⚡ electrical engineering

Improving roughness using plastic deformation treatment - Box-Behnken's experimental design approach

This study utilizes a Box-Behnken experimental design within Response Surface Methodology to optimize plastic deformation treatment parameters, demonstrating that the approach significantly reduces surface roughness while accurately predicting outcomes and preserving mechanical properties.

Original authors: Hichem Bounezour, youcef zennir, Hefaidh Hadef, lakhdar laouar

Published 2026-10-06

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CC BY 4.0

Original authors: Hichem Bounezour, youcef zennir, Hefaidh Hadef, lakhdar laouar

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

Every mechanical part that moves, rubs, or bears weight carries a hidden history written on its skin. Even a surface that looks smooth to the naked eye is actually a landscape of tiny peaks and valleys, a jagged terrain formed by the tools that shaped it. These microscopic irregularities are not just cosmetic; they dictate how long a machine lasts. Rough surfaces create friction, generate heat, and act as starting points for cracks that can eventually cause a component to fail. For decades, engineers have fought this roughness by grinding, polishing, or chemically stripping away material, essentially shaving off the peaks to create a flatter plane. While effective, these methods consume energy, wear down tools, and can sometimes weaken the part by introducing internal stresses or micro-cracks. A more elegant solution exists in the realm of plastic deformation, a process that does not remove material but instead reshapes it. By pressing a hard tool against the surface with controlled force, the material is coaxed to flow, filling in the valleys and flattening the peaks, leaving behind a smoother, stronger surface without losing any of the part's original dimensions.

In a recent study, researchers from universities in Algeria set out to master this reshaping process, specifically focusing on a technique known as burnishing. They wanted to find the perfect recipe for smoothing two very different metals: a common steel used in machinery and a lightweight aluminum alloy. The challenge was that the process depends on several variables that interact in complex ways. The team needed to determine exactly how much pressure to apply, how many times to pass the tool over the surface, and which type of tool motion worked best for each material. To solve this puzzle without running hundreds of trial-and-error tests, they employed a statistical strategy called the Box-Behnken design. This method allowed them to map out the relationships between the load, the number of passes, and the surface condition, creating a reliable model that could predict the outcome of any combination of these factors.

The researchers built a setup where they could treat cylindrical parts made of steel and aluminum on a standard lathe. They used two distinct methods of burnishing. The first involved a fixed ball that pressed against the spinning part, creating a tangential force that smoothed the surface by pushing material sideways. The second method used a moving ball, or roller, which rolled across the surface, applying a radial force that pressed directly into the peaks. They tested fifteen different scenarios for each metal, varying the pressure from 50 to 150 newtons and the number of passes from one to three. After each treatment, they measured the surface roughness with high precision, looking for the specific combination of settings that produced the smoothest finish.

The results revealed that there is no single "best" setting that works for every material. For the aluminum parts, the smoothest surfaces were achieved with a relatively low applied load and a minimal number of passes. Pushing harder or going over the surface more times actually made the aluminum rougher, likely because the softer metal was being deformed too aggressively. In contrast, the steel parts responded differently. While lower loads generally helped, the optimal conditions for steel were more nuanced and depended heavily on whether the surface had been prepared with the fixed ball or the moving roller. The study found that the fixed-ball method was particularly effective at smoothing the initial surface without damaging it, making it an excellent preparatory step. However, the moving-ball method, which creates a rolling action without the friction of a sliding tool, proved superior for the final finish, especially on the steel, where it could achieve a remarkably smooth texture.

Ultimately, the team demonstrated that by carefully tuning the pressure and the number of passes, plastic deformation can produce surface finishes that rival or even exceed those achieved by traditional grinding and polishing. The study confirmed that this approach not only smooths the surface but also strengthens the material by compressing the top layer, making it more resistant to wear and fatigue. The researchers concluded that while the specific settings must be tailored to the hardness of the metal, the technique offers a powerful, energy-efficient alternative to conventional finishing. It transforms the surface from a fragile, jagged landscape into a resilient, smooth plane, proving that sometimes the best way to improve a part is not to take anything away, but to press it just right.

Technical Summary: Improving Roughness Using Plastic Deformation Treatment via Box-Behnken Design

1. Problem Statement

Surface roughness is a critical determinant of mechanical component performance, directly influencing fatigue resistance, wear, friction, and corrosion susceptibility. While conventional finishing methods (grinding, polishing, electro-polishing) effectively reduce roughness, they are subtractive processes that consume significant energy, cause tool wear, and can introduce detrimental defects such as residual tensile stresses and micro-cracks.

