CN104537235A - Homogeneous coordinate method based micro-checker dynamic reliability analysis method - Google Patents

Homogeneous coordinate method based micro-checker dynamic reliability analysis method Download PDF

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CN104537235A
CN104537235A CN201410820168.7A CN201410820168A CN104537235A CN 104537235 A CN104537235 A CN 104537235A CN 201410820168 A CN201410820168 A CN 201410820168A CN 104537235 A CN104537235 A CN 104537235A
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micropositioner
error
theta
motion
reliability
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黄洪钟
付国忠
刘宇
李彦锋
米金华
罗大双
张龙龙
杨圆鉴
彭卫文
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University of Electronic Science and Technology of China
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a homogeneous coordinate method based micro-checker dynamic reliability analysis method. The homogeneous coordinate method based micro-checker dynamic reliability analysis method comprises the following steps of establishing a micro-checker geometric model, establishing a micro-checker motion error model, establishing a micro-checker motion reliability model, calculating the motion reliability and analyzing micro-checker dynamic reliability. According to the homogeneous coordinate method based micro-checker dynamic reliability analysis method, a micro-checker serves as a research object, a motion scheme of the micro-checker is analyzed by means of a motion analysis method, and the micro-checker geometric model is established; then the motion error model is established by means of a homogeneous coordinate method; finally a Monte-Carlo method is utilized to calculate the micro-checker motion reliability and analyze the relation between an original error mean of a driving motor of the micro-checker and dynamic accuracy in all directions; micro-checker dynamic reliability analysis is achieved under the situation that the nonlinearity and accuracy requirements of the micro-checker dynamic accuracy reliability model are high.

Description

Based on the micropositioner dynamic reliability analysis method of homogeneous coordinates method
Technical field
The invention belongs to photoetching machine technique field, particularly relate to a kind of litho machine micropositioner dynamic reliability analysis method based on homogeneous coordinates error analysis.
Background technology
Along with the high speed development of large scale integrated circuit, semi-conductor industry is more and more come high to the requirement of photoetching production technology.Litho machine is as the key equipment in integrated circuit production, and the dynamic accuracy reliability of its work stage will directly have influence on the lithography process performance of litho machine.Simultaneously, litho machine is as a kind of large-scale Complex Mechatronic Products, in the factors such as its environment for use, material property, physical dimension and load, ubiquity is uncertain, for the dynamic property and reliable operation degree that ensure litho machine under enchancement factor effect meet the demands, study its dynamic accuracy reliability tool and be of great significance.
Current facility precision reliability analytical approach mainly contains two kinds: 1) adopt the over-crossing theory in Structural Dynamics fail-safe analysis to solve, but to wear the joint probability density function needing reacting dose and speed thereof in the Rice formula of threshold rate at calculation expectation owing to crossing over procedural theory, use only two-dimentional united information in essence, namely the Reliability Theory based on over-crossing theory is certain second order theory in essence, and the DYNAMIC RELIABILITY value that thus this method obtains is coarse.Based on this method, there have been developed a kind of probability density function evolution method in recent years, it is by setting up the random evolution relation between " stochastic source " and " target " physical quantity, the essential connection of the probabilistic information between random sample can be disclosed, the statistical law of grasp mechanism kinematic output response quautity that can be meticulous.But it also has its limitation, when input motion interfere serious time or kinematic variables larger time, theory deduction process is very loaded down with trivial details, is even difficult to the result obtaining needs.2) the static analysis method for reliability of the structure improved is adopted, as analytical method, point estimations, function method of substitution and Monte-Carlo Digital Simulation Method etc., the statistical information of input parameter stochastic uncertainty can be passed to output response quautity by these methods, exported the parametric statistics amount of response quautity accordingly, low order statistical moment, output response quautity as exported response quautity meet certain probability etc. required.These methods all obtain good checking in the respective scope of application, but the problem of analytical method more difficult adaptation multi-mode nonlinearity, and point estimations is not suitable for higher-dimension and nonlinearity problem, and function method of substitution is difficult to the approximation to function of carrying out the overall situation.
