CN108819218B - A kind of electrofluid direct write nozzle and control method - Google Patents
A kind of electrofluid direct write nozzle and control method Download PDFInfo
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- CN108819218B CN108819218B CN201810533388.XA CN201810533388A CN108819218B CN 108819218 B CN108819218 B CN 108819218B CN 201810533388 A CN201810533388 A CN 201810533388A CN 108819218 B CN108819218 B CN 108819218B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
- B29C64/10—Processes of additive manufacturing
- B29C64/106—Processes of additive manufacturing using only liquids or viscous materials, e.g. depositing a continuous bead of viscous material
- B29C64/112—Processes of additive manufacturing using only liquids or viscous materials, e.g. depositing a continuous bead of viscous material using individual droplets, e.g. from jetting heads
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
- B29C64/20—Apparatus for additive manufacturing; Details thereof or accessories therefor
- B29C64/205—Means for applying layers
- B29C64/209—Heads; Nozzles
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
- B29C64/30—Auxiliary operations or equipment
- B29C64/386—Data acquisition or data processing for additive manufacturing
- B29C64/393—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B33—ADDITIVE MANUFACTURING TECHNOLOGY
- B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
- B33Y10/00—Processes of additive manufacturing
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B33—ADDITIVE MANUFACTURING TECHNOLOGY
- B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
- B33Y30/00—Apparatus for additive manufacturing; Details thereof or accessories therefor
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B33—ADDITIVE MANUFACTURING TECHNOLOGY
- B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
- B33Y50/00—Data acquisition or data processing for additive manufacturing
- B33Y50/02—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
Abstract
The invention discloses a kind of electrofluid direct write nozzles; including black liquid feed unit, black liquid import, middle part nozzle layer, stretch electrode layer, voltage generator, nozzle extended layer, jet stream protective layer, charged layer, lower nozzle, shielded layer and strabismus observation camera; lower nozzle inner wall is provided with inhibition electrod-array; also disclose a kind of control method of electrofluid direct write nozzle; the present invention realizes the high-precision control during jet stream direct write, guarantees the stabilization of the uniform injection of structure.
Description
Technical field
The invention belongs to micro nano structure manufacture EFI to print field, be more particularly to a kind of electrofluid direct write nozzle, also relate to
And a kind of control method of electrofluid direct write nozzle.
Background technique
The rise designed and manufactured with flexible electronic, functional polymer material, nano material etc. have special conduction
The brand-new material of property, ductility, chemical property is tatooed in flexibility, smart skins etc. show great application potential.But by
Material can be damaged by being different from traditional micro nanometer silicon sill, traditional micro-nano manufacturing process, such as photoetching, micro- casting in it
Attribute, and these materials are easily configured to solution, therefore solutionization manufacture micro nano structure becomes new research field.
In solutionization manufacture, traditional inkjet printing technology is had great potential.Traditional on-demand jet printing method belongs to energy
Amount method generates drop by extruded ink chamber, general liquid-drop diameter is nozzle using piezoelectricity or ultrasound or thermal as driving source
1.86 times, therefore drop size and jet size contact closely, and it is insufficient to be easy energy for high viscosity solution, is easy
Droplet inertia is insufficient when drop generates, and can not be broken.In contrast, electrohydrodynamic spray printing is pulled out solution by electric field force,
Taylor cone is generated, cone forms tiny jet stream, generally can achieve micron even Nano grade.Continuous electrohydrodynamic spray
If print can generate wild effects such as " whip are dynamic " when space is larger, the applications that can not be required in high position precision.
Summary of the invention
In view of the drawbacks of the prior art, the purpose of the present invention is to provide a kind of electrofluid direct write nozzle, one is additionally provided
The control method of kind electrofluid direct write nozzle.It realizes the high-precision control during jet stream direct write, guarantees the uniform spray of structure
The stabilization penetrated.
