Electric field modeling and evaluation method and system for ultrasonic vibration assisted electrostatic atomization milling

Abstract

The invention discloses an electric field modeling and evaluation method and system for ultrasonic vibration assisted electrostatic atomization milling, and the system comprises a model building module; a model importing module; a model setting module; the airflow field calculation module is used for calculating an airflow field generated during high-speed rotation of the milling cutter in the simulation model by adopting a frozen rotor method; the ultrasonic vibration excitation module introduces ultrasonic vibration; the energy transfer module is used for setting the milling cutter and the outer surface of the workpiece as a coupling boundary condition; the electric field simulation module is used for obtaining a simulation electric field dynamically changing along with the air conductivity; and the electric field evaluation module outputs a qualitative evaluation result and a quantitative evaluation result. According to the method, the influence of ultrasonic vibration and milling cutter rotation on an electric field between a nozzle and a cutter-workpiece is fully considered, and an ultrasonic vibration assisted electrostatic atomization milling electric field finite element model with solid medium vibration, sound pressure disturbance in an air medium and dynamic conductivity multi-physical field combination is constructed; and the dynamic evolution of the electric field distribution under the actual milling working condition can be truly reflected.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of sustainable processing, and particularly relates to an electric field modeling and evaluation method and system for ultrasonic vibration assisted electrostatic atomization milling. BACKGROUND

[0002] With the continuous promotion of the concept of green manufacturing, electrostatic atomization technology has gradually been applied in the field of advanced manufacturing due to its advantages such as good controllability of droplets, high utilization rate of lubricants, and environmental friendliness. The technology makes the cutting fluid charged through a high-voltage electric field, forms fine droplets under the action of electric field force, and realizes directional transport and precise deposition, thereby improving the lubrication efficiency and the surface quality of material processing. However, the contact area between the tool and the workpiece is small and the interface pressure is high during milling, and the penetration ability of the droplets is poor, making it difficult for the droplets to effectively penetrate into the cutting interface, thereby affecting the cooling and lubrication effect of the processing area.

[0003] In order to improve the problem that the droplets are difficult to effectively penetrate into the cutting interface, an ultrasonic vibration assisted machining technology has been proposed in recent years. The technology applies micron-level high-frequency vibration on the basis of traditional machining, so that periodic separation occurs between the tool and the workpiece, thereby changing the mode of continuous cutting to realize intermittent machining of materials. Due to the introduction of the periodic separation effect, the gap of the processing area can be periodically opened, promoting the penetration and transport of the droplets to the processing area and enhancing the electrostatic atomization lubrication and cooling effect. In addition, ultrasonic vibration will cause nonlinear acoustic disturbance of air. The periodic compression and expansion of the air medium leads to changes in local sound pressure, which changes the electrical conductivity of the air in the region, and further affects the electric field strength and its spatial distribution of electrostatic atomization milling. The change of the electric field affects the electrostatic atomization performance, the charging effect of the droplets, and the transport and deposition of the droplets to the cutting area, and finally brings changes in the lubrication and cooling effect. Therefore, it is of great significance to study the electric field distribution characteristics of ultrasonic vibration assisted electrostatic atomization milling for effectively improving the performance of electrostatic atomization machining. However, due to the complexity of the processing environment, the existing test detection methods are difficult to capture the dynamic evolution of the electric field of ultrasonic vibration assisted electrostatic atomization milling. SUMMARY

[0004] The first object of the present application is to provide an electric field modeling and evaluation method for ultrasonic vibration assisted electrostatic atomization milling capable of capturing the dynamic evolution of the electric field.

[0005] The second object of the present application is to provide an electric field modeling and evaluation system for ultrasonic vibration assisted electrostatic atomization milling.

[0006] Technical scheme: The present application discloses an electric field modeling and evaluation method for ultrasonic vibration assisted electrostatic atomization milling, comprising the following steps:

[0007] S1: constructing a three-dimensional simulation model of ultrasonic vibration assisted electrostatic atomization milling based on an actual milling operation, and the three-dimensional simulation model includes a workpiece to be milled, a milling cutter, a nozzle, and an air domain within a specified range of the milling cutter;

[0008] S2: importing the three-dimensional simulation model into a multi-physics field simulation software, and dividing the air domain into a rotating domain and a stationary domain;

[0009] S3: defining the material properties of the air domain of the three-dimensional simulation model as air medium, and defining the material properties of the workpiece, the milling cutter, and the nozzle as solid medium; and performing mesh division on the three-dimensional simulation model;

[0010] S4: calculating the airflow field generated when the milling cutter rotates at high speed in the simulation model by using the frozen rotor method, to obtain the pressure p1 of the airflow field;

[0011] S5: setting the workpiece as a fixed constraint, applying a vibration displacement on the surface of the milling cutter to introduce ultrasonic vibration, and calculating the displacement of the milling cutter in real time under the excitation of ultrasonic vibration to obtain the vector displacement field L of the milling cutter;

[0012] S6: based on the vector displacement field L, setting the milling cutter and the outer surface of the workpiece as a coupled boundary condition, the coupled boundary condition is used to realize energy transfer between the solid medium and the air medium, the vibration of the solid medium milling cutter under the excitation of ultrasonic vibration is transmitted to the air medium through the coupled boundary condition, and the sound pressure disturbance of the air medium is caused;

[0013] S7: applying an electric potential V on the nozzle to introduce an electrostatic field, setting the workpiece and the milling cutter as a grounding condition, the sound pressure disturbance causes the air conductivity σ in the electrostatic field to change dynamically, calculating the sound pressure p2 generated by the sound pressure disturbance in the air medium, constructing a correction model between the pressure p1 of the airflow field, the sound pressure p2 and the conductivity σ of the air, and calculating the simulation electric field based on the correction model as the air conductivity σ changes dynamically;

[0014] S8: evaluating the electric field intensity distribution of the simulation electric field in a qualitative and quantitative manner to obtain qualitative and quantitative evaluation results.

[0015] Further, the rotating domain is wrapped around the outer periphery of the milling cutter, and the stationary domain is wrapped around the rotating domain and the outer periphery of the workpiece.