Summary of the invention
Goal of the invention of the present invention is: in order to overcome the above problems, the present invention proposes a kind of micropositioner dynamic reliability analysis method based on homogeneous coordinates method, to when higher based on the non-linear and accuracy requirement of micropositioner dynamic accuracy reliability model, realize micropositioner dynamic reliability analysis.
Technical scheme of the present invention is: a kind of micropositioner dynamic reliability analysis method based on homogeneous coordinates method, comprises the following steps:
A, according to micropositioner motion scheme, adopt motion analytical method to analyze, set up micropositioner geometric model;
On B, the basis of micropositioner geometric model set up in step, adopt homogeneous coordinates method establishment micropositioner motion error model;
C, the micropositioner motion error model set up according to step B, set up micropositioner motion credibility model, and adopt Monte-Carlo method to calculate micropositioner movement reliability;
D, according to the micropositioner movement reliability calculated in step C, analyze the relation of micropositioner drive motor initial error average and micropositioner all directions dynamic accuracy fiduciary level.
Further, the micropositioner geometric model set up in described steps A, is specially:
If micropositioner coordinate is M-XYZ, world coordinates is 0-XYZ; Micropositioner coordinate origin is micropositioner center, and Z axis is perpendicular to micropositioner, and Y-axis is work stage Y-direction, and X-axis is determined by right-handed Cartesian coordinate system; Global coordinate system initial point is the subpoint of micropositioner center at frame floor level installed surface, and Z axis is vertical ground upward direction, and Y-axis is work stage Y-direction, and X-axis is determined by right-handed Cartesian coordinate system.
Further, described step B homogeneous coordinates method establishment micropositioner motion error model, is specially:
To set after micropositioner central motion in M-XYZ coordinate system homogeneous coordinates as (x 0, y 0, z 0, 1) t, actual homogeneous coordinates are (x 3, y 3, z 3, 1) t, be respectively (θ at the rotational angle of X, Y, Z-direction x, θ y, θ z), be respectively (θ in the actual rotation angle of X, Y, Z-direction xM, θ yM, θ zM); Two square motor movement margins of error are in X direction Δ x x, be Δ y along four square motor movement margins of error of Y-direction y, be Δ z along four cylinder motor movement margins of error of Z-direction z, calculated by homogeneous coordinates method:
Δx=x 3cosθ yMcosθ zM-y 3cosθ yMsinθ zM-Δx x
Δy = x 3 sin θ xM sin θ yM cos θ zM + cos θ xM sin θ zM + y 3 - sin θ xM sin θ yM sin θ zM + cos θ xM cos θ zM - Δy y
Δz = x 3 - cos θ xM sin θ yM cos θ zM + sin θ xM sin θ zM + y 3 cos θ xM sin θ yM sin θ zM + sin θ xM cos θ zM - Δz z .
Further, set up micropositioner motion credibility model in described step C, be specially:
Set-up function function is: G (Z)=δ-Δ Y > 0, determines that the expression formula of fiduciary level R is:
R=P(δ>ΔY)=Φ(β)
Wherein, Φ (i) is Standard Normal Distribution, g (Z)=δ-Δ Y, Δ Y are output error, and δ is tolerance limit error, μ μ, σ μbe respectively average and the standard deviation of stochastic variable Δ Y, μ 0, σ 0be respectively average and the standard deviation of stochastic variable δ.
The invention has the beneficial effects as follows: the micropositioner dynamic reliability analysis method based on homogeneous coordinates method of the present invention, using micropositioner as research object, is analyzed its motion scheme by motion analytical method, set up micropositioner geometric model; Again by its motion error model of homogeneous coordinates method establishment; Finally utilize Monte-Carlo method to calculate micropositioner movement reliability and analyze the relation of its drive motor initial error average and all directions dynamic accuracy fiduciary level; When higher based on the non-linear and accuracy requirement of micropositioner dynamic accuracy reliability model, realize micropositioner dynamic reliability analysis.
