Key takeaways: 1. The K-factor is a crucial variable in sheet metal design that quantifies the ratio of the distance from the inner surface to the neutral axis (where no compression or stretching occurs during bending) over the total material thickness; understanding and accurately calculating this ratio is essential for predicting the precise unfolded dimensions of the bent metal. 2. The K-factor cannot exceed 0.5 because it represents the position of the neutral layer within the material thickness, and by definition, the furthest the neutral layer can be is at the midpoint of the material's thickness, which would yield a K-factor of 0.5. 3. The article provides practical tools (calculators) and formulas for determining the K-factor based on different known variables, emphasizing the importance of this factor in achieving the desired dimensional accuracy in sheet metal fabrication, and thus underscoring its significance in the design and manufacturing process.
K Factor Calculator
We provide two different calculators to calculate the value of the k-factor. The final results may have slight differences, but they will definitely meet your needs.
If the bending allowance and inside bending radius are known, you can use the following calculator to calculate the k-factor as well as the distance from the inner surface to the neutral axis.
If only the inside bending radius and material thickness are known, you can use the following calculator to calculate the k-factor.
K Factor Calculation Formula
According to the above calculation, we can easily derive the formula for calculating the k-factor:
- BA=Bending allowance
- R=Inside bending radius
- K=k-factor, which is t/T
- T=Material thickness
- t=Distance from the inner surface to the neutral axis
- A=Bending angle (angle through which the material is bent)
Based on the given information:
Sheet metal thickness T = 1mm Bend angle A = 90° Bend radius R = 1mm Bend allowance factor BA = 2.1mm
The formula to calculate the K factor is:
Substituting the given values in the formula, we get:
K = (2.1 × 180/(3.14 × 90) – 1)/1
Simplifying this equation, we get:
K ≈ 0.337
Therefore, the K factor for the given parameters is approximately 0.337.
K Factor Chart
The following are K-factors for common metal materials.
- Soft copper or soft brass: K=0.35
- Semi-hard copper or brass, mild steel, aluminium etc.: K=0.41
- Bronze, hard bronze, cold rolled steel, spring steel, etc.: K=0.45
K factor chart
(All angles, including R angle)
(only applicable to 90 corners)
Note: The bend allowance for copper is the coefficient when the inner angle of the bend is R3. If an acute punch is used for bending, the bend allowance value should refer to the one for aluminum alloy or be determined through trial bending.
Why Can the K-factor Not Exceed 0.5?
To figure out the reason why the K-factor can’t exceed 0.5, you first need to know what the K-factor is.
To figure out the K-factor, it’s necessary to understand what the neutral layer is.
You understand that bending a sheet metal part involves creating a small arc, similar to roll bending, but with a smaller radius than that of sheet metal bending.
Regardless of the method used, it is impossible to achieve a perfect right angle in bending and there will always be a slight arc.
If the lower die radius is small, the workpiece radius is small; if the lower die radius is large, the workpiece radius is large.
Then we come to the neutral layer.
As you know, sheet metal parts have a thickness.
When bending it into an arc, you will notice that the length dimensions of its inner surface are reduced, while the length dimensions of its outer surface are enlarged.
This is where the bending allowance comes from.
For example, if you bend an angle-like part with an outside diameter of 20 x 20, it will always unfold to less than 40, no matter how thick the plate is.
This is because the dimensions of its outer surface become larger after bending.
So if you design the unfolded size to be 40, the bent size is 20 on one side and over 20 on the other.
However, in most cases, it is necessary to know the dimensions of the resulting bend (arc) ahead of time.
But in most cases, it is necessary to know the dimensions of the resulting bend (arc) to calculate its unfolded dimensions.
It has long been believed that no matter how thick the sheet is, no matter how much the inner dimensions get smaller and how much the outer dimensions get larger, the size of the middle layer of the sheet will not change.
The middle layer that remains constant is referred to as the neutral layer.
Due to the growing demand for product dimensional accuracy, it has been discovered that the amount of reduction on the inside does not necessarily match the amount of expansion on the outside.
