A method for calculating stress wave energy of a cutter tooth in milling a titanium alloy TC4 workpiece

Abstract

The application discloses a kind of milling titanium alloy TC4 workpiece cutter stress wave energy solving method, 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 processing workpiece is solved one by one, 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 No. 202310920770.7, with the filing date of July 26, 2023, and the original application name of "Milling titanium alloy stress wave superposition characteristics and tool tooth stress wave energy calculation method". TECHNICAL FIELD

[0002] The application relates to the technical field of calculating stress wave superposition equations in the surface and subsurface of a workpiece and calculating tool tooth relief energy characteristics, in particular to a tool tooth stress wave energy calculation method for milling titanium alloy TC4 workpieces. BACKGROUND

[0003] During the process of milling titanium alloy TC4 workpieces with high-efficiency milling tools, the tool-work interface friction acts on the surface of the workpiece, causing the internal particles of the workpiece to fluctuate and form stress waves. When different tool teeth mill the surface of the workpiece, different stress waves are generated along different paths in the surface and subsurface of the workpiece. If different stress waves meet in the interior of the workpiece and superimpose, the superimposed stress waves will propagate in the interior of the workpiece, causing damage to the surface layer and subsurface of the machined surface. These small damages will be amplified in the subsequent processing of the workpiece surface, affecting the workpiece surface topography, subsurface microstructure state and physical and mechanical properties, and further affecting the reliability and service life of the part. Therefore, it is of great significance to explore the superposition of stress waves in the surface and subsurface of the workpiece and to construct the stress wave superposition equation under the action of friction.

[0004] In order to reveal the superposition characteristics of stress waves in the surface and subsurface of the workpiece, the superposition equation of stress waves is constructed and solved. According to the analysis of the stress of the internal particles of the workpiece under the action of friction in the process of high-efficiency milling, the fluctuation equation of the particles is obtained, and the particular solution of the equation is solved. The vibration equation of the wave source is transformed and synthesized to obtain the superposition equation of the stress waves of the particles. The more significant the dynamic load in the process of high-efficiency milling, the more intense the vibration response of the tool. When the wave peaks or wave troughs superimpose at a certain particle, the intensity of the particle will be enhanced on the basis of the original, increasing the stress distribution depth of the particle, which will accelerate the damage of the tool and reduce the machining quality of the workpiece. When the wave peak and the wave trough meet and superimpose at a certain particle, the intensity of the particle will be reduced on the basis of the original, and at this time the damage at the particle will be reduced, thereby improving the surface quality of the machined workpiece. Therefore, solving the stress wave superposition characteristics in the interior of the machined workpiece has a guiding role in reducing the damage of the surface layer and subsurface of the machined surface and improving the surface quality of the workpiece.

[0005] The stress wave is often accompanied by energy change in the propagation process, and can also be a wave process of stress wave energy fluctuation. In addition to the disturbance between particles and particles, energy is also transmitted, which is also a kind of wave. The existing calculation method of stress wave characteristics is mostly for different rock joints and explosion stress waves, and the propagation characteristics of stress wave in the milling process and the energy evolution mechanism of the tooth relief under the action of stress wave need to be revealed. In the process of high efficiency milling, the energy propagation of stress wave has an important influence on the performance damage of the tooth relief. In order to further explore the energy loss of the tooth relief, a stress wave energy calculation method of the tooth relief of the titanium alloy TC4 workpiece is provided. SUMMARY

[0006] The purpose of the present application is to provide a kind of milling titanium alloy TC4 workpiece tooth stress wave energy calculation method, to solve the problems raised in the above background.

[0007] To achieve the above purpose, the present application provides the following technical scheme: a kind of milling titanium alloy TC4 workpiece tooth stress wave energy calculation method, the specific stress wave energy calculation method is as follows:

[0008] S1, the constraint of stress between particles in the machined workpiece makes the internal structure of the assembly in a stable state, and the stress between particles in the machined workpiece belongs to internal force action, and the internal structure is in a stable state when no external force is received;

[0009] S2, external force is applied to the surface of the machined workpiece through the tooth rake face, the particles in the workpiece produce displacement under the action of external force, stress is generated between adjacent particles, which causes stress transmission. Because the medium particles have inertia, the motion of some adjacent particles lags behind, and the disturbance of external load on the surface is thus propagated from near to far in the medium to form a stress wave;

[0010] S3, the particles in the machined workpiece form stress wave under the action of external force, 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, then the stress wave forms stress wave superposition in the machined workpiece. For elastic waves, the interaction of wave sources satisfies the linear superposition principle because they are all linear waves;

[0011] S4, the propagation process of stress wave in the third deformation zone of the machined workpiece in the milling process is the disturbance process of energy change in the propagation process of the particles between the tooth relief and the machined surface in the milling process of the machined workpiece.