Accompanying drawing explanation
Fig. 1 is the micropositioner dynamic reliability analysis method flow schematic diagram based on homogeneous coordinates method of the present invention.
Fig. 2 is micropositioner X-direction voice coil motor error information schematic diagram of the present invention.
Fig. 3 is micropositioner Y-direction voice coil motor error information schematic diagram of the present invention.
Fig. 4 is micropositioner Z-direction voice coil motor error information schematic diagram of the present invention.
Fig. 5 be in micropositioner X-direction of the present invention output accuracy reliability with Δ x xaverage change schematic diagram.
Fig. 6 be in micropositioner Y-direction of the present invention output accuracy reliability with Δ x xaverage change schematic diagram.
Fig. 7 be in micropositioner Z-direction of the present invention output accuracy reliability with Δ x xaverage change schematic diagram.
Fig. 8 is that micropositioner of the present invention to close on direction Δ output accuracy reliability with Δ x xaverage change schematic diagram.
Fig. 9 be in micropositioner X-direction of the present invention output accuracy reliability with Δ y yaverage change schematic diagram.
Figure 10 be in micropositioner Y-direction of the present invention output accuracy reliability with Δ y yaverage change schematic diagram.
Figure 11 be in micropositioner Z-direction of the present invention output accuracy reliability with Δ y yaverage change schematic diagram.
Figure 12 is that micropositioner of the present invention to close on direction Δ output accuracy reliability with Δ y yaverage change schematic diagram.
Figure 13 be in X-direction of the present invention output accuracy reliability with Δ z zaverage change schematic diagram.
Figure 14 be in Y-direction of the present invention output accuracy reliability with Δ z zaverage change schematic diagram.
Figure 15 be in Z-direction of the present invention output accuracy reliability with Δ z zaverage change schematic diagram.
Figure 16 be on the Δ of conjunction direction of the present invention output accuracy reliability with Δ z zaverage change schematic diagram.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.
As shown in Figure 1, for of the present invention based on the micropositioner dynamic reliability analysis method flow schematic diagram of homogeneous coordinates method.Be described with the magnetic levitation 6-freedom micro-motion platform of α 1 model litho machine model machine in the embodiment of the present invention.Based on a micropositioner dynamic reliability analysis method for homogeneous coordinates method, comprise the following steps:
A, according to micropositioner motion scheme, adopt motion analytical method to analyze, set up micropositioner geometric model.
Micropositioner geometric model of the present invention is specially: micropositioner coordinate is M-XYZ, and world coordinates is 0-XYZ; Micropositioner coordinate is six degree of freedom coordinate system, and initial point is micropositioner center, and Z axis is perpendicular to micropositioner and direction deviates from ground upwards, and Y-axis is work stage Y-direction, and X-axis is determined by right-handed Cartesian coordinate system; World coordinates is six degree of freedom coordinate system, is attached in frame, and initial point is frame floor level installed surface, is set to ground in the embodiment of the present invention, and Z axis is vertical ground upward direction, and Y-axis is work stage Y-direction, and X-axis is determined by right-handed Cartesian coordinate system.Four square motors along Y-direction arrangement are scan module, and scan module moves along mask bench scanning direction and work stage Y-direction; Two square motors arranged in X direction are stepper motor, and stepper motor moves along mask platform step direction and work stage X-direction.By the differential rotation realized around Z-direction of X, Y-direction drive motor.Four cylinder motors along Z-direction arrangement realize micropositioner around X-axis and the rotation of Y-axis and the movement of Z-direction.Whole micropositioner provides gravity compensation by magnetic levitation, realizes the location of nano-precision in short stroke.Final precision position is the intersection point of the contained mask plate of micropositioner and objective lens optical axis, sets the center that final precision position is micropositioner in embodiments of the present invention.
On B, the basis of micropositioner geometric model set up in step, adopt homogeneous coordinates method establishment micropositioner motion error model.
