Design of Vibration and Noise Reduction for Ultra-Thin Cemented Carbide Circular Saw Blades in Woodworking Based on Multi-Objective Optimization
Abstract
:1. Introduction
2. Mathematical Model
2.1. Circular Saw Blade Vibration and Noise Calculation Model
2.2. Multi-Objective Optimization Model
- Optimization objective.The optimization targets for ensuring machining quality, safety, and reducing vibration and noise following grooving are the maximum deformation (), the maximum equivalent stress (), and the cumulative sum of overall vibration intensity (). The maximum deformation represents the deflection deformation capacity of the circular saw blade during the cutting process. Excessive deformation can result in interference between the circular saw blade and the workpiece, affecting machining accuracy and surface quality. By regulating the level of deformation within an acceptable range, one may guarantee that the circular saw blades maintain high processing quality following grooving [22]. The maximum equivalent stress shows the general stress level experienced by the circular saw blade when subjected to a cutting load. Excessive equivalent stress can result in plastic deformation, cracking, and other failures of the circular saw blade, compromising its safety during use. Optimizing the maximum equivalent stress can increase the strength and service life of circular saw blades [23]. The cumulative sum of the overall vibration intensity () represents the total sum of the vibration intensity of the circular saw blade when subjected to various excitations. This target value effectively captures the vibration noise characteristics of the slotted circular saw blade across a wide range of frequencies.
- Design domain.The Variable Density Topology Optimization approach, based on the Solid Isotropic Material with Penalization (SIMP) technique, was employed to manipulate the cell pseudo-density of a finite element model of a circular saw blade. The objective was to achieve convergence to either 0 or 1 by incorporating a penalty factor. A pseudo-density close to 1 indicates material retention, while a value close to 0 signifies material removal. This method determines the design domain of the noise reduction slot on the circular saw blade [24].The topology optimization zone of the circular saw blade was defined as a substrate by removing the serrated and the flange clamping section. The goal of the optimization was to maximize the structural rigidity of the circular saw blade. During the optimization phase, the circular saw blade design was considered for its symmetry to provide evenness and stability during loading and utilization. The improved circular saw blade model underwent a surface trimming procedure, and the design domain for the slot holes was chosen to be the low-density zone with a significant area, as depicted in Figure 2.
- Design variables and parametric modeling.Due to the distribution of the low-density region along the radial direction of the circular saw blade, a radial slot was selected for opening. The circular saw blade’s shape parameters encompassed the slot’s position and size. The exact stages and outcomes of the parametric modeling approach are illustrated in Figure 3. Initially, the geometric characteristics of the key spots in the slot holes of the circular saw blade substrate were determined. This included identifying the starting point, finishing point, and the positioning information of the four equidistant intermediate locations. An interpolation technique was used to achieve the positional value addition and translation of the information points. The whole contour of the slot was formed by connecting these essential locations with a smooth curve. Subsequently, stress relief holes were strategically constructed and created at the two terminal positions of the slot in order to minimize stress concentration and improve the overall structural integrity [25]. The circular saw blade model was modified by incorporating a sound deadening slot with stress relief holes, resulting in the final circular saw blade model that included the noise reduction slot.This study developed nine important design factors to precisely characterize the geometric information of the critical spots, which were the initial radius , the final radius , the width of the slot , the starting point, the ending point, and the angles of the four equidistant intermediate key points to . The variables were consolidated into a shape parameter vector (Equation (10)), which acted as the independent variable in the optimization model:Table 2 displays the range of values for the constrained design variables. This was to ensure that the matrix slot holes were created within a specific design region and to prevent any negative impact on the mesh quality near the holes due to flanges or other restrictions.
- Multi-objective optimization model.Utilizing the aforementioned principles, a mathematical model for multi-objective optimization was formulated to design noise-reducing slots in circular saw blades. The objective was to create circular saw blades that satisfied the criteria of stiffness and strength, while also possessing low noise properties. The aim was to minimize the optimization objective function comprised of the maximum deformation, the maximum equivalent stress, and the cumulative sum of overall vibration intensity. Equation (11) defined the mathematical model:
3. Optimization Case Study
3.1. Materials
3.2. Analysis of Simulation Models
3.2.1. Thermal–Mechanical Coupling Sawing Model Analysis
3.2.2. Calculation Model for Stress and Natural Frequency of Circular Saw Blades
3.2.3. Calculation Model for Overall Vibration Intensity of Circular Saw Blades
3.3. ANSYS–MATLAB Collaborative Multi-Objective Optimization Method Based on NSGA-II
3.3.1. NSGA-II Multi-Objective Optimization Algorithm
3.3.2. ANSYS–MATLAB Co-Simulation Method
- Step 1
- MATLAB randomly generated a set of shape parameters within the design space as the initial population for the optimization process. Based on the radial distances and angles of the shape parameters, the corresponding Cartesian coordinates were calculated. Subsequently, the coordinate data underwent preprocessing, including data format unification, missing and duplicate value checking, and data sorting, to enhance the accuracy of curve fitting. Furthermore, the fitting curve type was defined as “poly4”, and the fit function was employed to perform curve fitting on the coordinate data, yielding the fitting results. Finally, the fitted curve was discretized into 100 equally spaced coordinate points, and the coordinate information was stored in the “crood.txt” file.