Especially when the resulting arc is small (such as a bend), it tends to get 0.3 smaller on the inside, but 1.7 larger on the outside.
It becomes apparent that the layer (neutral layer) that remains constant in size is not necessarily located in the middle of the sheet’s thickness, but rather is closer to the inside.
The distance from the inside to the neutral layer divided by the entire thickness of the sheet is referred to as the K-factor.
Yes, you’re right, the furthest the neutral layer can be from the inside is in the middle of the plate thickness.
Therefore, the distance from the inside to the middle divided by the entire plate thickness is 0.5, resulting in a K-factor of 0.5, which is the maximum value it can attain.
These are the reasons why the K-factor in sheet metal should not exceed 0.5. I hope this article has helped clarify your understanding.
What Is the K-Factor?
The K-factor is a fundamental concept in SolidWorks sheet metal design that is crucial to mastering sheet metal fabrication.
One must first understand the K-factor.
It is the ratio of the distance between the neutral layer and the bend’s inner surface to the sheet metal’s thickness.
As shown in the diagram below, K = t / T. From the definition of the K-factor, it is clear that it is a constant greater than 0 and less than 1.
Since the K-factor is related to the position of the neutral layer, what is the neutral layer?
In the bending deformation zone, the material near the inner surface is compressed and the compression is more severe the closer it is to the inner surface.
Similarly, the material near the outer surface is stretched, and the stretching is more severe the closer it is to the outer surface.
Transitioning from compression to stretching as going from the inner surface to the outer surface, assuming that the material is stacked in thin layers (most metal materials are layered), there must be a layer in the middle of the material that is neither compressed nor stretched. We call this layer the neutral layer.
In general, the neutral layer cannot be seen or touched because it is inside the metal. Its position is related to the material’s inherent properties, which means that the K-factor is related to the material. From the definition of the neutral layer, the unfolded size of the sheet metal is equal to the width of the neutral layer, as shown in the figure above.
The unfolded size of the sheet metal = straight line A + straight line B + arc C (length of the neutral layer in the deformation zone).
The K-factor is also referred to as the neutral layer position factor. For most materials, the K-factor is a number less than or equal to 0.5 in sheet metal design and processing.
How to Calculate K Factor?
The k-factor is an independent value that describes how sheet metal bending occurs in a wide range of geometric parameter situations and how it unfolds. It is also an independent value used to calculate the bending allowance (BA) under various situations, such as material thickness, bending radius/angle.
The figures below can help us better understand the detailed definition of the k-factor.
In the thickness of sheet metal parts, there is a neutral layer or axis. The sheet metal material in the neutral layer of the bending area neither stretches nor compresses, which is the only place in the bending area where it remains undeformed. It is represented as the intersection of the pink and blue areas in the diagram.
During the bending process, the pink area is compressed, while the blue area is stretched. If the neutral sheet metal layer remains undeformed, then the length of the neutral layer arc in the bending area is the same in its bent and flattened states.
Therefore, the bending allowance (BA) should be equal to the length of the neutral layer arc in the bending area of the sheet metal part. This arc is represented as green in the Figure.
The position of the neutral layer in sheet metal depends on specific material properties, such as ductility.
Assuming the distance between the neutral sheet metal layer and the surface is “t,” that is, the depth from the surface of the sheet metal part to the sheet metal material in the thickness direction is t.
Therefore, the radius of the neutral sheet metal layer arc can be expressed as (R+t).
Using this expression and the bending angle, the length of the neutral layer arc (BA) can be expressed as:
BA = Pi*(R+T)*A/180
To simplify the definition of the neutral layer in sheet metal and considering the applicability to all material thicknesses, the concept of the k-factor is introduced. Specifically, the k-factor is the ratio of the thickness of the neutral layer position to the overall thickness of the sheet metal part, that is:
K = t/T
Therefore, the value of K is always between 0 and 1. If a k-factor is 0.25, it means that the neutral layer is located 25% of the thickness of the sheet metal material, and if it is 0.5, it means that the neutral layer is located at the halfway point of the entire thickness, and so on.