A micropositioner dynamic reliability analysis method impact that analysis-driven error produces comprehensive output error based on homogeneous coordinates method of the present invention.Because micropositioner material is stupalith, set micropositioner rigidity in the embodiment of the present invention infinitely great, namely do not consider the distortion of micropositioner at the volley.For according to the motor with a collection of drawing processing and manufacturing, its machining precision is identical with production uncertain factor, therefore sets it in the embodiment of the present invention and drive error also identical.
Set the coordinate of micropositioner initial motion position in coordinate system M-XYZ as (0,0,0,0,0,0), the final precision position of post exercise is an A, when there is no error, mobile and rotate and can not introduce error, be (x in M-XYZ coordinate system middle ideal homogeneous coordinates after motion 0, y 0, z 0, 1) t, after motion, in M-XYZ coordinate system, actual homogeneous coordinates are (x 3, y 3, z 3, 1) t, be respectively (θ in the ideal rotation angle of X, Y, Z-direction x, θ y, θ z), be respectively (θ in the actual rotation angle of X, Y, Z-direction xM, θ yM, θ zM); Two square motor movement margins of error are in X direction Δ x x, be Δ y along four square motor movement margins of error of Y-direction y, be Δ z along four cylinder motor movement margins of error of Z-direction z.According to homogeneous coordinates method, ideally the homogeneous coordinates of A point under global coordinate system are:
Wherein, for the transformation matrix ideally between micropositioner coordinate system and global coordinate system,
T M O ( x , y , z , θ x , θ y , θ z ) + Trans ( a , b , c ) Rot ( x , θ x ) Rot ( y , θ y ) Rot ( z , θ z ) = 1 0 0 a 0 1 0 b 0 0 1 c 0 0 0 1 1 0 0 0 0 cos θ x - sin θ x 0 0 sin θ x cos θ x 0 0 0 0 1 cos θ y 0 sin θ y 0 0 1 0 0 - sin θ y 0 cos θ y 0 0 0 0 1 cos θ z - sin θ z 0 0 sin θ z cos θ z 0 0 0 0 1 0 0 0 0 1 .
According to homogeneous coordinates method, under actual conditions, the homogeneous coordinates of A point under global coordinate system are:
Wherein, for the transformation matrix under virtual condition between micropositioner coordinate system and global coordinate system,
T M O ( x M , y M , z M , θ xM , θ yM , θ zM ) = 1 0 0 x M 0 1 0 y M 0 0 1 z M 0 0 0 1 1 0 0 0 0 cos θ xM - sin θ xM 0 0 sin θ xM cos θ xM 0 0 0 0 1 cos θ yM 0 sin θ yM 0 0 1 0 0 - sin θ yM 0 cos θ yM 0 0 0 0 1 cos θ zM - sin θ zM 0 0 sin θ zM cos θ zM 0 0 0 0 1 0 0 0 0 1 .
According to kinematic chain error modeling principle, deduct desirable homogeneous coordinates by the actual homogeneous coordinates of final precision position, the margin of error on X, Y, Z tri-directions can be obtained, namely have:
Δx Δy Δz 0 = x 3 cos θ yM cos θ zM - y 3 cos θ yM sin θ zM + z 3 sin θ yM + x M x 3 sin θ xM sin θ yM cos θ zM + cos θ xM sin θ zM + y 3 - sin θ xM sin θ yM sin θ zM + cos θ x M cos θ zM - z 3 sin θ xM cos θ yM + y M x 3 - cos θ xM sin θ yM cos θ zM + sin θ xM sin θ zM + y 3 cos θ xM sin θ yM sin θ zM + sin θ xM cos θ zM + z 3 cos θ xM cos θ yM z M 1 - x y z 1 = x 3 cos θ yM cos θ zM - y 3 cos θ yM sin θ zM - Δx x x 3 sin θ xM sin θ yM cos θ zM + cos θ xM sin θ zM + y 3 - sin θ xM sin θ yM sin θ zM + cos θ xM cos θ zM - Δy y x 3 - cos θ xM sin θ yM cos θ zM + sin θ xM sin θ zM + y 3 cos θ xM sin θ yM sin θ zM + sin θ xM cos θ zM - Δz z 0
Solve and can obtain:
Δx=x 3cosθ yMcosθ zM-y 3cosθ yMsinθ zM-Δx x
Δy = x 3 sin θ xM sin θ yM cos θ zM + cos θ xM sin θ zM + y 3 - sin θ xM sin θ yM sin θ zM + cos θ xM cos θ zM - Δy y
Δz = x 3 - cos θ xM sin θ yM cos θ zM + sin θ xM sin θ zM + y 3 cos θ xM sin θ yM sin θ zM + sin θ xM cos θ zM - Δz z .
