In order to optimize the design of tool edge, an intelligent method was used for modeling and optimization. The tool edge design method based on Support Vector Regression (SVR) and Particle Swarm Optimization (PSO) was proposed. By combining tool edge parameters and processing condition parameters, and learning from empirical data, a functional model was established between tool life, edge parameters, and processing condition parameters. Taking the tool life as the objective function, the optimal edge profile design parameters were solved under different processing condition parameters. The T-shape tool validates was taken as a case for verification. The SVR-PSO function model was established and solved based on the processing condition parameters, and the optimized edge design parameters and predicted tool life were obtained. The results showed that the deviation between the calculated and actual tool life was less than 6.4%. This method was feasible and practical, and has been applied in the design department of tool manufacturing companies.
Research Article
Research on Cutting Tool Edge Geometry Design based on SVR-PSO
https://doi.org/10.21203/rs.3.rs-3214820/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 01 Mar, 2024
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Cutting tool
Tool edge parameters
Processing condition parameters
Support vector regression
Particle swarm optimization
The signing of the Paris Agreement [1] has had a profound impact on the course of world economic development, prompting the manufacturing industry to shift towards enhancing quality, resource efficiency, and energy conservation. As a crucial component of machine tools, the tool manufacturing industry plays a pivotal role in material processing, serving as the foundation for the machinery manufacturing and processing. In 2021, the global CNC tool market will be about USD 38 billion [2]. With the growing utilization of difficult-to-machine materials and the increasing demand for high-precision and complex parts processing, optimizing tool edge design and improving tool longevity have emerged as significant challenges for the entire industry. Consequently, the development of an efficient tool edge design becomes crucial in the field of machinery industry.
While traditional tool edge design methods have relied predominantly on experience and trial-and-error, they suffer from inefficiency and inadequate precision. Therefore, there is a pressing need to develop a fast, efficient, and accurate tool edge design method. Arifin et al. [3] investigated the design of a non-standard disc milling tool for machining screw rotors, considering the curvature of the tool edge and validating it through experiments. MU et al. [4] proposed tooth surface shaping method based on the tool edge design and the principles of differential geometry theory and gear meshing, substantiating it using finite element analysis. Fang et al. [5] designed a novel microfine-ball-end milling tool by converting the spatial curve of the tool edge into a machinable planar curve. Xue-Ming He et al. [6] introduced a tool edge design method based on the tool life cycle algorithm, successfully applying it to optimize the design at the Chinese Wuxi compressor plant. Additionally, Xie [7] conducted a study on tool edge design for bevel gear machining by formulating a mathematical model for the tool profile on the normal plane. Despite the advancements achieved in the existing research on tool edge design, they have been limited in their applicability and have not gained widespread popularity due to direct theoretical modeling errors.
With the rapid advancement of big data and artificial intelligence (AI) technology, various AI algorithms based on statistical theory have emerged. These intelligent algorithms share a common characteristic of autonomous learning from historical data, enabling them to circumvent the need for direct modeling of complex problems. As a result, they have effectively addressed numerous engineering challenges that were previously difficult to model and solve. Consequently, they have garnered significant attention in both research and application domains.
Support Vector Regression (SVR) and Particle Swarm Optimization (PSO) are two optimization algorithms that have gained substantial interest among researchers and are widely employed in optimization problems across various engineering disciplines. For instance, ALIZADEH et al. [8] utilized SVR to analyze temperature, velocity, Nusselt number, and shear stress, while employing the PSO algorithm to examine the relationship between Nusselt number and shear stress. Their work enhanced the analytical capabilities in the design process of thermal equipment. SHANGGUAN et al. [9] employed PSO-SVR to predict the icing time of road surfaces, thereby addressing efficiency challenges in road transportation systems in cold regions and improving prediction accuracy. IKRAM et al. [10] investigated the predictive capabilities of a coupled SVR model with PSO, validating their method using data from three meteorological stations in wet areas of northwestern Bangladesh. Their proposed hybrid machine learning model was recommended as a predictive tool for monthly reference evapotranspiration in similar wet areas globally. Yanbin Du et al. [11] explored a PSO and SVR-based method for predicting the dilution rate of 15-5PH alloy powder in laser cladding applications. Luo et al. [12] investigated the optimal combination of turning parameters by integrating the SVR method and PSO algorithm to minimize surface residual stresses during pure iron turning.
Lin Xiankun et al. [13] employed the PSO algorithm and SVR method to develop a prediction model for surface roughness, using speed, feed, dressing depth and dressing lead of grinding wheel as inputs. Their model exhibited superior prediction performance compared to the existing methods. These studies demonstrate that SVR method and PSO algorithm possess broad applicability and can yield improved model predictions and optimal design outcomes across diverse engineering disciplines.
