⚡ electrical engineering

Numerical study on the effect of blank-holding techniques on the countersinking process

This paper presents a numerical study demonstrating that innovative progressive blank-holding force models, utilizing elastic annular rings, significantly reduce geometric imperfections and energy consumption in the countersinking process compared to traditional displacement-imposed methods.

Original authors: Hassen Mosbah, Slimen Attyaoui, Rachid Nasri

Published 2026-09-14

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CC BY 4.0

Original authors: Hassen Mosbah, Slimen Attyaoui, Rachid Nasri

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of metalworking, creating a smooth, tapered seat for a screw or a rivet is a common but delicate task known as countersinking. Imagine a sheet of metal with a small hole in it; to make that hole ready for a fastener that sits flush with the surface, a conical tool pushes into the metal, forcing the edges to flare outward. This process seems simple, but it requires a careful balance of forces. If the metal sheet is not held down firmly enough, it will warp or lift, ruining the shape. If it is held down too hard, the machine wastes a tremendous amount of energy, and the metal might crack or deform in unwanted ways. For decades, engineers have struggled to find the perfect amount of pressure to apply to the edge of the sheet, a force known as the blank-holding force, to ensure the final product is flat, strong, and efficient to produce.

A team of researchers set out to solve this balancing act by simulating the process on a computer and testing their ideas with real metal sheets. They focused on three different ways to hold the sheet in place during the countersinking operation. The first method they examined was a traditional approach where the machine pushes the holding tool down with a fixed, unyielding pressure from the very start. Their simulations revealed a significant flaw in this technique: the force required to keep the sheet perfectly still was far too high, reaching levels nearly three times greater than the force needed to actually shape the hole. This excessive pressure meant the machine was working much harder than necessary, consuming extra energy and risking damage to the material.

To fix this inefficiency, the researchers proposed two new methods that use a flexible, spring-like ring made of a special plastic material to apply the holding force. Instead of pushing down with a constant, heavy hand, this ring allows the force to build up gradually as the shaping tool moves deeper into the metal. In the first new method, the ring sits directly against the holding tool, applying pressure immediately. In the second, slightly more refined method, a tiny gap is left between the ring and the tool. This gap acts as a brief delay, allowing the shaping process to begin before the holding pressure kicks in. The researchers found that both of these gradual approaches were far superior to the old, rigid method. They successfully reduced the total energy needed for the process and prevented the metal sheet from lifting or warping, resulting in a much flatter and more precise final shape.

The study confirmed that the key to success lies in timing and flexibility. By letting the holding force grow slowly and only applying it when truly needed, the machine avoids the waste of energy seen in the traditional method. The researchers validated their computer models by building physical tools and running actual tests, finding that the real-world results matched their simulations closely. They discovered that the best approach involved the delayed method, where the holding pressure starts just a fraction of a millimeter after the shaping begins. This specific adjustment reduced the energy consumption by about ten percent compared to the immediate-pressure method and kept the holding force well below the limit of what the shaping tool could handle. The findings suggest that by simply changing how the pressure is applied—using a smart, flexible ring instead of a rigid clamp—manufacturers can produce high-quality countersunk holes with less effort and less waste, a small but meaningful improvement for the industry.

Technical Summary: Numerical Study on the Effect of Blank-Holding Techniques on the Countersinking Process

Problem Statement
The countersinking process, widely used to enlarge pre-drilled holes for rivet or screw heads in sheet metal forming, is sensitive to the control of the Blank-Holding Force (BHF). In industrial applications, particularly with single-action press machines, controlling the BHF is critical to minimizing geometric imperfections (such as gaps and expansions) and reducing energy consumption. Previous studies have highlighted issues with existing blank-holding techniques; for instance, applying an imposed displacement to the blank-holder often results in an excessive BHF that exceeds the punch load, leading to unnecessary energy consumption and potential process inefficiencies. While research has extensively covered fatigue life, cracking behavior, and geometric parameter optimization, there is a lack of focused literature on optimizing the BHF application method itself to balance forming kinematics and energy efficiency.