Wherein, x 3 = Δx x 2 + Δy y 2 cos ( arctan Δy y Δx x + arctan 110 + y - Δy y 170 ) / cos ( arctan z - Δz z 170 )
y 3 = Δx x 2 + Δy y 2 sin ( arctan Δy y Δx x + arctan 110 + y - Δy y 170 ) / cos ( arctan z - Δz z 210 )
z 3=0
Δθ xM = arctan z - Δz z 210 - arctan z 210
Δθ yM = arctan z - Δz z 170 - arctan z 170
Δθ zM = arctan 110 + y - Δy y 170 - θ zM = arctan 110 + y - Δy y 170 - arctan 110 + y 170 .
C, the micropositioner motion error model set up according to step B, set up micropositioner motion credibility model, and adopt Monte-Carlo method to calculate micropositioner movement reliability.
For according to the mass-producted mechanism of same drawing, its site error is the function of stochastic variable, and mechanism position error is the linear function of separate each initial error.Law of great numbers is combined, the result still Normal Distribution of each initial error combined action, i.e. output error Δ Y Normal Distribution from probability distribution.According to the definition of mechanism kinematic precision fiduciary level, the probability that mechanism kinematic output error drops within the scope of permissible error is:
R=P(ε′ m<ΔY<ε″ m)
By normal distribution law, can formula of reliability be obtained:
R = P ( &epsiv; m &prime; < &Delta;Y < &epsiv; m &prime; &prime; ) = P ( &Delta;Y < &epsiv; m &prime; &prime; ) - P ( &Delta;Y < &epsiv; m &prime; ) = &Phi; ( &epsiv; m &prime; &prime; - &mu; &sigma; ) - &Phi; ( &epsiv; m &prime; - &mu; &sigma; )
Wherein, Φ (i) is Standard Normal Distribution, ε " mfor the higher limit of tolerance limit error, ε ' mfor the lower limit of tolerance limit error.
Especially, when definition tolerance limit error also Normal Distribution, according to the definition of mechanism kinematic reliability, carry out similar with Stress-Strength Interference Model, set-up function function is:
G(Z)=δ-ΔY>0
Wherein, δ is tolerance limit error.This power function represents that output error is less than tolerance limit error.
Due to output error Δ Y and tolerance limit error delta all Normal Distribution, then the probability density of output error Δ Y and tolerance limit error delta is respectively:
f 1 ( x 1 ) = &Delta;Y = 1 2 &pi; &sigma; &mu; exp [ - 1 2 ( x - x &mu; &sigma; &mu; ) 2 ]
f 2 ( x 2 ) = &delta; = 1 2 &pi; &sigma; 0 exp [ - 1 2 ( y - x 0 &sigma; 0 ) 2 ]
Wherein, μ μ, σ μbe respectively average and the standard deviation of stochastic variable Δ Y, μ 0, σ 0be respectively average and the standard deviation of stochastic variable δ.
