Optimization of Surface Roughness of Aluminium RSA 443 in Diamond Tool Turning †
Abstract
:1. Introduction
2. Literature on Diamond Machining Generally and RSA Specifically
2.1. Diamond Turning
2.1.1. Tool Wear
2.1.2. Tool Path Considerations
2.1.3. Hybrid Methods
2.2. Machining of RSA Materials
2.3. Optimization of Turning Parameters
3. Materials and Methods
3.1. Research Objectives
3.2. Approach
3.2.1. Experimental Design and Data Collection
3.2.2. Response Surface Methodology Model
3.2.3. Optimization Techniques
3.2.4. Genetic Algorithm (GA)
- A population of n individuals was created. The individuals were initialized with values on the interval of 15 individuals.
- The fitness of the population was evaluated. The fitness of the fittest chromosome was stored in the hall of fame.
- The fittest two chromosomes were carried over to the next generation (elitism).
- Eighty percent of the new generation was created by means of sexual reproduction with tournament selection as follows:
- Ten random individuals (tournament size) were selected from the population.
- Two of the fittest chromosomes were used in the crossover with a randomly generated mask to produce one child chromosome.
- Mutations applied at a probability of pm were applied to the genes of the chromosome.
- The fittest parent and child were carried over to the next generation.
- The remainder of the new generation was created by mutating the least fit chromosomes as follows:
- A random mask was created to determine which genes were to be mutated.
- These genes were mutated by a value on the interval of 15 individuals.
3.2.5. Particle Swarm Algorithm (PSO)
- A swarm of n particles was created, representing the cutting parameters. The position of the particles was initialized with random values on the interval of 15 particles. The initial velocity of the particles was set to 0.
- The fitness of the particles was evaluated.
- For each particle, if the fitness calculated was better than its previous personal best, the personal best () along with its position was updated.
- For each particle, if its personal best was better than the global best (), the global best along with its position was updated.
- The velocity () of each particle () was updated (for j dimensions) using the following equation:
- where w is the inertia weight, & are acceleration constants and and are random values on the interval (0; 1).
3.2.6. Differential Evolution (DE)
- The fitness of the population was evaluated. The fitness of the fittest chromosome was stored in the hall of fame.
- The same reproduction operator was used for each individual (target vector) of the population by carrying out the following:
- A trial vector was created from the parent vector and two randomly selected unique individuals and :
- , where is the scale factor which amplifies the differential variation.
- A binomial crossover was performed between the parent vector and trial vector to produce offspring .
- A randomly selected gene from the trial vector was transferred to the child vector.
- For the rest of the genes, genes from the trial vector were included at a crossover point at a probability, otherwise genes from the parent were included.
- The fitness of the offspring was then evaluated.
- The fitter individual between the parent and offspring was carried over to the next generation.
- Steps 2–5 were repeated for a fixed number of iterations.
4. Results for RSA 443
4.1. Response Transformation Check
4.2. Fit Summary
4.3. Development of a Model for Surface Roughness
4.4. Optimization
5. Discussion
5.1. Findings
5.2. Implications for Industry Practitioners
5.3. Limitations of the Study
5.4. Implications for Further Research
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Code Statement (MATLAB)
- Fitness functions
- -
- SurfaceRoughness_s500
- -
- SurfaceRoughness_s1750
- -
- SurfaceRoughness_s3000
- GA code
- PSO code:
- DE code:
Appendix B. Convergence Results
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Run | Cutting Speed (s) (rpm) | Cutting Feed Rate (f) (mm/min) | Cutting Depth (d) (μm) | Surface Roughness Ra (nm) |