[0016] Further, the frozen rotor method in step S4 is: taking the milling cutter axis as the rotation center, assigning a moving mesh to the rotating domain, and applying a counter-rotating reference frame to simulate the airflow field generated by the high-speed rotation of the milling cutter during actual milling operation; the rotating speed of the rotating domain is set to the rotating speed during the milling operation of the milling cutter; the surfaces of the workpiece, the milling cutter and the nozzle are set as no-slip walls; the outer wall interface of the stationary domain is set as an open boundary.

[0017] Further, the pressure p1 of the airflow field in step S4 is calculated based on the momentum conservation equation and the continuity equation, and the calculation is as follows:

[0018] The expression of the momentum conservation equation is as follows:

[0019] ,

[0020] The expression of the continuity equation is as follows:

[0021] ,

[0022] wherein, is the density of the air medium; u is the velocity of the airflow field; I is a unit matrix; represents a convection derivative operator, represents a calculation divergence; K is a total stress tensor, and the expression of the total stress tensor K is as follows:

[0023] ,

[0024] wherein, is a molecular dynamic viscosity, represents a gradient operator; is a turbulent viscosity, obtained through a k- turbulent model, and the expression of the turbulent viscosity is as follows:

[0025] ,

[0026] wherein, is a k- turbulent model constant; k is a turbulent kinetic energy; is a turbulent dissipation rate;

[0027] and the transport equation of the turbulent kinetic energy k is as follows:

[0028] ,

[0029] The transport equation of the turbulent dissipation rate ε is as follows:

[0030] ;

[0031] wherein, is a generation item of the turbulent kinetic energy, and the expression of the turbulent kinetic energy is as follows:

[0032]

[0033] wherein, , , , k-1 turbulence model constant.

[0034] Further, the vector displacement field L in step S5 is calculated by the following Navier equation:

[0035] ,

[0036] wherein, is the density of the solid medium; s is the Cauchy stress tensor, and the expression of the Cauchy stress tensor s is as follows:

[0037] s = C : η,

[0038] wherein, C is the elastic matrix, which is determined by the Young's modulus and Poisson's ratio of the material; η is the strain tensor, which is defined as the symmetric gradient of the vector displacement field L, and the expression of the strain tensor η is .

[0039] Further, the boundary condition equation of the coupling boundary condition is used to describe the energy transfer between the solid medium and the air medium in step S6, and the expression of the boundary condition equation is as follows:

[0040] ,

[0041] wherein, n is the boundary normal vector; p2 is the pressure gradient; q d is the volume force density.

[0042] L tt is the second-order time derivative of the vector displacement field L of the milling cutter, and the calculation formula of L tt is as follows:

[0043] .

[0044] Further, the formula for calculating the sound pressure p2 generated by the sound pressure disturbance in the air medium in step S7 is as follows,

[0045] ,

[0046] wherein, c is the sound speed in the air medium;

[0047] The expression of the correction model in step S7 is as follows:

[0048] ,

[0049] wherein, A1 is the maximum electrical conductivity of the air medium; B1 is the adjustment parameter; p t is the total sound pressure, and .

[0050] Further, the way of calculating the simulation electric field in step S7 is: the expression of the current continuity equation describing the dynamic electric field distribution is as follows: , Wherein, J is the current density; ρ e is the charge density; and the current density J and the electric field intensity E satisfy the following relationship: , Wherein, the electric field intensity E is the negative gradient of the electric potential V, that is, E=- ; The electric field intensity E and the charge density ρ e satisfy the following relationship: , Wherein, D is the electric displacement vector, and for isotropic medium, the expression of the electric displacement vector D is , wherein, δ is the dielectric constant; The potential function form of the charge density ρ e can be obtained from and , that is, ; The control equation for describing the transient electric field change can be obtained from , and : ; Substitute E=- into the control equation to obtain the electric field intensity distribution of the simulation electric field .

[0051] Further, the way of qualitative evaluation in step S8 is: obtaining the electric field intensity distribution in the air domain at a certain time point based on the simulation electric field, and taking the nephogram of the electric field intensity distribution as the qualitative evaluation result;

[0052] The way of quantitative evaluation in step S8 is:

[0053] A plurality of space cutting lines are drawn between the outlet end of the nozzle and the milling cutter; the way of drawing the plurality of space cutting lines is: a basic space cutting line coinciding with the center axis of the nozzle is drawn with the center of the outlet end of the nozzle as the starting point, and the length of the basic space cutting line is the straight line distance between the center and the cutter tip; a plurality of starting points are arranged in an annular array on a plurality of concentrically arranged circular rings at the outlet end of the nozzle, and other space cutting lines parallel to and equal in length to the basic space cutting line are drawn respectively from the plurality of starting points;

[0054] Based on the simulation electric field, the electric field intensity data on each space cutting line is extracted;

[0055] Based on the corresponding electric field intensity data, the electric field average values of each section line at different time points are calculated respectively, denoted as first electric field average values; the electric field average values of each section line in the full time domain are calculated respectively, denoted as second electric field average values;

[0056] The electric field difference values of the first electric field average values and the second electric field average values of each spatial section line at different time points are calculated, and the electric field difference values are used to represent the time sequence fluctuation amplitude of the electric field intensity, and the first electric field average values, the second electric field average values and the electric field difference values are taken as quantitative evaluation results.