[0012] Further, the machined workpiece is a titanium alloy TC4 workpiece.

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

[0014] Further, the stress wave fluctuation equation of the internal particle of the workpiece when the external force is applied is:

[0015]

[0016] Further, when the two cutter teeth generate the force to the machined workpiece surface, two wave sources are formed, the vibration equation of the wave source is the integral form of the wave fluctuation equation of the particle, and the vibration equation of the two wave sources can be obtained according to the wave fluctuation equation of the particle:

[0017] The vibration equation of the wave source 1 is:

[0018]

[0019] The vibration equation of the wave source 2 is:

[0020]

[0021] Further, the stress waves generated by the wave sources meet in the workpiece and are superimposed.

[0022] Further, according to the stress wave theory, S4 solves the elastic energy caused by the stress wave in the propagation process based on the one-dimensional elastic stress wave P wave energy solving method.

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

[0024] The milling titanium alloy stress wave superposition characteristics and the cutter stress wave energy solving method are mainly applied to different rock joints and explosion stress waves according to the existing theoretical research and experimental method about stress wave superposition and energy solving, the crack propagation process of the prefabricated crack rock is analyzed through the finite element simulation, the damage mechanism of the rock under different stress wave peak values and energy is researched, and the influence law of the rock damage is given.

[0025] The milling titanium alloy stress wave superposition characteristics and the cutter stress wave energy solving method can be applied to different rock joints, and the stress wave propagation characteristics of the machined workpiece surface layer and the energy evolution mechanism of the cutter back surface under the action of the stress wave need to be revealed. In the elastic medium, due to the frequent occurrence of instantaneous stress wave superposition, high local stress concentration is caused. Due to the complexity of the cutting process, the research on the stress wave superposition characteristics of the tool-work interface is very little, and it is difficult to directly apply the existing theory to the metal cutting process, so it is difficult to construct the stress wave superposition equation.

[0026] And according to the existing stress wave characteristics solving method is mostly for different rock joints and explosion stress wave, the propagation characteristics of stress wave in the milling process and the energy evolution mechanism of the tooth flank under the action of stress wave need to be revealed;

[0027] The stress wave superposition characteristics and the tooth stress wave energy solving method of the milling titanium alloy, in the efficient milling process, the internal particle of the workpiece is solved one by one, 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 stress wave superposition state under the action of external force (friction) is accurately described, and the strength of the superposition particle is analyzed. And aiming at the energy fluctuation of the tooth flank in the efficient milling process, the energy solving equation is constructed, the theoretical value of the stress wave energy of the corresponding position can be calculated, and the dynamic change characteristics of the friction stress wave energy in the milling cutter tooth are solved. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 It is the internal stress wave propagation mode and particle state diagram of the workpiece in the milling cutter cutting process in the application;

[0029] Figure 2 It is the amplitude change diagram of the wave peak and the wave peak superposition of two wave sources in the application when the frequencies are different;

[0030] Figure 3 It is the amplitude change diagram of the wave peak and the wave peak superposition of two wave sources in the application when the frequencies are the same;

[0031] Figure 4 It is the amplitude change diagram of the wave peak and the wave valley superposition of two wave sources in the application when the frequencies are different;

[0032] Figure 5 It is the amplitude change diagram of the wave peak and the wave valley superposition of two wave sources in the application when the frequencies are the same;

[0033] Figure 6 It is the instantaneous motion state diagram of a particle in the internal workpiece in the application;

[0034] Figure 7 It is the diagram that two wave sources act on the same particle in the workpiece in the application;

[0035] Figure 8 It is the diagram that the wave peak and the wave peak are superimposed when the frequencies of the tooth 1 and the tooth 2 are the same in the application;

[0036] Figure 9 It is the diagram that the wave peak and the wave valley are superimposed when the frequencies of the tooth 1 and the tooth 2 are the same in the application;