To achieve the above object, the invention adopts the following technical scheme:
A kind of electrofluid direct write nozzle, including black liquid feed unit further include black liquid import, the top of black liquid import and ink
The connection of liquid feed unit, the lower end of black liquid import are connect with the upper end of middle part nozzle layer, the lower end of middle part nozzle layer and stretching electricity
The outside of the upper end connection of pole layer, the outside of black liquid import and stretching electrode layer respectively with the supply voltage of voltage generator just
It pole and electrically connects, the lower end for stretching electrode layer is connect with the upper end of nozzle extended layer, and nozzle extended layer lower end and jet stream are protected
Charged layer, charged layer external connection voltage generator are bonded between the upper end of sheath, charged layer is that discoid and center opens up
There is jet stream circle via hole, shielded layer is bonded between jet stream protective layer lower end and the upper end of lower nozzle, shielded layer center, which offers, to be penetrated
Circle via hole is flowed, lower nozzle inner wall is provided with inhibition electrod-array, and shielded layer connection the earth inhibits electrod-array to be included in several
It further include straight for obtaining downward projection of the jet stream of lower nozzle outgoing on substrate to the symmetrically arranged inhibition electrode in center
Line, deflection distance and the strabismus observation camera for deflecting direction.
Black liquid import, middle part nozzle layer, stretching electrode layer, nozzle extended layer, jet stream protective layer, lower part spray as described above
Mouth is straight tube-like.
A kind of electrofluid direct write Jet control method, comprising the following steps:
Step 1, strabismus observation camera shooting jet stream squint perspective view, and jet stream downward projection figure is converted to jet stream vertical view and is thrown
Shadow figure, according to jet stream downward projection figure obtain jet stream project to jet stream downward projection straight line on substrate, jet deflection distance and
Jet deflection direction,
The direction of the line at the center of the projection of step 2, each pair of inhibition electrode on substrate is to inhibit electrode direction, is determined
Two pairs of inhibition electrode corresponding with two adjacent inhibition electrode directions of deflection direction, according to jet deflection distance and jet deflection
Direction obtains the size of opposite direction compensating electric field and the direction of opposite direction compensating electric field, then uses parallelogram method by negative side
It is scaled the size of the compensation supply voltage of above-mentioned two pairs of inhibition electrode to compensating electric field, gives above-mentioned two pairs of centrosymmetric inhibition
Electrode load compensation supply voltage.
Further include rectilinear print step:
Establish XYZ coordinate system, in XYZ coordinate system, plane is plane where substrate where X-axis and Y-axis, and Z axis is perpendicular to XY
Plane,
During rectilinear print, each point P of the straight line of printingiCoordinate be (Xi、Yi、Zi), Xi=vtcos θ, Yi=
Vtsin θ, Zi=0, wherein v is the speed of nozzle opposing substrate movement, and t is the time of nozzle movement, and θ is that x-axis and jet stream are overlooked
The angle of projection straight line, i are serial number,
During rectilinear print, the coordinate P of the bottom center of lower nozzleNi(XNi、YNi、ZNi) obtained by following formula
:
Wherein, H is vertical range of the lower nozzle bottom center to substrate, and L is jet deflection distance.
Further include circle printing step:
Establish XYZ coordinate system, in XYZ coordinate system, plane is plane where substrate where X-axis and Y-axis, and Z axis is perpendicular to XY
Plane,
In circle print procedure, the coordinate P of the bottom center of lower nozzleNi(XNi、YNi、ZNi) obtained by following formula
:
WhereinV is the speed of nozzle opposing substrate movement, and t is the time of nozzle movement, under H is
Portion nozzle bottom surface center is to the vertical range of substrate, and L is jet deflection distance, and r is circle radius, and i is serial number.
Further include curve printing step:
Establish XYZ coordinate system, in XYZ coordinate system, plane is plane where substrate where X-axis and Y-axis, and Z axis is perpendicular to XY
Plane,
Each point P of the curve of printingiCoordinate be (Xi、Yi、Zi), Zi=0,
The coordinate P of the bottom center of lower nozzleNi(XNi、YNi、ZNi) obtained by following formula:
Wherein,H is that lower nozzle bottom center arrives substrate
Vertical range, L are jet deflection distance, KiFor the point P on curveiTangential direction, i is serial number.