- Step 2
- In ANSYS, the circular saw blade model (without noise-reduction slots) was first constructed. Then, a macro file containing the coordinate information of the noise-reduction slots was read to complete the parametric modeling of the circular saw blade with noise-reduction slots, as illustrated in Figure 3. Subsequently, preprocessing commands such as mesh generation and boundary condition application were executed to prepare for the subsequent analysis.
- Step 3
- ANSYS conducted a static analysis, prestressed modal analysis, and harmonic response analysis. The maximum deformation, maximum equivalent stress, and cumulative sum of overall vibration intensity were computed, and the data were saved in a file named “res.txt”.
- Step 4
- MATLAB interpreted the analytical results and considered the calculated results as the fitness value of the genetic algorithm. Based on the computational procedure outlined in Figure 10, non-dominant sorting was performed to identify the most exceptional individuals.
- Step 5
- The shape parameter of the elite individual was considered as the fundamental parameter for optimizing the next generation. Step 1 to Step 4 were repeated until the predetermined algebraic condition was met.
4. Results and Discussion
4.1. Optimization Results and Analysis
4.2. Noise Test Results and Analysis
- The optimized circular saw blade, as depicted in Figure 18, demonstrated reduced sound radiation ability during the stable sawing phase. On average, there was a decrease in sound pressure level of approximately 2.4 dB to 3.0 dB. This outcome suggested that the design solution made some improvement in the overall noise level.During the idle stage of the circular saw blade, known as the saw-in and saw-out stages, there was minimal difference in the sound radiation capacity between the circular saw blade with noise reduction slots and the original circular saw blade. This suggested that the modifications made to the circular saw blade body had little impact on the equivalent sound pressure level during its idle stage, which aligns with the findings of the study conducted by Ján Svoren et al. [43]. Furthermore, the research conducted by Tian et al. [44] highlighted that decreasing the diameter of the saw blade, suitably increasing the number of teeth on the saw blade, and reducing the thickness of the saw blade were excellent methods for minimizing the idle noise produced by the saw blade.
- According to Figure 19, the noise radiation level of the optimized circular saw blade was lower than the initial design in most of the frequency bands. The reduction was particularly significant in the frequency range of 500 Hz to 1600 Hz. This reduction in noise was consistent with the decrease in overall vibration intensity of the circular saw blade after optimization, as shown in Figure 13.It is important to mention that while the noise levels of the optimized circular saw blades were typically lower than those of the original saw blades, the sound pressure level values of saw blade 2 in the frequency range of 1600 Hz–2000 Hz were slightly higher. This behavior could be attributed to the occurrence of excitation during the sawing process that aligned with a specific inherent frequency of the optimized circular saw blade 2. As a result, there was a notable increase in the emission of noise within this frequency range. Furthermore, minor variations in the design and composition of the circular saw blade and plate material could also have an impact on the noise level, making it difficult to completely avoid in the design process.
5. Conclusions
- A mathematical model for reducing vibration and noise in circular saw blades was derived. It established a mathematical relationship between the sound power emitted and the overall vibration intensity of the circular saw blade system. Furthermore, it established a direct mapping between the shape parameters of the noise reduction slot in the circular saw blade and the sawing deformation, equivalent stress, and overall vibration intensity. This led to the construction of a multi-objective optimization model for the noise reduction slot. This approach enhanced both the computational efficiency and the effectiveness of mathematical tools for controlling vibration noise in circular saw blade design and engineering applications.
- The suggested approach utilized a thermal–mechanical coupling analysis, prestress modal analysis, and harmonic response analysis to accurately determine the overall vibration intensity of circular saw blades. The method considered the impact of the stress state on the vibration characteristics of rotary circular saw blades. It could calculate the overall vibration intensity of various circular saw blades cutting different materials at any frequency range. This calculation can aid in the design and development of vibration and noise reduction for circular saw blades and other rotary cutters.
- A simulation platform was developed using ANSYS and MATLAB to determine the best shape parameters of noise reduction slots for ultra-thin circular saw blades used in cutting particleboards. NSGA-II was employed for this purpose. The multi-objective optimization method simultaneously achieved the design of reducing vibration and noise in the ultra-thin circular saw blade, while also ensuring that the circular saw blade maintained the requisite rigidity and strength requirements after grooving. The utilization of the joint simulation technique guaranteed precise data transmission, enhanced design efficiency, and showcased a broad scope of versatility and practicality. This served as a valuable reference for designing slots for various other types of circular saw blades.
- The preparation of slotted circular saw blades was carried out according to the optimization results. The experimental results demonstrated a reduction in sawing noise by 2.4 dB to 3.0 dB. Additionally, the noise levels of the optimized circular saw blades were generally lower than those of the initial saw blades across most of the design frequency bands. This finding aligned well with the overall reduction in vibration intensity, confirming the validity and practicality of the design scheme.