[0037] Figure 10 The stress wave superposition diagram for the different frequencies of the tool teeth 1 and 2 in the application;

[0038] Figure 11 The characteristic point position diagram of the tool tooth relief surface in the application;

[0039] Figure 12 The stress wave energy calculation method in the application is used to calculate the stress wave energy when the contact angle is 2°, and the change process diagram is shown in the figure;

[0040] Figure 13 The stress wave energy calculation method in the application is used to calculate the stress wave energy when the contact angle is 24.5°, and the change process diagram is shown in the figure;

[0041] Figure 14 The stress wave energy calculation method in the application is used to calculate the stress wave energy when the contact angle is 47°, and the change process diagram is shown in the figure;

[0042] Figure 15 The stress wave energy calculation method in the application is used to calculate the stress wave energy when the contact angle is 69.5°, and the change process diagram is shown in the figure;

[0043] Figure 16 The stress wave energy calculation method in the application is used to calculate the stress wave energy when the contact angle is 89.5°, and the change process diagram is shown in the figure. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0045] Please refer to Figures 1-16 The application provides a technical solution: a stress wave superposition characteristic and tool tooth stress wave energy calculation method for milling titanium alloy;

[0046] Embodiment one

[0047] The stress between the particles inside the processed workpiece is constrained, so that the inside of the assembly is in a stable state. The stress between the particles of the processed workpiece belongs to the internal force, and the internal structure is in a stable state when no external force is received. When the surface of the processed workpiece is subjected to an external force, the particles inside the workpiece are displaced under the action of the external force, so that stress is generated between the adjacent particles, causing stress transmission. However, due to the inertia of the medium particles, the motion of the adjacent particles lags behind, so that the disturbance of the external load on the surface is transmitted from near to far in the medium to form a stress wave.

[0048] The processed workpiece is titanium alloy TC4. When the stress wave is formed inside the processed workpiece, 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. Therefore, the stress wave is superimposed inside the processed workpiece. For elastic waves, since they are all linear waves, the interaction of the waves satisfies the linear superposition principle.

[0049] As shown in Figure 1 , the state of the particles when the stress wave is superimposed inside the processed workpiece during high-efficiency milling, the stress wave is the propagation of vibration state and vibration phase information. When the stress wave propagates inside the workpiece, the wave reaches a particle, causing the particle to vibrate. When a particle is subjected to the action of two stress waves, the vibration of the particle is the synthesis of the vibrations excited by the waves at the particle.

[0050] As shown in Figures 2-5 , c1 and c2 in Figures 2-5 respectively represent the wave speeds of the two waves, Figures 2-5 Each case shown in includes five stages: before the superposition of the two waves, initial superposition of the two waves, complete superposition of the two waves, end of superposition of the two waves, and separation of the two waves. The amplitude changes during the superposition of the two waves are shown through the five stages.

[0051] Figures 2-5 The wave shape of the transverse wave in Figure 1 is a sine curve or a cosine curve, and the vibration direction of the longitudinal wave particle is consistent with the propagation direction of the wave, so it cannot be directly seen. In order to obtain the propagation shape of the longitudinal wave, a static particle at a certain instant of longitudinal wave propagation is established, as shown in , the relationship between each particle at a certain instant and the equilibrium position particle can be obtained.

[0052] Figure 6 As shown in , the horizontal coordinate represents the distribution position of each particle, and the upper row represents the distribution of the particles when they are not subjected to an external force. At this time, the particles are uniformly distributed. The lower row represents the distribution of the particles when they are subjected to an external force. The vertical coordinate represents the displacement of the particles when they are subjected to an external force.

[0053] Take finite points for study, the displacement of the particle is analyzed, if the particle produces displacement to the right under the action of external force, the direction is positive, if it produces displacement to the left, the direction is negative, connecting each displacement point of the particle can obtain a curve;

[0054] It can be seen that the displacement of the particle under the action of external force is not equal, and the shape of the obtained curve is the same as the wave shape of the transverse wave; Figure 6

[0055] In the process of high efficiency milling of workpiece, the tooth flank of the cutter acts on the surface of the workpiece to produce friction force, and the friction force acts on the workpiece to produce stress wave, so the stress wave fluctuation equation of the particle in the workpiece is:

[0056]

[0057] The vibration equation of the wave source is the integral form of the wave equation of the particle, which can also be called the special solution form, so the vibration equations of the two wave sources can be obtained according to the wave equation of the particle:

[0058] The vibration equation of wave source 1 is:

[0059]

[0060] The vibration equation of wave source 2 is:

[0061]

[0062] Example two

[0063] As shown in Figure 1 , when two teeth act on the surface of the workpiece, two wave sources are formed, the stress waves generated by the two wave sources meet in the workpiece and are superimposed, the vibration equations of wave source 1 and wave source 2 are shown in example one, but when the wave source vibration is transmitted to P particle, a phase difference will be generated, that is Figure 7 Two rows of wave sources shown in

[0064] Figure 7 As shown in the figure, wave source 1 generates stress wave at O1 point, and transmits to particle P through the distance of r1, wave source 2 generates stress wave at O2, and transmits to particle P through the distance of r2, and meets and superimposes with the stress wave of wave source 1, O1 point is the first starting point, and O2 point is the first starting point;

[0065] That is, the vibration equation of wave source 1 at P particle is:

[0066]

[0067] The vibration equation of wave source 2 at P particle is:

[0068] ​

[0069] The combined vibration equation of P particle is:

[0070] y=y1+y2;

[0071] When the frequency of two waves is the same, the phase difference is constant, and the vibration direction is consistent, the two waves will interfere, and the vibration equation is:

[0072]

[0073] Wherein,

[0074]

[0075]

[0076] The phase difference is Independent of time t, r2-r1 is the wave path difference.

[0077] When the frequency of two waves is different, the two waves will not interfere, and the vibration equation is:

[0078]

[0079] By solving the stress wave fluctuation equation of the workpiece surface and subsurface in the milling process, the vibration equations of the two wave sources are obtained respectively. The propagation characteristics of the stress wave in the workpiece during cutting are studied, only the propagation process of the elastic longitudinal wave is considered, the coupling effect between the longitudinal waves is considered in the selected characteristic point position, and the superposition characteristics of one-dimensional elastic longitudinal wave in the processed workpiece are obtained;

[0080] Select the stress wave generated by different teeth, and use MATLAB to solve the stress wave superimposed at the same position at different times. The displacement of the particle at the same position after the superposition of tooth 1, tooth 2 and tooth 1 and tooth 2 is shown in Figures 8-10 .

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

[0082] Figure 8 As shown in the figure, two wave sources meet and superimpose, and the displacement after superimposition is the vector superposition of the displacement of each wave source. After meeting and superimposing, each wave source still maintains its original motion characteristics and continues to move;

[0083] As shown in Figure 9If the vibration frequency of the two wave sources is the same, the strengthened points are always strengthened, the weakened points are always weakened, a stable superposition is formed, it has periodicity, the frequency after superposition is the same as the original frequency, and the strengthened points and the weakened points are alternately present. At the superposition point of the two waves, when the wave peak meets the wave peak, the vibration at this time is strengthened, and when the wave peak meets the wave valley, the vibration is weakened.

[0084] If the vibration frequency of the two wave sources is the same, the strengthened points are always strengthened, the weakened points are always weakened, a stable superposition is formed, it has periodicity, the frequency after superposition is the same as the original frequency, and the strengthened points and the weakened points are alternately present. At the superposition point of the two waves, when the wave peak meets the wave peak, the vibration at this time is strengthened, and when the wave peak meets the wave valley, the vibration is weakened.

[0085] As shown in Figure 10 If the vibration frequency of the two waves is different, the displacement generated by the superposition of the points is the vector sum of the displacements generated by the two waves acting on the point alone, and it has a certain periodicity, but it is irrelevant to the original frequency.

[0086] Since the intensity of the wave is proportional to the square of the amplitude, that is, I∝A 2 Therefore, the intensity of the combined vibration is:

[0087]

[0088] If the wave is coherent, then:

[0089]

[0090] If the wave is incoherent, then:

[0091]

[0092] Example three

[0093] The propagation process of the stress wave in the third deformation zone in the milling process is essentially the disturbance process of the friction point between the tooth back surface and the machined transition surface in the milling process. In the propagation process, energy change often accompanies, which can also be called the fluctuation process of stress wave energy;

[0094] In addition to the disturbance of the point, energy is also transmitted as a way of fluctuation, so the study of the propagation characteristics of the stress wave in the milling process requires the study of the influence characteristics of the energy in the process;