[0057] Based on the same inventive concept, the application also discloses an electric field modeling and evaluation system for ultrasonic vibration assisted electrostatic atomization milling, comprising:

[0058] A model construction module is used to construct a three-dimensional simulation model of ultrasonic vibration assisted electrostatic atomization milling, and the three-dimensional simulation model comprises a workpiece to be milled, a milling cutter, a nozzle and an air domain in a specified range of the milling cutter;

[0059] A model import module is used to import the three-dimensional simulation model into a physical field simulation software, and divide the air domain into a rotating domain and a stationary domain;

[0060] A model setting module is used to define the material properties of the air domain of the three-dimensional simulation model as air medium, and define the material properties of the workpiece, the milling cutter and the nozzle as solid medium; and perform grid division on the three-dimensional simulation model;

[0061] An airflow field calculation module is used to calculate the airflow field generated when the milling cutter rotates at high speed in the simulation model by using a frozen rotor method, so as to obtain the pressure p1 of the airflow field;

[0062] An ultrasonic vibration excitation module is used to set the workpiece as a fixed constraint, apply a vibration displacement on the surface of the milling cutter to introduce ultrasonic vibration, and calculate the displacement of the milling cutter in real time under the excitation of ultrasonic vibration, so as to obtain the vector displacement field L of the milling cutter;

[0063] An energy transfer module is used to set the outer surfaces of the milling cutter and the workpiece as a coupling boundary condition based on the vector displacement field L, the coupling boundary condition is used to realize energy transfer between the solid medium and the air medium, the vibration of the solid medium milling cutter under the excitation of ultrasonic vibration is transferred to the air medium through the coupling boundary condition, and the acoustic pressure disturbance of the air medium is caused;

[0064] An electric field simulation module is used to apply an electric potential V on the nozzle to introduce an electrostatic field, set the workpiece and the milling cutter as a grounding condition, the acoustic pressure disturbance causes the air conductivity σ in the electrostatic field to change dynamically, calculate the acoustic pressure p2 generated by the acoustic pressure disturbance in the air medium, construct a correction model between the pressure p1 of the airflow field, the acoustic pressure p2 and the conductivity σ of the air, and calculate the simulation electric field based on the correction model with the dynamic change of the air conductivity σ;

[0065] The electric field evaluation module can evaluate the simulated electric field in both qualitative and quantitative manners, and output qualitative evaluation results and quantitative evaluation results.

[0066] Beneficial effects: Compared with the prior art, the present application has the following remarkable advantages: the present application fully considers the influence of ultrasonic vibration and milling cutter rotation on the electric field between the nozzle and the cutter-workpiece, constructs an electric field finite element model of ultrasonic vibration assisted electrostatic atomization milling in solid medium vibration, air medium sound pressure disturbance and dynamic electrical conductivity multi-physical field combination, which can truly reflect the dynamic evolution of the electric field distribution under actual milling working conditions. The present application comprehensively evaluates the electric field distribution and evolution law of ultrasonic vibration assisted electrostatic atomization milling through the electric field intensity distribution nephogram combined with the first electric field average value, the second electric field average value and the difference between the two of each spatial section line, which provides a basis for further understanding the electric field of ultrasonic vibration assisted electrostatic atomization milling. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is a flowchart of the method of the present application;

[0068] Figure 2 is a structural schematic diagram of the three-dimensional simulation model in the embodiment of the present application;

[0069] Figure 3 is a structural schematic diagram of the three-dimensional simulation model after meshing in the embodiment of the present application;

[0070] Figure 4 is a boundary condition schematic diagram of the three-dimensional simulation model in the embodiment of the present application;

[0071] Figure 5 is a pressure distribution diagram of the airflow field in the embodiment of the present application;

[0072] Figure 6 is a sound pressure broken line diagram of random two points in the rotating domain in the embodiment of the present application;

[0073] Figure 7 is an electric field intensity distribution nephogram in the embodiment of the present application;

[0074] Figure 8 is a schematic diagram of the outlet end of the nozzle in the embodiment of the present application;

[0075] Figure 9 is a schematic diagram of the spatial section line in the embodiment of the present application;

[0076] Figure 10 is a broken line diagram of the first electric field average value of 9 spatial section lines in the embodiment of the present application;

[0077] Figure 11 is a bar chart of the second electric field average value of 9 spatial section lines in the embodiment of the present application;

[0078] Figure 12 A schematic diagram of the electric field difference of 9 spatial section lines in the embodiment of the application. DETAILED DESCRIPTION

[0079] The technical solutions of the application are further described below with reference to the drawings.

[0080] Embodiment 1

[0081] The application discloses an electric field modeling and evaluation method for ultrasonic vibration assisted electrostatic atomization milling, as shown in the figure, comprising the following steps, Figure 1

[0082] S1: a three-dimensional simulation model of ultrasonic vibration assisted electrostatic atomization milling is constructed, and the three-dimensional simulation model comprises a workpiece to be milled 1, a milling cutter 2, a nozzle 3 and an air domain in a specified range of the milling cutter. The milling cutter 2 is located above the workpiece 1, and the nozzle 3 is located above the side of the milling cutter 2.

[0083] S2: the three-dimensional simulation model is imported into a multi-physical field simulation software, and the air domain is divided into a rotating domain 4 and a stationary domain 5. The rotating domain 4 is wrapped around the outer periphery of the milling cutter 2, and the stationary domain 5 is wrapped around the outer periphery of the rotating domain 4 and the workpiece 1.

[0084] Preferably, the rotating domain 4 is set as a cylindrical region, the height of the cylindrical region of the rotating domain 4 is consistent with the height of the milling cutter 2, the diameter of the cylindrical region of the rotating domain 4 is greater than the diameter of the milling cutter 2 and less than the diameter of the inscribed circle of the workpiece 1; the stationary domain 5 is also a cylindrical region, the height of the stationary domain 5 is greater than the total height of the rotating domain 4 and the workpiece 1, and the diameter of the stationary domain 5 is greater than the maximum size of the workpiece 1, that is, the stationary domain 5 is wrapped around the outer periphery of the rotating domain 4 and the workpiece 1.

[0085] S3: the material properties of the air domain of the three-dimensional simulation model are defined as air medium, and the material properties of the workpiece, the milling cutter and the nozzle are defined as solid medium; the three-dimensional simulation model is meshed.