Combining the above two equations, we can get the following equation (8):
BA = Pi*(R+K*T)*A/180 (8)
Where some values such as A, R, and T are determined by the actual geometric shape.
Variation Law of K Factor and Neutral Layer
1. Even for the same material, the K-factor in actual processing is not constant and its specific value is impacted by the processing technology.
In the elastic deformation stage of sheet metal bending, the neutral axis is situated in the middle of the plate thickness.
However, as the bending deformation of the stamped workpiece increases, the material undergoes mainly plastic deformation.
At this time, the plastic deformation is unrecoverable, and the neutral layer will shift to the inner side of the bending with the change of the deformation state.
The more severe the plastic deformation of the material, the greater the offset of the neutral layer to the inside of the bending.
So how can we reflect the intensity of plastic deformation during plate bending?
We can use the parameter R/T to reflect the intensity of plate deformation. R represents the inner radius of bending, and T stands for plate thickness.
A smaller R/T ratio indicates a higher level of plate deformation and a greater shift of the neutral layer inward.
The data in the table below apply to plates with a rectangular cross-section under specific processing conditions.
As shown in the table, the neutral layer’s position factor K increases as R/T increases.
Material properties and bending techniques can affect the position of the neutral layer.
At this time, the radius of the neutral layer can be calculated according to the following formula:
ρ = R + KT
- ρ – radius of the neutral layer
- R – bend inner radius
- K – neutral layer position factor
- T – material thickness
In simpler terms, once the radius of the neutral layer is determined, its development length can be calculated based on geometry, and then the sheet’s development length can be calculated.
2. Generally speaking, under the same bending conditions, the softer the sheet metal material, the lower its K value and the larger the offset of the neutral layer to the inside of the bend.
There are three standard bending tables applicable to 90-degree bending in Machinery’s Handbook.
K Factor Table for Different Materials
|Soft brass, copper
|Hard brass, copper, mild steel, aluminum
|Hard brass, bronze, cold rolled steel, spring steel
3. For smaller inner radius bends, the bending angle can also impact the change in the K factor.
The larger the bending deformation angle is, the greater the offset of the neutral layer to the inner side of the bend is.
Why Do We Need to Calibrate the K-Factor?
In the process of sheet metal bending calculation, we often need to calibrate the k-factor. So why do we need to calibrate the k-factor?
In SolidWorks, the deduction value for non-90-degree angle bending is only calculated by input. This can be very troublesome.
To avoid having to calculate the deduction value for non-90-degree angle bending, the k-factor is used instead.
However, how do we accurately determine the k-factor for different sheet metal thicknesses? This requires calibration.
Here is an analysis of how to calibrate:
- The first step is to determine the deduction value required for different sheet metal thicknesses in practice.
- The second step is to calibrate the k-factor in SolidWorks. When drawing sheet metal, set the inner radius to 0.1 for calibration because different inner radii have different k-factor unfoldings. Note that the inner radius must be set to 0.1 for calibration. Some may ask, what if the inner radius is not 0.1 after calibration? In this case, simply change it to 0.1 for unfolding.
- The third step is the calibration stage. In SolidWorks, bend a 10x10mm sheet metal with a thickness of 1.5mm at a 90-degree angle with an inner radius of 0.1 and a deduction value of 2.5mm to obtain an unfolding length of 17.5mm.
- The fourth step is to change the deduction value to the k-factor. Start by setting an approximate value, for example, 0.3. The unfolding length will not be 17.5mm. Then try adjusting the k-factor until the unfolding length is 17.5mm. In this way, the k-factor can be calibrated to 0.23, which will result in an unfolding length of 17.5mm.
- Repeat this process to calibrate different values and record them in a table.
- Sheet Metal Bending Calculator (Free to Use)
- Y Factor Calculator
- Bend Allowance Calculator
- Bend Deduction Calculator
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