CN107350558B - Umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device and track production method - Google Patents
Umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device and track production method Download PDFInfo
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- CN107350558B CN107350558B CN201710120587.3A CN201710120587A CN107350558B CN 107350558 B CN107350558 B CN 107350558B CN 201710120587 A CN201710120587 A CN 201710120587A CN 107350558 B CN107350558 B CN 107350558B
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- 238000005520 cutting process Methods 0.000 title claims abstract description 53
- 238000004519 manufacturing process Methods 0.000 title abstract description 6
- 239000000919 ceramic Substances 0.000 claims abstract description 98
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- 238000009434 installation Methods 0.000 claims abstract description 24
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23D—PLANING; SLOTTING; SHEARING; BROACHING; SAWING; FILING; SCRAPING; LIKE OPERATIONS FOR WORKING METAL BY REMOVING MATERIAL, NOT OTHERWISE PROVIDED FOR
- B23D79/00—Methods, machines, or devices not covered elsewhere, for working metal by removal of material
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B06—GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS IN GENERAL
- B06B—METHODS OR APPARATUS FOR GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS OF INFRASONIC, SONIC, OR ULTRASONIC FREQUENCY, e.g. FOR PERFORMING MECHANICAL WORK IN GENERAL
- B06B1/00—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency
- B06B1/02—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency making use of electrical energy
- B06B1/06—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency making use of electrical energy operating with piezoelectric effect or with electrostriction
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Abstract
The invention discloses a kind of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device and track production methods, belong to elliptical vibration assisted machining manufacture field.The device uses the design of three flexible hinge branch parallel connection umbrella arragement constructions, is made of umbrella parallel flexible hinge structure, folded plate, support plate, cushion block, cutter pre-loading screw, 5 interior hexagonal holding screws and piezoelectric ceramics, electrode slice, threaded bar, frequency modulation nut, location nut, locknut.The umbrella parallel flexible hinge structure is constituted by being uniformly distributed the 120 ° of branches in interval and Cutting tool installation manner platform on three circular conical surfaces, on three branches simultaneously input displacement, by the transmitting of flexible hinge umbrella parallel-connection structure and amplification, elliptical orbit is finally formed at point of a knife.The present invention has the advantages that apparatus structure is simple, resonant frequency is high and easily generates three-dimensional elliptical motion profile, can facilitate to be directly integrated with numerically-controlled machine tool and carries out auxiliary Precision Machining.
Description
Technical field
The invention belongs to ultrasonic elliptical vibratory assisted machining manufacture field, in particular to a kind of umbrella parallel-connection structure three-dimensional is super
Sound elliptical vibration cutting device and track production method.
Background technique
With accurate and Ultraprecision Machining fast development, elliptical vibration cutting reduces cutting force, raising due to it
Processing quality restrains Work-piece burr generation, increases the advantages that cutter life, has received significant attention.In view of to high-accuracy zero
The processing quality requirement of part is higher and higher, and the machined surface quality that scholars just further increase elliptical vibration cutting has devised
The method of a variety of elliptical vibration cuttings and matched vibration cutting device.In various elliptical vibration cutting forms, three-dimensional elliptical
The generation of the elliptical orbit in any space may be implemented in vibration cutting device, is very suitable to the Precision Machining of free form surface and certainly
By the micro-nano texture for configuring arbitrary shape on curved surface.
Three-dimensional elliptical vibration device is mainly using series connection and parallel-connection structure form at present, using serial mechanism as the three-dimensional of carrier
Elliptical vibration cutting device it is possible to prevente effectively from movement coupling, but serial mechanism will lead to device first natural frequency it is lower, drive
Dynamic difficulty.It can be to avoid disadvantages described above, patent by the three-dimensional elliptical vibration cutting device of carrier of parallel connection type compliant mechanism
(CN102059575A) and patent (CN102371359A) all respectively gives a kind of three-dimensional elliptical movement generation method and its dress
The patent set, although elliptical orbit can be generated, that there are working frequencies is low, impulse stroke is smaller, generates elliptical orbit shape
The problems such as formula is single, elliptical orbit range adjustability is poor.
In order to overcome the deficiencies of the prior art, in three groups of flexible hinges with more flexible cloth in the structure of parallel fashion parallel connection
The spatial distribution for having set flexible hinge keeps each branch of parallel-connection structure at an angle with the space symmetr axis of the structure, shape
At a kind of umbrella parallel-connection structure, along each branch input displacement can on Cutting tool installation manner platform it is more flexible compound, make knife
Cusp obtains various informative space ellipse motion profile.The characteristics of device, has: (1) it is simple and compact for structure, it is adapted to each
The machining form of seed type；(2) umbrella parallel flexible hinge is distributed the way of realization that can be convenient in space any angle
The elliptical orbit of multiplicity；(3) vibration frequency is high, available even closer micro-nano texture.
