A tool optimal edge form design method for chatter suppression under specific working conditions
By designing a critical axial depth of cut calculation function and optimizing the helix angle and pitch using a particle swarm optimization algorithm, the problem of chatter prevention before machining was solved, achieving efficient chatter suppression and improved machining efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2026-02-02
- Publication Date
- 2026-05-08
AI Technical Summary
Existing technologies make it difficult to prevent chatter before processing, and modifying the tool cutting edge is cumbersome and time-consuming, failing to effectively suppress chatter.
A critical axial depth of cut calculation function for arbitrary cutting edge shape was designed. Combined with particle swarm optimization algorithm, the helix angle and pitch were optimized to find the optimal cutting edge shape to suppress chatter.
The system can quickly find the optimal cutting edge shape under specific working conditions, improve processing efficiency and ensure surface quality, and avoid the tedious process of drawing stability lobe diagrams.
Smart Images
Figure CN121615282B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of cutting tool profile design technology, and in particular to an optimal cutting tool profile design method for chatter suppression under specific working conditions. Background Technology
[0002] Chatter, as one of the most complex problems in machining and the one with the greatest impact on machining quality, has always been a major concern for scholars in the field. Chatter is generated by the mutual excitation process of the changing cutting thickness and cutting force during the cutting process. Currently, chatter suppression methods can be mainly divided into active suppression and passive suppression. The essence of both suppression methods is to disrupt this mutually excitation regeneration mechanism through certain means.
[0003] In terms of passive suppression, the main method currently is to first collect signals during the processing, such as force signals, acoustic signals, and acceleration signals, and then analyze the signals to determine whether chatter occurs during processing. If chatter occurs, the process parameters are modified to eliminate it. The limitation of this method is that it can only perform post-process chatter suppression and cannot prevent chatter from occurring during processing by designing the process before processing.
[0004] In terms of active suppression, the main methods currently used are to actively increase the critical axial depth of cut for chatter by modifying the rotational speed, adding dampers, and modifying the tool profile, thereby improving machining efficiency while ensuring surface quality. Modifying the rotational speed by referencing the SLD (Self-Device Lamination) can achieve a higher critical stable depth of cut under the current operating conditions; however, the rotational speed must also change when the operating conditions change, which places high demands on machine tool performance. Furthermore, different tools have different recommended rotational speeds; if the actual rotational speed deviates from the recommended speed, it may accelerate tool wear or breakage. Adding a damper can increase the critical axial depth of cut at a global rotational speed, but adding a damper requires mounting the device on the machine tool spindle, which can disrupt the dynamic characteristics of the machine tool spindle and thus affect the SLD. Modifying the tool profile can increase the critical stable depth of cut at a specific rotational speed without affecting the dynamic characteristics of the machine tool spindle or placing special demands on machine tool performance. Therefore, many researchers have devoted themselves to research on suppressing chatter by modifying the tool profile.
[0005] Current optimization designs for cutting edge profiles primarily focus on tooth pitch design. Some researchers consider both the helix angle and tooth pitch in their tool design, but these optimizations are typically achieved using deep learning or heuristic algorithms without explaining the underlying physical mechanisms. Furthermore, the chatter frequency of the tool changes with the cutting edge profile, requiring iterative searching to find the new frequency. Additionally, a complete SLD (Search Detail Map) for all rotational speeds is necessary to obtain the critical axial depth of cut at a specific speed, a tedious and time-consuming process. Summary of the Invention
[0006] The purpose of this invention is to provide a tool optimal cutting edge design method for chatter suppression under specific working conditions. A critical axial depth of cut calculation function for arbitrary cutting edge is designed, eliminating the need to draw the complete SLD of the global rotational speed. Based on this function, a particle swarm optimization algorithm is used for optimization, thereby designing the optimal chatter suppression cutting edge that combines the helix angle and pitch under specific working conditions.
[0007] To achieve the above objectives, this invention provides a method for designing the optimal cutting edge profile for chatter suppression under specific working conditions, comprising the following steps:
[0008] S1. Set the helix angle and initial tooth pitch of the tool as optimization parameters;
[0009] S2. Based on the optimization parameters, the critical stable axial depth of cut is calculated using the critical depth of cut calculation function under specific working conditions. Specific working conditions include the current tool speed under non-ball end mill milling conditions. Radial immersion angle during milling process ;
[0010] S3. Using a heuristic algorithm, the local optimal cutting edge shape is found by using the critical axial cutting depth as the fitness function.