Hence, researchers have acknowledged the significance of employing intelligent methods to model and optimize tool edge design solutions. In light of the intricate structure of smartphone product mechanisms and the extensive use of shaped tools to enhance machining efficiency, Jingjiang Yunchuang Technology company has accumulated a wealth of practical data over the past 15 years concerning shaped tool design, manufacturing, and lifespan. Notably, the "one-stop" precision tool grinding app project, primarily developed by the company, received the first prize in the inaugural Chinese industrial internet competition [14]. Leveraging the existing grinding App, the research capabilities of Tsinghua mechanical department, and the actual demand for tool edge design, this paper proposes a tool edge optimization design method based on SVR and PSO. The method employs SVR algorithm to model the tool edge shape and processing condition parameters, establishing a functional relationship between the tool edge shape parameters, machining condition parameters, and tool life. Subsequently, PSO algorithm is employed to optimize the fitted function, thereby obtaining the optimized edge design parameters.
1.1 Overview of the tool edge design system
Once the tool material and coating selection are determined, the tool profile and processing condition parameters become crucial factors that affect tool life, and they exhibit a complex interrelationship. The life of a tool with the same profile can vary significantly under different processing condition parameters. Similarly, different processing condition parameters require appropriate adjustments to the tool profile in order to achieve optimal performance. Therefore, considering the processing condition parameters is essential for achieving optimal results in tool edge design.
This paper presents a tool edge optimization design method that utilizes support vector regression (SVR) and particle swarm optimization (PSO) to enhance the intelligence of the design process. The method treats the tool parameters and processing condition parameters as design variables. By utilizing the accumulated tool design cases and actual machining data as training samples, the correlation between tool edge parameters, processing condition parameters, and tool life is analyzed using the SVR algorithm, leading to the establishment of a regression function model. Subsequently, PSO algorithm is employed as an optimization tool, using tool life as the objective function to optimize the solution of the regression function and obtain the optimal tool edge parameters.
Through the integration of intelligent methods, the tool edge design system proposed in this paper surpasses the limitations of traditional experience-based and trial-and-error methods. It achieves autonomous learning and provides optimal solutions to complex engineering problems. This SVR-PSO based tool edge design method exhibits significant application potential and holds considerable academic and practical value in the field of tool design, manufacturing, and application.
1.2 Hierarchical structure of the tool edge optimization design
The tool edge optimization design program is structured into three layers: the display layer, logic layer, and data layer, as depicted in Fig. 1.
The display layer primarily provides the user with an intuitive interface for operation. It facilitates data input and output, and handles the display of tool design-related parameter data. This layer also offers various operation commands and menu interfaces to ensure user-friendly interaction.
The logic layer serves as the core component of the tool edge optimization design system and consists of two parts: case filtering and design optimization. Initially, a comprehensive database stores a large number of tools with different materials, coatings, edge types, and information regarding tool life under various machining conditions. The emphasis lies in establishing the correlation between tool edge parameters, machining conditions, and tool life. To obtain accurate data, tools with identical material, coating type, and machining object are selected from the database based on filtering conditions. The filtering conditions provided through the user interface are translated into database search commands, and the cases that satisfy the conditions are filtered from the database.
The design optimization part includes two steps: regression analysis and optimization solution. The goal of the regression analysis is to establish a regression function between the tool edge parameters, machining condition parameters, and tool life. This involves conducting regression analysis using data from the selected cases to establish an accurate relationship model. On the other hand, the optimization solution utilizes the Particle Swarm Optimization (PSO) algorithm to calculate the tool life regression function established based on Support Vector Regression (SVR). This process aims to obtain the optimal solution, which represents the best tool edge parameters.
The data layer, which forms the foundation for implementing the tool optimization design method, comprises a database of design cases. These design cases not only record parameters related to the tool edge profile but also include data on the machining conditions and performance of the tool. These data serve as crucial foundations for the regression analysis and optimization solution process.
With the above design system structure, the tool optimization design solution provides a user-friendly operation interface and enables efficient data processing and calculation. By combining the steps of case selection, regression analysis, and optimization solution, the solution delivers accurate tool design parameters and optimal combinations of processing condition parameters, thereby enhancing tool life.
1.3 Process for the realization of intelligent design solutions for tool edge
The process for implementing the intelligent design of tool edges, with the aim of achieving the highest tool life while ensuring machining quality, is illustrated in Fig. 2. It comprises the following four steps:
-
Determining the filter conditions and identifying the set of design cases that meet the requirements: initially, setting the filter conditions to select the set of design cases that satisfying the specified criteria. If there are no cases that fulfill the filter conditions, the tool edge parameters will be determined through manual design.
-
Establishing the regression function: Utilizing the tool edge parameters and processing condition parameters from the selected set of design cases as input vector, while considering the tool life as the output vector. Applying the support vector regression (SVR) algorithm is to establish the regression function. This function models and fits the relationship between the tool edge parameters, processing condition parameters, and tool life.