According to Stress-Strength Interference Model, mechanism kinematic fiduciary level R is:
R = P ( &delta; > &Delta;Y ) = &Integral; - &infin; + &infin; f 2 ( x 2 ) [ &Integral; - &infin; x 2 f 1 ( x 1 ) dx 1 ] dx 2 = &Integral; 0 + &infin; f ( z ) dx = &Integral; 0 + &infin; 1 2 &pi; &sigma; z exp [ - 1 2 ( z - &mu; z &sigma; z ) 2 dz
Above formula is turned to standardized normal distribution, and establishes be expressed as:
R = P ( &delta; > &Delta;Y ) = &Integral; 0 + &infin; f ( z ) dz = &Integral; 0 + &infin; 1 2 &pi; exp [ - 1 2 &mu; 2 ] d&mu; = &Phi; ( &beta; )
Wherein, f ( z ) = 1 2 &pi; &sigma; z exp [ - 1 2 ( z - &mu; z &sigma; z ) 2 ] , &beta; = &mu; z &sigma; z = &mu; 0 - &mu; &mu; &sigma; 0 2 + &sigma; &mu; 2 , Z = &delta; - &Delta;Y .
Conveniently the precision reliability analysis in later stage and the limiting error value of unified initial error in the embodiment of the present invention, get its absolute value as analysis data to the original dynamic value of drive motor.But in the result obtained, the output error average of all directions may be negative value, facilitate the limiting error limit of the analysis in later stage and unified output error, its absolute value also got to the output error of all directions and analyzes, namely have:
&beta; = &mu; z &sigma; z = &mu; 0 - | &mu; &mu; | &sigma; 0 2 + &sigma; &mu; 2
From above formula, when after known output error and tolerance limit error value feature, driven member movement locus can be obtained and fall into probability in accuracy rating allowable, i.e. fiduciary level R.The evaluation method adopting point to evaluate in invention calculates dynamic accuracy reliability.Namely some evaluation measures with probability the ability that mechanism end actuator accurately arrives certain some position in work space.With this point for the center of circle, the space sphere being radius with tolerance limit error delta and permissible error band.Mechanism end actuator deviations of actual position falls into the probability of permissible error band and the some evaluation of mechanism kinematic fiduciary level, and the computing method of fiduciary level are identical with the computing method of mechanism kinematic fiduciary level.Then fiduciary level R can be expressed as:
R = &Phi; ( &epsiv; m &prime; &prime; - &mu; &sigma; ) - &Phi; ( &epsiv; m &prime; - &mu; &sigma; ) = &Phi; ( &beta; )
Micropositioner drive motor driveability is tested, obtains voice coil motor track following accelerating sections error and positioning error on X, Y, Z tri-directions respectively, draw corresponding track following Error Graph.By analyzing and the test of fitness of fot test data, draw distribution pattern and the distribution parameter of motor initial error data.Again according to the limiting error in micropositioner X, Y, Z all directions and conjunction direction and average, calculated the dynamic accuracy fiduciary level of all directions under measured data of micropositioner by Monte-Carlo method.
D, according to the micropositioner motion credibility model set up in step C, analyze the relation of micropositioner drive motor initial error average and micropositioner all directions dynamic accuracy fiduciary level.
The embodiment of the present invention carries out calculating and matching on Matlab platform, according to the average of motor error in X, Y, Z all directions obtain the variation relation figure of output accuracy reliability on X, Y, Z all directions and conjunction direction, and analysis show that all directions motor initial error is on the impact of output accuracy.
As shown in Figures 2 to 4, micropositioner X of the present invention, Y, Z-direction voice coil motor error information schematic diagram is respectively.In embodiments of the present invention, micropositioner X-direction voice coil motor track following accelerating and decelerating part maximum error is ± 13nm, and positioning error is ± 5nm; Micropositioner Y-direction voice coil motor track following accelerating and decelerating part maximum error is ± 15nm, and positioning error is ± 6nm; Micropositioner Z-direction voice coil motor track following accelerating and decelerating part maximum error is ± 13nm, and positioning error is ± 5nm.By to obtained data analysis and the test of fitness of fot, this drive motor initial error data fit normal distribution, as shown in table 1.
The average of table 1 drive motor initial error data and mean square deviation
It is fixed that X, Y, Z all directions and the limiting error of closing on direction and average are got according to the design performance index ultimate value of micropositioner, and according to each data obtained in table 1, the dynamic accuracy fiduciary level of all directions under measured data of micropositioner is calculated by Monte-Carlo method, as shown in table 2.