[0095] With the cutting process continues to deepen, the interaction between the milling cutter and the workpiece makes the teeth from the complete state until the peeling so that the upper boundary occurs, and then with the workpiece material is removed by the process of occurrence, through the analysis found that the equivalent stress changes and then give the lower boundary basis, so select the four characteristic points of the tooth flank, and according to the experimental scheme using DEFORM simulation to extract the normal stress under the action of friction force;

[0096] The simulation conditions are shown in the following table:

[0097] Table 1 Simulation boundary conditions

[0098]

[0099] In the simulation process, the number of mesh division of the tooth is 500,000. In order to make the simulation results more accurate, when the workpiece is divided into absolute size grid, the step distance is not more than 1 / 3 of the minimum unit size of the workpiece grid unit. The position of the characteristic point of the tooth flank and the stress wave propagation are shown in Figure 11 The friction stress of the propagation path of the four characteristic points is calculated, which prepares for the energy calculation of the tooth flank. The instantaneous contact angle is selected at different times, that is, the effective cutting period reached by the tooth cutting into the workpiece is divided into five instantaneous contact angles. Therefore, according to the influence of stress wave propagation under different conditions, the calculation method of stress wave energy is given and its influence characteristics are studied.

[0100] In the process of milling, the position of the particle is disturbed to form a stress wave due to the action of external load, and the stress wave propagates to the inside of the tooth in this form. According to the stress wave theory, the elastic energy caused by the stress wave in the propagation process is solved based on the energy calculation method of one-dimensional elastic stress wave P wave.

[0101] The kinetic energy and potential energy produced in the process of stress wave propagation are the same. For the disturbance of the particles inside the tooth, the wave propagates in the form of wave, and the kinetic energy and potential energy are the same in energy transmission. Therefore, the total energy in the propagation process is the sum of the elastic energy and the kinetic energy.

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

[0103]

[0104] In the equation: σ ij is the stress of the unit body; E is the elastic modulus of the material;

[0105] In the milling process, the same elastic potential energy and kinetic energy of the particles on the chord line at any time during the change process of the stress wave propagation. Therefore, the key factor for distinguishing the wave motion of the particles in the material and the particle vibration is this. For any microelement, the energy generated by the stress wave during the propagation process does not follow the energy conservation law. The disturbance of the wave source particle gradually increases with the increase of the load, so that the energy generated increases, and gradually decreases as the energy is gradually transferred to the interior of the medium during the milling process. Therefore, for the transmission process of the stress wave, the wave motion is also a way of energy transmission.

[0106] According to the stress wave energy solving method of the above formula, the stress wave energy at the positions of the four characteristic points is solved, and the change process is as shown in Figures 2-16 It can be seen from the figure that the attenuation trend of the stress wave energy at different characteristic point positions is roughly the same, Figures 2-16 The figure shows that the overall energy size order is P3>P1>P4>P2.

[0107] The third characteristic point is different from the first characteristic point of the tool tooth in that the installation angle of the tool tooth is considered. During processing, it first contacts the workpiece and participates in cutting, so the stress of the particles in the third deformation zone (tool-work contact zone) is higher than that of the other characteristic points. With the passage of time, the friction between the tool tooth relief surface and the machined transition surface becomes more intense, so the stress at the second characteristic point position and the fourth characteristic point position in the friction area is smaller than that at the characteristic point on the cutting edge. Therefore, the energy is lower than that at other positions.

[0108] The present application establishes the superposition equation of the stress wave generated in the machined workpiece surface and subsurface due to the action of friction in the milling process, analyzes the energy dissipation caused by the stress wave propagation of the tool tooth relief surface in the high-efficiency milling process, and thus constructs the energy solving method of the stress wave propagation of the tool tooth relief surface.

[0109] And through the solving of the superposition of the stress wave in the workpiece, the main propagation characteristics of the stress wave in the workpiece in the high-efficiency milling process are reflected, so that the influence range of the stress wave in the machined workpiece can be identified by solving the superposition characteristics of the stress wave, and a theoretical basis for exploring the generation mechanism of the damage of the milling cutter to the internal structure of the workpiece in the milling process is provided.