[0011] Preferably, in S1, by The distribution defines the initial tooth pitch at the cutting edge tip, i.e., the axial angle between each cutting edge, through... The distribution defines the helix angle of each cutting edge of the tool, that is, the angle between the normal of each cutting edge and the tool axis.
[0012] Preferably, in S2, the milling conditions include side milling, end milling, and plunge milling.
[0013] Preferably, in S2, the critical stable axial cutting depth is calculated using a critical cutting depth calculation function by comprehensively considering the optimization parameters and specific working conditions. Critical stable axial depth of cut The calculation formula is as follows:
[0014] ;
[0015] in, This represents the total number of cutting edges on the tool that participate in the cutting process. These are characteristic values during the dynamic cutting process. This is the normal coefficient of the cutting force. For the first The cutting angle of each cutting edge This refers to the chatter frequency, which is the vibration frequency when chatter occurs during the cutting process. For the first The tooth-passing cycle of a micro-element of the cutting edge.
[0016] Preferably, in S2, during the critical stable axial cutting depth... Before calculation, determine the tool geometry, the tool dynamic characteristic FRF frequency domain response function, the cutting force coefficient, and the current tool speed. The geometry of a cutting tool includes its diameter, cutting edge angle, cutting edge radius, and cutting edge inclination angle.
[0017] Preferably, in S2, during the critical stable axial cutting depth... Before calculation, the process also includes reading tool cutting edge characteristic parameters from the user-provided configuration file, including the number of cutting edges, the length of the discretized micro-element of the cutting edge, the direction of the helix angle, the direction of rotation, whether there is a cutting edge at the bottom, and the distance between the starting point of the cutting edge and the blank space; the three-dimensional coordinates, normal vector, and tangent vector of each cutting edge micro-element; and material and dynamic parameters, including natural frequencies. Stiffness coefficient Damping ratio Cutting force coefficient Sum of forces .
[0018] Preferably, in S2, the critical stable axial cutting depth During the calculation process, the definition Flutter factor ,in For the first The first cutting edge and the first The angle difference between each cutting edge; for tools with variable helix angles, after multiple uniform slices along different heights of the tool axis, the chatter factor of each slice is calculated. With corresponding helix angle The critical stable axial shear depth is obtained by adding the cosine values and taking the average. The denominator in the calculation formula ,in That is .
[0019] Preferably, in S3, the heuristic algorithm uses the initial tooth pitch of the tool and the helix angle of each cutting edge as input to the optimization algorithm. It explores in the parameter space, calculates the critical depth of cut for each set of parameters during the optimization process through the critical depth of cut calculation function, and selects the set of parameters with the largest critical depth of cut as the optimal parameter combination to obtain the optimal helix angle. and optimal initial tooth pitch The optimal cutting edge shape is determined by this combination of parameters.
[0020] Preferably, in S3, the heuristic algorithm used is the Particle Swarm Optimization (PSO) algorithm, which treats each problem to be solved as a particle in the search space. The optimization process is as follows:
[0021] Initialize a group of particles with random positions and velocities;
[0022] During the iteration process, each particle calculates its fitness value based on its current position and compares it with its own historical best position and the global best position of the entire population.
[0023] The particle then dynamically adjusts its forward speed and position based on its own historical best position and the global best position of the entire swarm.
[0024] After iteration, the particle swarm finds the optimal solution to the problem.
[0025] Therefore, the present invention employs the above-mentioned optimal cutting edge design method for chatter suppression under specific working conditions, and the beneficial effects are as follows:
[0026] (1) The present invention designs a critical axial cutting depth calculation function for arbitrary blade shape. This function can obtain a relatively accurate chatter frequency while calculating the critical stable cutting depth, and does not require drawing all stability lobe diagrams (SLD). Then, the particle swarm optimization algorithm is used to find the optimal blade shape based on this function. The whole process greatly reduces the search time for the optimal blade shape.
[0027] (2) Furthermore, this invention provides the physical mechanism behind the critical stable depth of cut calculation function under arbitrary cutting edge, thereby combining the helix angle and pitch for cutting edge design, which improves processing efficiency while ensuring the surface quality of the workpiece.
[0028] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0029] Figure 1 This is a schematic diagram of the overall framework of an embodiment of the optimal cutting edge design method for chatter suppression under specific working conditions according to the present invention.