-
Solving for the optimal tool parameters: Employing the particle swarm optimization (PSO) algorithm is to solve for the optimal tool parameters that can maximize the tool life for a specific machining parameter. By undergoing the optimization solution process, a new tool design solution is obtained, which represents the optimal edge parameters for a given machining parameter.
-
Evaluating and validating the design solution: Evaluating the obtained design solution using appropriate evaluation metrics is to ensure its effectiveness and feasibility. Validating the solution through practical experiments or simulations is to confirm its performance.
By following this process, the intelligent design solution for tool edges can be realized, enabling the achievement of improved tool life while maintaining machining quality.
2.1 Vector Representation of Tool Edge Parameters and Processing condition parameters
Tool design involves numerous parameters, and calculating the precise impact of each parameter on tool life using equations is challenging. Moreover, these parameters exhibit a certain level of correlation. Additionally, tool life is inherently imprecise, obtained through testing and subject to certain volatility. Consequently, tool designers typically rely on their experience to initially determine these design parameters. To address the relationship between tool life and design parameters, and to circumvent the need for exact modeling, artificial intelligence algorithms can be employed. These algorithms facilitate the identification of patterns between tool life and design parameters by establishing a regression function using statistical learning. In this process, it is crucial to establish a vector representing the tool edge parameters, a vector representing the processing condition parameters, and an objective function for tool life.
(1) Tool edge parameter vector
$${{\mathbf{x}}_1}={\{ {a_1},{a_2},...,{a_l}\} ^T}$$
1
The tool edge parameters vector comprises various parameters involved in tool design, such as tool diameter, radial rake angle, radial clearance angle, core diameter, and helix angle. These parameters, denoted by \({a_i}\), have a significant influence on the machining performance of the tool. There exists a complex nonlinear correlation among these design parameters, where each parameter's effect on the final tool life is interdependent with the others. Consequently, accurately describing and solving this multidimensional constraint relationship using traditional exact calculation models is challenging.
In practical tool design, engineers often prioritize optimizing the tool edge parameters that strongly impact performance based on the specific usage requirements of the tool. Conversely, parameters with lesser influence on performance are frequently assigned empirical values. This design strategy has proven to be practical and widely adopted within the industry.
(2) Tool machining parameter vector
$${{\mathbf{x}}_2}={\{ {b_1},{b_2},...,{b_l}\} ^T}$$
2
The machining parameter vector encompasses spindle speed, feed rate, lateral depth of cut, and radial depth of cut, denoted by \({b_i}\). These parameters are primarily determined based on the machining equipment's performance, efficiency and quality requirements of the processed product, and the cutting edge parameters of the tool. They exert a significant influence on the tool life, and the appropriate selection of processing condition parameters can prolong the tool life. Conversely, improper selection of processing condition parameters may reduce the tool life.
Determining the optimal range of processing condition parameters for a newly designed tool typically involves extensive testing and experimentation. Engineers continuously adjust and optimize the processing condition parameters during actual machining to assess the tool's performance under different parameter combinations. Through this iterative process, they aim to identify the optimal combination of processing condition parameters that achieves the desired machining efficiency and meets product quality requirements. This optimization process requires a comprehensive consideration and trade-off among key indicators such as tool life, cutting forces, surface quality, and machining efficiency.
(3) Objective Function for Tool Life
$${F_{\hbox{max} }}={\text{Max}}\{ F({\mathbf{X}})\}$$
3
The tool life objective function is defined as follows:\(F\left(x\right)=F({x}_{1},{x}_{2})\), where X is the design vector comprising the tool edge parameters and processing condition parameters, denoted by \({x}_{1}\) and \({x}_{2}\), respectively. The function \(F\left(x\right)\) represents the nonlinear regression function calculated based on a set of cases. The objective is to determine the optimal value, denoted as \({F_{\hbox{max} }}\), that maximizes the tool life. By optimizing the values of \({x}_{1}\) and \({x}_{2}\) within the design vector \(X\), the goal is to find the combination of tool edge parameters and processing condition parameters that leads to the highest tool life performance.
2.2 Support vector regression algorithm
The Support Vector Regression (SVR) algorithm, initially derived from the principles of Support Vector Machine (SVM) [15], was further developed by Vapnik [16] for data regression analysis. Unlike traditional regression algorithms, SVR takes into consideration the upper and lower bounds of prediction errors, enabling it to effectively handle linear and nonlinear data. The SVR algorithm has witnessed significant advancements in both theoretical research and practical applications [17–19], positioning it as one of the leading methods for addressing multidimensional nonlinear regression problems. Notably, SVR offers distinct advantages and practical feasibility.
