CN115007431A - Ultrasonic vibration auxiliary cutting device with two-stage amplification ultrasonic transducer and design method of two-stage amplification ultrasonic transducer - Google Patents
Ultrasonic vibration auxiliary cutting device with two-stage amplification ultrasonic transducer and design method of two-stage amplification ultrasonic transducer Download PDFInfo
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Abstract
The invention discloses an ultrasonic vibration auxiliary cutting device with a secondary amplification ultrasonic transducer and a design method of the secondary amplification ultrasonic transducer. The design method mainly comprises the following steps: according to the input end radius R of the conical part of a preset conical transition ladder-shaped amplitude transformer (504) 1 Radius of output end R 2 The cross-sectional radius R of the tool head (507) 3 Length l of cross section of piezoelectric ceramic group (503) 2 And the number of circles k calculated from the material properties n Harmonic impedance Z n And determining the size parameter of the two-stage amplification ultrasonic transducer. The ultrasonic vibration auxiliary processing device provided by the invention can be applied to milling of typical difficult-to-process materials, so that the processing efficiency is improved, the processing surface quality is improved, and the cutting is reducedForce and cutting heat.
Description
Technical Field
The invention relates to the technical field of ultrasonic auxiliary milling, in particular to an ultrasonic vibration auxiliary cutting device with a two-stage amplification ultrasonic transducer and a design method of the two-stage amplification ultrasonic transducer.
Background
Advanced materials such as high-performance alloys (such as high-temperature alloys, Qinzi alloys, high-strength steel and the like), composite materials, hard and brittle materials (such as optical glass, engineering ceramics and functional product bodies) and the like have excellent performance, and are increasingly widely applied to the fields of aviation, aerospace, war industry, electronics, automobiles and the like. The composite material has the advantages of low density, high specific strength and specific modulus, strong designability, good corrosion resistance, good fatigue resistance, good structural size stability and the like.
These structural members and parts not only have high requirements on machining accuracy and quality, but also have high requirements on machining efficiency. Because the hard and brittle materials of the composite materials have the characteristics of high hardness, large brittleness, good wear resistance and the like, the cutting processability of the materials is poor, the processing requirement of parts is high, and the processing by using the traditional mechanical processing method and the processing tool is difficult. Therefore, how to realize high-quality and high-efficiency precision machining of parts made of difficult-to-machine materials has become a subject of current domestic and foreign attention.
The traditional processing technical method can not meet the technical requirements of processing typical parts made of difficult-to-process materials in the fields of aerospace and the like, so that a one-dimensional longitudinal ultrasonic vibration cutting device is provided in the prior art.
However, the device has the problems of inconvenient observation, inconvenient tool clamping, difficult tool setting and the like, and can only be used for processing cylindrical surfaces and end surfaces generally, and can not process irregular surfaces such as free curved surfaces or grooves.
Disclosure of Invention
The invention aims to provide an ultrasonic vibration auxiliary cutting device with a two-stage amplification ultrasonic transducer, which comprises a pull nail, a rotation stopping body, a cutter handle shell, a power transmission system, the two-stage amplification ultrasonic transducer and an ultrasonic generator.
The blind rivet is in threaded connection with the knife handle shell.
The rotation stopping body is connected with the stator of the power transmission system, so that the stator of the power transmission system is fixed.
The handle housing is bolted to the rotor of the power transmission system.
The cutter handle shell is connected with the second-stage amplification ultrasonic transducer through bolts.
And the ultrasonic generator outputs an ultrasonic signal to the secondary amplification ultrasonic transducer.
The rotation stopping body comprises a rotation stopping ring, a plurality of fastening screws and a plurality of rotation stopping rods.
A plurality of first threaded holes and a plurality of second threaded holes are formed in the rotation stopping ring.
And the fastening screw fixes the rotation stopping ring on the main shaft of the machining center through the second threaded hole.
The rotation stopping rod is used for connecting the rotation stopping body with a stator of a power transmission system through a first threaded hole.
The anti-rotation ring is a circular ring, wherein a plurality of first threaded holes are formed in the upper surface of the circular ring, and a plurality of second threaded holes are formed in the side wall of the circular ring.
The power transmission system comprises a motor and a rotation stopping sheet.
The rotation stopping sheet is fixed on the motor stator through a rotation stopping rod of the rotation stopping body.
The two-stage amplification ultrasonic transducer comprises a pre-tightening bolt, a countersunk head type rear cover plate, a piezoelectric ceramic group, a conical transition ladder-shaped amplitude transformer, a pressing cap, a clamp spring and a cutter head.
The countersunk head type rear cover plate, the piezoelectric ceramic group and the conical transition trapezoidal amplitude transformer are sequentially connected through a pre-tightening bolt.
The pre-tightening bolt provides pre-tightening force for the piezoelectric ceramic group.
The clamp spring is positioned in a groove at the output end of the conical transition trapezoidal amplitude transformer, and the cutter head and the conical transition trapezoidal amplitude transformer are connected and fixed through the pressing cap.
The input end of the conical transition ladder-shaped amplitude transformer is connected with the piezoelectric ceramic group, and the output end of the conical transition ladder-shaped amplitude transformer is connected with the cutter head.
When the ultrasonic vibration auxiliary cutting device works, the ultrasonic generator outputs a high-frequency ultrasonic signal to the secondary amplification ultrasonic transducer.
The two-stage amplification ultrasonic transducer converts high-frequency ultrasonic signals into mechanical vibration with corresponding frequency, the amplitude of the mechanical vibration is increased through the conical transition ladder-shaped amplitude transformer and is transmitted to the tip of the cutter head, so that the cutter head generates ultrasonic vibration, and ultrasonic-assisted cutting machining is realized.
