to 125 per cent of the material thickness. If your radius is 125 per cent of the material thickness or more, you have a radius bend.

Even if you are producing a sharp bend, the smallest radius you can use for your bend calculations is the minimum bend radius, if you want your numbers to work out in practice. Note also that air forming a sharp bend usually is very detrimental to consistency. The crease in the centre of the bend tends to amplify any angular variations caused by changes in material grain direction, hardness, thickness, and tensile strength—the sharper and deeper the crease, the greater the effect.

Your punch nose radius comes into play here too. If the bend turns sharp at an inside radius of 0.078 in., then punch nose radii of 1/16 in. (0.062 in.), 1/32 in. (0.032 in.), and 1/64 in. (0.015 in.) are all too sharp. As the punch nose radius gets smaller in relation to material thickness, the more significant the total amount of angle variation you will experience.

There's a lot more to know about sharp bends. For more on the subject, check out "Predicting the inside radius when bending on a press brake," "How to calculate an air formed radius of different bend angles," "Minimum versus recommended inside bend radius," "How an air bend turns sharp," as well as the four-part series "A grand unifying theory of bending," all archived on thefabricator.com. And years' worth of articles is linked on my website under the media tab at theArtofPressBrake.com.

But, I digress. Now that we've discussed what types of bends there are and how we create them, we can move on to the K-factor. You'll notice how the different methods of forming wait a minute—we haven't defined the forming methods yet: air forming, bottom bending, and coining.

**METAL BENDING ALLOWANCE**

To calculate the bend allowance, the K factor and the derived coefficient called the Y factor, insert the thickness and initial length of the sheet into the cells on the left. After bending the sheet, insert the inner radius, and flanges A and B. Bending angle is 90°.

Bend allowance is similar to bend deduction. It is the material required to add to the Flange length (A1 and B1) to develop a flat length.

Flat Length = Length A1 + Length B1 + Bend Allowance

Bend allowance and bend deduction are directly related. Sum of bend allowance and bend deduction is equal to two times of outside set back.

BA + BD = 2 X OSSB

Outside Setback = (Tan (A / 2) ) X (T + R)

Where ;

BA; Bend Allowance

BD; Bend Deduction

OSSB: Outside Setback

A: Bend Angle

T: Sheet Thickness

R: Inside Bend Radius

**BEND DEDUCTION**

After bending, the total length of the sheet metal part increases.

During bending, the inside surface of the bend is compressed, and the outer surface is stretched. As a result, the total surface area of sheet metal parts increases. In other words, Total length (A + B) is more significant than sheet metal Flat Length.

The difference in the total length after bending and flat length is known as Bend Deduction.

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## What is metal bending forming?

How you bend the metal makes a difference too. You have three main forming methods to choose from — coining, bottom bending and air bending. Among these, coining is the oldest and now mostly obsolete. This method uses a punched nose that presses into the metal and through the neutral radius. In this way, coining thins the material, negatively affecting its integrity.

Bottom bending, while similar to coining, does not ruin the material. The material presses around the punch nose instead of the nose pushing into the metal. The radius of the punch nose determines the radius inside the bend, just as it does with coining.

Air bending does not have a direct correlation between the punch nose radius and the bend radius. Instead, the bend radius is a percentage of the die's opening. Most engineers favour the 20% rule, which uses percentages around 20% for various metals. For example, for 304 stainless steel, the percentage ranges from 20% to 22%, but for H-series soft aluminium, the range is between 13% and 15%.

And yes, there is a difference between bottom bending and coining. Coining forces the punch nose into the material, penetrating the neutral axis. Bottoming occurs at about 20 per cent above the material thickness, as measured from the bottom of the die. (Note: For more on the forming methods, including illustrations, see "How the inside bend radius forms," archived at thefabricator.com.)