Compared to other intelligent algorithms, SVR stands out by providing a definitive regression analytic equation. Moreover, this equation exhibits stability even after repeated calculations, ensuring consistent and reliable regression outcomes. These qualities have contributed to the widespread adoption of SVR as a preferred method across various domains.
The fundamental concept of SVR involves mapping a variable x from a low-dimensional space to a high-dimensional feature space through a nonlinear transformation function. By employing this transformation, the nonlinear problem in the low-dimensional space can be effectively addressed by finding a linear regression hyperplane in the high-dimensional space. This mapping is accomplished using a kernel function, denoted as \(K\left(x,{x}^{{\prime }}\right)\), which operates on \({R}^{n}\times {R}^{n}\). A kernel function is considered valid if there exists an H-transform, denoted as \({\phi }_{\bullet x\to \phi \left(x\right)}^{\bullet {R}^{n}\to H}\), capable of mapping \({R}^{n}\) to a Hilbert space, such that \(K\left(x,{x}^{{\prime }}\right)=\left(\phi \right(x)\bullet \phi (x{\prime }\left)\right)\). Utilizing the kernel function, it becomes possible to construct a linear function based on the sample feature vectors within the high-dimensional feature space.
$$y={\mathbf{\omega }} \cdot \varphi ({{\mathbf{x}}_i})+b$$
4
In SVR, y represents the output quantity, ω represents the weight vector, x represents the input vector, and b represents the bias constant. By introducing the relaxation variable ξ and considering the Karush-Kuhn-Tucker (KKT) condition, the support vector regression problem can be expressed as follows:
$$\mathop {{\text{Min}}}\limits_{{\varvec{\omega},b,{\xi ^*}}} \;\{ \frac{1}{2}||\varvec{\omega}|{|^2}+C\sum\limits_{{i=1}}^{i} {({\xi _i}+{\xi _i}^{*})} \}$$
5
$$\begin{gathered} {\text{s}}{\text{.}}\;{\text{t}}.\;\;({\mathbf{\omega }}\varphi ({{\mathbf{x}}_i})+b) - {y_i} \leqslant \varepsilon +\xi _{i}^{{}},i=1, \ldots l \hfill \\ \mathop {}\limits^{{}} \mathop {}\limits^{{}} \mathop {}\limits^{{}} {y_i} - \mathop {({\mathbf{\omega }}\varphi ({{\mathbf{x}}_i})+b) \leqslant \varepsilon +\xi _{i}^{*},i=1, \ldots l}\limits^{{}} \hfill \\ \mathop {}\limits^{{}} \mathop {}\limits^{{}} \mathop {}\limits^{{}} \xi _{i}^{{}},\xi _{i}^{*} \geqslant 0 \hfill \\ \end{gathered}$$
6
By introducing the Lagrange function, the original problem is transformed into a quadratic optimization problem. The Lagrange function incorporates the constraints and converts the problem into a maximization problem. The objective is to maximize the Lagrange dual function, which is defined as the difference between the primal objective function and the sum of the Lagrange multipliers multiplied by the constraints. This transformation enables the application of optimization techniques to find the optimal values of the Lagrange multipliers. The quadratic optimization problem can be efficiently solved using various optimization algorithms, such as the Sequential Minimal Optimization (SMO) algorithm. The solution to the quadratic optimization problem provides the optimal values for the Lagrange multipliers, which can then be used to determine the solution to the original problem.
$$\mathop {{\text{Max}}}\limits_{{\mathbf{a}}} \mathop {\{ - \frac{1}{2}\sum\limits_{{j={\text{1}}}}^{l} {\sum\limits_{{i=1}}^{l} {({a_i} - {a_i}^{*})} } ({a_j} - {a_j}^{*})K({{\mathbf{x}}_i},{{\mathbf{x}}_j}) - \varepsilon \sum\limits_{{i=1}}^{l} {({a_i}+{a_i}^{*})} +\sum\limits_{{i=1}}^{l} {{y_i}({a_i} - {a_i}^{*})} \} }\nolimits^{{}}$$
7
$$\begin{gathered} {\text{s}}{\text{.}}\;{\text{t}}.\;\;\sum\limits_{{i=1}}^{l} {({a_i} - {a_i}^{*})} =0 \hfill \\ \;\quad \;{\kern 1pt} {\kern 1pt} a{}_{i},{a_i}^{*} \in [0,C] \hfill \\ \end{gathered}$$
8
Solving for the regression function results in determining the optimal values for the parameters, weights, and bias in the model. The regression function represents the relationship between the input variables and the output quantity. It can be obtained by minimizing the objective function, which measures the discrepancy between the predicted output and the actual output in the training data. Various optimization techniques can be employed to solve for the regression function, such as gradient descent, least squares, or maximum likelihood estimation. The ultimate goal is to find the best-fit regression function that accurately captures the underlying patterns and provides reliable predictions for new input data.
