CN104537235A  Homogeneous coordinate method based microchecker dynamic reliability analysis method  Google Patents
Homogeneous coordinate method based microchecker dynamic reliability analysis method Download PDFInfo
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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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Abstract
The invention discloses a homogeneous coordinate method based microchecker dynamic reliability analysis method. The homogeneous coordinate method based microchecker dynamic reliability analysis method comprises the following steps of establishing a microchecker geometric model, establishing a microchecker motion error model, establishing a microchecker motion reliability model, calculating the motion reliability and analyzing microchecker dynamic reliability. According to the homogeneous coordinate method based microchecker dynamic reliability analysis method, a microchecker serves as a research object, a motion scheme of the microchecker is analyzed by means of a motion analysis method, and the microchecker geometric model is established; then the motion error model is established by means of a homogeneous coordinate method; finally a MonteCarlo method is utilized to calculate the microchecker motion reliability and analyze the relation between an original error mean of a driving motor of the microchecker and dynamic accuracy in all directions; microchecker dynamic reliability analysis is achieved under the situation that the nonlinearity and accuracy requirements of the microchecker dynamic accuracy reliability model are high.
Description
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, semiconductor 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 largescale 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 overcrossing theory in Structural Dynamics failsafe 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 twodimentional united information in essence, namely the Reliability Theory based on overcrossing 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 MonteCarlo 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 multimode nonlinearity, and point estimations is not suitable for higherdimension 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 nonlinear 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 MonteCarlo 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 MXYZ, world coordinates is 0XYZ; Micropositioner coordinate origin is micropositioner center, and Z axis is perpendicular to micropositioner, and Yaxis is work stage Ydirection, and Xaxis is determined by righthanded 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 Yaxis is work stage Ydirection, and Xaxis is determined by righthanded Cartesian coordinate system.
Further, described step B homogeneous coordinates method establishment micropositioner motion error model, is specially:
To set after micropositioner central motion in MXYZ 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, Zdirection
_{x}, θ
_{y}, θ
_{z}), be respectively (θ in the actual rotation angle of X, Y, Zdirection
_{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 Ydirection
_{y}, be Δ z along four cylinder motor movement margins of error of Zdirection
_{z}, calculated by homogeneous coordinates method:
Δx＝x
_{3}cosθ
_{yM}cosθ
_{zM}y
_{3}cosθ
_{yM}sinθ
_{zM}Δx
_{x}
Further, set up micropositioner motion credibility model in described step C, be specially:
Setup function function is: G (Z)=δΔ 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)=δΔ Y, Δ Y are output error, and δ is tolerance limit error, μ
_{μ}, σ
_{μ}be respectively average and the standard deviation of stochastic variable Δ Y, μ
_{0}, σ
_{0}be 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 MonteCarlo 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 nonlinear 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 Xdirection voice coil motor error information schematic diagram of the present invention.
Fig. 3 is micropositioner Ydirection voice coil motor error information schematic diagram of the present invention.
Fig. 4 is micropositioner Zdirection voice coil motor error information schematic diagram of the present invention.
Fig. 5 be in micropositioner Xdirection of the present invention output accuracy reliability with Δ x
_{x}average
change schematic diagram.
Fig. 6 be in micropositioner Ydirection of the present invention output accuracy reliability with Δ x
_{x}average
change schematic diagram.
Fig. 7 be in micropositioner Zdirection of the present invention output accuracy reliability with Δ x
_{x}average
change schematic diagram.
Fig. 8 is that micropositioner of the present invention to close on direction Δ output accuracy reliability with Δ x
_{x}average
change schematic diagram.
Fig. 9 be in micropositioner Xdirection of the present invention output accuracy reliability with Δ y
_{y}average
change schematic diagram.
Figure 10 be in micropositioner Ydirection of the present invention output accuracy reliability with Δ y
_{y}average
change schematic diagram.
Figure 11 be in micropositioner Zdirection of the present invention output accuracy reliability with Δ y
_{y}average
change schematic diagram.
Figure 12 is that micropositioner of the present invention to close on direction Δ output accuracy reliability with Δ y
_{y}average
change schematic diagram.
Figure 13 be in Xdirection of the present invention output accuracy reliability with Δ z
_{z}average
change schematic diagram.
Figure 14 be in Ydirection of the present invention output accuracy reliability with Δ z
_{z}average
change schematic diagram.
Figure 15 be in Zdirection of the present invention output accuracy reliability with Δ z
_{z}average
change schematic diagram.