Summary of the invention
The purpose of the present invention, is to provide a kind of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device and is produced from track
Generation method solves the problems, such as the generation of three-D ultrasonic elliptical vibration track.
In order to achieve the above objectives, solution of the invention is:
A kind of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device, it is characterised in that:
The device includes cutter, umbrella parallel flexible hinge structure, folded plate, support plate, cushion block；
Above-mentioned umbrella parallel flexible hinge structure includes the first branch, the second branch, third branch and Cutting tool installation manner platform.
Above three branched structure is identical, by straight round flexible hinge (1021) structure and displacement input lever
(1022) it forms；Wherein displacement input lever (1022) cross sectional shape can simplify flexible hinge structure mechanical property using square
Analysis；Straight round flexible hinge (1021) is located between displacement input lever (1022) and Cutting tool installation manner platform (104)；Three branch institutes
Identical as the axis angle size of Cutting tool installation manner platform in space in axis, theoretically its value all can produce ellipse at 0-90 °
Circular test, but the ellipse long and short shaft axial length that when value is placed in the middle obtains is bigger, the oval length generated when value is 0 ° or 90 ° partially nearly
Axis axial length difference is larger, and trajectory shape deviates three-dimensional elliptical, by theory analysis, takes the preferred section that 28-56 ° is the angle；
And each branch is distributed along the axis direction mode of being centrosymmetric of Cutting tool installation manner platform, is successively separated by a circumferential direction
120°；Three branches spatially unanimously polymerize, and support Cutting tool installation manner platform jointly, in the rack arrangement form of umbrella；
The device further includes the first threaded bar being installed in the first branch bottom surface threaded hole, is installed under the second branch
The second threaded bar in the threaded hole of bottom surface, the third threaded bar being installed in third branch bottom surface threaded hole；
Above-mentioned first threaded bar is by the first piezoelectric ceramics, first electrode sheet, the second piezoelectric ceramics, second electrode sheet, first
Frequency modulation nut, the first location nut and the first locknut are sequentially connected in series, and are positioned on the first folded plate；First location nut
It is in contact with one end face of the first folded plate, the first locknut is in contact with the first folded plate other end, and two nuts are mutually tightened, and makes
The component of first threaded bar and series connection on it is all fixed on the first folded plate；First holding screw again fixes the first folded plate
On the supporting plate；
Above-mentioned second threaded bar is by third piezoelectric ceramics, third electrode slice, the 4th piezoelectric ceramics, the 4th electrode slice, second
Frequency modulation nut, the second location nut and the second locknut are sequentially connected in series, and are positioned on the second folded plate；Second location nut
It is in contact with one end face of the second folded plate, the second locknut is in contact with the second folded plate other end, and two nuts are mutually tightened, and makes
The component of second threaded bar and series connection on it is all fixed on the second folded plate；Second holding screw again fixes the second folded plate
On the supporting plate；
Above-mentioned third threaded bar is by the 5th piezoelectric ceramics, the 5th electrode slice, the 6th piezoelectric ceramics, the 6th electrode slice, third
Frequency modulation nut, third location nut and third locknut are sequentially connected in series, and are positioned on third folded plate；Third location nut
It is in contact with one end face of third folded plate, third locknut is in contact with third folded plate other end, and two nuts are mutually tightened, and makes
The component of third threaded bar and series connection on it is all fixed on third folded plate；Third holding screw again fixes third folded plate
On the supporting plate；
The device further includes the 4th holding screw and the 5th holding screw, and cushion block is fixed under support plate by two screws
End, in order to positioning of the whole device on lathe and clamping.