$$F(x)=\sum\limits_{{i=1}}^{l} {({a_i} - {a_i}^{*})} K({{\mathbf{x}}_i},{\mathbf{x}})+b$$
9
$$b=\left\{ {\begin{array}{*{20}{c}} {{y_i} - \sum\limits_{{{{\mathbf{x}}_j} \in SV}} {({a_j} - {a_j}^{*})} K({{\mathbf{x}}_i},{{\mathbf{x}}_j}) - \varepsilon \;\;(0<{a_i}<C({a_i}^{*}=0))} \\ {{y_i} - \sum\limits_{{{{\mathbf{x}}_j} \in SV}} {({a_j} - {a_j}^{*})} K({{\mathbf{x}}_i},{{\mathbf{x}}_j})+\varepsilon \;\;(0<{a_i}^{*}<C({a_i}=0))} \end{array}} \right.$$
10
The b-values are individually calculated for each standard support vector and subsequently averaged. This process involves determining the bias constant, b, which is an important parameter in SVR. By considering each standard support vector separately, their corresponding b-values are calculated, and then these values are averaged to obtain the final value for b. This method ensures that the bias constant is appropriately estimated and takes into account the contributions of all standard support vectors in the regression model.
$$b=\frac{1}{{{N_{NSV}}}}\{ \sum\limits_{{0<{a_i}<C}} {[{y_i} - \sum\limits_{{{x_j} \in SV}} {({a_j} - {a_j}^{*})} K({{\mathbf{x}}_i},{{\mathbf{x}}_j}) - \varepsilon ]} +\sum\limits_{{0<{a_i}^{*}<C}} {[{y_i} - \sum\limits_{{{{\mathbf{x}}_j} \in SV}} {({a_j} - {a_j}^{*})} K({{\mathbf{x}}_i},{{\mathbf{x}}_j})+\varepsilon ]} \}$$
11
The set of standard support vectors, SV is utilized, and the number of standard support vectors is denoted as NNSV. In support vector regression (SVR), generalized kernel functions play a crucial role, with the main options being Gaussian radial basis kernel functions and polynomial kernel functions. Each type has its own strengths and weaknesses. The Gaussian radial basis kernel function, a local kernel function, exhibits excellent learning capability and convergence properties; however, its generalization effect may be limited. On the other hand, the polynomial kernel function, a global kernel function, offers superior generalization; nevertheless, it may be more challenging to achieve convergence and requires more complex parameter adjustments.
In the SVR algorithm, the choice of appropriate parameters significantly affects the accuracy of fitting and the generalization performance. Specifically, the Gaussian radial basis kernel function is represented by \(K({\mathbf{x}},{\mathbf{x}}')\)=\({e^{ - \frac{{||{\mathbf{x}} - {\mathbf{x}}'|{|^2}}}{{2{\sigma ^2}}}}}\), where \({\sigma ^2}\) denotes the kernel function parameter. Additionally, the insensitive loss coefficient ε and the error penalty factor C also contribute to the overall fitting accuracy and generalization performance of the SVR algorithm. It is imperative to select suitable parameter values to optimize the regression effect and achieve improved accuracy and generalization in SVR.
2.3 Particle swarm optimization algorithm
The fitted function \(F({\mathbf{X}})\) obtained through the SVR algorithm represents a complex multivariate function, making the search for the optimal solution quite challenging. To tackle such complex problems, intelligent search algorithms like neural networks, genetic algorithms, ant colony algorithms, and particle swarm algorithms are commonly employed. These algorithms bypass the need for complex equation derivation and solution processes and have shown promising results.
Among these algorithms, PSO algorithm, jointly proposed by Drs. Kennedy and Eberhart in 1995 [20], draws inspiration from the foraging behavior of bird flocks. It leverages the information exchange between individuals within a group and between individuals and the optimal individual to guide the entire group toward convergence to the optimal solution while preserving individual diversity. Through continuous updates, the algorithm gradually identifies the optimal solution. Over time, the PSO algorithm has undergone continuous improvements and has found widespread applications across various domains [21–22].
In the PSO algorithm, all particles adjust their velocity and position based on their individual optimal values and the global optimal values of the particle swarm. The velocity and position update equations are as follows:
$$v_{{id}}^{{k+1}}=\omega v_{{id}}^{k}+{c_1}{r_1}{\text{(}}p_{{id}}^{k}-x_{{id}}^{k}{\text{)}}+{c_2}{r_2}{\text{(}}g_{d}^{k}-x_{{id}}^{k}{\text{)}}$$
12
In the given equations, \({p}_{id}^{k}\)represents the individual optimal value of the ith particle in the d-dimensional space at the kth iteration, while \({g}_{d}^{k}\) denotes the global optimal value of all particles in the d-dimensional space at the kth iteration. The parameters ω, c1, and c2 refer to the inertia weight factor, individual learning factor, and social learning factor, respectively. Additionally, r1 and r2 represent random numbers between 0 and 1, while \({x}_{id}^{k+1}\) represents the current position of the ith particle in the d-dimensional space at the \((k+1)\)th iteration.