[0086] S4: the frozen rotor method is used to calculate the air flow field generated when the milling cutter 2 rotates at high speed in the simulation model, and the pressure p1 of the air flow field is obtained;

[0087] The frozen rotor method is: taking the milling cutter axis as the rotation center, the dynamic mesh is given to the rotating domain 4, and the reverse rotating reference system is applied to simulate the air flow field generated by the high-speed rotation of the milling cutter in the actual milling process, and the related parameters of the steady air flow field are set based on the actual milling operation. The related parameters of the steady air flow field include: setting the rotating speed of the rotating domain 4, and the rotating speed of the rotating domain 4 is consistent with the rotating speed of the milling cutter 2 during the milling operation; setting the surface of the workpiece 1, the milling cutter 2 and the nozzle 3 as a no-slip wall; setting the outer wall interface of the stationary domain 5 as an open boundary. ​

[0088] The pressure p1 is calculated based on the momentum conservation equation and the continuity equation, and the calculation is as follows:

[0089] The expression of the momentum conservation equation is as follows:

[0090] ,

[0091] The expression of the continuity equation is as follows:

[0092] ,

[0093] wherein, is the density of the air medium, the density is kg / m 3 ; is the velocity of the airflow field, the unit is m / s; p1 is the pressure of the airflow field, the unit is Pa; I is a unit matrix; K is the total stress tensor; represents the convection derivative operator, represents the calculation of divergence.

[0094] wherein, the stress tensor refers to the internal friction force in the airflow caused by molecules and turbulence, and the expression of the total stress tensor K is as follows:

[0095]

[0096] wherein, is the molecular dynamic viscosity, represents the gradient operator; is the turbulence viscosity, and can be obtained by k- turbulence model;

[0097] The specific calculation formula of is as follows:

[0098]

[0099] wherein, is the k- turbulence model constant, k is the turbulence kinetic energy, is the turbulence dissipation rate;

[0100] and the transport equation of the turbulence kinetic energy k is as follows:

[0101] ,

[0102] The transport equation of the turbulence dissipation rate ε is as follows:

[0103] ;

[0104] wherein, is the generation term of turbulent kinetic energy, and the expression of turbulent kinetic energy is as follows:

[0105]

[0106] wherein, , , , are k- turbulent model constants.

[0107] The pressure p1 of the airflow field is obtained through the above calculation.

[0108] S5: Set the workpiece 1 as a fixed constraint, apply a vibration displacement on the milling cutter 2 to introduce ultrasonic vibration, and calculate the displacement of the milling cutter 2 occurring under the excitation of ultrasonic vibration in real time to obtain the vector displacement field L of the milling cutter 2.

[0109] The expression of the Navier equation for calculating the vector displacement field L is as follows:

[0110]

[0111] wherein, is the density of the solid medium, with the unit of kg / m3; L is the vector displacement field of the milling cutter 2, with the unit of m; s is the Cauchy stress tensor, with the unit of Pa;

[0112] wherein, the expression of the Cauchy stress tensor s is as follows:

[0113] s = C:η,

[0114] wherein, C is an elastic matrix, which is determined by the Young's modulus and Poisson's ratio of the material; η is a strain tensor, which is defined as the symmetric gradient of the vector displacement field L, and the expression of the strain tensor η is .

[0115] The vector displacement field L of the milling cutter 2 under the excitation of ultrasonic vibration is obtained through the above Navier equation, and the vector displacement field L provides a driving boundary in the form of acceleration as a coupled boundary condition.

[0116] S6: Based on the vector displacement field L, set the milling cutter 2 and the outer surface of the workpiece 1 as a coupled boundary condition, which is used to realize the energy transfer between the solid medium and the air medium, and the vibration of the solid medium milling cutter 2 under the excitation of ultrasonic vibration is transmitted to the air medium through the coupled boundary condition, and causes the acoustic pressure disturbance of the air medium.

[0117] In the ultrasonic vibration assisted electrostatic atomization milling, the milling cutter 2 generates high frequency periodic mechanical vibration, and then causes the sound pressure disturbance of the nozzle 3 and the air medium around the milling cutter 2, so as to cause the dynamic change of the air conductivity in the local space, and finally cause the dynamic change of the electric field. The sound pressure disturbance refers to a rapid and small change of the local air pressure relative to the static air pressure. The ultrasonic vibration displacement is applied to the milling cutter 2, that is, the vibration is generated on the solid medium, while the sound pressure disturbance is propagated in the air medium. The vibration and the sound pressure disturbance occur in different physical domains, and the coupling boundary condition is needed to transfer the energy, convert the normal acceleration of the solid medium under the ultrasonic vibration into the normal acceleration in the air medium, so as to cause the sound pressure change in the air medium. Without the coupling boundary condition, the vibration cannot affect the sound pressure field, and the sound pressure field cannot react on the solid medium. Specifically, the coupling boundary condition can ensure the physical consistency of the solid medium and the air medium, and avoid the non-physical condition of “vibration without sound” or “sound without source”.

[0118] The boundary condition equation of the coupling boundary condition is used to describe the energy transfer between the solid medium and the air medium in step S6, and the expression of the boundary condition equation is as follows:

[0119] ,

[0120] Wherein, n is the boundary normal vector; p2 is the pressure gradient, with the unit of Pa / m; q d is the volume force density, with the unit of N / m 3 .

[0121] L tt is the second order time derivative of the vector displacement field L of the milling cutter, that is, the acceleration, with the unit of m / s 2 , and the calculation formula of L tt is as follows:

[0122] .

[0123] In the normal direction of the boundary, that is, in the boundary normal vector, the acceleration of the air medium is equal to the acceleration of the wall surface of the solid medium, so as to realize the continuity of the velocity and the displacement, and thus couple the ultrasonic vibration of the solid medium and the sound pressure disturbance of the air medium. The boundary condition equation of the coupling boundary condition is the bridge connecting the solid medium and the air medium, which defines how the two interact on the boundary where the solid medium and the air medium contact.

[0124] S7: A potential V is applied on the nozzle 3 to introduce an electrostatic field, the workpiece 1 and the milling cutter 2 are set as ground conditions, the air conductivity σ in the electrostatic field dynamically changes due to the acoustic pressure disturbance, the acoustic pressure p2 generated by the acoustic pressure disturbance in the air medium is calculated, a correction model between the pressure p1 of the airflow field, the acoustic pressure p2 and the conductivity σ of the air is constructed, and a simulation electric field changing with the dynamic change of the air conductivity σ is calculated based on the correction model.