[0030] Figure 2 This is a critical axial depth of cut distribution diagram of an embodiment of the optimal cutting edge design method for chatter suppression under specific working conditions of the present invention;
[0031] Figure 3 This is an embodiment of the optimal cutting edge design method for chatter suppression under specific working conditions of the present invention, which is the optimal cutting edge shape under a specific input.
[0032] Figure 4 This is a schematic diagram of the calculation logic of the critical axial depth of cut calculation function in an embodiment of the present invention, which is a tool optimal cutting edge design method for chatter suppression under specific working conditions.
[0033] Figure 5This is a schematic diagram illustrating the physical principle behind the application of the critical axial depth of cut calculation function of the present invention, which is used to design the optimal cutting edge shape for chatter suppression under specific working conditions, to any cutting edge shape. Detailed Implementation
[0034] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0035] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.
[0036] like Figure 1 As shown, an optimal cutting edge design method for chatter suppression under specific working conditions includes the following steps:
[0037] S1. Set the helix angle and initial tooth pitch of the tool as optimization parameters, where, The distribution defines the initial tooth pitch at the cutting edge tip, that is, the axial angle between each cutting edge. The distribution defines the helix angle of each cutting edge of the tool, that is, the angle between the normal of each cutting edge and the tool axis.
[0038] S2. Based on the optimization parameters, the critical stable axial depth of cut is calculated using the critical depth of cut calculation function under specific working conditions. This embodiment takes side milling with a four-flute tool as an example. There are eight optimization parameters in total, namely four helix angles and four initial tooth pitches. The specific working conditions include the tool speed under milling conditions not related to ball end mills, such as side milling, end milling, and plunge milling. Radial immersion angle during milling process The cutting edge shape of a ball end mill is a spherical profile, and its helix angle is not a constant value but varies along the cutting edge. The critical depth of cut calculation method based on axial layer micro-element analysis adopted in this invention discretizes each layer of the cutting edge by slicing along the tool axis, which can accurately adapt to the complex and changing cutting edge geometry of ball end mills. Therefore, this method is still applicable to various three-axis and five-axis milling operations with ball end mills.
[0039] By combining the optimization parameters and specific operating conditions, it can be passed The calculation function is obtained , and then The fitness function is used to find the best local optimum blade shape until a good local optimum is found.
[0040] like Figure 4 As shown, during the critical stable axial cutting depth... Before calculation, the helix angle and pitch parameters for each cutting edge are required, i.e. Figure 1In addition to the eight parameters shown, it is also necessary to determine the tool geometry, the tool dynamic characteristic FRF frequency domain response function, the cutting force coefficient, and the current tool speed. All the above parameters and information determine the critical stable axial depth of cut. The result of the calculation formula is the final critical stable axial cutting depth.
[0041] First, the configuration file in INI format provided by the user is read. The geometric parameters defining the tool are read from the [geometry] section of the configuration file, including diameter DC, cutting edge angle APMX, cutting edge radius RE, and cutting edge inclination angle PSIR.
[0042] Extract the parameters that define the characteristics of the cutting edge from [edges], including the number of cutting edges num_flute, the length of the discretized micro-element delta_length, the direction of the helix angle positive_helix, the direction of rotation, whether there is a bottom, whether there is a cutting edge bottom, and the distance between the starting point of the cutting edge and the blank space.
[0043] The core helper function `cutting_edges_init_seperate` is called, which outputs a series of arrays containing information such as the three-dimensional coordinates, normal vector, tangent vector, and curvature of the tiny line segments (micro-elements) that make up each cutting edge.
[0044] Then, a dynamic model is constructed based on the fundamental properties of the cutting tool, as follows:
[0045] Import material and dynamic parameters. From the [material] section of the configuration file, read parameters related to the tool material and dynamic properties, including natural frequencies. Stiffness coefficient Damping ratio Cutting force coefficient Sum of forces .
[0046] Based on the aforementioned material and dynamic parameters, the critical depth of cut calculation function is further transformed into an equivalent dynamic parameter model of the tool through a parameterization method, forming a simplified mass-damping-stiffness MCK model, where M represents mass and stiffness is... and natural frequency Calculations show that C represents damping, derived from the damping ratio. Stiffness The result is calculated from the mass M; The normal coefficient of the cutting force is derived from the cutting force coefficient. Sum of forces The calculations show that this is a key coefficient connecting the cutting force and the cutting width. This is then combined with the user-inputted angle of entry. and cut-out angle The dynamic cutting force coefficient describing the coupling relationship between cutting force and vibration was calculated. .