Plastic deformation treatments, specifically burnishing, offer a non-subtractive alternative that improves surface finish and mechanical properties simultaneously by flattening surface asperities and inducing compressive residual stresses. However, optimizing these processes is challenging due to the complex, non-linear interactions between process parameters (e.g., applied load, number of passes, surface state). Traditional trial-and-error approaches are inefficient for navigating these interactions, necessitating a robust statistical framework to model and predict optimal conditions without extensive experimental trials.

2. Methodology

The study employs a Box-Behnken Design (BBD) within the framework of Response Surface Methodology (RSM) to optimize surface roughness ( $R_a$ ) through controlled plastic deformation.

Experimental Setup

Materials: Two materials were tested: Steel (XC38) and Aluminum (AL).
Process: Ball burnishing was performed on a lathe using two distinct regimes:
- Fixed-ball burnishing: Generates tangential forces.
- Moving-ball (roller) burnishing: Generates radial forces.
Factors and Levels: Three independent variables were investigated at three levels:
1. Surface Type (S): Machined (M), Fixed-ball burnished (B), or Moving-ball burnished (R).
2. Applied Load ( $P_y$ ): 50 N, 100 N, and 150 N.
3. Number of Passes (n): 1, 2, and 3.
Design Matrix: A standard 15-run BBD matrix was utilized, including 12 factorial points and 3 center-point replicates to estimate experimental error and model curvature.
Measurement: Surface roughness ( $R_a$ ) was measured using a Surftest SJ-210 device.
Modeling: A second-order quadratic polynomial model was fitted to the experimental data to predict $R_a$ as a function of the input factors and their interactions.

3. Key Contributions

Statistical Modeling: The study successfully developed predictive mathematical models for surface roughness under plastic deformation, capturing both individual factor effects and their interactions using the Box-Behnken approach.
Comparative Analysis of Burnishing Modes: The research distinguishes the mechanical effects of fixed-ball (tangential force) versus moving-ball (radial force) burnishing, analyzing how these force vectors interact with material properties (ductile aluminum vs. harder steel).
Optimization of Process Parameters: The work identifies specific optimal regimes for minimizing $R_a$ for different material and surface combinations, demonstrating that a "one-size-fits-all" approach is insufficient.
Validation of BBD-RSM: The study validates the efficacy of the Box-Behnken design in reducing the number of required experimental trials while maintaining high predictive accuracy ( $R^2$ values ranging from 0.96 to 0.97).

4. Results

The experimental results and statistical analysis yielded the following findings:

Model Accuracy: The quadratic models demonstrated excellent agreement with experimental data, with $R^2$ values between 0.96 and 0.97, confirming the reliability of the BBD approach for this application.
Material-Specific Behavior:
- Aluminum: Consistent behavior was observed across surface types. Optimal results (lowest $R_a$ ) were achieved with low applied loads and a reduced number of passes. Increasing these parameters led to surface degradation.
- Steel: The response was more complex and fluctuating. For fixed-ball treatment, low loads and fewer passes were optimal. For moving-ball treatment, the interaction between load and passes was significant; generally, higher loads and pass counts improved results for certain surface types, while low loads were preferred for others.
Burnishing Mechanism:
- Fixed-Ball: The tangential forces effectively smooth peaks without significantly propagating microscopic cracks, making it highly effective for initial surface preparation.
- Moving-Ball: The radial forces create a smoother surface with less friction and heat buildup, yielding superior final finishes and mechanical property improvements.
Optimal Regimes:
- Aluminum (Fixed Ball): Load = 50 N, Passes = 1.
- Steel (Moving Ball): Load = ~62.85 N, Passes = 3.
- The study noted that for aluminum, the fixed-ball method yielded the best results, whereas for steel, the moving-ball method showed significant potential for improvement when parameters were correctly tuned.

5. Significance and Claims

The paper claims that surface treatment via plastic deformation, when optimized using a Box-Behnken experimental design, serves as an excellent finishing process. Its significance lies in the ability to:

Achieve Superior Finishes: The optimized process can yield surface finishes potentially superior to conventional superfinishing methods without material removal.
Enhance Mechanical Properties: Beyond roughness reduction, the process improves surface hardness and yield strength through work hardening and compressive residual stress induction.
Efficient Optimization: The BBD-RSM approach provides a reliable, low-cost method to navigate complex parameter interactions, avoiding the need for exhaustive trial-and-error experimentation.

The authors conclude that the choice of optimal conditions is strictly dependent on the material's behavior (ductile vs. hard) and the specific force vector (tangential vs. radial) applied during burnishing. The study positions plastic deformation as a sustainable, high-performance alternative to traditional subtractive finishing, particularly when guided by robust statistical modeling.