A method for calculating stress wave energy of a milling titanium alloy cutter based on simulation

Abstract

The application discloses a kind of based on milling titanium alloy cutter tooth stress wave energy solving method of simulation, according to the existing about stress wave characteristics solving method is mostly for different rock joints and explosion stress wave etc., for the propagation characteristics of stress wave in milling process and the energy evolution mechanism of the relief of cutter tooth under the action of stress wave, it needs to be revealed, in the process of high efficiency milling, using the internal particle of workpiece processing one by one solving method, the friction stress wave fluctuation equation constructed by one-dimensional string theory is converted into vibration wave source equation, the wave source vibration equation under the action of friction is obtained, the accurate description of the superposition state of stress wave under external force is realized, and the strength of superposition particle is analyzed, and for the energy fluctuation of the relief of cutter tooth in the process of high efficiency milling, energy solving equation is constructed, the theoretical value of corresponding position stress wave energy can be calculated, the dynamic change characteristics of friction stress wave energy in cutter tooth is solved.

Description

[0001] This application is a divisional application of application number 202310920770.7, filed on July 26, 2023, with the invention title "Superposition Characteristics of Stress Waves in Milled Titanium Alloys and Method for Calculating the Energy of Stress Waves in Cutting Teeth". Technical Field

[0002] This invention relates to the technical field of solving the superposition equation of stress waves in the surface and subsurface layers of machined workpieces and the method for calculating the energy characteristics of the rake face of cutting tools, specifically a simulation-based method for calculating the stress wave energy of milling titanium alloy cutting tools. Background Technology

[0003] During the milling of TC4 titanium alloy workpieces with high-efficiency end mills, the frictional force at the tool interface acts on the workpiece surface, causing fluctuations in the internal particles of the workpiece, thus forming stress waves. When different cutter teeth mill the workpiece surface, different stress waves are generated along different paths in the surface and subsurface layers of the workpiece. If different stress waves meet inside the workpiece and superimpose, the superimposed stress waves propagate inside the workpiece, causing surface and subsurface damage to the machined surface. These minor damages will be amplified during subsequent surface treatments, affecting the surface morphology, subsurface microstructure, and physical and mechanical properties of the workpiece, thereby impacting the reliability and service life of the parts. Therefore, exploring the superposition of stress waves in the surface and subsurface layers of the workpiece and constructing a stress wave superposition equation under the action of friction is of great significance.

[0004] To reveal the superposition characteristics of stress waves in the surface and subsurface layers of a workpiece, a superposition equation for stress waves was constructed and solved. Based on the effect of friction during high-efficiency milling, this equation analyzes the forces acting on particles within the workpiece, deriving the wave equation for the particles. A particular solution to this equation is then calculated, transformed into the vibration equation of the wave source, and synthesized to obtain the superposition equation for the stress waves of the particles. In high-efficiency milling, the more significant the dynamic load, the more intense the vibration response of the cutting tool. When wave crests and troughs superimpose at a certain particle, the strength of the particle is enhanced, increasing the stress distribution depth and leading to microcrack propagation. This accelerates tool damage and reduces the machining quality of the workpiece. Conversely, when wave crests and troughs meet and superimpose at a certain particle, the strength of that particle decreases, reducing damage and improving the surface quality of the machined workpiece. Therefore, solving for the superposition characteristics of stress waves within the machined workpiece provides guidance for reducing damage in the surface and subsurface layers and improving the surface quality of the workpiece.

[0005] Stress waves often undergo energy changes during propagation, which can be considered a fluctuation process of stress wave energy. Besides the disturbance between particles, energy is also transferred, which is also a form of wave motion. Existing methods for calculating the characteristics of stress waves are mostly aimed at different rock joints and explosive stress waves. The propagation characteristics of stress waves during milling and the energy evolution mechanism of the rake face under stress wave action remain to be revealed. In high-efficiency milling, the energy propagation of stress waves has a significant impact on the performance degradation of the rake face. To further explore the energy loss of the rake face, a method for calculating the stress wave energy of the rake face is proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a simulation-based method for calculating the stress wave energy of milled titanium alloy cutting tools, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a simulation-based method for calculating the stress wave energy of milled titanium alloy cutting tools, wherein the specific stress wave energy calculation method is as follows:

[0008] S1. The constraint of stress between internal particles of the machined workpiece keeps its internal components in a stable state. The stress constraining the particles of the machined workpiece is an internal force. When no external force is applied, the internal structure is in a stable state.