---|---|---|---|---|
1 | 1750 | 25 | 25 | 39.33 |
2 | 1750 | 25 | 5 | 35.55 |
3 | 3000 | 5 | 15 | 14.48 |
4 | 1750 | 15 | 15 | 23.94 |
5 | 1750 | 15 | 15 | 24.0 |
6 | 1750 | 5 | 25 | 17.45 |
7 | 500 | 15 | 25 | 76.82 |
8 | 3000 | 25 | 15 | 26.22 |
9 | 3000 | 15 | 25 | 22.05 |
10 | 500 | 15 | 15 | 187.18 |
11 | 3000 | 15 | 5 | 26.20 |
12 | 500 | 5 | 15 | 28.42 |
13 | 1750 | 5 | 5 | 17.35 |
14 | 1750 | 15 | 15 | 23.8 |
15 | 500 | 15 | 5 | 66.81 |
Type of Fit | F-Value | p-Value, Prob > F | Lack of Fit, Sum of Squares | Df for Lack of Fit | R-Squared | Evaluation |
---|---|---|---|---|---|---|
Linear | 24.70 | <0.0001 | 5.541 × 10−4 | 9 | 0.8707 | |
2FI | 0.11 | 0.9499 | 5.316 × 10−4 | 6 | 0.8760 | |
Quadratic | 35.01 | 0.0009 | 2.409 × 10−5 | 3 | 0.9944 | Suggested |
Cubic | 248.55 | 0.0040 | 0.000 | 0 | 1.0000 | Aliased |
Source | Sum of Squares | Degree of Freedom | Mean Square | F-Value | p-Value Prob > F | Characteristics |
---|---|---|---|---|---|---|
Model | 4.265 × 10−3 | 9 | 4.736 × 10−4 | 98.02 | <0.0001 | Significant |
A-Speed | 1.867 × 10−3 | 1 | 1.867 × 10−3 | 386.35 | <0.0001 | Significant |
B-Feed | 1.865 × 10−3 | 1 | 1.865 × 10−3 | 386.03 | <0.0001 | Significant |
C-Depth | 6.046 × 10−7 | 1 | 6.046 × 10−7 | 0.13 | 0.7380 | |
A2 | 3.380 × 10−4 | 1 | 3.380 × 10−4 | 69.95 | 0.0004 | Significant |
B2 | 8.091 × 10−5 | 1 | 8.091 × 10−5 | 16.75 | 0.0094 | Significant |
C2 | 7.066 × 10−5 | 1 | 7.066 × 10−5 | 14.63 | 0.0123 | Significant |
AB | 2.905 × 10−7 | 1 | 2.905 × 10−7 | 0.060 | 0.8161 | |
AC | 2.086 × 10−5 | 1 | 2.086 × 10−6 | 4.32 | 0.0923 | |
BC | 1.408 × 10−6 | 1 | 1.408 × 10−6 | 0.29 | 0.6125 | |
Residuals | 2.416 × 10−5 | 5 | 4.832 × 10−6 | |||
Lack of fit | 2.409 × 10−5 | 3 | 8.031 × 10−6 | 248.55 | 0.0040 | Significant |
Pure Error | 6.463 × 10−8 | 2 | 3.231 × 10−8 | |||
Corr. Total | 4.287 × 10−3 | 14 |
Std. Dev. | 2.198 × 10−3 | R-Squared | 0.9944 |
Mean | 0.037 | Adj R-Squared | 0.9842 |
C.V | 5.96 | Pred R-Squared | 0.9100 |
PRESS | 3.856 × 10−4 | Adeq Precision | 34.038 |
Source | Sum of Squares | Degree of Freedom | Mean Square | F-Value | p-Value Prob > F | Characteristics |
---|---|---|---|---|---|---|
Model | 4.265 × 10−3 | 9 | 4.736 × 10−4 | 98.02 | <0.0001 | Significant |
A-Speed | 1.867 × 10−3 | 1 | 1.867 × 10−3 | 386.35 | <0.0001 | Significant |
B-Feed | 1.865 × 10−3 | 1 | 1.865 × 10−3 | 386.03 | <0.0001 | Significant |
A2 | 3.380 × 10−4 | 1 | 3.380 × 10−4 | 69.95 | 0.0004 | Significant |
B2 | 8.091 × 10−5 | 1 | 8.091 × 10−5 | 16.75 | 0.0094 | Significant |
C2 | 7.066 × 10−5 | 1 | 7.066 × 10−5 | 14.63 | 0.0123 | Significant |
Residuals | 2.416 × 10−5 | 5 | 4.832 × 10−6 | |||
Lack of fit | 2.409 × 10−5 | 3 | 8.031 × 10−6 | 248.55 | 0.0040 | |
Pure Error | 6.463 × 10−8 | 2 | 3.231 × 10−8 | |||
Corr. Total | 4.287 × 10−3 | 14 |
Function | Cutting Speed (rpm) | Iterations or Generations | |||
---|---|---|---|---|---|
150 | 500 | 1500 | |||
GA | Ra_s500 | 500 | - | - | - |
Ra_s1500 | 1500 | 44.21 nm | - | 22.15 nm | |
Ra_s3000 | 3000 | - | 14.02 nm | - | |
PSO | Ra_s500 | 500 | - | - | - |
Ra_s1500 | 1500 | - | - | - | |
Ra_s3000 | 3000 | 211.0 nm | 121.84 nm | 211.0 nm | |
DE | Ra_s500 | 500 | - | - | - |
Ra_s1500 | 1500 | - | 37.38 nm | - | |
Ra_s3000 | 3000 | 36.28 nm | - | 67.87 nm |
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Mbangu Tambwe, G.; Pons, D. Optimization of Surface Roughness of Aluminium RSA 443 in Diamond Tool Turning. J. Manuf. Mater. Process. 2024, 8, 61. https://doi.org/10.3390/jmmp8020061
Mbangu Tambwe G, Pons D. Optimization of Surface Roughness of Aluminium RSA 443 in Diamond Tool Turning. Journal of Manufacturing and Materials Processing. 2024; 8(2):61. https://doi.org/10.3390/jmmp8020061
Chicago/Turabian StyleMbangu Tambwe, Gregoire, and Dirk Pons. 2024. "Optimization of Surface Roughness of Aluminium RSA 443 in Diamond Tool Turning" Journal of Manufacturing and Materials Processing 8, no. 2: 61. https://doi.org/10.3390/jmmp8020061