[0125] Under the action of the coupling boundary condition, the vibration generated by the milling cutter 2 during milling, that is, the vibration of the solid medium, will cause the acoustic pressure disturbance of the air medium. The acoustic pressure disturbance is described by an acoustic wave equation, that is, a formula for calculating the acoustic pressure p2 generated by the acoustic pressure disturbance in the air medium, and the expression of the acoustic wave equation is as follows:

[0126]

[0127] Wherein, p2 is the pressure caused by air flow, with the unit of Pa; is the pressure gradient, with the unit of Pa / m; c is the sound speed in the air medium, with the unit of m / s.

[0128] The correction model is an exponential model, and the expression of the correction model is as follows:

[0129] ,

[0130] Wherein, A1 is the maximum conductivity of the air medium, with the unit of S / m; B1 is an adjustment parameter, with the unit of Pa; p t Total sound pressure, the total sound pressure is composed of the pressure p1 generated by the rotation of the milling cutter 2 and the acoustic pressure p2 generated by the acoustic pressure disturbance, that is ;

[0131] Considering the influence of the acoustic pressure disturbance on the conductivity σ of the air medium, the conductivity based on the dynamic change of the acoustic pressure disturbance needs to be introduced to replace the conductivity of the static air, and the conductivity caused by the acoustic pressure disturbance is mapped to the current continuity equation for describing the dynamic electric field distribution. The expression of the current continuity equation is as follows:

[0132]

[0133] Wherein, J is the current density, with the unit of A / m²; ρ e is the charge density, with the unit of C / m 3 . The current density J satisfies Ohm's law, that is, the current density J and the electric field strength E satisfy the following relationship:

[0134]

[0135] Wherein, E is electric field intensity, unit is V / m; Sigma is conductivity, S / m; Wherein V is electric potential, and electric field intensity E is the negative gradient of electric potential V, that is, E= .

[0136] Therefore, the current continuity equation can be expressed as .

[0137] In order to further describe the relationship between electric field intensity E and charge density p e , the Gauss law in Maxwell equation group is introduced, and its differential form is as follows:

[0138]

[0139] Wherein, D is electric displacement vector, unit is C / m 2 . For isotropic medium, the expression of electric displacement vector D is as follows:

[0140]

[0141] Wherein, delta is dielectric constant, unit is F / m.

[0142] From And , the potential function form of charge density p e can be obtained, that is, .

[0143] From And , the following control equation for describing transient electric field change can be obtained:

[0144] ;

[0145] Substitute E=- Into the control equation, the electric field intensity distribution .

[0146] The electric field modeling method of the ultrasonic vibration assisted electrostatic atomization milling of the application has high universality and expandability, and can simulate the electric field of ultrasonic vibration assisted electrostatic atomization milling under different ultrasonic vibration forms, ultrasonic parameters, milling cutter rotating speed, voltage (electric potential) and milling cutter structure, thereby providing support for optimizing ultrasonic vibration assisted electrostatic atomization milling.

[0147] S8: Qualitative and quantitative methods are used to evaluate the electric field intensity distribution of the simulated electric field, and qualitative evaluation results and quantitative evaluation results are obtained.

[0148] Wherein the qualitative evaluation method is: based on the simulated electric field, the electric field intensity distribution in the air domain at a certain time point is obtained, and the nephogram of the electric field intensity distribution is taken as the qualitative evaluation result;

[0149] The quantitative evaluation is as follows:

[0150] A plurality of space cross-sections are drawn between the outlet end of the nozzle 3 and the milling cutter 2; the electric field intensity of the space cross-sections can reflect the electric field intensity distribution among the nozzle 3, the milling cutter 2 and the workpiece 1.

[0151] The plurality of space cross-sections are drawn in the following manner: a basic space cross-section coinciding with the central axis of the nozzle 3 is drawn with the center of the outlet end of the nozzle 3 as the starting point, and the length of the basic space cross-section is the straight-line distance between the center and the tip of the milling cutter 2; a plurality of starting points are arranged in a ring array on a plurality of concentrically arranged circular rings at the outlet end of the nozzle 3, and other space cross-sections parallel to and equal in length to the basic space cross-section are drawn respectively with the plurality of starting points.

[0152] The electric field intensity data on each space cross-section are extracted based on the simulated electric field.

[0153] Based on the corresponding electric field intensity data, the electric field mean values of each cross-section at different time points are calculated respectively, denoted as first electric field mean values; further, the electric field mean values of each cross-section in the full time domain are calculated respectively, denoted as second electric field mean values. The full time domain refers to the time from the start of milling to the end of milling; preferably, the full time domain is the time for one rotation of the milling cutter 2.

[0154] The electric field difference values between the first electric field mean values and the second electric field mean values of each space cross-section at different time points are calculated, and the electric field difference values are used to represent the time sequence fluctuation amplitude of the electric field intensity, and the first electric field mean values, the second electric field mean values and the electric field difference values are taken as the quantitative evaluation results.

[0155] Embodiment 2

[0156] The application discloses an electric field modeling and evaluation system for ultrasonic vibration assisted electrostatic atomization milling, which comprises a model construction module, a model import module, a model setting module, an airflow field calculation module, an ultrasonic vibration excitation module, an energy transmission module, an electric field simulation module and an electric field evaluation module.

[0157] The model construction module is used to construct a three-dimensional simulation model of ultrasonic vibration assisted electrostatic atomization milling, and the model comprises a workpiece 1 to be milled, a milling cutter 2, a nozzle 3 and an air domain within a specified range of the milling cutter; the model construction module performs step S1 in the embodiment 1.

[0158] The model import module is used to import the three-dimensional simulation model into a multi-physical field simulation software, and divide the air domain into a rotating domain 4 and a stationary domain 5; the model import module performs step S2 in the embodiment 1.

[0159] A model setting module is configured to define material properties of an air domain of the three-dimensional simulation model as air medium, and define material properties of the workpiece 1, the milling cutter 2 and the nozzle 3 as solid medium, and perform meshing on the three-dimensional simulation model; the model setting module performs step S3 in Embodiment 1.