The design method of the two-stage amplification ultrasonic transducer in the ultrasonic vibration auxiliary cutting device comprises the following steps:
1) and establishing a simulation model of the two-stage amplification ultrasonic transducer, wherein the cross section of the simulation model comprises a first equal cross section, a variable cross section of conical transition, a second equal cross section and a third equal cross section.
2) Establishing a cross-sectional area function S of a conical transition ladder variable amplitude transformer n (x n ) Namely:
in the formula, R 1 、R 2 、R 3 Respectively showing the input end radius, the output end radius and the cross section radius of the cutter head of the conical part of the conical transition ladder-shaped variable amplitude rod. l 1 、l 2 、l 3 、l 4 、l 5 、l 6 The length of the cross section of the countersunk head type rear cover plate, the length of the cross section of the piezoelectric ceramic group, the length of the cylindrical surface of the conical transition trapezoidal amplitude transformer, the length of the cross section of the input end of the conical part of the conical transition trapezoidal amplitude transformer, the length of the cross section of the output end of the conical part of the conical transition trapezoidal amplitude transformer and the length of the cross section of the cutter head are respectively shown. x is the number of n Are particles.
3) The longitudinal vibration wave equation of the variable cross-section ultrasonic transducer is as follows:
in the formula, mu n (x n ) As a function of particle displacement. S n (x n ) Is a function of the cross-sectional area of the variable amplitude rod of the conical transition ladder. Number of circles
ω n Is the circular frequency.
The propagation velocities of longitudinal waves in different media. E n The young's modulus of different materials. Rho n The densities of different dielectric materials.
4) A nodal plane is designed at the input end of a conical surface of the conical transition ladder amplitude transformer, the left side of the nodal plane comprises a first equal section, and the right side of the nodal plane comprises a variable section, a second equal section and a third equal section of conical transition.
Simplifying equation (2) yields:
5) according to formula (3), the general formula is solved:
in the formula, F n (x n ) Is a longitudinal elastic force. Z n ＝ρ n c n S (x) is the acoustic impedance of each part of the two-stage amplification ultrasonic transducer. A. the n 、B n Are coefficients.
6) Establishing boundary conditions of the vibration speed and the force of the equal cylindrical section parts of the conical transition ladder-shaped amplitude transformer, namely:
in the formula, v f The vibration speed of the output end surface of the countersunk head type rear cover plate is adopted. Mu.s 1 (0)、μ 1 (l 1 )、μ 2 (0)、μ 2 (l 2 )、μ 3 (0)、μ 3 (l 3 )、F 1 (0)、F 2 (0)、F 1 (l 1 )、F 2 (l 2 )、F 3 (0) Representing a boundary parameter;
7) the method comprises the following steps of (4) and (5) in a combined mode, establishing a frequency equation of cylindrical section parts such as a conical transition ladder deformation amplitude rod and the like, namely:
in the formula, Z 1 、Z 2 Is the impedance;
8) establishing a longitudinal vibration wave equation of the variable cross section of the conical transition, namely:
in the formula, parameter
R 1 、R 2 And l 4 Respectively the input end radius, the output end radius and the length of the conical structure of the conical part.
9) According to formula (7), the general formula is solved:
in the formula, v n (x n ) Variable section vibration velocity for conical transition, F n (x n ) A longitudinal elastic force of a variable cross section of a conical transition. C n 、D n Are coefficients.
10) Establishing boundary conditions of vibration speed and force of the variable section, the second equal section and the third equal section of the conical transition, namely:
in the formula, v e For two-stage amplification of the vibration velocity v at the output end of the ultrasonic transducer 0 The vibration speed of the input end of the variable amplitude rod of the conical transition ladder is adopted. Mu.s 4 (0)、μ 4 (l 4 )、μ 5 (0)、μ 5 (l 5 )、F 4 (0)、F 4 (l 4 )、F 5 (0)、F 5 (l 5 )、F 6 (0)、F 6 (l 6 ) Representing a boundary parameter; z 3 Is the impedance;
11) and (3) combining (4), an equation (8) and an equation (9), and solving to obtain a frequency equation of the right conical section and the equal cylindrical section of the pitch surface, namely:
wherein the number of circles k is k 4 ＝k 5 。
12) Calculating the amplitude amplification coefficient M of the two-stage amplification ultrasonic transducer, namely:
13) according to the preset input end radius R of the conical part of the conical transition ladder variable amplitude rod 1 Radius of output end R 2 The cross-sectional radius R of the tool head 3 Length l of cross section of piezoelectric ceramic group 2 And the number of circles k calculated from the material properties n Harmonic impedance Z n Determining the size parameters of the two-stage amplification ultrasonic transducer, including the length l of the cross section of the countersunk head type back cover plate 1 Length l of cylindrical surface of conical transition trapezoidal amplitude transformer 3 Input end cross section length l of conical part of conical transition ladder variable amplitude rod 4 The length l of the cross section of the output end of the conical part of the conical transition ladder variable amplitude rod 5 The cross-sectional length l of the tool head 6 And an amplitude amplification factor M.
14) Determining the outer diameter size of the piezoelectric ceramic group; the outer diameter of the piezoelectric ceramic group is not more than
Wherein, the wavelength λ of the ultrasonic wave in the piezoelectric ceramic material is as follows:
wherein c is the sound velocity in the piezoceramic material, f is the ultrasonic frequency,
is the elastic characteristic parameter of the piezoelectric ceramic material.
The first constant section comprises a countersunk head type rear cover plate cross section, a piezoelectric ceramic group cross section and a conical transition ladder amplitude-changing rod cylindrical surface.
The variable cross section of the conical transition comprises the input end cross section of the conical part of the conical transition trapezoidal amplitude transformer.
The second equal section comprises the cross section of the output end of the conical part of the conical transition trapezoidal amplitude transformer.
The third constant cross-section comprises a cross-section of the cutter head.