The method for generating elliptical vibration track using the umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device；
When the sinusoidal displacement input of frequencies such as existing simultaneously in the end of three branches, it is mounted on umbrella parallel flexible hinge
The point of a knife of cutter in chain structure draws out a three-dimensional elliptical track；
First piezoelectric ceramics and the second piezoelectric ceramics, will by inverse piezoelectric effect in by voltage course in described above
Displacement output is generated, the output displacement of generation acts in the displacement input lever of the first branch of parallel flexible hinge structure, generates
Output displacement size are as follows:
In formula, A1Indicate the amplitude of the output displacement in displacement input lever by the first piezoelectric ceramics and the second piezoelectric ceramics, f
Indicate the vibration frequency generated in displacement input lever by the first piezoelectric ceramics and the second piezoelectric ceramics,It indicates by the first piezoelectricity
The initial phase of ceramics and the second piezoelectric ceramics output displacement in displacement input lever, t indicate the time；
It is defeated that third piezoelectric ceramics and the 4th piezoelectric ceramics will generate displacement in by voltage course, through inverse piezoelectric effect
Out, the output displacement of generation acts in the displacement input lever of the second branch of parallel flexible hinge structure, the output displacement of generation
Size are as follows:
In formula, A2Indicate the amplitude of the output displacement in displacement input lever by third piezoelectric ceramics and the 4th piezoelectric ceramics, f
Indicate the vibration frequency generated in displacement input lever by third piezoelectric ceramics and the 4th piezoelectric ceramics,It indicates by third piezoelectricity
The initial phase of ceramics and the 4th piezoelectric ceramics output displacement in displacement input lever, t indicate the time；
It is defeated that 5th piezoelectric ceramics and the 6th piezoelectric ceramics will generate displacement in by voltage course, through inverse piezoelectric effect
Out, the output displacement of generation acts in the displacement input lever of parallel flexible hinge structure third branch, the output displacement of generation
Size are as follows:
In formula, A2Indicate the amplitude of the output displacement in displacement input lever by the 5th piezoelectric ceramics and the 6th piezoelectric ceramics, f
Indicate the vibration frequency generated in displacement input lever by the 5th piezoelectric ceramics and the 6th piezoelectric ceramics,It indicates by the 5th piezoelectricity
The initial phase of ceramics and the 6th piezoelectric ceramics output displacement in displacement input lever, t indicate the time；
XYZ coordinate system is defined, the flexible hinge sections on each branch of umbrella parallel flexible hinge structure are reduced to
A bit, three simplified points are linked to be a triangle, and using the center of this triangle as origin, Z axis is perpendicular to where this triangle
Plane, and point of a knife side is directed toward in direction, X-direction is parallel to flexible hinge simplifies on the second branch and third branch two
The straight line that point is linked to be, and direction is by the simplification for simplifying point and being directed toward flexible hinge on third branch of flexible hinge on the second branch
Point, Y direction can be determined by right-handed Cartesian coordinate system.
At any time when t, if AtFor point of a knife point position, BtFor the center position of above-mentioned constructed triangle,
B can be obtained by analytic geometry methodtCoordinate are as follows:
Use Btx、Bty、BtzRespectively indicate BtEach coordinate components, then have:
Wherein θ indicates axis where any branch of umbrella parallel flexible hinge structure and Cutting tool installation manner platform when initial position
The angle of axis；
The normal vector of plane where equally can be calculated the above-mentioned constructed triangle of t momentWherein
nx、ny、nzRespectively
Wherein b indicate center of the flexible hinge away from above-mentioned constructed triangle when initial position on any branch away from
From；
Due to line segment AtBtPerpendicular to plane where above-mentioned constructed triangle, by BtThe coordinate of point and the method for the plane
VectorAny time t point of a knife point A can be calculatedt(Atx,Aty,Atz) each coordinate components are as follows:
Wherein l indicates vertical range of the point of a knife point away from plane where above-mentioned constructed triangle, i.e. line segment when initial position
AtBtLength；
When each branch cross sectional shape of umbrella parallel flexible hinge structure is designed using 10 × 10mm, structure size b
Too small to make three branches at Cutting tool installation manner platform apart from less than normal, structure is difficult to, and b is too big, the three-dimensional elliptical that device generates
Track scale is less than normal, show that the preferred scope of b is 8-18mm by simulation optimization；Structure size l is too small, the three-dimensional that device generates
Elliptical orbit is less than normal along Z-direction scale, and l is too big, and the rigidity of structure reduces obviously, and the preferred model of l is obtained by simulation optimization
It encloses for 23-38mm.
According to the optimization structure of device, the value for determining b, θ, l is taken in optimization range, by formula (1), (2), (3), (4), (5)
It successively brings formula (6) into, the incremental point of a knife point A with time t can be obtained under matlab softwaret(Atx,Aty,Atz) draw out one
Elliptic curve.
The advantages of the invention patent: (1) it is simple and compact for structure, it is adapted to various types of machining forms；(2) umbrella
The elliptical orbit for the way of realization multiplicity that shape parallel flexible hinge can be convenient in the distribution of space any angle；(3) vibration frequency
Height, available even closer micro-nano texture.