The fitness function plays a crucial role in evaluating the quality of each particle's position in the algorithm. The appropriate selection of the fitness function significantly impacts the convergence speed and accuracy of the algorithm. In our method, Eq. (9) is utilized as the fitness function. This choice enables a more accurate evaluation of the advantages and disadvantages of each particle's position, leading to a significant acceleration in the convergence speed of the algorithm.
The selection of initial values in the PSO algorithm is another critical factor affecting its convergence. In our method, a strategy of using filtered cases as the initial particles is adopted, rather than randomly initialized particles. This deliberate choice aims to enhance the convergence of the algorithm and expedite the attainment of the optimal solution. By leveraging pre-filtered cases as the initial particles, the method has demonstrated a faster convergence rate compared to random initialization methods. The main flow of the particle swarm algorithm is shown in Fig. 3.
To validate the proposed tool edge design method, a tool edge optimization design system was developed, as illustrated in Fig. 4. This system leverages the accumulated tool design and machining data, utilizing the calculated tool edge parameters generated by the software. Subsequently, a representative tool is manufactured for conducting actual machining tests, thereby assessing the conformity between the lifes of the design method and the actual machining .
In this study, a T-shape tool was selected for machining the stainless steel center frame of a cell phone, serving as a case study. The primary objective was to determine the optimal tool edge parameters, considering a prescribed tool diameter and specific machining conditions, in order to achieve the maximum tool life.
The tool edge optimization design system incorporates a modeling method to establish the relationship between the tool edge parameters and tool life. This model takes into consideration the nonlinear correlation among the tool edge parameters and utilizes a SVR algorithm for effective modeling. By leveraging statistical learning techniques, the model identifies potential patterns between tool life and the tool edge parameters, enabling the establishment of a regression function to predict tool life.
Building upon this model, an tool edge optimization algorithm is devised to maximize tool life by optimizing the combination of tool edge parameters. This algorithm facilitates the search for the optimal tool edge parameter combination that satisfies machining requirements and enhances tool life, given the tool edge diameter and machining conditions. To validate the feasibility and effectiveness of the optimization results, physical prototype tools are manufactured and subjected to machining tests. By comparing and verifying the achieved machining life with actual machining operations, the accuracy and reliability of the design method can be evaluated.
The development of this tool edge optimization design system presents tool manufacturers and engineers with a scientific and viable method to design and optimize tool edge parameters, thereby extending tool life and meeting actual machining requirements. This advancement holds great significance in enhancing tool machining performance and reducing production costs.
3.1 Case selection
In the implementation of the tool edge design method, the selection of cases is a crucial step to investigate the impact of tool edge parameters and processing condition parameters on tool life. To ensure a focused analysis, certain filtering conditions are applied to qualify and choose the influencing factors. Table 1 presents the specific filtering conditions used in this study. These conditions help identify and prioritize the key factors that will be further examined in relation to their influence on tool life.
| Filter condition | Indices |
|---|---|
| Tool material | Tungsten steel |
| Processing material | SUS316 |
| Coating type | TiAlN |
| Tool type | T-shape tool |
| Processing type | Finishing |
| Tool edge range/mm | φ2-φ9 |
After applying the screening conditions outlined in Table 1, a total of 310 design cases that meet the conditions were identified from the case database, where the first 290 sample cases were chosen as training data for regression analysis. This dataset will be utilized to establish the regression function and model the relationship between the selected factors and tool life. The remaining 20 sample cases will be used as evaluation data to assess the performance and accuracy of the regression function. By dividing the dataset into training and evaluation sets, the effectiveness and reliability of the regression analysis can be thoroughly examined.
3.2 Regression analysis
(1) Tool edge parameters selection
The T-shape tool is primarily utilized for machining the recess in the middle frame, and its key edge parameters are depicted in Fig. 5. Among these edge parameters, tool edge thickness is predetermined based on the product structure, while the helix angle and core diameter have minimal impact on the tool's machining life. Consequently, they are typically assigned fixed values, with the helix angle set at 30° and the core diameter set to 50% of tool edge diameter. The three edge parameters that exert a more substantial influence on the tool life are selected as tool edge design parameters. These design parameters are outlined in Table 2, resulting in the edge parameter vector \({x}_{1}={\{{a}_{1},{a}_{2}{,a}_{3}\}}^{T}\).