The material of the countersunk head type rear cover plate comprises 40Cr alloy steel.
The material of the piezoelectric ceramic group comprises lead zirconate titanate (PZT-8).
The material of the conical transition ladder-shaped amplitude transformer comprises 40Cr alloy steel.
The size parameters of the two-stage amplification ultrasonic transducer are verified by harmonic response analysis.
The technical effects of the invention are undoubted, and the beneficial effects of the invention are as follows:
1) the ultrasonic vibration auxiliary processing device provided by the invention can be applied to milling of typical difficult-to-process materials, so that the processing efficiency is improved, the processing surface quality is improved, and the cutting force and the cutting heat are reduced.
2) The invention considers the characteristics of the cutter structure and the like, comprehensively provides a design method of a two-stage amplification ultrasonic transducer, designs the two-stage amplification ultrasonic transducer according to the method, and improves the output amplitude of the ultrasonic vibration auxiliary cutting device;
3) based on the ANSYS modal simulation harmonic response analysis, the designed two-stage amplification ultrasonic transducer has stable longitudinal vibration and meets the performance requirement of the ultrasonic vibration auxiliary cutting device, and the modal analysis frequency and the design frequency deviate by 1.33 percent and the harmonic response frequency and the design frequency deviate by 1 percent in the simulation result, which indicates that the transducer is reasonable in design;
4) the output amplitude of the designed and processed secondary ultrasonic transducer is measured by a laser vibration meter, and the transducer has the amplitude of 14.5 micrometers when the ultrasonic generator outputs 50% of power and 25.01 micrometers when the ultrasonic generator outputs 100% of power, so that the function of amplitude adjustment is realized;
5) the overall structure of the ultrasonic vibration auxiliary cutting device is designed by combining working conditions of a machining center, and the ultrasonic vibration auxiliary cutting device with the working frequency of 20kHz and the output amplitude of more than 15 mu m is designed;
6) compared with the transducer structure in the conventional ultrasonic vibration auxiliary cutting device, the design parameters obtained by the design method of the two-stage amplification ultrasonic transducer considering the cutter structure and the size provided by the invention can ensure that the output of longitudinal vibration is gathered at the tip of the cutter head, and simultaneously, the size of the whole transducer can be reduced as much as possible and the working is stable.
Drawings
FIG. 1 is a schematic structural view of an ultrasonic vibration-assisted machining apparatus according to the present invention;
FIG. 2 is a schematic view of a rotation stop body according to the present invention;
FIG. 3 is an exploded view of the ultrasonic vibration assisted machining apparatus of the present invention;
FIG. 4 is an exploded view of the two-stage amplified ultrasound transducer of the present invention;
FIG. 5 is a schematic diagram of a two-stage amplified ultrasound transducer according to the present invention;
FIG. 6 is a cloud of mode shapes under modal analysis for a two-stage amplified ultrasound transducer of the present invention;
FIG. 7 is a vector diagram of the longitudinal vibration velocity of the two-stage amplified ultrasonic transducer of the present invention;
FIG. 8 is a cloud of the resonance response analysis mode of the two-stage amplified ultrasonic transducer of the present invention;
FIG. 9 is a two-stage amplified ultrasonic transducer harmonic response analysis deformation displacement of the present invention;
FIG. 10 is a graph of power percentage of an ultrasonic generator versus transducer amplitude for the present invention;
FIG. 11 is a frequency domain diagram of the longitudinal vibration of the two-stage amplified ultrasonic transducer of the present invention;
in the figure: the device comprises a rivet 1, a rotation stopping body 2, a knife handle shell 3, a power transmission system 4, a two-stage amplification ultrasonic transducer 5, an ultrasonic generator 6, a rotation stopping ring 201, a set screw 202, a rotation stopping rod 203, a first threaded hole 201a, a second threaded hole 201B, a rotation stopping sheet 401, a pre-tightening bolt 501, a countersunk back cover plate 502, a piezoelectric ceramic group 503, a conical transition ladder-shaped amplitude-changing rod 504, a pressing cap 505, a snap spring 506, a knife head 507, a first uniform section A, a conical transition variable section B, a second uniform section C and a third uniform section D.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 11, the ultrasonic vibration assisted cutting device with the two-stage amplification ultrasonic transducer comprises a rivet 1, a rotation stopping body 2, a tool shank shell 3, a power transmission system 4, a two-stage amplification ultrasonic transducer 5 and an ultrasonic generator 6.
The blind rivet 1 is in threaded connection with the knife handle shell 3.
The swivel 2 is connected to the stator of the power transmission system 4, thereby fixing the stator of the power transmission system 4.
The handle housing 3 is bolted to the rotor of the power transmission system 4.
The handle shell 3 is connected with a second-stage amplification ultrasonic transducer 5 through a bolt.
The ultrasonic generator 6 outputs an ultrasonic signal to the secondary amplification ultrasonic transducer 5.
The rotation stopping body 2 comprises a rotation stopping ring 201, a plurality of set screws 202 and a plurality of rotation stopping rods 203.
The anti-rotation ring 201 is provided with a plurality of first threaded holes 201a and a plurality of second threaded holes 201 b.
The set screw 202 fixes the rotation stop ring 201 to the machining center spindle through the second screw hole 201 b.
The rotation preventing rod 203 connects the rotation preventing body 2 to the stator of the power transmission system 4 through the first screw hole 201 a.
The rotation stopping ring 201 is a circular ring, wherein the upper surface of the circular ring is provided with a plurality of first threaded holes 201a, and the side wall of the circular ring is provided with a plurality of second threaded holes 201 b.
The power transmission system 4 includes a motor and a rotation stop tab 401.
The rotation stopping sheet 401 is fixed on the motor stator through the rotation stopping rod 203 of the rotation stopping body 2.