Detailed description of the invention
Fig. 1 is the isometric views of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device in the present invention；
Fig. 2 is that umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device removes support plate and with lower component in the present invention
Isometric views；
Fig. 3 be in the present invention umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device removal folded plate, support plate and with
The isometric views of lower component；
Fig. 4 is the umbrella parallel flexible hinge knot of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device in the present invention
Structure isometric views；
Fig. 5 is that umbrella parallel flexible hinge structure is not applying the kinematics simplified model figure for being displaced input in the present invention；
Fig. 6 is that umbrella parallel flexible hinge structure is applying the kinematics simplified model figure for being displaced input in the present invention；
Fig. 7 is that the examples of parameters substitution generation of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device in the present invention is ellipse
The elliptical orbit figure generated in Circular test expression formula；
Figure label title: 1- umbrella parallel flexible hinge structure；2- cutter holding screw；3- cutter；The first folded plate of 4-；
The second folded plate of 5-；6- third folded plate；7- support plate；8- cushion block；The 4th holding screw of 9-；The 5th holding screw of 10-；11- first
Holding screw；The second holding screw of 12-；13- third holding screw；The first piezoelectric ceramics of 14-；15- first electrode sheet；16-
Two piezoelectric ceramics；17- second electrode sheet；18- the first frequency modulation nut；The first location nut of 19-；The first threaded bar of 20-；21-
One locknut；22- third piezoelectric ceramics；23- third electrode slice；The 4th piezoelectric ceramics of 24-；The 4th electrode slice of 25-；26-
Two frequency modulation nuts；The second location nut of 27-；The second threaded bar of 28-；The second locknut of 29-；The 5th piezoelectric ceramics of 30-；31-
5th electrode slice；The 6th piezoelectric ceramics of 32-；The 6th electrode slice of 33-；34- third frequency modulation nut；35- third location nut；36-
Third threaded bar；37- third locknut；The first branch of 101-；The second branch of 102-；103- third branch；104- cutter peace
Fill platform；1021- directly round flexible hinge；1022- is displaced input lever.
Specific embodiment
Below in conjunction with attached drawing, technical solution of the present invention is described in detail.
In order to achieve the above objectives, solution of the invention is:
1. a kind of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device, it is characterised in that:
The device include umbrella parallel flexible hinge structure 1, cutter 3, the first folded plate 4, the second folded plate 5, third folded plate 6,
Support plate 7, cushion block 8, as shown in Figure 1；
Above-mentioned umbrella parallel flexible hinge structure 1 include the first branch 101, the second branch 102, third branch 103 and
Cutting tool installation manner platform 104, as shown in Figure 4.
Above-mentioned three branched structures shown in Fig. 4 are identical, by straight round 1021 structure of flexible hinge and displacement
Input lever 1022 forms；Wherein displacement 1022 cross sectional shape of input lever can simplify flexible hinge structure mechanical property using square
It can analysis；Straight round flexible hinge 1021 is located between displacement input lever 1022 and Cutting tool installation manner platform 104；Axis where three branches
Line is identical as the axis angle size of Cutting tool installation manner platform in space, and theoretically its value all can produce oval rail at 0-90 °
Mark, but the ellipse long and short shaft axial length that when value is placed in the middle obtains is bigger, the ellipse long and short shaft axis generated when value is 0 ° or 90 ° partially nearly
Long difference is larger, and trajectory shape deviates three-dimensional elliptical, by theory analysis, takes the preferred section that 28-56 ° is the angle；And
Each branch is distributed along the axis direction mode of being centrosymmetric of Cutting tool installation manner platform, is successively separated by 120 ° in a circumferential direction；Three
A branch spatially unanimously polymerize, and supports Cutting tool installation manner platform jointly, in the rack arrangement form of umbrella；
The device further includes the first threaded bar 20 being installed in 101 bottom surface threaded hole of the first branch, is installed on second
The second threaded bar 28 in 102 bottom surface threaded hole of branch, the third screw thread being installed in 103 bottom surface threaded hole of third branch
Stick 36, as shown in Figure 1, Figure 2, Figure 3 shows；
Above-mentioned first threaded bar 20 is by the first piezoelectric ceramics 14, first electrode sheet 15, the second piezoelectric ceramics 16, second electrode
Piece 17, the first frequency modulation nut 18, the first location nut 19 and the first locknut 21 are sequentially connected in series, and are positioned at the first folded plate
On 4；First location nut 19 is in contact with 4 one end face of the first folded plate, the first locknut 21 and 4 other end phase of the first folded plate
Contact, two nuts are mutually tightened, and are fixed on the component of the first threaded bar 20 and series connection on it all on the first folded plate 4；The
First folded plate 4 is fixed in support plate 7 by one holding screw 11 again, as shown in Figure 3.
Above-mentioned second threaded bar 28 is by third piezoelectric ceramics 22, third electrode slice 23, the 4th piezoelectric ceramics 24, the 4th electrode
Piece 25, the second frequency modulation nut 26, the second location nut 27 and the second locknut 29 are sequentially connected in series, and are positioned at the second folded plate
On 5；Second location nut 27 is in contact with 5 one end face of the second folded plate, the second locknut 29 and 5 other end phase of the second folded plate
Contact, two nuts are mutually tightened, and are fixed on the component of the second threaded bar 28 and series connection on it all on the second folded plate 5；The
Second folded plate 5 is fixed in support plate 7 by two holding screws 12 again, as shown in Figure 3.
