Application of the NSGA-II Algorithm and Kriging Model to Optimise the Process Parameters for the Improvement of the Quality of Fresnel Lenses
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2023-08-14 |
| Journal | Polymers |
| Authors | Hanjui Chang, Yue Sun, Rui Wang, Shuzhou Lu |
| Institutions | Shantou University |
| Citations | 5 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study successfully optimized the injection molding process for Polymethyl Methacrylate (PMMA) Fresnel lenses using a hybrid computational approach to enhance product quality and optical performance.
- Core Achievement: Minimized nodal displacement and residual stress in PMMA Fresnel lenses, achieving a 59.64% optimization rate for displacement.
- Methodology: A Kriging surrogate model was combined with the NSGA-II (Non-Dominated Sorting Genetic Algorithm II) for multi-objective optimization, effectively mapping process parameters to quality objectives.
- Optimal Parameters: The best results were achieved with a holding pressure of 320.35 MPa and a melt temperature of 251.40 °C.
- Process Selection: In-Mould Decoration (IMD) technology was selected over Injection Compression Molding (ICM) and Two-stage Injection Molding, as IMD is better suited for protecting the delicate serrated microstructure of the Fresnel lens surface.
- Optical Performance: The optimized lenses demonstrated excellent optical quality, achieving an average transmittance of 95.43% in the near-infrared (NIR) wavelength range.
- Key Influencing Factors: Holding pressure was determined to be the dominant factor affecting both nodal displacement and residual stress, followed by melt temperature.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Optimized Holding Pressure (P) | 320.35 | MPa | Optimal injection parameter |
| Optimized Melt Temperature (T) | 251.40 | °C | Optimal injection parameter |
| Optimized Avg Nodal Displacement | 0.393 | mm | Average displacement after optimization |
| Initial Avg Nodal Displacement | 0.659 | mm | Average displacement using initial IMD settings |
| Displacement Optimization Rate | 59.64 | % | Improvement achieved via NSGA-II/Kriging |
| Simulated Avg Residual Stress | 0.075 | MPa | Simulated average stress at optimal parameters |
| Measured Transmittance | 95.43 | % | Average transmittance in the near-infrared range |
| PMMA Glass Transition Temp (Tg) | 105-110 | °C | Material property (Polymethyl Methacrylate) |
| PMMA Compressive Modulus | 2-3 | GPa | Material property |
| NSGA-II Population Size | 50 | - | Genetic algorithm setting |
| NSGA-II Terminating Generations | 200 | - | Genetic algorithm setting |
| NSGA-II Crossover Rate | 80 | % | Genetic algorithm setting |
Key Methodologies
Section titled âKey MethodologiesâThe optimization process combined simulation, surrogate modeling, and multi-objective genetic algorithms to determine the ideal injection molding parameters for PMMA Fresnel lenses manufactured via IMD.
- Process Comparison and Selection:
- Simulations were performed comparing In-Mould Decoration (IMD), Injection Compression Molding (ICM), and Two-stage Injection Molding based on V-groove nodal displacement.
- ICM yielded the lowest displacement (0.251 mm average) but risked damaging the serrated microstructure. IMD (0.659 mm average initial displacement) was selected due to its protective coating layer, which enhances surface quality and optical performance.
- Parameter Screening:
- Holding pressure and melt temperature were identified as the two most significant variables influencing nodal displacement and residual stress, based on response surface analysis.
- Kriging Surrogate Model Establishment:
- 20 sets of sample data points (varying holding pressure and melt temperature) were generated via simulation.
- A Kriging proxy model was constructed using MATLAB and a Gaussian spatial correlation function to create a high-accuracy, non-linear response surface mapping parameters to the objectives (R1: nodal displacement, R2: residual stress).
- Multi-Objective Optimization (NSGA-II):
- The NSGA-II algorithm was applied to the Kriging model to solve the black-box optimization problem, minimizing the objective function F = Min{R1, R2}.