The two-stage amplification ultrasonic transducer 5 comprises a pre-tightening bolt 501, a countersunk head type rear cover plate 502, a piezoelectric ceramic group 503, a conical transition ladder-shaped amplitude transformer 504, a pressing cap 505, a clamp spring 506 and a cutter head 507.
The countersunk rear cover plate 502, the piezoelectric ceramic group 503 and the conical transition ladder amplitude transformer 504 are sequentially connected through a pretightening bolt 501.
The pre-tightening bolt 501 provides pre-tightening force for the piezoelectric ceramic group 503.
The clamp spring 506 is positioned in a groove at the output end of the conical transition ladder-shaped amplitude transformer 504, and the cutter head 507 and the conical transition ladder-shaped amplitude transformer 504 are fixedly connected through the pressing cap 505.
The input end of the conical transition ladder-shaped amplitude transformer 504 is connected with the piezoelectric ceramic group 503, and the output end is connected with the cutter head 507.
When the ultrasonic vibration auxiliary cutting device works, the ultrasonic generator 6 outputs a high-frequency ultrasonic signal to the secondary amplification ultrasonic transducer 5.
The two-stage amplification ultrasonic transducer 5 converts a high-frequency ultrasonic signal into mechanical vibration with corresponding frequency, the amplitude of the mechanical vibration is increased through the conical transition ladder-shaped amplitude transformer 504 and is transmitted to the tip of the cutter head, so that the cutter head generates ultrasonic vibration, and ultrasonic-assisted cutting machining is realized.
The design method of the two-stage amplification ultrasonic transducer in the ultrasonic vibration auxiliary cutting device comprises the following steps:
1) and establishing a simulation model of the two-stage amplification ultrasonic transducer 5, wherein the cross section of the simulation model comprises a first equal cross section A, a variable cross section B of conical transition, a second equal cross section C and a third equal cross section D.
2) Establishing a cross-sectional area function S of the conical transition ladder variable amplitude transformer 504 n (x n ) Namely:
in the formula, R 1 、R 2 、R 3 Respectively showing the input end radius, the output end radius and the cross section radius of the cutter head 507 of the conical part of the conical transition ladder-shaped amplitude transformer 504. l. the 1 、l 2 、l 3 、l 4 、l 5 、l 6 The length of the cross section of the countersunk head type rear cover plate 502, the length of the cross section of the piezoelectric ceramic group 503, the length of the cylindrical surface of the conical transition ladder deformation amplitude rod 504, the length of the cross section of the input end of the conical part of the conical transition ladder deformation amplitude rod 504, the length of the cross section of the output end of the conical part of the conical transition ladder deformation amplitude rod 504 and the length of the cross section of the cutter head 507 are respectively shown. x is the number of n Are particles.
3) The longitudinal vibration wave equation of the variable cross-section ultrasonic transducer is as follows:
in the formula, mu n (x n ) As a function of particle displacement. S n (x n ) Is a function of the cross-sectional area of the variable amplitude rod of the conical transition ladder. Number of circles
ω n Is the circular frequency.
The propagation speeds of longitudinal waves in different media. E n The young's modulus of different materials. Rho n The densities of different dielectric materials.
4) A nodal plane is designed at the input end of the conical surface of the conical transition ladder amplitude transformer 504, the left side of the nodal plane comprises a first equal section, and the right side of the nodal plane comprises a variable section, a second equal section and a third equal section of conical transition.
Simplifying equation 2 yields:
5) according to formula 3, the general formula:
in the formula, F n (x n ) Is a longitudinal elastic force. Z n ＝ρ n c n S (x) is the acoustic impedance of each part of the two-stage amplification ultrasonic transducer 5. A. the n 、B n Are coefficients.
6) Establishing boundary conditions of the vibration speed and the force of the cylindrical section parts of the conical transition ladder-shaped amplitude transformer 504 and the like, namely:
in the formula, v f Is the vibration velocity of the output end surface of the countersunk back cover plate 502.
7) Combining the vertical type 4 and the formula 5, establishing a frequency equation of the cylindrical section parts of the conical transition ladder-shaped variable amplitude rod 504 and the like, namely:
in the formula, Z 1 、Z 2 Is the impedance;
8) establishing a longitudinal vibration wave equation of the variable cross section of the conical transition, namely:
in the formula, parameter
R 1 、R 2 And l 4 Respectively the input end radius, the output end radius and the length of the conical structure of the conical part.
9) According to formula 7, the general formula:
in the formula, v n (x n ) Variable section vibration velocity for conical transition, F n (x n ) A longitudinal elastic force of a variable cross section of a conical transition. C n 、D n Are coefficients.
10) Establishing boundary conditions of the vibration speed and the force of the variable section, the second equal section and the third equal section of the conical transition, namely:
in the formula, v e For two-stage amplification of the vibration velocity v at the output end of the ultrasonic transducer 5 0 The input end vibration velocity of the amplitude transformer 504 of the conical transition ladder. Mu.s 4 (0)、μ 4 (l 4 )、μ 5 (0)、μ 5 (l 5 )、F 4 (0)、F 4 (l 4 )、F 5 (0)、F 5 (l 5 )、F 6 (0)、F 6 (l 6 ) Representing a boundary parameter; z 3 Is the impedance;
11) and (3) solving joint vertical equations 4, 8 and 9 to obtain a pitch surface right conical and equal cylindrical section part frequency equation, namely:
wherein the number of circles k is k 4 ＝k 5 。
12) Calculating the amplitude amplification factor M of the two-stage amplification ultrasonic transducer 5, namely:
13) according to the preset input end radius R of the conical part of the conical transition ladder-shaped amplitude transformer 504 1 Radius R of the output end 2 The cross-sectional radius R of the tool head 507 3 Length l of cross section of piezoelectric ceramic group 503 2 And the number of circles k calculated from the material properties n Harmonic impedance Z n Determining the dimension parameters of the two-stage amplification ultrasonic transducer, including the length l of the cross section of the countersunk head type back cover plate 502 1 The length l of the cylindrical surface of the amplitude transformer 504 of the conical transition ladder 3 The length l of the cross section of the input end of the conical part of the conical transition ladder-shaped amplitude-change rod 504 4 The length l of the cross section of the output end of the conical part of the conical transition ladder amplitude-change rod 504 5 The cross-sectional length l of the tool head 507 6 And an amplitude amplification factor M.