[0110] Although embodiments of the present application 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 therein without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the stress wave energy of a milling cutter tooth for milling a titanium alloy TC4 workpiece, characterized in that: S1, the constraint of the stress between the internal particles of the machined workpiece makes the internal components thereof in a stable state, the stress between the internal particles of the machined workpiece belongs to internal force action, and the internal structure is in a stable state when no external force is received; S2, an external force is applied to the workpiece surface through the tooth surface of the cutter tooth, the particles in the workpiece interior generate displacement under the action of the external force, stress is generated between adjacent particles, and stress transmission is caused; due to the inertia of the medium particles, the motion of certain adjacent particles lags behind, and 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, the particles in the interior of the machined workpiece form a stress wave under the action of the external force, the stress waves generated by several wave sources propagate in the same medium and simultaneously act on the same particle in the workpiece, and then the stress wave forms stress wave superposition in the interior of the machined workpiece; for elastic waves, since they are all linear waves, the interaction of the wave sources satisfies the linear superposition principle; S4, the transmission and propagation process of the stress wave in the third deformation zone in the milling process is essentially a disturbance process of the particles between the cutter tooth relief surface and the machined transition surface in the milling process; with the continuous deepening of the cutting process, the interaction of the milling cutter and the workpiece causes the tooth to be peeled off from the complete state to generate an upper boundary, and then with the occurrence of the process of cutting off the workpiece material, the change of the equivalent stress is found through analysis and the lower boundary is given, therefore, four feature points of the cutter tooth relief surface are selected, and the normal stress under the action of the friction force is extracted; in order to make the simulation result more accurate, when the workpiece is divided into grids in an absolute size, the step is not more than 1 / 3 of the minimum unit size of the workpiece grid unit, the positions of the feature points of the cutter tooth relief surface and the stress wave propagation are obtained, the friction stress of the propagation path of the four feature points is calculated to prepare for the energy calculation of the cutter tooth relief surface in the subsequent process, the instantaneous contact angles under different time conditions, i.e., the effective cutting periods reached by the tooth cutting into the workpiece, are divided into five instantaneous contact angles, and therefore the calculation method of the stress wave energy and the influence characteristics thereof are given according to the influence of the parameters under different conditions on the stress wave propagation; in the milling process, the position of the particle is disturbed to form a stress wave due to the action of the external load, and the stress wave propagates to the interior of the tooth in this form; according to the stress wave theory, the elastic energy caused by the stress wave in the propagation process is solved based on the one-dimensional elastic stress wave P wave energy calculation method; Since the kinetic energy and the potential energy generated in the stress wave propagation process are the same, the disturbance of the particles in the interior of the tooth propagates in the form of a wave, and the kinetic energy and the potential energy are the same in energy transmission, so the total energy in the propagation process is the sum of the elastic energy and the kinetic energy; Therefore, the total energy of the stress wave propagation is: ​ ​ ​ ​ ​ ​ ​ In the equation: σ ij is the unit stress; E is the modulus of elasticity of the material; According to the stress wave energy calculation method of the above formula, the stress wave energy at the positions of the four characteristic points is calculated respectively. The characteristic point three position is on the cutting edge, which is different from the characteristic point one of the tool tooth in considering the effect of the tool tooth installation angle. The stress of the tool-work contact area particle which first contacts the workpiece and participates in cutting during machining is higher than that of other characteristic points. With the passage of time, the friction between the tool tooth back surface and the machined transition surface becomes more intense, which makes the stress at the positions of the characteristic point two and the characteristic point four in the friction area smaller than that on the cutting edge. Therefore, the energy at the positions of the characteristic point two and the characteristic point four is lower than that at other positions. The machined workpiece is a titanium alloy TC4 workpiece. The stress wave is the vibration state and vibration phase information propagation when an external force is applied to the machined workpiece surface.

2. The method of claim 1, wherein the method is used for milling titanium alloy TC4 workpiece. The stress wave fluctuation equation of the internal particle of the workpiece when an external force is applied to the workpiece is:

3. The method of claim 2, wherein the method is used for milling titanium alloy TC4 workpiece. When the two tool teeth generate an acting force on the machined workpiece surface, two wave sources are formed. The vibration equation of the wave source is the integral form of the wave fluctuation equation of the particle. The vibration equation of the two wave sources can be obtained according to the wave fluctuation equation of the particle. The vibration equation of the wave source 1 is: The vibration equation of the wave source 2 is:

4. The method of claim 3, wherein the method is used for calculating the stress wave energy of a cutter tooth when milling a titanium alloy TC4 workpiece. The stress waves generated by the two wave sources meet in the workpiece and are superimposed.

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