- The algorithm utilized non-dominated sorting and crowding distance to maintain population diversity and accelerate convergence toward the Pareto optimal frontier.
- Optimal Solution Determination:
- Analysis of the Pareto frontier identified the optimal parameter combination: 320.35 MPa holding pressure and 251.40 °C melt temperature.
- Validation and Testing:
- Simulations confirmed the optimal parameters yielded low average displacement (0.675 mm) and residual stress (0.075 MPa).
- Physical lenses were produced using an all-electric injection molding machine and tested using a Lambda 950 UV/Vis spectrophotometer, confirming 95.43% transmittance.
Commercial Applications
Section titled âCommercial ApplicationsâThe optimized manufacturing process for high-quality, high-transmittance PMMA Fresnel lenses supports several high-tech and mass-market sectors:
- Infrared (IR) Technology:
- Infrared thermal imagers and sensors, leveraging the lensâs high transmittance (95.43%) in the near-infrared spectrum.
- Infrared communication systems, improving signal focusing and stability.
- Infrared thermometry instruments.
- Optical Systems and Displays:
- Projector lenses and rear projection displays, where thin, lightweight, and efficient focusing elements are required.
- Miniaturized optical components and micro-lenses for consumer electronics and medical devices.
- Renewable Energy:
- Solar concentrators and linear Fresnel collectors, where high optical efficiency and material cost-effectiveness are crucial.
- High-Volume Manufacturing:
- The use of IMD combined with NSGA-II optimization ensures high yield and quality control for mass-produced plastic optical parts, reducing waste and improving production efficiency.
View Original Abstract
The Fresnel lens is an optical system consisting of a series of concentric diamond grooves. One surface of the lens is smooth, while the other is engraved with concentric circles of increasing size. Optical interference, diffraction, and sensitivity to the angle of incidence are used to design the microstructure on the lens surface. The imaging of the optical surface depends on its curvature. By reducing the thickness of the lens, light can still be focused at the same focal point as with a thicker lens. Previously, lenses, including Fresnel lenses, were made of glass due to material limitations. However, the traditional grinding and polishing methods for making Fresnel lenses were not only time-consuming, but also labour-intensive. As a result, costs were high. Later, a thermal pressing process using metal moulds was invented. However, the high surface tension of glass caused some detailed parts to be deformed during the pressing process, resulting in unsatisfactory Fresnel lens performance. In addition, the complex manufacturing process and unstable processing accuracy hindered mass production. This resulted in high prices and limited applications for Fresnel lenses. These factors prevented the widespread use of early Fresnel lenses. In contrast, polymer materials offer advantages, such as low density, light weight, high strength-to-weight ratios, and corrosion resistance. They are also cost effective and available in a wide range of grades. Polymer materials have gradually replaced optical glass and other materials in the manufacture of micro-optical lenses and other miniaturised devices. Therefore, this study focuses on investigating the manufacturing parameters of Fresnel lenses in the injection moulding process. We compare the quality of products obtained by two-stage injection moulding, injection compression moulding, and IMD (in-mould decoration) techniques. The results show that the optimal method is IMD, which reduces the nodal displacement on the Fresnel lens surface and improves the transmission performance. To achieve this, we first establish a Kriging model to correlate the process parameters with optimisation objectives, mapping the design parameters and optimisation objectives. Based on the Kriging model, we integrate the NSGA-II algorithm with the predictive model to obtain the Pareto optimal solutions. By analysing the Pareto frontier, we identify the best process parameters. Finally, it is determined that the average nodal displacement on the Fresnel surface is 0.393 mm, at a holding pressure of 320.35 MPa and a melt temperature of 251.40 °C. Combined with IMD technology, product testing shows a transmittance of 95.43% and an optimisation rate of 59.64%.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 2012 - Surface wear of TiN coated nickel tool during the injection moulding of polymer micro Fresnel lenses [Crossref]
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