14, determining the outer diameter size of the piezoelectric ceramic group 503; the outer diameter of the piezoelectric ceramic group 503 is not more than
Wherein, the wavelength λ of the ultrasonic wave in the piezoelectric ceramic material is as follows:
wherein c is the sound velocity in the piezoceramic material, f is the ultrasonic frequency,
is the elastic characteristic parameter of the piezoelectric ceramic material.
The first equal section comprises the cross section of a countersunk head type rear cover plate 502, the cross section of a piezoelectric ceramic group 503 and the cylindrical surface of a conical transition ladder-shaped amplitude transformer 504.
The variable cross-section of the conical transition comprises the input end cross-section of the conical portion of the conical transition ladder horn 504.
The second equal section comprises the output end cross section of the conical portion of the conical transition ladder horn 504.
The third constant cross-section comprises the cross-section of the cutter head 507.
The material of the countersunk back cover plate 502 includes 40Cr alloy steel.
The material of the piezo-ceramic stack 503 includes lead zirconate titanate (PZT-8).
The material of the conical transition ladder-shaped horn 504 comprises 40Cr alloy steel.
The size parameters of the two-stage amplification ultrasonic transducer are verified by harmonic response analysis.
Example 2:
as shown in fig. 1, the ultrasonic vibration assisted cutting device comprises a rivet 1, a rotation stopping body 2, a tool shank housing 3, a power transmission system 4, a two-stage amplification ultrasonic transducer 5 and an ultrasonic generator 6. The ultrasonic generator 6 is connected with a stator part in the power transmission system 4 for power transmission. As shown in fig. 2, first the stationary part: the rotation stopping body 2 is fixed on a main shaft of the vertical machining center through six set screws 202 and is connected with a rotation stopping sheet on the power transmission system 4 through a rotation stopping rod 203, so that the stator part of the power transmission system 4 is guaranteed to be fixed. As shown in fig. 3, next is the moving rotating part: the blind rivet 1 is connected with the knife handle shell through surface threads; a rotor in the power transmission system 4 is connected with the cutter handle shell through four positioning screws; and four threaded holes on the lower end surface of the cutter handle shell are used for being connected with a flange structure of the secondary amplification ultrasonic transducer 5 through four bolts. As shown in fig. 4, the countersunk head type rear cover plate 502, the piezoelectric ceramic plate 503 and the conical transition ladder deformation amplitude rod 504 are connected through a pretightening bolt 501, and provide a pretightening force of 50N · m; the clamp spring 506 is positioned in a groove at the output end of the conical transition ladder-shaped amplitude transformer 504, and the cutter head 507 and the conical transition ladder-shaped amplitude transformer 504 are fixedly connected through the pressing cap 505.
As shown in fig. 5, which is a schematic structural diagram of the two-stage amplified ultrasound transducer 5, in the design, the conical transition ladder-shaped horn 504 is directly used as a front cover plate portion of the transducer, so that the area function of the two-stage amplified ultrasound transducer 5 is:
according to the design theory, the longitudinal vibration wave equation of the ultrasonic transducer with any variable cross section is as follows:
in the formula (2), mu n (x n ) Is a particle displacement function; s n (x n ) As a function of the cross-sectional area of the horn;
k n is the number of circles, ω n Is the frequency of the circle, c n Is the propagation velocity of longitudinal waves in different media, wherein
E n Is the Young's modulus, ρ, of different materials n Density of different dielectric materials;
as shown in fig. 5, the nodal plane is designed at the conical surface input end of the conical transition ladder amplitude transformer 504, the nodal plane is the position where the deformation displacement is 0, the left side of the nodal plane is the countersunk head type rear cover plate 502, the piezoelectric ceramic plate 503 and the cylindrical surface of the input end of the amplitude transformer, which are all equal sections a, i.e., S n (x n ) Equation (2) can be simplified to constant:
according to formula (3), the general formula is:
in the formula F n (x n ) Longitudinal elastic force; z n ＝ρ n c n S (x) the acoustic impedance of each part of the two-stage amplification ultrasonic transducer (5); a. the n 、B n Is a coefficient;
according to the nodal surface designed as shown in fig. 5, the boundary conditions of the vibration velocity and the force of the equal cylindrical cross section portion on the left side of the nodal surface are:
in the formula v f The vibration speed of the output end surface of the rear cover plate. Mu.s 1 (0)、μ 1 (l 1 )、μ 2 (0)、μ 2 (l 2 )、μ 3 (0)、μ 3 (l 3 )、F 1 (0)、F 2 (0)、F 1 (l 1 )、F 2 (l 2 )、F 3 (0) Representing a boundary parameter;
the frequency equation of the cylindrical section part such as the left side of the section can be obtained according to each boundary condition in the joint type (4) and the formula (5) as follows:
as shown in fig. 5, the variable cross-section (B) longitudinal vibration wave equation of the conical transition on the right side of the nodal plane is:
in the formula
R 1 、R 2 And l 4 The input end radius, the output end radius and the conical structure length of the conical part are respectively;
the general solution can be found from equation (7) as:
in the formula v n (x n ) The vibration speed, F, of the portion of variable cross-section (B) which is a conical transition n (x n ) Longitudinal elastic force of the variable cross section (B) part of the conical transition; c n 、D n Is a coefficient;
the boundary conditions of the vibration speed and the force of the variable section (B), the equal section (C) and the equal section (D) of the conical transition on the right side of the nodal surface are as follows:
in the formula v e For two-stage amplification of the vibration velocity v at the output end of the ultrasonic transducer (5) 0 The input end of the conical transition ladder variable amplitude rod (504) vibrates. The frequency equation of the right conical section and the equal cylindrical section of the nodal surface can be obtained by solving equations of a united type (4), an equation (8) and an equation (9) and is as follows:
in the formula, the amplitude transformer 504 of the conical transition ladder is made of the same material, i.e., k is k 4 ＝k 5 ；
In consideration of the whole transducer structure, the secondary amplification ultrasonic transducer 5 is composed of an M10 pre-tightening bolt 501, a countersunk head type rear cover plate 502, four piezoelectric ceramic plates 503, a conical transition ladder-shaped amplitude transformer 504, a pressing cap 505, a clamp spring 506 and a cutter head 507. The pre-tightening bolt is used for providing pre-tightening force for the piezoelectric ceramics. The amplitude transformer structure mainly ensures that mechanical vibration energy is effectively transmitted forwards, and the rear cover plate mainly ensures that the energy is transmitted forwards, so that the materials of the cone transition ladder amplitude transformer 504 and the countersunk rear cover plate 502 in the design are both 40 Cr. The overall transducer material properties are shown in table 1.