[0009] S2. When an external force is applied to the surface of a machined workpiece through the upper face of the cutting teeth, the particles inside the workpiece are displaced under the action of the external force, and stress is generated between them and adjacent particles, resulting in stress transmission. Due to the inertia of the medium particles, the motion of a certain adjacent particle lags behind. The disturbance of the external load on the surface is thus propagated from near to far in the medium to form a stress wave.

[0010] S3. When the particles inside the processed workpiece form stress waves under the action of external force, and the stress waves generated by several wave sources propagate in the same medium and act on the same particle in the workpiece at the same time, the stress waves form a superposition of stress waves inside the processed workpiece. For elastic waves, since they are all linear waves, the interaction of their wave sources satisfies the principle of linear superposition.

[0011] S4. The propagation process of stress waves in the third deformation zone of the machined workpiece during milling. The propagation process is the friction between the cutting edge and the machining transition surface after the cutting tooth during the milling process of the machined workpiece. The propagation process is often accompanied by a disturbance process of energy change.

[0012] Furthermore, the processed workpiece is a titanium alloy TC4 workpiece.

[0013] Furthermore, the stress wave refers to the propagation of vibration state and vibration phase information when an external force is applied to the surface of the machined workpiece.

[0014] Furthermore, the stress wave fluctuation equation of the internal mass points of the workpiece when an external force is applied is:

[0015]

[0016] Furthermore, when the two cutting teeth exert force on the surface of the workpiece, they form two wave sources. The vibration equation of the wave sources is the integral form of the wave equation of the particle. The vibration equations of the two wave sources can be obtained from the wave equation of the particle.

[0017] The vibration equation of wave source 1:

[0018]

[0019] The vibration equation of wave source 2:

[0020]

[0021] Furthermore, the stress waves generated by the wave sources meet and superimpose inside the workpiece.

[0022] Furthermore, based on stress wave theory, S4 uses a one-dimensional elastic stress wave P-wave energy calculation method to solve for the elastic energy caused by the stress wave during propagation.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] The superposition characteristics of stress waves in milling titanium alloys and the method for calculating the stress wave energy of cutting teeth are based on existing theoretical research and experimental methods on stress wave superposition and energy calculation. These methods are mainly applied to different rock joints and explosive stress waves. The crack propagation process of pre-cracked rocks is analyzed through finite element simulation. The damage mechanism of rocks with different stress wave peak values ​​and energies is studied, and the influence law of rock damage is given.

[0025] The superposition characteristics of stress waves in milling titanium alloys and the method for calculating the energy of stress waves in cutting tools can be applied to different rock joints. However, the propagation characteristics of stress waves in the surface and subsurface layers of the workpiece during milling and the energy evolution mechanism generated on the back face of the cutting tools under the action of stress waves need to be revealed. In elastic media, the superposition of instantaneous stress waves often occurs, resulting in high local stress concentration. Due to the complexity of the cutting process, there is very little research on the superposition characteristics of stress waves at the tool interface, making it difficult to directly apply existing theories to the metal cutting process. Therefore, the process of constructing the superposition equation of stress waves is quite difficult.

[0026] Furthermore, most existing methods for calculating the characteristics of stress waves are designed for different rock joints and explosive stress waves. The propagation characteristics of stress waves during milling and the energy evolution mechanism of the back face of the cutting teeth under the action of stress waves need to be revealed.