- Multi-scale multi-physical field coupling problem of sawing system: There are certain simplifications in the currently adopted finite element model, such as ignoring the chip formation process, contact nonlinearity problem, etc. The establishment of a high precision multi-scale simulation model of the wood sawing system, from the microscopic material behavior to the macroscopic cutting process for a comprehensive description, to provide a more reliable theoretical basis for the optimal design. In addition, the comprehensive use of mechanics, acoustics, fluids, and other related disciplines to reveal the vibration and noise generation mechanism of circular saw blades under the conditions of multi-physical field coupling is still the focus of the current research issues.
- Broader frequency analysis: This study focused on a specific frequency range, and future research could extend the analysis to a broader frequency range, especially frequencies outside the current range. This would ensure that the circular saw blade is optimized for a wider range of operating conditions.
- Machine learning method: This optimization calculation method allows saw blade design for specific materials or cutting requirements but requires complex code adjustments each time. The application of machine learning technology would reduce the computational time and resources required for simulation studies by accumulating a large quantity of simulation and experimental data under cutting conditions and predicting performance results based on historical data to refine the optimization process.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Diameter (mm) | Aperture (mm) | Tooth Number (T) | Tooth Width (mm) | Saw Blade Thickness (mm) | Flange Diameter (mm) | Serration Type |
---|---|---|---|---|---|---|
305 | 30 | 100 | 2 | 1.5 mm | 120 | Trapezoidal serrated |
Design Variable | Variable Description | Minimum Value | Maximum Value |
---|---|---|---|
Starting radius | 95 mm | 105 mm | |
Terminal radius | 125 mm | 135 mm | |
Slot width | 0.5 mm | 1 mm | |
Key point angle | −9.41° | 9.41° |
Materials | SKS51 (Saw Body) | YG6 (Serrated) |
---|---|---|
Density () | 7850 | 14,800 |
Poisson’s ratio | 0.28 | 0.30 |
Modulus of elasticity () | 210 | 510 |
Coefficient of thermal expansion () | 11.2 × 10−6 | 6 × 10−6 |
Specific heat () | 460 | 220 |
Thermal conductivity () | 51.9 | 75.0 |
Property | Density (g/cm3) | Poisson’s Ratio | Modulus of Elasticity (MPa) | Bending Strength (MPa) | Coefficient of Thermal Expansion (1/K) | Specific Heat () | Thermal Conductivity () |
---|---|---|---|---|---|---|---|
Particleboard | 0.65 | 0.342 | 5204 | 79 | 6.9 × 10−6 | 1900 | 0.165 |
Number | Origin Radius (mm) | Endpoint Radius (mm) | Slot Width (mm) | Initial Angle | Key Point One Angle | Key Point Two Angle | Key Point Three Angle | Key Point Four Angle | Terminal Angle |
---|---|---|---|---|---|---|---|---|---|
1 | 103.05 | 126.66 | 0.30 | −6.71 | −0.12 | −8.20 | 4.72 | −1.14 | 6.05 |
2 | 97.62 | 125.91 | 0.84 | −6.89 | −5.91 | −7.94 | −7.69 | −4.82 | 8.85 |
3 | 98.20 | 126.64 | 0.76 | −1.35 | −4.72 | 4.24 | −2.84 | 6.46 | 0.37 |
4 | 101.47 | 126.20 | 0.84 | 3.78 | −3.76 | −2.16 | −3.20 | 2.91 | 0.31 |
Number | Maximum Deformation (μm) | Maximum Equivalent Stress (MPa) | Cumulative Sum of Overall Vibration Intensity |
---|---|---|---|
0 | 10.26 | 23.38 | 766,423 |
1 | 10.40 | 27.87 | 360,482 |
2 | 10.38 | 28.98 | 394,876 |
3 | 10.37 | 26.80 | 460,954 |
4 | 10.39 | 26.75 | 578,410 |
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Jia, N.; Guo, L.; Wang, R.; Liu, J. Design of Vibration and Noise Reduction for Ultra-Thin Cemented Carbide Circular Saw Blades in Woodworking Based on Multi-Objective Optimization. Forests 2024, 15, 1554. https://doi.org/10.3390/f15091554
Jia N, Guo L, Wang R, Liu J. Design of Vibration and Noise Reduction for Ultra-Thin Cemented Carbide Circular Saw Blades in Woodworking Based on Multi-Objective Optimization. Forests. 2024; 15(9):1554. https://doi.org/10.3390/f15091554
Chicago/Turabian StyleJia, Na, Lei Guo, Ruisen Wang, and Jiuqing Liu. 2024. "Design of Vibration and Noise Reduction for Ultra-Thin Cemented Carbide Circular Saw Blades in Woodworking Based on Multi-Objective Optimization" Forests 15, no. 9: 1554. https://doi.org/10.3390/f15091554