TABLE 1 two-stage amplification ultrasonic transducer horn and backplate Material Properties
After the materials of the ultrasonic transducer horn and the rear cover plate are determined, other sizes of the whole transducer need to be designed. The outer diameter of the piezoelectric ceramic plate is not designed to be larger than one quarter of the wavelength of the ultrasonic wave in the piezoelectric ceramic material, wherein the expression of the wavelength is
Wherein c is 3150m/s, f is 20kHz and ultrasonic frequency,
is the elastic characteristic parameter of the piezoelectric ceramic material. R 1 The ultrasonic signal input end of the amplitude transformer is required to be the same as the piezoelectric ceramic piece in size. And the most central part of the transducer is the piezoceramic material, and the performance parameters of the piezoceramic material determine the performance of the whole transducer structure. Therefore, as an application scenario of the ultrasonic vibration assisting device, lead zirconate titanate (PZT-8) materials with high electromechanical coupling coefficient and small dielectric loss are required to be selected, the sizes are outer diameter phi 38mm, inner diameter phi 15mm and height 5mm, and the material properties are shown in table 2.
TABLE 2 piezoceramic PZT-8 Material Properties
R 2 The size of the output end of the ultrasonic signal of the amplitude transformer takes the amplitude magnification factor and the size of the ER16 tool handle head standard part into consideration. The overall structure of the transducer is based on the design principle, values are taken according to the traditional design method, and the design size parameters of the two-stage amplification ultrasonic transducer 5 can be obtained by combining the formula and are shown in table 3.
TABLE 3 design size parameters of two-stage amplified ultrasonic transducer (unit: mm)
The amplification structure in the whole two-stage amplification ultrasonic transducer (5) is a cone transition ladder-shaped amplitude transformer (504) for the first-stage amplification and a third uniform-section part for the second-stage amplification, and the amplitude amplification coefficient is as follows:
as shown in fig. 6, for the model established by theoretical design, the established model is subjected to modal analysis and harmonic response analysis by using ANSYS simulation software. Corresponding material attributes of different parts are given to ANSYS simulation software, then self-adaptive grid division is carried out on the model by adopting the setting of the maximum size of 3mm, and finally free modal solution can be carried out on the model. The longitudinal vibration mode frequency of the two-stage amplification ultrasonic transducer 5 is 19734Hz, so that when the external excitation frequency is within the range of 19734Hz, the two-stage amplification ultrasonic transducer 5 realizes longitudinal vibration, the error between the design frequency and the longitudinal vibration mode frequency is 1.33%, and the correctness of theoretical design is verified. Meanwhile, as shown in fig. 7, the longitudinal vibration velocity vector diagram of the two-stage amplified ultrasonic transducer 5 is shown, the maximum axial value of the output end is located at the tip of the tool head 507, the vibration effect is good, and the nodal plane position with the deformation displacement of 0 coincides with the pre-designed flange structure, that is, the design result coincides with the simulation result. And by combining the harmonic response analysis result of the two-stage amplification ultrasonic transducer 5 shown in fig. 8, the piezoelectric ceramic material is endowed with piezoelectric characteristics in ANSYS, and after a corresponding voltage of 300V is applied, the resonant frequency of the piezoelectric ceramic material is 19800Hz, the resonant frequency is close to the longitudinal vibration modal frequency of the two-stage amplification ultrasonic transducer, the error is 1% of the designed frequency, and meanwhile, the theoretical maximum amplitude under the resonant frequency is 16 μm as shown in fig. 9, thereby showing that the theoretical design of the transducer is correct.
For the ultrasonic generator 6 with different output powers, the longitudinal vibration amplitude of the corresponding two-stage amplified ultrasonic transducer 5 is measured, and the measurement result and the change rule thereof are shown in fig. 10. The output amplitude of the longitudinal vibration of the two-stage amplification ultrasonic transducer 5 is increased along with the increase of the power, and the amplitude of the longitudinal vibration of the ultrasonic transducer reaches 25.01 μm when the output power is 100%.
The ultrasonic generator 6 can realize normal and stable operation of the two-stage amplification ultrasonic transducer 5 by selecting 50% of output power, and a longitudinal vibration time domain diagram of the ultrasonic generator is shown in fig. 11. The test of the laser vibration meter shows that under the conditions of 650 percent of output power of the ultrasonic generator and 18110Hz working frequency, the longitudinal vibration amplitude of the two-stage amplification ultrasonic transducer is 14.5 mu m, the amplitude output is stable, the requirement of an ultrasonic vibration auxiliary processing device is met, and the two-stage amplification ultrasonic transducer is suitable for ultrasonic processing.