Figure 16 be on the Δ of conjunction direction of the present invention output accuracy reliability with Δ z
_{z}average
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 6freedom micromotion 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 MXYZ, and world coordinates is 0XYZ; 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 Yaxis is work stage Ydirection, and Xaxis is determined by righthanded 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 Yaxis is work stage Ydirection, and Xaxis is determined by righthanded Cartesian coordinate system.Four square motors along Ydirection arrangement are scan module, and scan module moves along mask bench scanning direction and work stage Ydirection; Two square motors arranged in X direction are stepper motor, and stepper motor moves along mask platform step direction and work stage Xdirection.By the differential rotation realized around Zdirection of X, Ydirection drive motor.Four cylinder motors along Zdirection arrangement realize micropositioner around Xaxis and the rotation of Yaxis and the movement of Zdirection.Whole micropositioner provides gravity compensation by magnetic levitation, realizes the location of nanoprecision 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 analysisdriven 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 MXYZ 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 MXYZ coordinate system middle ideal homogeneous coordinates after motion
_{0}, y
_{0}, z
_{0}, 1)
^{t}, after motion, in MXYZ 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, Zdirection
_{x}, θ
_{y}, θ
_{z}), be respectively (θ in the actual rotation angle of X, Y, Zdirection
_{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 Ydirection
_{y}, be Δ z along four cylinder motor movement margins of error of Zdirection
_{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,
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,
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 tridirections can be obtained, namely have:
Solve and can obtain:
Δx＝x
_{3}cosθ
_{yM}cosθ
_{zM}y
_{3}cosθ
_{yM}sinθ
_{zM}Δx
_{x}
Wherein,
${x}_{3}=\sqrt{{{\mathrm{\Δx}}_{x}}^{2}+{{\mathrm{\Δy}}_{y}}^{2}}\mathrm{cos}(\mathrm{arctan}\frac{{\mathrm{\Δy}}_{y}}{{\mathrm{\Δx}}_{x}}+\mathrm{arctan}\frac{110+y{\mathrm{\Δy}}_{y}}{170})/\mathrm{cos}\left(\mathrm{arctan}\frac{z{\mathrm{\Δz}}_{z}}{170}\right)$
z
_{3}＝0
C, the micropositioner motion error model set up according to step B, set up micropositioner motion credibility model, and adopt MonteCarlo method to calculate micropositioner movement reliability.
For according to the massproducted 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:
Wherein, Φ (i) is Standard Normal Distribution, ε "
_{m}for the higher limit of tolerance limit error, ε '
_{m}for 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 StressStrength Interference Model, setup function function is:
G(Z)＝δΔY＞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:
Wherein, μ
_{μ}, σ
_{μ}be respectively average and the standard deviation of stochastic variable Δ Y, μ
_{0}, σ
_{0}be respectively average and the standard deviation of stochastic variable δ.
According to StressStrength Interference Model, mechanism kinematic fiduciary level R is:
Above formula is turned to standardized normal distribution, and establishes
be expressed as:
Wherein,
$f\left(z\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_{z}}\mathrm{exp}[\frac{1}{2}{\left(\frac{z{\mathrm{\μ}}_{z}}{{\mathrm{\σ}}_{z}}\right)}^{2}],\mathrm{\β}=\frac{{\mathrm{\μ}}_{z}}{{\mathrm{\σ}}_{z}}=\frac{{\mathrm{\μ}}_{0}{\mathrm{\μ}}_{\mathrm{\μ}}}{\sqrt{{\mathrm{\σ}}_{0}^{2}+{\mathrm{\σ}}_{\mathrm{\μ}}^{2}}},Z=\mathrm{\δ}\mathrm{\ΔY}.$
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:
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:
Micropositioner drive motor driveability is tested, obtains voice coil motor track following accelerating sections error and positioning error on X, Y, Z tridirections 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 MonteCarlo 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, Zdirection voice coil motor error information schematic diagram is respectively.In embodiments of the present invention, micropositioner Xdirection voice coil motor track following accelerating and decelerating part maximum error is ± 13nm, and positioning error is ± 5nm; Micropositioner Ydirection voice coil motor track following accelerating and decelerating part maximum error is ± 15nm, and positioning error is ± 6nm; Micropositioner Zdirection 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 MonteCarlo 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
_{x}average
the variation relation figure of change, as shown in Fig. 5 to Fig. 8, is respectively micropositioner X of the present invention, Y, Zdirection and closes on direction Δ output accuracy reliability with Δ x
_{x}average
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 Xdirection 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
_{y}average
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
_{y}average
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
${\mathrm{\μ}}_{{\mathrm{\Δy}}_{y}}=4.5$ 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
_{z}average
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
_{z}average
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 MonteCarlo 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 MXYZ, world coordinates is 0XYZ; Micropositioner coordinate origin is micropositioner center, and Z axis is perpendicular to micropositioner, and Yaxis is work stage Ydirection, and Xaxis is determined by righthanded 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 Yaxis is work stage Ydirection, and Xaxis is determined by righthanded 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 MXYZ 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, Zdirection
_{x}, θ
_{y}, θ
_{z}), be respectively (θ in the actual rotation angle of X, Y, Zdirection
_{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 Ydirection
_{y}, be Δ z along four cylinder motor movement margins of error of Zdirection
_{z}, calculated the margin of error Δ x of X, Y, Zdirection 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:
Setup function function is: G (Z)=δΔ 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)=δΔ Y, Δ Y are output error, and δ is tolerance limit error, μ
_{μ}, σ
_{μ}be respectively average and the standard deviation of stochastic variable Δ Y, μ
_{0}, σ
_{0}be respectively average and the standard deviation of stochastic variable δ.
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Application publication date: 20150422 