[0027] This method for calculating the superposition characteristics of stress waves in milling titanium alloys and the energy of stress waves in milling cutter teeth employs a point-by-point calculation method within the workpiece during high-efficiency milling. The frictional stress wave fluctuation equation, constructed using one-dimensional string theory, is transformed into a vibration source equation, deriving the vibration equation of the wave source under frictional force. This achieves an accurate description of the superposition state of stress waves under external force (friction) and analyzes the strength of the superimposed particles. Furthermore, for the energy fluctuation on the flank face of the milling cutter teeth during high-efficiency milling, an energy calculation equation is constructed, capable of calculating the theoretical value of the stress wave energy at the corresponding position and solving for the dynamic variation characteristics of frictional stress wave energy in the milling cutter teeth. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the propagation mode of internal stress waves and the state of mass points in the workpiece during the milling process of the milling cutter in this invention.

[0029] Figure 2 This is a schematic diagram showing the amplitude variation of the superposition of wave crests at different frequencies of the two wave sources in this invention.

[0030] Figure 3 This is a schematic diagram showing the amplitude variation of the superposition of wave crests when the two wave sources have the same frequency in this invention.

[0031] Figure 4 This is a schematic diagram showing the amplitude variation of the superposition of wave peaks and troughs when the two wave sources in this invention are at different frequencies;

[0032] Figure 5 This is a schematic diagram showing the amplitude variation of the superposition of wave crests and troughs when the two wave sources in this invention have the same frequency.

[0033] Figure 6 This is a schematic diagram of the instantaneous motion state of a certain mass point inside the workpiece being processed in this invention;

[0034] Figure 7 This is a schematic diagram showing two wave sources acting simultaneously on the same particle in a workpiece in this invention.

[0035] Figure 8 This is a schematic diagram showing the superposition of wave peaks when the frequencies of cutter teeth 1 and 2 are the same in this invention;

[0036] Figure 9 This is a schematic diagram showing the superposition of peaks and troughs when the frequencies of cutter teeth 1 and 2 are the same in this invention;

[0037] Figure 10 This is a schematic diagram of stress wave superposition when the frequencies of cutter teeth 1 and 2 are different in this invention;

[0038] Figure 11 This is a schematic diagram showing the location of the feature points on the back face of the cutting tooth in this invention;

[0039] Figure 12 This is a schematic diagram illustrating the process of calculating the stress wave energy change at a contact angle of 2° using the stress wave energy calculation method of the present invention.

[0040] Figure 13 This is a schematic diagram illustrating the process of calculating the stress wave energy variation at a contact angle of 24.5° using the stress wave energy calculation method of this invention.

[0041] Figure 14 This is a schematic diagram illustrating the process of calculating the stress wave energy change at a contact angle of 47° using the stress wave energy calculation method of this invention.

[0042] Figure 15 This is a schematic diagram illustrating the process of calculating the stress wave energy variation at a contact angle of 69.5° using the stress wave energy calculation method of this invention.

[0043] Figure 16 This is a schematic diagram illustrating the process of calculating the stress wave energy change at a contact angle of 89.5° using the stress wave energy calculation method of this invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] Please see Figure 1-16 The present invention provides a technical solution: a method for calculating the superposition characteristics of stress waves in milled titanium alloys and the energy of stress waves in cutting tools;

[0046] Example 1

[0047] By constraining the stress between the particles inside the machined workpiece, the internal components are kept in a stable state. The stress constraining the particles of the machined workpiece is an internal force. When no external force is applied, the internal structure is in a stable state. When the surface of the machined workpiece is subjected to an external force, the particles inside the workpiece are displaced under the action of the external force, thereby generating stress between adjacent particles and causing stress transmission. However, due to the inertia of the medium particles, the motion of a certain adjacent particle lags behind. The disturbance of the external load on the surface is thus propagated from near to far in the medium to form a stress wave.

[0048] The workpiece is made of titanium alloy TC4. When the particles inside the workpiece are subjected to external force, stress waves are formed. When the stress waves generated by several wave sources propagate in the same medium and act on the same particle in the workpiece at the same time, the stress waves are superimposed inside the workpiece. For elastic waves, since they are all linear waves, their interaction satisfies the principle of linear superposition.

