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K-Factor Impact: Bending Methods, Die Width, and Friction

The k-factor, crucial in metal bending, mirrors the shift of the neutral axis in bending. Diverse factors influence it, impacting bend accuracy. In this article, we explore these factors’ effects on metal fabrication. Maybe you also want to check out our Section Bending Machine page.

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The k-factor, a critical parameter in the metal bending process, reflects the displacement of the neutral axis during the bending process. Numerous factors influence the k-factor, each playing a distinct role in determining the accuracy and precision of bends. In this comprehensive analysis, we delve into the various factors affecting the k-factor and their implications for metal fabrication.


The k-factor, a crucial parameter in metal bending, embodies the displacement of the neutral axis during the bending process. Originating as a theoretical construct positioned at 50 percent of the material thickness (Mt) in its unstressed and flat state, the neutral axis undergoes a shift toward the inside of the bend upon bending. This displacement is quantified by the k-factor value, representing the ratio of the neutral axis’ post-bend position, denoted as “t” in Figure 1, to the material thickness (k-factor = t/Mt).

Figure 1: The k-factor is defined as the neutral-axis shift during bending (t) divided by the material thickness (Mt)

A multitude of factors influence the k-factor, each playing a pivotal role in shaping its value. Previously discussed factors, such as the minimum bend radius and its correlation with material thickness, remain integral to k-factor determination. Additionally, distinctions between “sharp” and “minimum” bends in air forming, where the pressure to form surpasses that of piercing, significantly impact the k-factor by inducing creases at the bend’s center.

Moreover, grain direction, material thickness, and hardness emerge as key determinants of the k-factor. The orientation of grain within the material, alongside its thickness and hardness properties, influences the degree of neutral axis displacement during bending. As we delve deeper into understanding the k-factor, it becomes evident that a comprehensive assessment of these factors is essential for accurate k-factor estimation.

In the subsequent discussion, we will explore additional factors that contribute to the determination of the k-factor, further elucidating its significance in metal bending processes. Additionally, we will navigate through a manual calculation to demonstrate the practical application of these factors in determining the k-factor value. Stay tuned as we unravel the intricacies of the k-factor and its profound implications in the realm of metal fabrication.

Bending Method

bottom bending for sheet metal bending
When bottoming (which is different from coining), the material wraps around the descending punch. Continued pressure then forces the metal open against the die angle. Material deformation at the radius during bottoming causes the k-factor to be higher than it would be during an air form.

The choice of bending method significantly impacts the k-factor value. Air bending, bottoming, and coining represent distinct approaches to forming metal bends, each with its unique characteristics. While air bending is characterized by controlled compression and expansion, bottoming and coining involve extreme force and material thinning. Coining, in particular, results in a lower k-factor due to stress relief and internal realignment, leading to a sharper inside bend radius. Conversely, bottoming relies on material compression and deformation, resulting in a higher k-factor value. Understanding the differences between these bending methods is crucial for optimizing bend accuracy and minimizing material wastage.

air bending in sheet metal bending
Air bending has a floated radius that forms as a percentage of the die opening.

In addition to the k-factor variables previously discussed, the forming method plays a crucial role in shaping the k-factor value. Three primary bending techniques—air bending, bottoming, and coining—each exert distinct influences on the neutral axis displacement and, consequently, the k-factor.

Let’s delve into each method:


In coining, the material interfaces fully with both the punch and die surfaces, subjecting it to extreme forces that exceed the material’s yield point. As a result, the punch tip penetrates the neutral axis, compressing the material and creating a sharp inside bend radius (Ir). This severe thinning and realignment of the metallurgical structure alleviate material stress, ultimately reducing the k-factor value compared to bottoming.


Unlike coining, bottoming involves clearance between the punch and die angle. As the descending punch tip forces the material to wrap around it, the material is gradually forced to conform to the die angle, particularly at the inside bend radius. Bottoming occurs within the material thickness to approximately 20 percent above it, compressing the inside bend radius and further thinning the material. This process, although less extreme than coining, contributes to a higher k-factor value due to increased material deformation.

coining for sheet metal bending
When coining, the material comes in full contact with both the punch and die. The severe thinning relieves material stress and, in turn, causes the k-factor to be less than it would be during bottoming.

Air Forming:

Air forming, a prevalent technique in modern precision bending, differs significantly from coining and bottoming. It operates on a three-point bend principle, with the punch tip and two radii leading into the die opening contacting the bend. Unlike the direct contact observed in coining and bottoming, air forming creates a floated radius based on a percentage of the die opening. The punch’s depth of penetration into the die space determines the bend angle, resulting in relatively small tonnages compared to other methods. Air forming serves as the baseline method for defining the k-factor, neutral axis, and Bend Allowance (BA).

How do these bending methods influence the k-factor value?

  • Air Forming vs. Bottoming: Research indicates that transitioning from air forming to bottoming, utilizing the same material and tooling, elevates the k-factor value by approximately 15 percent. This escalation is attributed to the substantial deformation occurring at the bend radius during bottoming.
  • Coining vs. Bottoming: While coining yields a reduced k-factor due to stress alleviation and realignment of the metallurgical structure, bottoming contributes to a higher k-factor value through material compression and thinning at the bend point.

The k-factor value serves as a critical metric in metal bending, reflecting the intricate interplay between forming methods, material properties, and geometric factors. Understanding these nuances is imperative for optimizing bending processes and achieving precise fabrication outcomes.

Die Width

Die width plays a critical role in determining the k-factor, especially when considering material thickness variations. Increasing material thickness with a constant punch and die combination leads to greater friction and reduced material slide over the die radius. Consequently, this results in increased material deformation and a higher k-factor value. Conversely, decreasing die width while keeping material thickness constant amplifies the bending force required, leading to a larger k-factor. Experimental studies have demonstrated a direct correlation between die width and k-factor, highlighting the importance of die selection in achieving desired bend characteristics.

Coefficient of Friction

The coefficient of friction between metal surfaces and tooling components significantly influences the k-factor. As the metal becomes harder and thicker, the coefficient of friction increases, leading to greater resistance to movement during bending. This elevated frictional force induces higher stress and pressure on the metal, ultimately reducing the k-factor. Conversely, lower coefficients of friction result in smoother material movement and reduced deformation, contributing to a higher k-factor value. Understanding the interplay between material properties and friction coefficients is essential for accurately predicting bend behavior and optimizing bending processes.

Implications for Metal Fabrication

The factors affecting the k-factor have profound implications for metal fabrication, ranging from part accuracy to tooling selection and manufacturing efficiency. By comprehensively understanding the influence of bending methods, die width, and friction coefficients, fabricators can make informed decisions to achieve desired bend characteristics and meet stringent quality standards. Additionally, accurate k-factor estimation facilitates precise bend allowance calculations, minimizing material wastage and optimizing production costs.


The k-factor serves as a fundamental parameter in metal bending, reflecting the displacement of the neutral axis during the bending process. Factors such as bending method, die width, and coefficient of friction exert a significant influence on the k-factor value, shaping bend accuracy and precision. By systematically analyzing these factors and their implications, fabricators can enhance bend quality, optimize manufacturing processes, and achieve superior results in metal fabrication applications.

Works Cited and Img Resources: Analyzing the k-factor in sheet metal bending