Above-mentioned third threaded bar 36 is by the 5th piezoelectric ceramics 30, the 5th electrode slice 31, the 6th piezoelectric ceramics 32, the 6th electrode
Piece 33, third frequency modulation nut 34, third location nut 35 and third locknut 37 are sequentially connected in series, and are positioned at third folded plate
On 6；Third location nut 35 is in contact with 6 one end face of third folded plate, third locknut 37 and 6 other end phase of third folded plate
Contact, two nuts are mutually tightened, and are fixed on the component of third threaded bar 36 and series connection on it all on third folded plate 6；The
Third folded plate 6 is fixed in support plate 7 by three holding screws 13 again, as shown in Figure 3.
The device further includes cutter holding screw 2 and the 4th holding screw 9 and the 5th holding screw 10, and two screws will pad
Block 8 is fixed on the lower end of support plate 7, in order to positioning of the whole device on lathe and clamping.
The method that the umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device generates elliptical vibration track, it is special
Sign is:
When the sinusoidal displacement input of frequencies such as existing simultaneously in the end of three branches, it is mounted on umbrella parallel flexible hinge
The point of a knife of cutter in chain structure draws out a three-dimensional elliptical track；
First piezoelectric ceramics 14 and the second piezoelectric ceramics 16 are imitated in by voltage course by inverse piezoelectricity in described above
Displacement output should will be generated, the output displacement of generation acts on the displacement input lever of 1 first branch 101 of parallel flexible hinge structure
On, the output displacement size of generation are as follows:
In formula, A1Indicate the vibration of the output displacement in displacement input lever by the first piezoelectric ceramics 14 and the second piezoelectric ceramics 16
Width, f indicate the vibration frequency generated in displacement input lever by the first piezoelectric ceramics 14 and the second piezoelectric ceramics 16,Indicate by
The initial phase of first piezoelectric ceramics 14 and the second piezoelectric ceramics 16 output displacement in displacement input lever, t indicate the time；
Third piezoelectric ceramics 22 and the 4th piezoelectric ceramics 24 will generate position in by voltage course, through inverse piezoelectric effect
Output is moved, the output displacement of generation acts in the displacement input lever of 1 second branch 102 of parallel flexible hinge structure, generation
Output displacement size are as follows:
In formula, A2Indicate the vibration of the output displacement in displacement input lever by third piezoelectric ceramics 22 and the 4th piezoelectric ceramics 24
Width, f indicate the vibration frequency generated in displacement input lever by third piezoelectric ceramics 22 and the 4th piezoelectric ceramics 24,Indicate by
The initial phase of third piezoelectric ceramics 22 and the 4th piezoelectric ceramics 24 output displacement in displacement input lever, t indicate the time；
5th piezoelectric ceramics 30 and the 6th piezoelectric ceramics 32 will generate position in by voltage course, through inverse piezoelectric effect
Output is moved, the output displacement of generation acts in the displacement input lever of 1 third branch 103 of parallel flexible hinge structure, generation
Output displacement size are as follows:
In formula, A2Indicate the vibration of the output displacement in displacement input lever by the 5th piezoelectric ceramics 30 and the 6th piezoelectric ceramics 32
Width, f indicate the vibration frequency generated in displacement input lever by the 5th piezoelectric ceramics 30 and the 6th piezoelectric ceramics 32,Indicate by
The initial phase of 5th piezoelectric ceramics 30 and the 6th piezoelectric ceramics 32 output displacement in displacement input lever, t indicate the time；
XYZ coordinate system is defined, Fig. 5 indicates t=0 (piezoelectric ceramics is not passed through voltage) moment umbrella parallel flexible hinge knot
The structure diagram of structure, P10Indicate the flexible hinge position on the first branch 101, P20Indicate the flexibility on the second branch 102
Hinge position, P30Indicate the flexible hinge position on third branch 103, A0For point of a knife point position, with point P10、
P20、P30The center B for the triangle being formed by connecting0Point is origin, with straight line B0A0For Z axis, direction is by B0It is directed toward A0, Z axis hangs down at this time
Directly in triangle P10P20P30Place plane defines X-axis and is located at triangle P10P20P30Place plane, and with straight line P20P30In parallel,
Direction is by P20It is directed toward P30, Y-axis can determine by right-handed Cartesian coordinate system.