In summary, the invention designs the core part transducer in the ultrasonic vibration auxiliary cutting device by adopting the design method of the two-stage amplification ultrasonic transducer, and then realizes the overall design of the ultrasonic vibration auxiliary cutting device by designing the rotation stopping body, the power transmission system and the cutter handle shell structure, thereby being suitable for ultrasonic vibration auxiliary milling of typical difficult-to-machine materials.
Claims (10)
1. Ultrasonic vibration auxiliary cutting device with two-stage amplification ultrasonic transducer is characterized in that: the pull nail comprises a pull nail (1), a rotation stopping body (2), a cutter handle shell (3), a power transmission system (4), a two-stage amplification ultrasonic transducer (5) and an ultrasonic generator (6).
The blind rivet (1) is connected with the knife handle shell (3).
The rotation stopping body (2) is connected with a stator of the power transmission system (4) so as to fix the stator of the power transmission system (4);
the cutter handle shell (3) is connected with a rotor of a power transmission system (4);
the cutter handle shell (3) is connected with a secondary amplification ultrasonic transducer (5);
the ultrasonic generator (6) outputs ultrasonic signals to the two-stage amplification ultrasonic transducer (5).
2. The ultrasonic vibration assisted cutting device with a two-stage amplified ultrasonic transducer of claim 1, characterized in that: the rotation stopping body (2) comprises a rotation stopping ring (201), a plurality of set screws (202) and a plurality of rotation stopping rods (203);
a plurality of first threaded holes (201a) and a plurality of second threaded holes (201b) are formed in the anti-rotation ring (201);
the fastening screw (202) fixes the rotation stopping ring (201) on the main shaft of the machining center through a second threaded hole (201 b);
the rotation stopping rod (203) connects the rotation stopping body (2) with a stator of a power transmission system (4) through a first threaded hole (201 a).
3. The ultrasonic vibration assisted cutting device with a two-stage amplified ultrasonic transducer of claim 2, characterized in that: the anti-rotation ring (201) is a circular ring, wherein a plurality of first threaded holes (201a) are formed in the upper surface of the circular ring, and a plurality of second threaded holes (201b) are formed in the side wall of the circular ring.
4. The ultrasonic vibration assisted cutting device with a two-stage amplified ultrasonic transducer of claim 1, characterized in that: the power transmission system (4) comprises a motor and a rotation stopping sheet (401);
the rotation stopping sheet (401) is fixed on the motor stator through a rotation stopping rod (203) of the rotation stopping body (2).
5. The ultrasonic vibration assisted cutting device with a two-stage amplified ultrasonic transducer of claim 1, characterized in that: the two-stage amplification ultrasonic transducer (5) comprises a pre-tightening bolt (501), a countersunk head type rear cover plate (502), a piezoelectric ceramic group (503), a conical transition ladder-shaped amplitude transformer (504), a pressing cap (505), a clamp spring (506) and a cutter head (507);
the countersunk head type rear cover plate (502), the piezoelectric ceramic group (503) and the conical transition ladder deformation amplitude transformer (504) are sequentially connected through a pretightening bolt (501);
the pre-tightening bolt (501) provides pre-tightening force for the piezoelectric ceramic group (503);
the clamp spring (506) is positioned in a groove at the output end of the conical transition ladder amplitude-changing rod (504), and the cutter head (507) is fixedly connected with the conical transition ladder amplitude-changing rod (504) through a pressing cap (505);
the input end of the conical transition ladder-shaped amplitude transformer (504) is connected with the piezoelectric ceramic group (503), and the output end is connected with the cutter head (507).
6. The ultrasonic vibration assisted cutting device with a two-stage amplified ultrasonic transducer of claim 1, characterized in that: when the ultrasonic vibration auxiliary cutting device works, the ultrasonic generator (6) outputs a high-frequency ultrasonic signal to the secondary amplification ultrasonic transducer (5);
the two-stage amplification ultrasonic transducer (5) converts high-frequency ultrasonic signals into mechanical vibration with corresponding frequency, the amplitude of the mechanical vibration is increased through the conical transition ladder-shaped amplitude transformer (504) and is transmitted to the tip of the cutter head, so that ultrasonic vibration is generated, and ultrasonic-assisted cutting machining is realized.