[0160] An airflow field calculation module is configured to calculate an airflow field generated by high-speed rotation of the milling cutter 2 in the simulation model by using a frozen rotor method, and obtain a pressure p1 of the airflow field; the airflow field calculation module performs step S4 in Embodiment 1.

[0161] An ultrasonic vibration excitation module is configured to set the workpiece 1 as a fixed constraint, apply a vibration displacement on a surface of the milling cutter 2 to introduce ultrasonic vibration, and calculate a displacement of the milling cutter 2 occurring under excitation of the ultrasonic vibration in real time, and obtain a vector displacement field L of the milling cutter 2; the ultrasonic vibration excitation module performs step S5 in Embodiment 1.

[0162] An energy transfer module is configured to set the milling cutter 2 and an outer surface of the workpiece 1 as a coupling boundary condition based on the vector displacement field L, the coupling boundary condition is used to realize energy transfer between the solid medium and the air medium, vibration of the solid medium milling cutter 2 under excitation of the ultrasonic vibration is transferred to the air medium through the coupling boundary condition, and acoustic pressure disturbance of the air medium is caused; the energy transfer module performs step S6 in Embodiment 1.

[0163] An electric field simulation module is configured to apply an electric potential V on the nozzle 3 to introduce an electrostatic field, and set the workpiece 1 and the milling cutter 2 as a grounding condition, the acoustic pressure disturbance causes dynamic change of air conductivity σ in the electrostatic field, calculate acoustic pressure p2 generated by the acoustic pressure disturbance in the air medium, construct a correction model between the pressure p1 of the airflow field, the acoustic pressure p2 and the air conductivity σ, and obtain a simulation electric field changing with the dynamic change of the air conductivity σ based on the correction model; the electric field simulation module performs step S7 in Embodiment 1.

[0164] An electric field evaluation module is configured to evaluate the simulation electric field in a qualitative and quantitative manner, and output qualitative evaluation results and quantitative evaluation results. The electric field evaluation module performs step S8 in Embodiment 1.

[0165] Embodiment 3

[0166] The application discloses an electric field modeling and evaluation method for practical application of ultrasonic vibration assisted electrostatic atomization milling, comprising the following steps:

[0167] Step S1 in Embodiment 1 is performed. In the embodiment, the nozzle 3 is arranged obliquely on the right side of the milling cutter 2. The three-dimensional simulation model is as shown in FIG. 1, and related parameters are set according to actual milling conditions, and specific values are shown in Table 1. Figure 2

[0168] Table 1 related parameters of the three-dimensional simulation model​

[0169] The interpole spacing in Table 1 refers to the distance between the milling cutter 2 and the nozzle 3 along the nozzle axis.

[0170] Perform step S2 in Example 1. In this example, the rotation domain 4 is set as a cylindrical region, and the height of the cylindrical region of the rotation domain 4 is the same as the height of the milling cutter 2. The diameter of the cylinder of the rotation domain 4 is greater than the diameter of the milling cutter 2 and smaller than the diameter of the inscribed circle of the workpiece 1. The stationary domain 5 is also a cylindrical region, and the height of the stationary domain 5 is greater than the total height of the rotation domain 4 and the workpiece 1, and the diameter of the stationary domain 5 is greater than the maximum size of the workpiece 1. That is, the stationary domain 5 surrounds the outer periphery of the rotation domain 4 and the workpiece 1.

[0171] Perform step S3 in Example 1. In this example, the workpiece material is titanium alloy TC4, the milling cutter material is cemented carbide YG8, and the nozzle material is stainless steel 304.

[0172] This embodiment uses a free tetrahedral mesh to mesh the entire 3D simulation model. Because the milling cutter wall and nozzle have relatively small volumes, local meshing is applied to the milling cutter wall, nozzle exit, and surrounding areas. The 3D simulation model after meshing in this embodiment is as follows: Figure 3 As shown.

[0173] Perform step S4 in Example 1. In this example, the rotational speed and direction of the rotational domain 4 are set to 2000 r / min and clockwise, respectively. The surfaces of workpiece 1, milling cutter 2, and nozzle 3 are set as non-slip walls; the outer wall interface of the stationary domain 5 is set as an open boundary, and the boundary conditions of the three-dimensional simulation model in this example are as follows: Figure 4 As shown.

[0174] The turbulence model constants in this embodiment are shown in Table 2 below.

[0175] Table 2. Constants for the Turbulence Model

[0176] The airflow pressure p1 calculated in this embodiment is as follows: Figure 5 As shown, its maximum value is 0.136229 Pa and its minimum value is -0.273389 Pa.

[0177] Perform step S5 in Example 1, and the fixed constraint conditions and vibration displacement conditions applied in this example are as follows: Figure 4The vibration displacement conditions applied in this embodiment are shown in Table 3, and the vibration displacement conditions applied in this embodiment are as follows: (B x sin(2 x pi x f0 x t + (pi / 2))) is applied in the X direction, and (A x sin(2 x pi x f0 x t)) is applied in the Z direction, where t represents time, and the related parameters of the vibration displacement conditions are set as shown in Table 3.

[0178] Table 3 Displacement vibration condition parameter table

[0179]

[0180] L is the vector displacement field of the milling cutter 2, which includes three spatial components (x, y, and z directions) and represents the displacement of each point on the milling cutter 2 under the action of ultrasonic vibration. The expression of the vector displacement field L calculated in this embodiment is L(x, y, z, t), where t represents time.

[0181] Steps S6 and S7 in Embodiment 1 are performed, and the potential conditions and grounding conditions applied in this embodiment are as shown in Figure 4 . The change of the sound pressure p2 of the random two points in the rotation domain with time calculated in this embodiment is as shown in Figure 6 .

[0182] Considering the influence of the sound pressure disturbance caused by the longitudinal torsional ultrasonic vibration on the air conductivity, the conductivity based on the sound pressure field is introduced to replace the conductivity of the static air for subsequent electric field calculation. The expression of the modified model is as follows:

[0183] ,

[0184] In this embodiment, A1 is 10 -7 S / m, and B1 is 108.6 Pa.