[0049] like Figure 1 As shown, the workpiece being machined during high-efficiency milling is in the state of a particle when internal stress waves are superimposed. Stress waves are the propagation of vibration state and vibration phase information. When a stress wave propagates inside the workpiece, it causes a particle to vibrate when it reaches a certain particle. When a particle is subjected to two stress waves, the vibration of that particle is the synthesis of the vibrations excited by each wave at that point.

[0050] like Figure 2-5 As shown, Figure 2-5 In this context, c1 and c2 represent the wave velocities of the two waves, respectively. Figure 2-5 Each case shown includes five stages: before the two waves are superimposed, the initial superposition of the two waves, the complete superposition of the two waves, the end of the superposition of the two waves, and the separation of the two waves from superposition. These five stages demonstrate the amplitude changes during the superposition process of the two waves.

[0051] Figure 2-5 The transverse wave in a longitudinal wave has a sinusoidal or cosine curve shape, while the vibration direction of the longitudinal wave particles is the same as the wave propagation direction, and its propagation shape cannot be directly observed. To determine the propagation shape of the longitudinal wave, a static particle at a certain instant of the longitudinal wave propagation is established, such as... Figure 1 As shown, the relationship between each particle at a certain instant and the particle at the equilibrium position can be obtained.

[0052] Figure 6 As shown, the horizontal axis represents the distribution of each particle. The top row shows the distribution of particles when they are not subjected to external forces, in which case the particles are uniformly distributed. The bottom row shows the distribution of particles under the action of external forces. The vertical axis represents the displacement of particles when they are subjected to external forces.

[0053] By studying a finite number of points and analyzing the displacement of the particle, if the particle is displaced to the right under the action of an external force, the direction is set to positive; if it is displaced to the left, the direction is set to negative. Connecting the displacement points of the particle will yield a curve.

[0054] Depend on Figure 6 It can be seen that the displacements of particles under the action of external forces are not equal, and the resulting curve shape is the same as the wave shape of a transverse wave.

[0055] In the high-efficiency milling process of machining, the flank face of the cutting teeth on the tool acts on the workpiece surface, generating frictional force. This frictional force acts on the workpiece to generate stress waves. The stress wave fluctuation equation of the internal particles of the workpiece is:

[0056]

[0057] The vibration equation of a wave source is the integral form of the wave equation of a particle, or its particular solution form. Therefore, the vibration equations of two wave sources can be obtained from the wave equation of a particle:

[0058] The vibration equation of wave source 1:

[0059]

[0060] The vibration equation of wave source 2:

[0061]

[0062] Example 2

[0063] like Figure 1 As shown, when the two cutting teeth act on the workpiece surface, two wave sources are formed. The stress waves generated by these two wave sources meet and superimpose inside the workpiece. The vibration equations for wave source 1 and wave source 2 are shown in Example 1. However, when the vibration of the wave source is transmitted to particle P, a phase difference will be generated, i.e. Figure 7 The two wave sources shown in the diagram act simultaneously on the same particle in the workpiece;

[0064] Figure 7 As shown, wave source 1 generates a stress wave at point O1, which travels a distance of r1 to particle P. Wave source 2 generates a stress wave at point O2, which travels a distance of r2 to particle P and meets and superimposes with the stress wave from wave source 1. Point O1 is the first starting point and point O2 is the first starting point.

[0065] Therefore, the vibration equation of particle wave source 1 at point P can be derived as follows:

[0066]

[0067] The vibration equation for particle wave source 2 is:

[0068]

[0069] The equation of the resultant vibration of particle P is:

[0070] y = y1 + y2;

[0071] When two waves have the same frequency, a constant phase difference, and the same direction of vibration, they will interfere with each other. The vibration equation at this time is:

[0072]

[0073] in,

[0074]

[0075]

[0076] Phase difference is Regardless of time t, r2-r1 is the path difference.