Contemplated above technical scheme through the invention flows when by thus according to actual ejection compared with prior art
The variation of body controls the deflection of jet stream, and improves spinning positioning accuracy.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of electrofluid direct write nozzle,
Wherein, 1- black liquid import, the middle part 2- nozzle layer, 3- stretching electrode layer, 4- nozzle extended layer, the charged layer of 5-, 6- are penetrated
Protective layer, 7- shielded layer are flowed, 8- inhibits electrod-array;9- lower nozzle;
Fig. 2 is the distribution schematic diagram for inhibiting electrod-array;
Fig. 3 is the schematic diagram of fluidic spaces description,
21- taylor cone, 22- electrofluid injection in jet stream, 23- substrate.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
It is as shown in Figure 1 the cross-sectional view of nozzle, fluidic vectoring thrust area includes black liquid import 1, and middle part nozzle layer 2 stretches electrode
Layer 3, wherein black liquid import 1 be glass material, middle part nozzle layer 2 be glass material, stretch electrode layer 3 be metal material (such as
Copper).The top of black liquid import 1 connect (such as air pressure, syringe pump) with other black liquid feed units, and the lower end of black liquid import 1 is straight
It connects and is connect with the upper end of middle part nozzle layer 2.Middle part nozzle layer 2 uses straight pipe shape, and lower end is bonded with the upper end for stretching electrode layer 3
Connection, the outside of black liquid import 1 and the outside for stretching electrode layer 3 are positive and electrical with the supply voltage of voltage generator respectively
Ground connection.The upper end of the lower end and nozzle extended layer 4 that stretch electrode layer 3 is fitted and connected, and is stretched electrode layer 3 and is used glass material,
It is bonded charged layer 5 between 4 lower end of nozzle extended layer and the upper end of jet stream protective layer 6, charged 5 external connection voltage generator of layer,
Voltage generator is that charged layer 5 provides charge, charged layer 5 be it is discoid, center offers jet stream circle via hole, for by penetrating
Stream, charged layer 5 are metal material (such as copper), and shielded layer 7 is bonded between 6 lower end of jet stream protective layer and the upper end of lower nozzle 9, under
Nozzle 9 inner wall in portion's, which is provided with, inhibits electrod-array 8, and wherein shielded layer 7 connects the earth always, and 7 center of shielded layer, which offers, to be penetrated
Circle via hole is flowed, is used to inhibit electrod-array 8 to be included in the symmetrically arranged inhibition electrode in several pairs of centers, every centering by jet stream
The heart symmetrically inhibits the external control unit of electrode to carry out individually addressing power control, power control include access voltage size and
It is positive and negative.
Black liquid import 1, middle part nozzle layer 2 stretch electrode layer 3, nozzle extended layer 4, jet stream protective layer 6, lower nozzle 9
For straight tube-like.
Fig. 3 is status diagram of the jet stream in nozzle, and 21 be taylor cone, and 22 be the jet stream in electrofluid injection, and 23 are
Substrate.Detailed process is that marking ink is delivered to black liquid import 1 by black liquid feed unit, makes black liquid full of black liquid import 1, outside
It connects voltage generator and supply voltage is provided, be separately connected black liquid import 1 and stretch electrode layer 3, be then powered, due to polarization
It acts on black liquid and rheological behaviour occurs, after voltage is more than critical voltage, black liquid forms jet stream and sprays, and jet stream is along nozzle centerline
It flies in middle part nozzle layer 2, then passes through and stretch electrode layer 3, into nozzle extended layer 4, although being deposited at this time without electric field force
, but since there are inertia for jet stream, still fly along former direction, subsequently into charged layer 5, charged layer connects outside always
Voltage generator increase jet stream unit charge density for the jet stream that polarizes again, jet stream continues to fly through jet stream protective layer
6, shielded layer 7 and inhibition electrod-array 8, are eventually deposited on substrate 23.Electrod-array 8 is inhibited to pass through to each pair of centrosymmetric
Inhibit the power on/off of electrode, realizes the control minimized to jet deflection.
As an implementation, inhibiting electrod-array 8 is 4 pairs of centrosymmetric inhibition electrodes, as shown in Fig. 2, 4 centerings
The heart symmetrically inhibit electrode be respectively the first inhibition electrode to, second inhibit electric grade to, third inhibit electric grade to, the 4th inhibit electricity
Grade is right.
It further include strabismus observation camera, it is always viscous by substrate when being deposited on substrate since jet stream is viscous liquid
The effect of power, strabismus observation camera shooting jet stream squints perspective view, since the optical axis of strabismus observation camera is not located at vertically
The direction of substrate needs to be converted to jet stream strabismus perspective view into jet stream downward projection figure (technology is the prior art), and jet stream is bowed
It is located at the jet stream downward projection figure that the direction shooting of vertical substrate obtains depending on the optical axis that perspective view is equivalent to strabismus observation camera.Root
Jet stream downward projection straight line, jet deflection distance and jet deflection direction are obtained according to jet stream downward projection figure.