[0185] Step S8 in Embodiment 1 is performed, and the qualitative evaluation method is to visually present the overall situation of the electric field of the ultrasonic vibration assisted electrostatic atomization milling by using the electric field intensity distribution cloud map. The electric field intensity distribution cloud map at the time of 0.025 ms after the start of milling in this embodiment is as shown in Figure 7 .

[0186] The quantitative evaluation method is as follows:

[0187] In this embodiment, a nozzle with coaxial structure of the outer nozzle and the inner nozzle is used, and a schematic view of the outlet end thereof is as shown in Figure 8 . Four points are arranged in a counterclockwise annular array around N0 at the outlet end of the inner nozzle, with the ring radius being d1 / 4 (d1 is the inner wall diameter of the inner nozzle); and four points are arranged in a counterclockwise annular array around N0 at the outlet end between the outer nozzle and the inner nozzle. ​Four points, ring radius is (D+d2) / 4 (D is the outer nozzle inner wall diameter, d2 is the inner nozzle outer wall diameter).

[0188] With the nozzle outlet end as the starting plane, 9 line segments parallel to the nozzle center axis are constructed, respectively denoted as lineN0, . Among them, lineN0 coincides with the nozzle center axis, and the length is the straight line distance from point N0 to the cutter tip; and are parallel to lineN0 and equal in length. The schematic diagram of the space section is shown in Figure 9 .

[0189] The first electric field average of the 9 space section lines of this embodiment at different time points is shown in Figure 10 , and the second electric field average of the 9 space section lines in the full time domain is shown in Figure 11 .

[0190] The electric field difference of the 9 space section lines of this embodiment at different time points is shown in Figure 12 .

Claims

1. A method for electric field modeling and evaluation in ultrasonic vibration-assisted electrostatic atomization milling, characterized in that: Includes the following steps: S1: Based on actual milling operations, construct a three-dimensional simulation model of ultrasonic vibration-assisted electrostatic atomization milling, and the three-dimensional simulation model includes the workpiece to be milled (1), milling cutter (2), nozzle (3) and air domain within the specified range of the milling cutter. S2: Import the three-dimensional simulation model into the multiphysics simulation software and divide the air domain into a rotating domain (4) and a stationary domain (5). S3: Define the material properties of the air domain in the three-dimensional simulation model as air medium, and define the material properties of the workpiece (1), milling cutter (2), and nozzle (3) as solid medium; and perform mesh generation on the three-dimensional simulation model; S4: The airflow field generated by the high-speed rotation of the milling cutter (2) in the simulation model is calculated using the frozen rotor method, and the pressure p1 of the airflow field is obtained; S5: Set the workpiece (1) as a fixed constraint, apply vibration displacement to the surface of the milling cutter (2) to introduce ultrasonic vibration, and calculate the displacement of the milling cutter (2) under ultrasonic vibration excitation in real time to obtain the vector displacement field L of the milling cutter (2); S6: Based on the vector displacement field L, the outer surfaces of the milling cutter (2) and the workpiece (1) are set as coupled boundary conditions. The coupled boundary conditions are used to realize the energy transfer between the solid medium and the air medium. The vibration generated by the solid medium milling cutter (2) under the excitation of ultrasonic vibration is transmitted to the air medium through the coupled boundary conditions, and causes the sound pressure disturbance of the air medium. S7: Apply potential V to the nozzle (3) to introduce an electrostatic field. Set the workpiece (1) and the milling cutter (2) to ground conditions. The sound pressure disturbance causes the air conductivity σ in the electrostatic field to change dynamically. Calculate the sound pressure p2 generated by the sound pressure disturbance in the air medium. Construct a correction model between the pressure p1 and sound pressure p2 of the airflow field and the air conductivity σ. Calculate the simulated electric field that changes dynamically with the air conductivity σ based on the correction model. S8: The electric field intensity distribution of the simulated electric field is evaluated using both qualitative and quantitative methods to obtain qualitative and quantitative evaluation results.

2. The method for electric field modeling and evaluation in ultrasonic vibration-assisted electrostatic atomization milling according to claim 1, characterized in that: The rotating domain (4) encloses the outer periphery of the milling cutter (2), and the stationary domain (5) encloses the outer periphery of the rotating domain (4) and the workpiece (1).

3. The method for electric field modeling and evaluation in ultrasonic vibration-assisted electrostatic atomization milling according to claim 1, characterized in that: The frozen rotor method described in step S4 is as follows: with the axis of the milling cutter (2) as the rotation center, the moving mesh is assigned to the rotation domain (4), and a reverse rotation reference frame is applied to simulate the airflow field generated by the high-speed rotation of the milling cutter (2) during actual milling operations; the rotation speed of the rotation domain (4) is set to the rotation speed of the milling cutter (2) during milling operations; the surfaces of the workpiece (1), the milling cutter (2) and the nozzle (3) are set as non-slip walls; and the outer wall interface of the stationary domain (5) is set as an open boundary.

4. The electric field modeling and evaluation method for ultrasonic vibration-assisted electrostatic atomization milling according to claim 3, characterized in that: The pressure p1 of the airflow field in step S4 is calculated based on the momentum conservation equation and the continuity equation. The calculation method is as follows: The equation for the conservation of momentum is expressed as follows: ， The expression for the continuity equation is as follows: ， in, ρ is the density of the air medium; u is the velocity of the airflow field; I is the identity matrix; Represents the convection derivative operator. This indicates the calculation of divergence; K is the total stress tensor, and the expression for the total stress tensor K is as follows: ， in, For molecular dynamic viscosity, Represents the gradient operator; For turbulent viscosity, via k- Obtained from turbulence models, and The expression is as follows: ， in, For k- Turbulence model constants; k is the turbulent kinetic energy; The turbulent dissipation rate; The transport equation for turbulent kinetic energy k is as follows: ， The transport equation for the turbulent dissipation rate ε is as follows: ； in, This is the term that generates turbulent kinetic energy, and turbulent kinetic energy... The expression is as follows: ， in, , , , All are k- Turbulence model constants.