[0077] When the frequencies of the two waves are different, the two waves will not interfere. In this case, the vibration equation is:

[0078]

[0079] By solving the stress wave equations of the surface and subsurface layers of the workpiece during milling, vibration equations for the two wave sources are obtained. The propagation characteristics of stress waves inside the workpiece during cutting are studied, considering only the propagation process of its elastic longitudinal waves. The selected feature point locations take into account the coupling effect between the longitudinal waves, thus obtaining the superposition characteristics of one-dimensional elastic longitudinal waves inside the machined workpiece.

[0080] Stress waves generated by different cutting teeth were selected, and MATLAB was used to calculate the superimposed stress waves of a particle at the same location at different times. The displacements of the particle after the superposition of cutting teeth 1 and 2 are shown in the figure. Figures 8-10 As shown:

[0081] Wherein, H1 represents the displacement generated when the stress wave generated by cutter tooth 1 propagates to the same particle at different times, H2 represents the displacement generated when the stress wave generated by cutter tooth 2 propagates to the same particle at different times, and H3 represents the displacement generated at the same particle when cutter tooth 1 and cutter tooth 2 act on the same particle at different times.

[0082] Figure 8 As shown, when two wave sources meet and superimpose, the resulting displacement is a vector superposition of the displacements generated by each of the two wave sources. After meeting and superimposing, each wave source retains its original motion characteristics. Please continue.

[0083] like Figure 9As shown, if the vibration frequencies of the two wave sources are the same, the point of reinforcement will always be reinforced and the point of weakening will always be weakened, forming a stable superposition with periodicity. The frequency after superposition is the same as the original frequency, and the points of vibration reinforcement and vibration weakening occur alternately. At the particle where the two waves superimpose, when the wave crests meet, the vibration is reinforced, and when the wave troughs meet, the vibration of the particle is also reinforced.

[0084] If the vibration frequencies of the two wave sources are the same, the point of reinforcement will always be reinforced and the point of weakening will always be weakened, forming a stable superposition with periodicity. The frequency of the superposition is the same as the original frequency, and the points of reinforcement and weakening of vibration appear alternately. At the particle where the two waves superimpose, when the wave crests meet, the vibration is reinforced, and when the wave crests meet the wave troughs, the vibration is weakened.

[0085] like Figure 10 As shown, if the vibration frequencies of the two waves are different, the displacement produced when the particles are superimposed is the vector sum of the displacements produced when the two waves act on the particle individually, and it exhibits a certain periodicity, but is independent of its original frequency.

[0086] Since the intensity of a wave is proportional to the square of its amplitude, i.e.: I∝A 2 Therefore, the intensity of the resultant vibration is:

[0087]

[0088] If the wave is a coherent wave, then:

[0089]

[0090] If the wave is incoherent, then:

[0091] I = I1 + I2.

[0092] Example 3

[0093] The propagation process of stress waves in the third deformation zone during milling is essentially a study of the disturbance process of the particles rubbing between the back face of the cutting tool and the machining transition surface during milling. The propagation process is often accompanied by energy changes, which can also be called the stress wave energy fluctuation process.

[0094] In addition to the disturbance of particles, energy is also transferred as a form of wave. Therefore, to study the propagation characteristics of stress waves during milling, it is necessary to study the influence characteristics of energy in the process.

[0095] As the cutting process continues, the interaction between the milling cutter and the workpiece causes the cutter teeth to peel off from their intact state, thus creating the upper boundary. Subsequently, as the workpiece material is removed, the change in its equivalent stress is analyzed, thus providing the basis for the lower boundary. Therefore, four characteristic points on the back face of the cutter teeth are selected, and the normal stress under the action of friction is extracted using DEFORM simulation according to the experimental scheme.