7. A method of designing a two-stage amplification ultrasonic transducer in an ultrasonic vibration-assisted cutting apparatus as set forth in any one of claims 1 to 6, wherein: the method comprises the following steps:
1) establishing a simulation model of a two-stage amplification ultrasonic transducer (5), wherein the cross section of the simulation model comprises a first equal cross section, a variable cross section of conical transition, a second equal cross section and a third equal cross section;
2) establishing a cross-sectional area function S of a conical transition ladder deformation amplitude transformer (504) n (x n ) Namely:
in the formula, R 1 、R 2 、R 3 Respectively representing the input end radius, the output end radius and the cross section radius of a cutter head (507) of the conical part of the conical transition ladder-shaped amplitude transformer (504); l 1 、l 2 、l 3 、l 4 、l 5 、l 6 Respectively showing the cross section length of the countersunk head type rear cover plate (502), the cross section length of the piezoelectric ceramic group (503), the cylindrical surface length of the conical transition ladder-shaped amplitude transformer (504), the input end cross section length of the conical part of the conical transition ladder-shaped amplitude transformer (504), the output end cross section length of the conical part of the conical transition ladder-shaped amplitude transformer (504), and the cross section of the cutter head (507)A length; x is the number of n Are particles;
3) the longitudinal vibration wave equation of the variable cross-section ultrasonic transducer is as follows:
in the formula, mu n (x n ) Is a particle displacement function; s n (x n ) Is a function of the cross section area of the variable amplitude rod of the conical transition ladder; number of circles
ω n Is the circular frequency;
the propagation speeds of longitudinal waves in different media; e n Young's modulus for different materials; rho n Density of different dielectric materials;
4) designing a nodal surface at the input end of a conical surface of a conical transition ladder-shaped amplitude transformer (504), wherein the left side of the nodal surface comprises a first equal section, and the right side of the nodal surface comprises a variable section, a second equal section and a third equal section of conical transition;
simplifying equation (2) yields:
5) according to formula (3), the general formula:
in the formula, F n (x n ) Longitudinal elastic force; z n ＝ρ n c n S (x) is the acoustic impedance of each part of the two-stage amplification ultrasonic transducer (5); a. the n 、B n Is a coefficient;
6) establishing boundary conditions of the vibration speed and the force of the cylindrical section parts of the conical transition ladder-shaped amplitude transformer (504), namely:
in the formula, v f The vibration speed of the surface of the output end of the countersunk head type rear cover plate (502); mu.s 1 (0)、μ 1 (l 1 )、μ 2 (0)、μ 2 (l 2 )、μ 3 (0)、μ 3 (l 3 )、F 1 (0)、F 2 (0)、F 1 (l 1 )、F 2 (l 2 )、F 3 (0) Representing a boundary parameter;
7) combining the vertical type (4) and the formula (5), establishing a frequency equation of the cylindrical section parts of the conical transition ladder-shaped amplitude transformer (504) and the like, namely:
in the formula, Z 1 、Z 2 Is the impedance;
8) establishing a longitudinal vibration wave equation of the variable cross section of the conical transition, namely:
in the formula, parameter
R 1 、R 2 And l 4 The input end radius, the output end radius and the length of the conical structure of the conical part are respectively;
9) according to formula (7), the general formula:
in the formula，v n (x n ) Variable section vibration velocity for conical transition, F n (x n ) A longitudinal elastic force of a variable cross section of a conical transition; c n 、D n Is a coefficient;
10) establishing boundary conditions of the vibration speed and the force of the variable section, the second equal section and the third equal section of the conical transition, namely:
in the formula, v e For two-stage amplification of the vibration velocity v at the output end of the ultrasonic transducer (5) 0 The input end of a conical transition ladder amplitude transformer (504) vibrates; mu.s 4 (0)、μ 4 (l 4 )、μ 5 (0)、μ 5 (l 5 )、F 4 (0)、F 4 (l 4 )、F 5 (0)、F 5 (l 5 )、F 6 (0)、F 6 (l 6 ) Representing a boundary parameter; z 3 Is the impedance;
11) the joint vertical type (4), the formula (8) and the formula (9) equations are solved to obtain the frequency equations of the right conical section and the equal cylindrical section of the pitch surface, namely:
wherein the number of circles k is k 4 ＝k 5 ；
12) Calculating the amplitude amplification factor M of the two-stage amplification ultrasonic transducer (5), namely:
13) according to the input end radius R of the conical part of a preset conical transition ladder-shaped amplitude transformer (504) 1 Radius of output end R 2 The cross-sectional radius R of the tool head (507) 3 Length l of cross section of piezoelectric ceramic group (503) 2 And calculated from material propertiesNumber of arrival circles k n Harmonic impedance Z n Determining the size parameters of the two-stage amplification ultrasonic transducer, including the length l of the cross section of the countersunk head type back cover plate (502) 1 The length l of the cylindrical surface of the variable amplitude rod (504) of the conical transition ladder 3 The input end cross section length l of the conical part of the conical transition ladder deformation amplitude transformer (504) 4 The length l of the cross section of the output end of the conical part of the conical transition ladder amplitude-change rod (504) 5 The cross-sectional length l of the tool head (507) 6 And an amplitude amplification factor M;
14) determining the outer diameter size of the piezoelectric ceramic group (503); the outer diameter of the piezoelectric ceramic group (503) is not more than
Wherein, the wavelength λ of the ultrasonic wave in the piezoelectric ceramic material is as follows:
wherein c is the sound velocity in the piezoceramic material, f is the ultrasonic frequency,
is the elastic characteristic parameter of the piezoelectric ceramic material.
8. The design method of the two-stage amplification ultrasonic transducer according to claim 7, wherein: the first equal section comprises the cross section of a countersunk head type rear cover plate (502), the cross section of a piezoelectric ceramic group (503) and the cylindrical surface of a conical transition ladder amplitude transformer (504);
the variable cross section of the conical transition comprises the input end cross section of the conical part of a conical transition ladder variable amplitude transformer (504);
the second equal section comprises the cross section of the output end of the conical part of the conical transition ladder-shaped amplitude transformer (504);
the third constant cross-section comprises a cross-section of a cutter head (507).
9. The design method of the two-stage amplification ultrasonic transducer according to claim 7, wherein: the material of the countersunk rear cover plate (502) comprises 40Cr alloy steel;
the material of the piezoelectric ceramic group (503) comprises lead zirconate titanate (PZT) -8;
the material of the conical transition ladder-shaped amplitude transformer (504) comprises 40Cr alloy steel.
10. The design method of the two-stage amplification ultrasonic transducer according to claim 7, wherein: the size parameters of the two-stage amplification ultrasonic transducer are verified by harmonic response analysis.
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| CN104647147A (en) * | 2013-11-25 | 2015-05-27 | 大连康赛谱科技发展有限公司 | Carbon fiber composite rotary ultrasonic milling and grinding device and method |
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| US11107455B1 (en) * | 2018-09-19 | 2021-08-31 | The United States Of America As Represented By The Secretary Of The Navy | Constant beam pattern array method |
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