There is a fair probability that the die sets on your stamping press are actually coining the material, pushing the die to less than the material thickness. Otherwise, you're probably bottom bending, which again occurs at about 20 per cent above the material thickness. One forces tighter radii than the other, but both force the material to a certain radius. Regardless of the type of bend you have—sharp, minimum, perfect, or radius—if you're bottoming or coining, the punch nose value determines the resulting radius and, hence, is what we use in our bend calculations.

This is not the case in air forming, however. In an air form, the produced radius is a percentage of the die opening. An air-formed bend floats across the width of the die, and the inside radius is established as a percentage of that width. The percentage depends on the material's tensile strength. This is called the 20 per cent rule. It's only a title, though, because of the percentage changes with the material type and tensile strength.

For instance, 304 stainless steel forms a radius 20 to 22 per cent of the die width, while a radius in 5052-H32 aluminium forms at 13 to 15 per cent of the width. The general rule here is this: The softer the material, the tighter the inside radius.

By the way, 60-KSI mild cold-rolled steel is our baseline material for most calculations, including the 20 per cent rule. That material forms a radius between 15 and 17 per cent of the die width. We start with the median, 16 per cent, then adjust as necessary. Say we need to work with 120-KSI material. That's double the 60 KSI of our baseline material; hence, this 120-KSI sheet will air-form a radius that's about double that of mild cold-rolled steel—or 32 per cent of the die opening (16 per cent × 2).

## How to calculate K- and Y-Factors?

You can calculate K-factor and Y-factor for various metals, but they will require more involved math when you're doing them by hand rather than using the simple ratio found in reference materials.

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**How to determine K-factor?**

If you want to find the K-factor value on your own, you'll need to take some measurements with several pieces of metal. You must know the inside radius in addition to the dimensions before and after bending. You can use gauge pins and radius gauges to find these values or try an optical comparator. First, use this information to find the bend allowance, BA. (BA = total of inside formed dimensions – flat dimensions.)

Bend allowance is a fundamental parameter to calculate sheet elongation. This is defined as the length of the neutral fibre from the beginning to the end of the arc generated by the bend.

Next, measure the inside radius, Ir, and the complementary bend angle, which is 180 degrees minus the included angle. Find the material thickness, Mt, and you'll have the information you need for calculating the K-factor for sheet metal bending.

To find the K-factor, divide the product of 180 and BA by the difference between the product of pi, Mt and the complementary bend angle to the ratio of Ir to Mt. Mathematically, this formula looks like this:

K-factor = {(180 x BA) ÷ [(π x Complementary Bend Angle x Mt) – (Ir ÷ Mt)]}

**How to find Y-Factor for sheet metal bending?**

You'll need the K-factor to find the Y-factor. To calculate Y-factor, you should multiply K-factor by pi and divide the result by two.

Y-factor = (K-factor x π) ÷ 2

## What are the factors in K- and Y-Factors to consider in designing custom metal parts?

Because not all materials have K-factors or Y-factors on a chart, you can calculate these values on your own with your particular choice of metal. Using the calculations mentioned above, you won't need to rely on preset values when you're customizing your own designs. This ability will allow you to branch out from standards on tables.

When you're calculating bend deduction, you can use the K-factor or Y-factor. The bend deduction comes from the bend allowance and the outside setback, OSSB. Multiply the outside setback by two and subtract the bend allowance from that product to find the bend deduction, BD. The OSSB is the tangent of the bend angle divided by two times the sum of the inside radius and the material thickness.

BD = (2 x OSSB) – BA

OSSB = tan (bend angle ÷ 2) x (Ir + Mt)

Recall that BA is the difference between the total formed dimensions and the flat dimensions. Another way to calculate this value is with the K-factor or Y-factor.

With the K-factor, the BA is equal to the following: BA = {[(π ÷ 180) x Ir] + [(π ÷ 180) x K-factor] x Mt}

With the Y-factor, the BA is equal to the following: BA = [(π ÷ 2) x Ir + (Y-factor x Mt)]

With these formulas, you can use your calculated K-factor and Y-factor to find the bend deduction.