5. The electric field modeling and evaluation method for ultrasonic vibration-assisted electrostatic atomization milling according to claim 4, characterized in that: In step S5, the vector displacement field L is calculated using the following Navierian equation: ， in, Let be the density of the solid medium; s be the Cauchy stress tensor, and the expression for the Cauchy stress tensor s is as follows: s=C:η, Where C is the elasticity matrix, determined by the Young's modulus and Poisson's ratio of the material; η is the strain tensor, defined as the symmetric gradient of the vector displacement field L, and the expression for the strain tensor η is: .

6. The electric field modeling and evaluation method for ultrasonic vibration-assisted electrostatic atomization milling according to claim 5, characterized in that: The energy transfer mechanism between the solid medium and the air medium in step S6 is described by the boundary condition equations with coupled boundary conditions, and the expression of the boundary condition equations is as follows: ， Where n is the boundary normal vector; p2 is the pressure gradient; q d It is the volumetric force density; L tt Let L be the second-order time derivative of the vector displacement field L of the milling cutter, and L tt The calculation formula is as follows: 。 7. The electric field modeling and evaluation method for ultrasonic vibration-assisted electrostatic atomization milling according to claim 6, characterized in that: The formula for calculating the sound pressure p2 generated by the sound pressure disturbance in the air medium in step S7 is as follows: ， Where c is the speed of sound in air; The expression for the corrected model in step S7 is as follows: ， Where A1 is the maximum conductivity of the air medium; B1 is the adjustment parameter; p t Total sound pressure, and .

8. The electric field modeling and evaluation method for ultrasonic vibration-assisted electrostatic atomization milling according to claim 7, characterized in that: The method for calculating the simulated electric field in step S7 is as follows: The expression for the current continuity equation describing the dynamic electric field distribution is as follows: ， Where J is the current density; ρ e Let J be the charge density; and let J be the current density and E be the electric field strength, satisfying the following relationship: ， Wherein, the electric field strength E is the negative gradient of the electric potential V, i.e., E = - ; Electric field strength E and charge density ρ e The following relationship must be satisfied: ， Where D is the electric displacement vector, and for an isotropic medium, the expression for the electric displacement vector D is: Where δ is the dielectric constant; Depend on and The charge density ρ can be obtained e The potential function form, i.e. ; Depend on , and The following governing equations can be obtained to describe the transient electric field change: ； E=- Substituting into the governing equations, we obtain the electric field intensity distribution of the simulated electric field. .

9. The method for electric field modeling and evaluation in ultrasonic vibration-assisted electrostatic atomization milling according to claim 1, characterized in that: The qualitative evaluation method described in step S8 is as follows: the electric field intensity distribution in the air domain at a certain time point is obtained based on the simulated electric field, and the cloud map of the electric field intensity distribution is used as the qualitative evaluation result. The quantitative evaluation method described in step S8 is as follows: Multiple spatial lines are drawn between the outlet end of the nozzle (3) and the milling cutter (2). The method for drawing multiple spatial lines is as follows: draw a basic spatial line that coincides with the central axis of the nozzle (3) with the center of the outlet end of the nozzle (3) as the starting point, and the length of the basic spatial line is the straight distance between the center and the tip of the milling cutter (2). Select several concentric rings at the outlet end of the nozzle (3), set multiple starting points in a ring array on the rings, and draw other spatial lines that are parallel to the basic spatial line and of equal length with multiple starting points. Electric field intensity data is extracted from each spatial cutoff line based on the simulated electric field. Based on the corresponding electric field intensity data, the average electric field value of each cross section at different time points is calculated and denoted as the first average electric field value. Calculate the mean electric field of each section in the entire time domain, and denote it as the second mean electric field. The electric field difference between the first and second electric field mean values ​​at different time points is calculated for each spatial intercept. The electric field difference is used to characterize the temporal fluctuation amplitude of the electric field intensity, and the first electric field mean value, the second electric field mean value, and the electric field difference are used as quantitative evaluation results.

10. An electric field modeling and evaluation system for ultrasonic vibration-assisted electrostatic atomization milling according to any one of claims 1 to 9, characterized in that: include, The model building module is used to build a three-dimensional simulation model of ultrasonic vibration-assisted electrostatic atomization milling. The three-dimensional simulation model includes the workpiece to be milled (1), the milling cutter (2), the nozzle (3), and the air domain within the specified range of the milling cutter. The model import module is used to import the three-dimensional simulation model into the physics simulation software and divide the air domain into the rotation domain (4) and the stationary domain (5). The model setting module is used to define the material properties of the air domain of the three-dimensional simulation model as air medium, and the material properties of the workpiece (1), milling cutter (2), and nozzle (3) as solid medium; and to perform mesh generation on the three-dimensional simulation model; The airflow field calculation module uses the frozen rotor method to calculate the airflow field generated when the milling cutter (2) in the simulation model rotates at high speed, and obtains the pressure p1 of the airflow field. The ultrasonic vibration excitation module is used to set the workpiece (1) as a fixed constraint, apply vibration displacement to the surface of the milling cutter (2) to introduce ultrasonic vibration, and calculate the displacement of the milling cutter (2) under ultrasonic vibration excitation in real time to obtain the vector displacement field L of the milling cutter (2); The energy transfer module, based on the vector displacement field L, sets the outer surfaces of the milling cutter (2) and the workpiece (1) as coupled boundary conditions. The coupled boundary conditions are used to realize energy transfer between the solid medium and the air medium. The vibration generated by the solid medium milling cutter (2) under the excitation of ultrasonic vibration is transmitted to the air medium through the coupled boundary conditions, and causes acoustic pressure disturbance of the air medium. The electric field simulation module is used to apply a potential V to the nozzle (3) to introduce an electrostatic field. The workpiece (1) and the milling cutter (2) are set as grounded conditions. The sound pressure disturbance causes the air conductivity σ in the electrostatic field to change dynamically. The sound pressure p2 generated by the sound pressure disturbance in the air medium is calculated. A correction model between the pressure p1, sound pressure p2 and air conductivity σ of the airflow field is constructed. Based on the correction model, the simulated electric field that changes dynamically with the air conductivity σ is calculated. The electric field evaluation module can evaluate the simulated electric field using both qualitative and quantitative methods, and output qualitative and quantitative evaluation results.

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