[0047] Then, define a flutter frequency as the unknown quantity to be determined. Using the model parameters of MCK, the tool frequency is calculated. The tool dynamic characteristic FRF frequency domain response function value is used to describe the vibration response of the tool at a specific frequency.
[0048] Dynamic cutting force coefficient The characteristic equation is constructed by combining the tool's dynamic characteristic FRF frequency domain response function, and the complex eigenvalues in the dynamic cutting process are obtained by solving it. And by checking the chatter phase condition at the tool's natural frequency Search for all possible flutter frequencies in the vicinity, and for each valid flutter frequency... Finally, a corresponding critical depth of cut is calculated, and the minimum value among all valid positive values is output as the upper limit of the stable depth of cut under this processing condition.
[0049] The critical stable axial cutting depth is calculated using a critical cutting depth calculation function by combining the optimization parameters and specific working conditions. Critical stable axial depth of cut The calculation formula is as follows:
[0050] ;
[0051] in, This represents the total number of cutting edges on the tool that participate in the cutting process. These are characteristic values during the dynamic cutting process, derived from the system's dynamic response function FRF and the cutting force coefficient matrix. They reflect the transmission relationship between cutting force and vibration displacement and are core parameters for measuring system stability. It is the normal coefficient of cutting force, which is related to the tool material, workpiece material and cutting conditions, and reflects the magnitude of the normal cutting force generated per unit cutting area during the cutting process.
[0052] For the first The cutting angle of each cutting edge describes the spatial orientation of the cutting edge when it contacts the workpiece, and affects the direction and distribution of the cutting force. The chatter frequency is the vibration frequency at which chatter occurs during the cutting process, and it is determined by the dynamic characteristics of the tool-workpiece system, such as natural frequency and damping. For the first The tooth-passing cycle of a micro-element of the cutting edge is usually related to the tool speed and tooth pitch, representing the time difference between adjacent cutting edges passing through the same machining position.
[0053] like Figure 5 As shown, the critical cutting depth calculation function of this invention The underlying physical principle for applying arbitrary cutting edge profiles is: the depth of cut along the critical stable axis. During the calculation process, the definition The chatter factor (CF) is the factor where For the first The first cutting edge and the first The angle difference between the cutting edges; and for tools with variable helix angles, the chatter factor of different slices varies depending on the height of the cutter axis. Therefore, it is necessary to perform multiple uniform slices along a plane perpendicular to the cutter axis within the axial cutting depth.
[0054] After making multiple uniform slices at different heights along the blade axis, the dizziness factor CF of each layer is determined. With corresponding helix angle The critical stable axial shear depth is obtained by adding the cosine values and taking the average. The denominator in the calculation formula ,in That is And finally obtain the average chatter factor of the tool at the current cutting depth, thus realizing the ability to operate on tools with arbitrary helix angles and pitches. Calculation, such as Figure 2 As shown.
[0055] S3. Using the particle swarm optimization algorithm with the critical axial cutting depth as the fitness function, find the locally optimal cutting edge shape, such as... Figure 3 The heuristic algorithm used in this study takes the initial tooth pitch of the tool and the helix angle of each cutting edge as input to the optimization algorithm. It explores the parameter space and calculates the critical depth of cut for each set of parameters during the optimization process using a critical depth of cut calculation function. The set of parameters with the largest critical depth of cut is selected as the optimal parameter combination to obtain the optimal helix angle. and optimal initial tooth pitch The optimal cutting edge shape is determined by this combination of parameters.
[0056] Particle Swarm Optimization (PSO) is a collaborative optimization method that treats each possible solution to a problem as a particle in the search space. The optimization process begins by initializing a swarm of particles with random positions and velocities. During iteration, each particle calculates its fitness value based on its current position and compares it to its own historical best position and the global best position of the entire swarm. The particle then dynamically adjusts its velocity and position based on these two optimal positions. This adjustment mechanism simulates information sharing and imitation, causing the particle swarm to gradually converge towards the global optimum. Through repeated iterations, the particle swarm can eventually find the optimal or near-optimal solution to the problem with high efficiency.