| Parameters | Variables | Ranges |
|---|---|---|
| Tool edge diameter/(mm) | a1 | 2–9 |
| Racial rake angle/(°) | a2 | 4–8 |
| Racial clearance angle/(°) | a3 | 8–12 |
(2) Tool processing condition parameters selection
The selection of tool processing condition parameters includes spindle speed, feed rate, cutting width, and cutting depth. These parameters are closely related to the magnitude of the tool edge diameter. In general, when the tool edge diameter is larger, larger feed rates, cutting widths, and cutting depth are chosen to enhance material cutting and removal efficiency. According to Equations (14–15), the spindle speed determines the linear velocity of the tool, while the feed rate, cutting width, and depth of cut collectively determine the material removal rate of the tool. To simplify the model's complexity, the tool's linear velocity and material removal rate per minute are chosen as the processing condition parameters. The specific parameter design is presented in Table 3. The cutting linear velocity of the tool is calculated as follows:
$${V_c}=\frac{{\pi DS}}{{1000}}$$
14
Where Vc is the linear velocity (m/min), D is the tool diameter (mm), and S is the rotational speed (r/min). The material removal rate per minute is calculated using the equation:
$$V=F{a_e}{a_p}$$
15
Where V is the material removal rate (mm³/min), F is the feed rate (mm/min), ae is the width of cut (mm), and ap is the depth of cut (mm).
| Parameters | Variables |
|---|---|
| Linear velocity(m/min) | b1 |
| Removal rate(mm3/min) | b2 |
(2) Normalization of tool design parameters
Due to the significant differences in magnitude and value range among the design parameters, it is important to normalize these parameters before applying them to the regression analysis model. By normalizing the design vector values of the sample data to the range of [-1, 1], the following equation is used for normalization:
$$y=\frac{{2(x - {x_{\hbox{min} }})}}{{{x_{\hbox{max} }} - {x_{\hbox{min} }}}} - 1$$
16
(3) Support vector regression model construction
In this case, the Gaussian radial basis kernel function is selected as \(K\left(x,{x}^{{\prime }}\right)={e}^{-\frac{{\left|\left|x-{x}^{{\prime }}\right|\right|}^{2}}{2{\sigma }^{2}}}\), and the model construction relies on determining the values of three parameters. Using an iterative method of fixed step traversal with an insensitivity loss factor of \(\epsilon =0.03\), the optimal parameters \({\sigma }^{2}=0.65\) and \(C=20\) were obtained. The range for kernel function parameter \({\sigma }^{2}\) is set from 0 to 1, while the range for parameter \(C\) was set from 0 to 100.
290 training sample fitting error plot is shown in Fig. 6.Twenty sample cases are utilized to evaluate the regression function, and the evaluation results are presented in Fig. 7. The errors for the training and evaluation samples are summarized in Table 4. For the 290 training samples, the average absolute value error was 4.8% with a mean square error of 7.7 m. Regarding the 20 evaluation samples, the average absolute value error is 7.0% with a mean square error of 9.6 m. The disparity between the errors of the training and evaluation samples is minimal, thus confirming the validity of the fitted life model.
| Sample type | Average absolute percentage error/% | Mean square error/% |
|---|---|---|
| 290 training samples | 4.8 | 7.7 |
| 20 evaluation samples | 7.0 | 9.6 |
3.3 PSO algorithm optimization solution
The example imposes a constraint on the cutting edge diameter and processing condition parameters of the tool. The processing condition parameters are set as follows: spindle speed of 10,000 rpm, feed rate of 1,000 mm/min, cutting width of 0.76 mm, cutting depth of 1.4 mm, and tool cutting edge diameter of 4.6 mm. After performing the necessary conversions, the design variables listed in Table 5 are obtained. The objective is to determine the optimal values for the radial rake angle and radial clearance angle parameters that maximize the tool life.
| Parameters | Variables | Set values |
|---|---|---|
| Tool edge diameter/(mm) | a1 | 4.6 |
| Racial rake angle/(°) | a2 | — |
| Racial clearance angle/(°) | a3 | — |
| Linear velocity/(m/min) | b1 | 130 |
| Removal rate/(mm3/min) | b2 | 1064 |
The fitness function used in the particle swarm algorithm is the regression function obtained in Section 3.2. The algorithm is configured with 100 particles, an inertia weight (ω) of 0.7, an individual learning factor \(\left({c}_{1}\right)\) of 0.5, and a social learning factor \(\left({c}_{2}\right)\) of 1. The maximum number of iterations is set to 50. After the calculations, the optimal fitness value is found to be \({F}_{best}=264\), and the corresponding optimal design parameter vector is \({X}_{best}={\left[4.6 6.5 10.8 130 1064\right]}^{T}\), representing the tool's radial rake angle and radial clearance angle parameters. The convergence curve of PSO is shown in Fig. 8, demonstrating that the objective function value converges after 19 iterations, indicating that the PSO algorithm can quickly converge to the optimal solution.