Reduce deflection distance mechanism be, by strabismus observation camera survey jet stream downward projection straight line, jet deflection away from
From with jet deflection direction, the opposite direction along deflection direction applies electric field, reduces deflection distance.Concrete mode is each pair of suppression
The direction of the line at the center of projection of the electrode processed on substrate is to inhibit electrode direction, and determination is adjacent with jet deflection direction
The corresponding two pairs of inhibition electrode of two inhibition electrode directions obtains opposite direction according to jet deflection distance and jet deflection direction and mends
The size of electric field and the direction of opposite direction compensating electric field are repaid, is then arrived using parallelogram method by opposite direction compensating electric field is equivalent
Two pairs of centrosymmetric compensation supply voltage sizes for inhibiting electrode, control unit control external electricity according to supply voltage size
It presses generator to provide corresponding compensation supply voltage to corresponding inhibition electrode, and then reduces deflection distance, control unit is repeatedly
After adjustment, so that the saltation point of jet stream is in control within the scope of precision prescribed.
Establish XYZ coordinate system, in XYZ coordinate system, plane is plane where substrate where X-axis and Y-axis, and Z axis is perpendicular to XY
Plane.In print procedure, nozzle can be regarded as relative to substrate motion.
Rectilinear print
In XYZ coordinate system, during rectilinear print, the track of the straight line of printing can be regarded as from initial point P0(0,0,
0) final goal point P is arrivednMotion profile, therefore initial point P0To final goal point PnUpper each point PiCoordinate be (Xi、Yi、
Zi), Xi=vtcos θ, Yi=vtsin θ, Zi=0, wherein v be nozzle opposing substrate movement speed, t be nozzle movement when
Between, i is serial number a little.
During rectilinear print, the coordinate P of the bottom center of lower nozzle 9Ni(XNi、YNi、ZNi) can be by following formula
It obtains:
Wherein, H be 9 bottom center of lower nozzle arrive substrate 23 vertical range, L be jet deflection distance, θ be x-axis with
The angle of jet stream downward projection straight line.
Circular path
In XYZ coordinate system, in circle print procedure, the track of the circle of printing can be regarded as from initial point P0(0,0,
0) final goal point P is arrivednMotion profile, initial point P0To final goal point PnUpper each point PiCoordinate be (Xi、Yi、Zi), Xi
=rcos α, Yi=rsin α, Zi=0, wherein r is circle radius, and α is rotation angle, and α is the parameter about time t, and i is a little
Serial number,
In circle print procedure, the coordinate P of the bottom center of lower nozzle 9Ni(XNi、YNi、ZNi) can be by following formula
It obtains:
θ be X-axis and jet stream downward projection straight line angle, H be 9 bottom center of lower nozzle to substrate 23 it is vertical away from
From L is jet deflection distance.
Since α and θ are mutually remaining, can be obtained by transformation
WhereinV is the speed of nozzle opposing substrate movement, and t is the time of nozzle movement.
Arbitrary curve
In XYZ coordinate system, in curve F print procedure, the track of the curve of printing can be regarded as from initial point P0(0,0,
0) final goal point P is arrivednMotion profile, initial point P0To final goal point PnUpper each point PiCoordinate be (Xi、Yi、Zi), Zi
=0, i are serial number a little,
For the point P on curve FiTangential direction be defined as Ki,
In curve F print procedure, the coordinate P of the bottom center of lower nozzle 9Ni(XNi、YNi、ZNi) can be by following public affairs
Formula obtains:
Wherein,H is 9 bottom center of lower nozzle to substrate 23
Vertical range, L be jet deflection distance.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (6)
1. a kind of electrofluid direct write nozzle, including black liquid feed unit, which is characterized in that further include black liquid import (1), black liquid into
The top of mouth (1) is connect with black liquid feed unit, and the lower end of black liquid import (1) is connect with the upper end of middle part nozzle layer (2), middle part
The lower end of nozzle layer (2) connect with the upper end for stretching electrode layer (3), the outside of black liquid import (1) and stretch electrode layer (3) outside
Portion is connect with the anode of the supply voltage of voltage generator and electrically respectively, and the lower end and nozzle for stretching electrode layer (3) extend
The upper end connection of layer (4), is bonded charged layer (5) between nozzle extended layer (4) lower end and the upper end of jet stream protective layer (6), charged
Layer (5) external connection voltage generator, charged layer (5) are that discoid and center offers jet stream circle via hole, jet stream protective layer
(6) shielded layer (7) being bonded between lower end and the upper end of lower nozzle (9), shielded layer (7) center offers jet stream circle via hole, under
Portion's nozzle (9) inner wall, which is provided with, inhibits electrod-array (8), and shielded layer (7) connection the earth inhibits electrod-array (8) if being included in
It is dry to the symmetrically arranged inhibition electrode in center, further include the vertical view for obtaining the jet stream of lower nozzle (9) outgoing on substrate
Projection straight line, deflection distance and the strabismus observation camera for deflecting direction.