[0096] The simulation conditions are set as shown in the table below:

[0097] Table 1 Simulation boundary conditions

[0098]

[0099] The simulation involved dividing the milling cutter teeth into 500,000 meshes. To ensure more accurate simulation results, when using absolute-size meshing for the workpiece, the step size was set to no more than 1 / 3 of the smallest mesh element size. This allowed for the determination of the feature points on the flank face of the milling cutter teeth and the propagation of stress waves. Figure 11 As shown, the frictional stress along the propagation path at four characteristic points is calculated to prepare for the subsequent energy calculation of the rake face of the cutting tooth. Five instantaneous contact angles are selected based on the instantaneous contact angles at different times, i.e., the effective cutting cycle reached when the cutting tooth enters the workpiece. Therefore, based on the influence of parameters under these different conditions on stress wave propagation, a method for calculating stress wave energy is given, and its influence characteristics are studied.

[0100] During milling, the external load causes disturbances in the position of particles, forming stress waves that propagate into the cutting teeth. Based on stress wave theory, the elastic energy induced by the stress wave during propagation is calculated using a one-dimensional elastic stress wave P-wave energy calculation method.

[0101] Since the kinetic energy and potential energy generated during the propagation of stress waves are the same, the kinetic energy and potential energy are the same for the perturbation of particles inside the cutting teeth in the form of waves. Therefore, the total energy during the propagation process is the sum of elastic energy and kinetic energy.

[0102] The total energy of stress wave propagation is:

[0103]

[0104] In the equation: σ ij E represents the element stress; E is the elastic modulus of the material.

[0105] During milling, the propagation of stress waves involves the same elastic potential energy and kinetic energy at any given moment for the particles along the string. Therefore, this is the key factor in distinguishing between wave motion and particle vibration within a material. For any infinitesimal element, the energy generated by the stress wave under load does not follow the law of conservation of energy during propagation. As the load increases, the disturbance of the wave source particle gradually increases, leading to an increase in energy. As the milling process continues, the energy gradually decreases as it is transferred into the medium. Therefore, wave motion is also a form of energy transfer in the propagation of stress waves.

[0106] The stress wave energy at the four characteristic points is calculated using the above formula and the change process is as follows: Figure 2-16 As shown in the figure, the attenuation trend of stress wave energy is roughly the same at different characteristic point locations. Figure 2-16 The overall energy order is P3 > P1 > P4 > P2;

[0107] Because feature point three is located on the cutting edge, unlike feature point one, it is the first to contact the workpiece and participate in cutting due to the effect of the cutting tooth installation angle. Therefore, the stress of the mass point in the third deformation zone (tool contact zone) is higher than that of other feature point positions. As time goes by, the friction between the back face of the cutting tooth and the machining transition surface becomes more intense, causing the stress at feature point two and feature point four in the friction area to be smaller than that at feature points on the cutting edge. Therefore, the energy is lower than that at other positions.

[0108] This invention establishes a superposition equation for stress waves generated on the surface and subsurface of the workpiece due to friction during milling, and analyzes the energy dissipation caused by stress wave propagation on the back face of the cutting tooth during high-efficiency milling, thereby constructing an energy calculation method for stress wave propagation on the back face of the cutting tooth.

[0109] By calculating the superposition of stress waves inside the workpiece, the main propagation characteristics of stress waves inside the workpiece during high-efficiency milling are reflected. Thus, by calculating the superposition characteristics of stress waves, the influence range of stress waves in the machined workpiece can be identified, providing a theoretical basis for exploring the generation mechanism of milling cutter damage to the internal structure of the workpiece during milling.