Table 2 dynamic error result of calculation in all directions and DYNAMIC RELIABILITY
By carrying out calculating and matching on matlab platform, obtaining X, Y, Z all directions and closing on direction output accuracy reliability with Δ x xaverage the variation relation figure of change, as shown in Fig. 5 to Fig. 8, is respectively micropositioner X of the present invention, Y, Z-direction and closes on direction Δ output accuracy reliability with Δ x xaverage change schematic diagram.Can find out by analyzing these figure, comparatively large on the impact of the output accuracy reliability in Δ x, Δ y, Δ direction, less on the impact of the output accuracy reliability in Δ z direction.Making the output accuracy reliability of all directions higher, is not that the error of X-direction motor is the smaller the better.Know by analyzing, when time, the precision reliability of all directions is the highest.
By carrying out calculating and matching on matlab platform, obtaining X, Y, Z all directions and closing on direction output accuracy reliability with Δ y yaverage the variation relation figure of change, as shown in Fig. 9 to Figure 12, is respectively micropositioner X, Y, Z all directions of the present invention and closes on direction Δ output accuracy reliability with Δ y yaverage change schematic diagram.Can find out by analyzing these figure, comparatively large on the impact of Δ x, Δ y, Δ direction output accuracy reliability, less on the impact of Δ z direction output accuracy reliability.Now can find out, Δ x, Δ direction output accuracy reliability and Δ y direction output accuracy reliability are conflicting, can not improve the precision reliability in these three directions simultaneously.Because the precision reliability in Δ direction is more important than the precision reliability of Δ x, Δ y, therefore the precision reliability in Δ direction is preferentially made to be guaranteed.Can be drawn by optimality analysis &mu; &Delta;y y = 4.5 Time result optimum.
By carrying out calculating and matching on matlab platform, obtaining X, Y, Z all directions and closing on direction output accuracy reliability with Δ z zaverage the variation relation figure of change, as shown in Figure 13 to Figure 16, is respectively X, Y, Z all directions of the present invention and closes on direction Δ output accuracy reliability with Δ z zaverage change schematic diagram.Can find out by analyzing these figure, comparatively large on the impact of Δ z, Δ direction output accuracy reliability, less on the impact of Δ x, Δ y direction output accuracy reliability.The change of Δ z, Δ direction output accuracy reliability is consistent, but asynchronous.Because the precision reliability in Δ direction is more important than the precision reliability in Δ z direction, therefore the precision reliability in Δ direction is preferentially made to be guaranteed.Can be drawn by optimality analysis time result optimum.
Finally by the relation of the dynamic accuracy fiduciary level of the average with micropositioner all directions of analyzing micropositioner drive motor initial error, discovery respectively when time can obtain optimum dynamic accuracy fiduciary level.
Those of ordinary skill in the art will appreciate that, embodiment described here is to help reader understanding's principle of the present invention, should be understood to that protection scope of the present invention is not limited to so special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combination of not departing from essence of the present invention according to these technology enlightenment disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (4)

1., based on a micropositioner dynamic reliability analysis method for homogeneous coordinates method, it is characterized in that: comprise the following steps:
A, according to micropositioner motion scheme, adopt motion analytical method to analyze, set up micropositioner geometric model;
On B, the basis of micropositioner geometric model set up in step, adopt homogeneous coordinates method establishment micropositioner motion error model;
C, the micropositioner motion error model set up according to step B, set up micropositioner motion credibility model, and adopt Monte-Carlo method to calculate micropositioner movement reliability;
D, according to the micropositioner movement reliability calculated in step C, analyze the relation of micropositioner drive motor initial error average and micropositioner all directions dynamic accuracy fiduciary level.