Methodology
This study employs a comprehensive numerical approach using axisymmetric elasto-plastic finite element models developed in Abaqus/Standard®. The research utilizes S235 hot-rolled steel (2.7 mm thickness) and investigates three distinct blank-holding scenarios:

Case C1 (Imposed Displacement): A traditional model where a specific displacement is imposed on the blank-holder. A sub-case with zero imposed displacement (maintained blank-holder) serves as a baseline for reaction force determination.
Case C2 (Progressive BHF, No Clearance): A novel model utilizing an elastic annular ring positioned between the punch and the blank-holder to generate a progressive BHF from the start of the process. The stiffness of the ring is varied by changing its Young's Modulus ( $E_S$ ).
Case C3 (Progressive BHF with Clearance): An extension of Case C2 where a clearance ( $C \neq 0$ ) is introduced between the blank-holder and the workpiece. This creates a delay in the application of the BHF, allowing it to engage only after the punch has traveled a specific distance.

The models incorporate Coulomb friction (coefficient = 0.12) and adaptive meshing to handle large plastic deformations. Experimental validation was conducted using a 200 kN universal compression machine. For the progressive force models, a Polytetrafluoroethylene (PTFE) annular ring was manufactured to approximate the required stiffness, and shims were used to control the clearance.

Key Contributions and Results
The study systematically compares the three cases regarding load evolution, forming kinematics, and energy consumption:

Excessive Force in Case C1: The traditional imposed displacement method (specifically with $\delta_b = 1\mu m$ ) resulted in a maximum BHF of approximately 59 kN. This value is roughly 144% of the punch load (41 kN), confirming that this technique leads to excessive energy consumption and is unsuitable for manufacturing where BHF should not exceed punch load.
Effectiveness of Progressive BHF (Cases C2 and C3): The introduction of an elastic annular ring successfully reduced the BHF to manageable levels.
- In Case C2, the maximum BHF was reduced to 19 kN (approx. 45% of the punch load).
- In Case C3, with the addition of a 0.45 mm clearance, the maximum BHF was 24 kN (approx. 60% of the punch load).
Kinematic Improvements: The progressive BHF significantly improved the quality of the formed part. Compared to the reference case (C1 with zero displacement), the progressive methods reduced the inferior gap ( $G_i$ ) to one-third of its original value and decreased axial expansion, thereby enhancing the flatness of the final surface. The use of the annular ring also increased material retraction, which is beneficial for hole formation.
Energy Efficiency: Energy consumption, calculated as the area under the BHF curve, was minimized in Case C3. The introduction of the clearance resulted in a 10% reduction in energy usage compared to Case C2.
Experimental Validation: Experimental tests using a PTFE ring (approximating $E_S = 540$ MPa) showed good agreement with numerical simulations, with a maximum difference of 14% in the progressive BHF curves. The experiments confirmed that progressive blank holding reduces cumulative plastic strain (PEEQ) by 25% compared to the traditional method and eliminates circular scratches around the countersunk hole caused by high contact pressure.

Significance and Claims
The authors conclude that the proposed progressive blank-holding techniques (specifically Cases C2 and C3) offer a viable solution for optimizing the countersinking process in single-action machines. By utilizing an elastic annular ring, the BHF can be controlled to remain below the punch load, thereby reducing energy consumption and geometric defects without altering the punch load requirements.

The study claims that Case C3 represents the optimal configuration, balancing the lowest energy consumption with effective control over forming kinematics (retraction, gaps, and expansion). The research validates that finite element models, when coupled with experimental verification, are reliable tools for predicting loads and kinematics in countersinking. The authors state that these methodologies can be directly integrated into existing low-cost single-action punch machines to produce standardized countersunk holes with improved quality and efficiency. Future work is identified as focusing on further process optimization to achieve fully normalized countersunk holes.

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