3.4 Comparison of actual tool machining life and calculated predicted life
Two tool samples are produced based on the optimal design parameters obtained. The life-time machining tests are conducted using FANUC RoboDrill as the testing equipment. The tool life is determined by monitoring the tool edge wear, specifically when the wear reaches 0.05 mm, on SUS316 stainless steel. During the test, the machining length reaches 220 m, and, the edge wear condition is checked using Keyence edge wear testing equipment every 2 m. The machining test setup and the equipments for edge wear inspection are depicted in Fig. 9, respectively.
The predicted and actual values of tool life for the two sample tools are presented in Table 6. Additionally, Fig. 10 displays the machining edge profile of the two sample tools.
| Sample number | Predicted life/(m) | Actual life/(m) | Absolute percentage error/(%) |
|---|---|---|---|
| 1 | 264 | 248 | 6.4 |
| 2 | 264 | 252 | 4.7 |
The actual test results demonstrate that the actual machining life of the two sample tools, produced with as the design parameter, aligns with the fluctuation trend of the fitting error observed in the training and evaluation samples in Table 4. The absolute error between the predicted and actual values of tool life is ≤ 6.4%. These findings affirm the feasibility and effectiveness of the adopted tool design method and the excellent fit of SVR in capturing the correlation between tool edge parameters, processing condition parameters, and tool life. The tool edge design method proves to be highly valuable in practical tool design.
The test results provide validation for the actual application and accuracy of the tool edge design method in machining operations. By establishing a model that relates edge type parameters, processing condition parameters, and tool life, and utilizing the SVR algorithm for optimization, tool designers can obtain a tool design solution that aligns with actual machining results. This method offers a reliable and efficient method for tool designers to optimize cutting edge parameters and determine processing condition parameters, thereby extending tool life and enhancing design and machining efficiency.
The "one-stop" tool grinding App presents an intelligent method to tool life modeling and optimization, specifically focusing on tool edge design. By employing the Support Vector Regression (SVR) algorithm, the relationship between tool edge parameters, processing condition parameters, and tool life is effectively modeled. Furthermore, Particle Swarm Optimization (PSO) algorithm is utilized to optimize the parameters involved. The proposed method is validated using a case study involving a T-shape tool for stainless steel machining.
The optimization objective in this case is tool life, and under the specified processing condition parameters, the optimized tool edge parameters are calculated. The actual machining tests confirm that the predicted tool life of 264m closely aligns with the actual life values of 248m and 252m, within 6.4% error. This demonstrates the effectiveness and practicality of the tool edge design method.
By leveraging historical experience data, the proposed method empowers tool designers to leverage past knowledge for intelligent design, enhancing tool design capabilities. The established tool edge design model offers practical value by facilitating optimization not only of tool edge design parameters under specified processing condition parameters but also of processing condition parameters under specified tool edge design parameters. The research results have been applied in the tool design department of Shenzhen Jingjiang Yunchuang Technology Co., Ltd.. Further improvements and refinements are anticipated, with the aim of promoting the method within the industry.
Indeed, there are certain limitations to consider in this study. Firstly, the data collection and experimental testing might be constrained by the specific experimental conditions, which could impact the generalizability of the results. Expanding the sample size and testing range would be beneficial to enhance the reliability and robustness of the findings.
Secondly, the model developed in this study relies on historical empirical data, which means that further research and validation would be necessary for new tool design, particularly under unique machining conditions. It is crucial to continually refine and validate the model to ensure its applicability and accuracy across different conditions.
Future research directions could involve improving the accuracy and reliability of the model by exploring additional tool edge design parameters and processing condition parameters. Additionally, considering more complex tool machining situations would contribute to a more comprehensive understanding of the tool edge. Incorporating emerging technologies such as machine learning and artificial intelligence, and integrating data-driven methods with physical modeling methods, could also enhance the efficiency and quality of tool design and machining processes.
In conclusion, the proposed tool edge design method presents a valuable tool and method for tool designers, aiding in enhancing tool performance, extending tool life, and offering scientific guidance for tool design and machining. It also opens up new avenues for future research, providing fresh ideas and directions for further exploration in the field.
Author contribution
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Yimin Jiang, Wei Huang, Yu Tian, Mingyang Yang, Wenwu Xu, Yanjie An, Jing Li, Junqi Li, Ming Zhou. The first draft of the manuscript was written by Yimin Jiang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Disclosure statements
No potential conflict of interest was reported by the authors.
Funding information
We thank the supports from the Guangdong Province Key Area R&D Program of China (NO. 2019B010154002) and Shenzhen Technology Tackling Key Projects of China (NO. 2020N003).
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