2., as claimed in claim 1 based on the micropositioner dynamic reliability analysis method of homogeneous coordinates method, it is characterized in that, the micropositioner geometric model set up in described steps A, is specially:
If micropositioner coordinate is M-XYZ, world coordinates is 0-XYZ; Micropositioner coordinate origin is micropositioner center, and Z axis is perpendicular to micropositioner, and Y-axis is work stage Y-direction, and X-axis is determined by right-handed Cartesian coordinate system; Global coordinate system initial point is the subpoint of micropositioner center at frame floor level installed surface, and Z axis is vertical ground upward direction, and Y-axis is work stage Y-direction, and X-axis is determined by right-handed Cartesian coordinate system.
3., as claimed in claim 1 based on the micropositioner dynamic reliability analysis method of homogeneous coordinates method, it is characterized in that, described step B homogeneous coordinates method establishment micropositioner motion error model, is specially:
To set after micropositioner central motion in M-XYZ coordinate system middle ideal homogeneous coordinates as (x 0, y 0, z 0, 1) t, actual homogeneous coordinates are (x 3, y 3, z 3,1) t, be respectively (θ in the ideal rotation angle of X, Y, Z-direction x, θ y, θ z), be respectively (θ in the actual rotation angle of X, Y, Z-direction xM, θ yM, θ zM); Two square motor movement margins of error are in X direction Δ x x, be Δ y along four square motor movement margins of error of Y-direction y, be Δ z along four cylinder motor movement margins of error of Z-direction z, calculated the margin of error Δ x of X, Y, Z-direction by homogeneous coordinates method, Δ y, Δ z.
4., as claimed in claim 1 based on the micropositioner dynamic reliability analysis method of homogeneous coordinates method, it is characterized in that, set up micropositioner motion credibility model in described step C, be specially:
Set-up function function is: G (Z)=δ-Δ Y, determines that the expression formula of fiduciary level R is:
R=P(δ>ΔY)=Φ(β)
Wherein, Φ () is Standard Normal Distribution, g (Z)=δ-Δ Y, Δ Y are output error, and δ is tolerance limit error, μ μ, σ μbe respectively average and the standard deviation of stochastic variable Δ Y, μ 0, σ 0be respectively average and the standard deviation of stochastic variable δ.
CN201410820168.7A 2014-12-25 2014-12-25 Homogeneous coordinate method based micro-checker dynamic reliability analysis method Pending CN104537235A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106959667A (en) * 2017-04-11 2017-07-18 西南交通大学 A kind of lathe translation shaft error of perpendicularity modeling method

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1760760A (en) * 2004-10-14 2006-04-19 中国科学院电工研究所 The accurate magnetic levitation work stage of extreme ultraviolet photolithographic
CN101078889A (en) * 2007-06-29 2007-11-28 清华大学 6 freedom degree micromotion operating platform
US20080109184A1 (en) * 2006-11-06 2008-05-08 Canon Kabushiki Kaisha Position and orientation measurement method and apparatus
US20080240616A1 (en) * 2007-04-02 2008-10-02 Objectvideo, Inc. Automatic camera calibration and geo-registration using objects that provide positional information

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1760760A (en) * 2004-10-14 2006-04-19 中国科学院电工研究所 The accurate magnetic levitation work stage of extreme ultraviolet photolithographic
US20080109184A1 (en) * 2006-11-06 2008-05-08 Canon Kabushiki Kaisha Position and orientation measurement method and apparatus
US20080240616A1 (en) * 2007-04-02 2008-10-02 Objectvideo, Inc. Automatic camera calibration and geo-registration using objects that provide positional information
CN101078889A (en) * 2007-06-29 2007-11-28 清华大学 6 freedom degree micromotion operating platform

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
DASHUANG LUO 等: "《Dynamic Precision Reliability Analysis for Six Degree of Freedom Micro-Diplacement Mechanism of Reticle Stage in Lithography Machine Based on Monte-Carlo》", 《QR2MSE 2013》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106959667A (en) * 2017-04-11 2017-07-18 西南交通大学 A kind of lathe translation shaft error of perpendicularity modeling method

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Application publication date: 20150422