As shown in figure 5, being illustrated to design parameter each in figure: θ is three branches of umbrella parallel flexible hinge structure
Angle of the place axis in space and the axis of Cutting tool installation manner platform；A is the distance of flexible hinge on any two branch；B is three
Distance of the center for the triangle that flexible hinge connects into away from any flexible hinge, then there are relationships；L is point of a knife o'clock away from three
The distance of plane where the triangle that flexible hinge connects into.
It the following is the detailed step that elliptical orbit derivation is carried out in conjunction with the kinematic sketch of umbrella parallel flexible hinge structure:
(1) when carving (t=0) at the beginning, the kinematics simplified model (as shown in Figure 5) of umbrella parallel flexible hinge structure
The coordinate of each point is respectively as follows:
A0(0,0, l), B0(0,0,0),
P10(0, b, 0),
The direction vector difference of axis where three branches of umbrella parallel flexible hinge structure can be released by geometrical relationship
Are as follows:
(2) at any time t when, umbrella parallel flexible hinge structure three branches displacement input terminal there are input bits
It moves, structure motion dotted line position into such as Fig. 6, is respectively present input displacement s on three branches1、s2、s3, P1t、P2t、
P2tRespectively indicate flexible hinge position on three branches at this time, AtIndicate point of a knife point position at this time, BtIndicate point P1t、
P2t、P3tThe center for the triangle being linked to be；It can be obtained a little according to the input displacement on three branches and the direction vector where it
P1t、P2t、P3tCoordinate be respectively as follows:
P1t(0, b-s1Sin θ, s1cosθ)
Due to BtIt is triangle P1tP2tP3tCenter, the coordinate of t moment B point can be obtained are as follows:
Use Btx、Bty、BtzRespectively indicate BtEach coordinate components, then have:
(3) due to straight line AtBtAlways perpendicular to point P1t、P2t、P3tThe plane of composition, therefore only demand obtains the normal direction of the plane
Amount, then by B in step (2)tCoordinate and straightway AtBtLong l can be written any time point of a knife point AtEach coordinate point
Amount.
Three point P of t moment1t、P2t、P3tThe normal vector of the plane of composition can be expressed as
The point P that step (2) is obtained1t、P2t、P3tCoordinate bring above formula into, outgoing vector can be calculatedThree coordinate components
For
By vectorAnd BtAny time t point of a knife point A can be written in the coordinate of pointt(Atx,Aty,Atz) each coordinate components
Are as follows:
When each branch cross sectional shape of umbrella parallel flexible hinge structure is designed using 10 × 10mm, structure size b
Too small to make three branches at Cutting tool installation manner platform apart from less than normal, structure is difficult to, and b is too big, the three-dimensional elliptical that device generates
Track scale is less than normal, show that the preferred scope of b is 8-18mm by simulation optimization；Structure size l is too small, the three-dimensional that device generates
Elliptical orbit is less than normal along Z-direction scale, and l is too big, and the rigidity of structure reduces obviously, and the preferred model of l is obtained by simulation optimization
It encloses for 23-38mm.
According to the optimization structure of device, the value for determining b (a and b of equal value), θ, l is taken in optimization range, by formula (1), (2),
(3), (4), (5) successively bring formula (6) into, and the incremental point of a knife point A with time t can be obtained under matlab softwaret(Atx,Aty,
Atz) draw out an elliptic curve.If Fig. 7 is the elliptical orbit curve generated under a particular parameter value.
3. umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device under resonant conditions using cutting, frequency modulation nut can
With regulating device resonant frequency.
Above example is merely illustrative of the invention's technical idea, and this does not limit the scope of protection of the present invention, all to press
According to technical idea proposed by the present invention, any changes made on the basis of the technical scheme, each fall within the scope of the present invention it
It is interior.