[0110] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A simulation-based method for calculating the stress wave energy of milled titanium alloy cutting tools, characterized in that: S1. The constraint of stress between internal particles of the machined workpiece keeps its internal components in a stable state. The stress constraining the particles of the machined workpiece is an internal force. When no external force is applied, the internal structure is in a stable state. S2. When an external force is applied to the surface of a machined workpiece through the upper face of the cutting teeth, the particles inside the workpiece are displaced under the action of the external force, and stress is generated between them and adjacent particles, resulting in stress transmission. Due to the inertia of the medium particles, the motion of a certain adjacent particle lags behind. The disturbance of the external load on the surface is thus propagated from near to far in the medium to form a stress wave. S3. When the particles inside the processed workpiece form stress waves under the action of external force, and the stress waves generated by several wave sources propagate in the same medium and act on the same particle in the workpiece at the same time, the stress waves form a superposition of stress waves inside the processed workpiece. For elastic waves, since they are all linear waves, the interaction of their wave sources satisfies the principle of linear superposition. S4. The propagation and distribution process of stress waves in the third deformation zone during milling is essentially a study of the disturbance process of particles rubbing between the back face of the cutting tooth and the machining transition surface during milling. As the cutting process progresses, the interaction between the milling cutter and the workpiece causes the cutter teeth to peel off from their intact state, resulting in the upper boundary. Subsequently, as the workpiece material is removed, the change in equivalent stress is analyzed, thus providing the basis for the lower boundary. Therefore, four characteristic points on the flank face of the cutter teeth are selected, and the normal stress under friction is extracted using simulation. The simulation conditions are: milling cutter material WC; coating material Ti-CN; workpiece material TC4; thermal conductivity 45 W / m·℃; milling stroke 5 m. Feed rate: 500 mm / min; Milling width: 16 mm; Milling depth: 0.5 mm; To make the simulation results more accurate, when the workpiece is meshed using absolute dimensions, the step size does not exceed 1 / 3 of the smallest unit size of the workpiece mesh. The positions of the feature points on the back face of the milling cutter teeth and the propagation of stress waves are obtained. The frictional stress of the propagation path at the four feature points is calculated to prepare for the subsequent energy calculation of the back face of the cutter teeth. The instantaneous contact angles at different times, i.e., the effective cutting cycles reached when the cutter teeth cut into the workpiece, are divided into five instantaneous contact angles. Therefore, based on the influence of parameters under different conditions on the propagation of stress waves, the calculation method of stress wave energy is given and its influence characteristics are studied. During milling, the position of the mass point is disturbed due to the action of external load, forming a stress wave, which propagates into the inside of the cutting tooth in this form. According to the stress wave theory, the elastic energy caused by the stress wave during propagation is solved based on the one-dimensional elastic stress wave P-wave energy calculation method. Since the kinetic energy and potential energy generated during the propagation of stress waves are the same, the kinetic energy and potential energy are the same in terms of energy transfer when the disturbance of particles inside the cutting teeth propagates in the form of waves. Therefore, the total energy during the propagation process is the sum of elastic energy and kinetic energy. Therefore, the total energy of the stress wave propagation is: In the equation: σ ij E represents the element stress; E is the elastic modulus of the material. According to the stress wave energy calculation method above, the stress wave energy at the four characteristic points is calculated respectively. Since the characteristic point three is on the cutting edge, unlike the characteristic point one which takes into account the cutting tooth installation angle, the stress of the particle in the tool-work contact area that first contacts the workpiece and participates in cutting during machining is higher than that of other characteristic points. As time goes by, the friction between the back face of the cutting tooth and the machining transition surface becomes more intense, causing the stress at the characteristic points two and four in the friction area to be smaller than that at the characteristic points on the cutting edge. Therefore, the energy is lower than that at other locations. The processed workpiece is a titanium alloy TC4 workpiece; The stress wave refers to the propagation of vibration state and vibration phase information when an external force is applied to the surface of a machined workpiece.

2. The simulation-based method for calculating the stress wave energy of milled titanium alloy cutting tools according to claim 1, characterized in that: The stress wave equation for the internal particles of the workpiece when an external force is applied is:

3. The method for calculating stress wave energy of milled titanium alloy cutting tools based on simulation according to claim 2, characterized in that: When the two cutting teeth exert force on the surface of the workpiece, two wave sources are formed. The vibration equation of the wave source is the integral form of the wave equation of the particle. The vibration equations of the two wave sources can be obtained from the wave equation of the particle. The vibration equation of wave source 1: The vibration equation of wave source 2:

4. The simulation-based method for calculating the stress wave energy of milled titanium alloy cutting tools according to claim 3, characterized in that: The stress waves generated by the two wave sources meet and superimpose inside the workpiece.

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