2. a kind of electrofluid direct write nozzle according to claim 1, which is characterized in that the black liquid import (1), middle part
Nozzle layer (2), stretching electrode layer (3), nozzle extended layer (4), jet stream protective layer (6), lower nozzle (9) are straight tube-like.
3. a kind of utilize electrofluid direct write Jet control method described in claim 1, which comprises the following steps:
Step 1, strabismus observation camera shooting jet stream squint perspective view, and jet stream strabismus perspective view is converted to jet stream downward projection
Figure obtains jet stream downward projection straight line that jet stream projects on substrate according to jet stream downward projection figure, jet deflection distance and penetrates
Stream deflection direction,
The direction of the line at the center of the projection of step 2, each pair of inhibition electrode on substrate is to inhibit electrode direction, determining and inclined
Turn the adjacent corresponding two pairs of inhibition electrode of two inhibition electrode directions in direction, according to jet deflection distance and jet deflection direction
The size of opposite direction compensating electric field and the direction of opposite direction compensating electric field are obtained, is then mended opposite direction using parallelogram method
The size that electric field is scaled the compensation supply voltage of above-mentioned two pairs of inhibition electrode is repaid, above-mentioned two pairs centrosymmetric inhibition electrodes are given
Load compensation supply voltage.
4. a kind of utilize electrofluid direct write Jet control method described in claim 1, which is characterized in that walked including rectilinear print
It is rapid:
Establish XYZ coordinate system, in XYZ coordinate system, plane where X-axis and Y-axis is plane where substrate, Z axis perpendicular to X/Y plane,
During rectilinear print, each point P of the straight line of printingiCoordinate be (Xi、Yi、Zi), Xi=vtcos θ, Yi=
Vtsin θ, Zi=0, wherein v is the speed of nozzle opposing substrate movement, and t is the time of nozzle movement, and θ is bowing for x-axis and jet stream
Depending on the angle of projection straight line, i is serial number,
During rectilinear print, the coordinate P of the bottom center of lower nozzle (9)Ni(XNi、YNi、ZNi) obtained by following formula
:
Wherein, H is vertical range of lower nozzle (9) bottom center to substrate, and L is jet deflection distance.
5. a kind of utilize electrofluid direct write Jet control method described in claim 1, which is characterized in that print and walk including circle
It is rapid:
Establish XYZ coordinate system, in XYZ coordinate system, plane where X-axis and Y-axis is plane where substrate, Z axis perpendicular to X/Y plane,
In circle print procedure, the coordinate P of the bottom center of lower nozzle (9)Ni(XNi、YNi、ZNi) obtained by following formula
:
WhereinV is the speed of nozzle opposing substrate movement, and t is the time of nozzle movement, and H is lower nozzle
(9) bottom center is to the vertical range of substrate, and L is jet deflection distance, and r is circle radius, and i is serial number.
6. a kind of utilize electrofluid direct write Jet control method described in claim 1, which is characterized in that walked including curve printing
It is rapid:
Establish XYZ coordinate system, in XYZ coordinate system, plane where X-axis and Y-axis is plane where substrate, Z axis perpendicular to X/Y plane,
Each point P of the curve of printingiCoordinate be (Xi、Yi、Zi), Zi=0,
The coordinate P of the bottom center of lower nozzle (9)Ni(XNi、YNi、ZNi) obtained by following formula:
Wherein,H is lower nozzle (9) bottom center hanging down to substrate
Straight distance, L are jet deflection distance, KiFor the point P on curveiTangential direction, i is serial number.
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