Claims (5)
1. a kind of umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device, it is characterised in that:
The device includes umbrella parallel flexible hinge structure (1), cutter (3), the first folded plate (4), the second folded plate (5), third folding
Plate (6), support plate (7)；
Above-mentioned umbrella parallel flexible hinge structure (1) includes the first branch (101), the second branch (102), third branch (103)
And Cutting tool installation manner platform (104)；
Above three branched structure is identical, by straight round flexible hinge (1021) structure and displacement input lever (1022)
Composition；Wherein displacement input lever (1022) cross sectional shape is square；Straight round flexible hinge (1021) is located at displacement input lever
(1022) between Cutting tool installation manner platform (104)；Axis angle of the axis in space and Cutting tool installation manner platform where three branches
Size is identical, and value is between 0-90 °, and each branch is centrosymmetric mode point along the axis direction of Cutting tool installation manner platform
Cloth is successively separated by 120 ° in a circumferential direction；Three branches spatially unanimously polymerize, and support Cutting tool installation manner platform jointly, are in
The rack arrangement form of umbrella；
The device further includes the first threaded bar (20) being installed in the first branch (101) bottom surface threaded hole, is installed on second
The second threaded bar (28) in branch (102) bottom surface threaded hole, be installed in third branch (103) bottom surface threaded hole
Three threaded bars (36)；
Above-mentioned first threaded bar (20) is by the first piezoelectric ceramics (14), first electrode sheet (15), the second piezoelectric ceramics (16), second
Electrode slice (17), the first frequency modulation nut (18), the first location nut (19) and the first locknut (21) are sequentially connected in series, fixed
On the first folded plate (4)；First location nut (19) is in contact with (4) one end face of the first folded plate, the first locknut (21)
It is in contact with the first folded plate (4) other end, two nuts are mutually tightened, and the component of the first threaded bar (20) and series connection on it is made
All it is fixed on the first folded plate (4)；First folded plate (4) is fixed on support plate (7) by the first holding screw (11) again；
Above-mentioned second threaded bar (28) is by third piezoelectric ceramics (22), third electrode slice (23), the 4th piezoelectric ceramics (24), the 4th
Electrode slice (25), the second frequency modulation nut (26), the second location nut (27) and the second locknut (29) are sequentially connected in series, fixed
On the second folded plate (5)；Second location nut (27) is in contact with (5) one end face of the second folded plate, the second locknut (29)
It is in contact with the second folded plate (5) other end, two nuts are mutually tightened, and the component of the second threaded bar (28) and series connection on it is made
All it is fixed on the second folded plate (5)；Second folded plate (5) is fixed on support plate (7) by the second holding screw (12) again；
Above-mentioned third threaded bar (36) is by the 5th piezoelectric ceramics (30), the 5th electrode slice (31), the 6th piezoelectric ceramics (32), the 6th
Electrode slice (33), third frequency modulation nut (34), third location nut (35) and third locknut (37) are sequentially connected in series, fixed
On third folded plate (6)；Third location nut (35) is in contact with (6) one end face of third folded plate, third locknut (37)
It is in contact with third folded plate (6) other end, two nuts are mutually tightened, and the component of third threaded bar (36) and series connection on it is made
All it is fixed on third folded plate (6)；Third folded plate (6) is fixed on support plate (7) by third holding screw (13) again.
2. umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device according to claim 1, it is characterised in that:
Axis where three branches of umbrella parallel flexible hinge structure exists in the axis angle of space and Cutting tool installation manner platform
Between 28-56 °.
3. generating elliptical vibration track using umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device described in claim 1
Method, it is characterised in that:
When the sinusoidal displacement input of frequencies such as existing simultaneously in the end of three branches, it is mounted on umbrella parallel flexible hinge knot
The point of a knife of cutter on structure draws out a three-dimensional elliptical track；
First piezoelectric ceramics (14) and the second piezoelectric ceramics (16) are imitated in by voltage course by inverse piezoelectricity in described above
Displacement output should will be generated, the displacement that the output displacement of generation acts on (1) first branch (101) of parallel flexible hinge structure is defeated
Enter on bar, the output displacement size of generation are as follows:
In formula, A1Indicate the vibration of the output displacement in displacement input lever by the first piezoelectric ceramics (14) and the second piezoelectric ceramics (16)
Width, f indicate the vibration frequency generated in displacement input lever by the first piezoelectric ceramics (14) and the second piezoelectric ceramics (16),Table
The initial phase for showing the output displacement in displacement input lever by the first piezoelectric ceramics (14) and the second piezoelectric ceramics (16), when t is indicated
Between；
Third piezoelectric ceramics (22) and the 4th piezoelectric ceramics (24) will generate position by inverse piezoelectric effect in by voltage course
Output is moved, the output displacement of generation acts in the displacement input lever of (1) second branch (102) of parallel flexible hinge structure, produces
Raw output displacement size are as follows:
In formula, A2It indicates by the vibration of third piezoelectric ceramics (22) and the 4th piezoelectric ceramics (24) output displacement in displacement input lever