[0057] Therefore, this invention adopts the above-mentioned optimal cutting edge design method for chatter suppression under specific working conditions. By theoretically extending the zero-order analysis method of milling cutter chatter, a critical axial depth of cut calculation function for arbitrary cutting edge is designed. This function does not require drawing the entire stability leaf plot (SLD) when calculating the critical depth of cut for arbitrary cutting edge. Based on this function, a particle swarm optimization algorithm is used for optimization, thereby finding the cutting edge with the largest critical axial cutting depth under specified working conditions, especially under specific tool speeds. This is the optimal cutting edge for chatter suppression under specific working conditions, which improves machining efficiency while ensuring the surface quality of the workpiece.
[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A method for designing the optimal cutting edge profile of a tool to suppress chatter under specific working conditions, characterized in that, Includes the following steps: S1. Set the helix angle and initial tooth pitch of the tool as optimization parameters; S2. Based on the optimization parameters, the critical stable axial depth of cut is calculated using the critical depth of cut calculation function under specific working conditions. Specific working conditions include the current tool speed under non-ball end mill milling conditions. Radial immersion angle during milling process ; S3. Using a heuristic algorithm, the local optimal cutting edge shape is found by using the critical axial cutting depth as the fitness function. In S2, the critical stable axial cutting depth is calculated using the critical cutting depth calculation function by comprehensively considering the optimization parameters and specific working conditions. Critical stable axial depth of cut The calculation formula is as follows: ； in, This represents the total number of cutting edges on the tool that participate in the cutting process. These are characteristic values during the dynamic cutting process. This is the normal coefficient of the cutting force. For the first The cutting angle of each cutting edge This refers to the chatter frequency, which is the vibration frequency when chatter occurs during the cutting process. For the first The tooth-passing cycle of a micro-element of the cutting edge.
2. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 1, characterized in that, In S1, through The distribution defines the initial tooth pitch at the cutting edge tip, i.e., the axial angle between each cutting edge, through... The distribution defines the helix angle of each cutting edge of the tool, that is, the angle between the normal of each cutting edge and the tool axis.
3. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 1, characterized in that, S2 Milling machining conditions include side milling, end milling, and plunge milling.
4. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 3, characterized in that, In S2, during the critical stable axial cutting depth... Before calculation, determine the tool geometry, the tool dynamic characteristic FRF frequency domain response function, the cutting force coefficient, and the current tool speed. The geometry of a cutting tool includes its diameter, cutting edge angle, cutting edge radius, and cutting edge inclination angle.
5. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 4, characterized in that, In S2, during the critical stable axial cutting depth... Before calculation, the process also includes reading tool cutting edge characteristic parameters from the user-provided configuration file, including the number of cutting edges, the length of the discretized micro-element of the cutting edge, the direction of the helix angle, the direction of rotation, whether there is a cutting edge at the bottom, and the distance between the starting point of the cutting edge and the blank space; the three-dimensional coordinates, normal vector, and tangent vector of each cutting edge micro-element; and material and dynamic parameters, including natural frequencies. Stiffness coefficient Damping ratio Cutting force coefficient Sum of forces .
6. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 1, characterized in that, In S2, at the critical stable axial depth of cut During the calculation process, the definition Flutter factor ,in For the first The first cutting edge and the first The angle difference between each cutting edge; for tools with variable helix angles, after multiple uniform slices along different heights of the tool axis, the chatter factor of each slice is calculated. With corresponding helix angle The critical stable axial shear depth is obtained by adding the cosine values and taking the average. The denominator in the calculation formula ,in That is .
7. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 1, characterized in that, In S3, the heuristic algorithm uses the initial tooth pitch of the tool and the helix angle of each cutting edge as input to the optimization algorithm. It explores in the parameter space, calculates the critical depth of cut for each set of parameters during the optimization process through the critical depth of cut calculation function, and selects the set of parameters with the largest critical depth of cut as the optimal parameter combination to obtain the optimal helix angle. and optimal initial tooth pitch The optimal cutting edge shape is determined by this combination of parameters.
8. The optimal cutting edge design method for chatter suppression under specific working conditions according to claim 7, characterized in that, In S3, the heuristic algorithm uses the Particle Swarm Optimization (PSO) algorithm, treating each problem to be solved as a particle in the search space. The optimization process is as follows: Initialize a group of particles with random positions and velocities; During the iteration process, each particle calculates its fitness value based on its current position and compares it with its own historical best position and the global best position of the entire population. The particle then dynamically adjusts its forward speed and position based on its own historical best position and the global best position of the entire swarm. After iteration, the particle swarm finds the optimal solution to the problem.