Width, f indicate the vibration frequency generated in displacement input lever by third piezoelectric ceramics (22) and the 4th piezoelectric ceramics (24),Table
Show by the initial phase of third piezoelectric ceramics (22) and the 4th piezoelectric ceramics (24) output displacement in displacement input lever, when t is indicated
Between；
5th piezoelectric ceramics (30) and the 6th piezoelectric ceramics (32) will generate position by inverse piezoelectric effect in by voltage course
Output is moved, the output displacement of generation acts in the displacement input lever of parallel flexible hinge structure (1) third branch (103), produces
Raw output displacement size are as follows:
In formula, A3Indicate the vibration of the output displacement in displacement input lever by the 5th piezoelectric ceramics (30) and the 6th piezoelectric ceramics (32)
Width, f indicate the vibration frequency generated in displacement input lever by the 5th piezoelectric ceramics (30) and the 6th piezoelectric ceramics (32),Table
The initial phase for showing the output displacement in displacement input lever by the 5th piezoelectric ceramics (30) and the 6th piezoelectric ceramics (32), when t is indicated
Between；
XYZ coordinate system is defined, the flexible hinge sections on each branch of umbrella parallel flexible hinge structure are reduced to a bit,
Three simplified points are linked to be a triangle, using the center of this triangle as origin, Z axis perpendicular to plane where this triangle,
And point of a knife side is directed toward in direction, X-direction is parallel to the two o'clock that flexible hinge simplifies on the second branch and third branch and connects
At straight line, and direction by the second branch flexible hinge simplify point be directed toward third branch on flexible hinge a simplification point, Y-axis
Direction can be determined by right-handed Cartesian coordinate system；
At any time when t, if AtFor point of a knife point position, DtFor the center position of above-mentioned constructed triangle, by solving
Analysis method of geometry can obtain BtCoordinate are as follows:
Use Btx、Bty、BtzRespectively indicate BtEach coordinate components, then have:
Wherein θ indicates the axis of axis and Cutting tool installation manner platform where any branch of umbrella parallel flexible hinge structure when initial position
Angle；
The normal vector of plane where equally can be calculated the above-mentioned constructed triangle of t momentWherein nx、ny、
nzRespectively
Wherein b indicates the distance at center of the flexible hinge away from above-mentioned constructed triangle when initial position on any branch；
Due to line segment AtBtPerpendicular to plane where above-mentioned constructed triangle, by BtThe coordinate of point and the normal vector of the plane
Any time t point of a knife point A can be calculatedt(Atx,Aty,Atz) each coordinate components are as follows:
Wherein l indicates vertical range of the point of a knife point away from plane where above-mentioned constructed triangle, i.e. line segment A when initial positiontBt's
It is long.
4. umbrella parallel-connection structure three-D ultrasonic elliptical vibration cutting device according to claim 3 generates elliptical vibration track
Method, it is characterised in that:
Axis where three branches of umbrella parallel flexible hinge structure exists in the axis angle of space and Cutting tool installation manner platform
Between 28-56 °；
When each branch cross sectional shape of umbrella parallel flexible hinge structure is designed using 10 × 10mm, when above-mentioned initial position
The distance b optimization range value at center of the flexible hinge away from above-mentioned constructed triangle on any branch is 8-18mm；
Vertical range l optimization range value of the point of a knife point away from plane where above-mentioned constructed triangle is when above-mentioned initial position
23-38mm。
5. the method according to claim 4 for generating elliptical vibration track, it is characterised in that:
According to the optimization structure of device, the value for determining b, θ, l is taken in optimization range, successively by formula (1), (2), (3), (4), (5)
It brings formula (6) into, the incremental point of a knife point A with time t can be obtained under matlab softwaret(Atx,Aty,Atz) draw out an ellipse
Curve.
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| CN108381306B (en) * | 2018-05-02 | 2023-04-07 | 吉林大学 | Ultrasonic machining tool with three groups of ultrasonic vibrators in cone structure and control method |
| CN109648098B (en) * | 2019-01-15 | 2020-01-14 | 东北大学 | Ultrasonic auxiliary turning device capable of improving ultrasonic vibration dimension |
| CN109940171B (en) * | 2019-01-29 | 2020-04-24 | 南京航空航天大学 | Real-time synchronous control method of elliptical vibration cutting device based on corner |
| CN109866074A (en) * | 2019-03-06 | 2019-06-11 | 天津理工大学 | A kind of variable element three-D ultrasonic vibration processing device and processing method |
| CN110000416B (en) * | 2019-05-21 | 2023-12-22 | 吉林大学 | Radial vibration-assisted force position control milling and grinding machine tool and control method thereof |
| CN110681877B (en) * | 2019-09-30 | 2020-07-31 | 东北大学 | Parallel and spiral groove combined type single-excitation three-dimensional curved surface ultrasonic auxiliary turning device |
| CN111014737B (en) * | 2019-12-14 | 2021-06-22 | 大连理工大学 | Single-excitation ultrasonic elliptical turning device |
| CN111014738B (en) * | 2019-12-14 | 2021-06-08 | 大连理工大学 | Single-excitation three-dimensional ultrasonic elliptical turning device |
| CN111730075B (en) * | 2020-05-29 | 2021-07-09 | 南京航空航天大学 | Variable-dimension vibration auxiliary turning device and track generation method thereof |
| CN111880471B (en) * | 2020-07-03 | 2022-06-10 | 哈尔滨工业大学 | Calculation method for cutting track of ultrasonic elliptical vibration cutting technology |
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