Raise the research  that the law measured precision at 3 o'clock

The method analysed the reading that measure a head and horn position error each to circularity humorous affects each bits more circumferential the effect that measures precision; Put forward what the law surveyed a system at 3 o'clock to optimize strategy and algorithm; Studied what the law measured an error at 3 o'clock to distributing with pass the law; Put forward to overcome error of the fixed position that measure a head and 3 sensitivity that measure a head the software method of correction of abhorrent influence.

Result circularity of each harmonic the biggest measure an error opposite at the tradition the law was reduced at 3 o'clock 67% , circularity reachs his the measurement of each harmonic uncertainty is reduced apparently.

This method can raise conclusion apparently the law measured precision at 3 o'clock.

Keyword at 3 o'clock law; Circularity; Shafting motion error; Error depart classifies Wang Xiaolin(Department Of Optical Engineering of 　 of 　 of date TG806 A Study On Improving The Accuracy Of(for Roundness And Spindle Motion Error Measurements With Three-Point MethodZhang Yuhua, beijing Institute Of Technology, li Zhen(Precision Instrument And Opto-electronics Engineering College Of Tianjin University of 　 of 　 of Beijing 　 100081)Zhang Guoxiong, to Improve The Accuracy Of Measuring Roundness And Spindle Mo-tion Error With Three-point Method of 　 of Aim of 　 of Tianjin 　 300072)Abstract.

Methods 　 The Effects Of The Reading Error And The Misalignment Of The Probes On The Accuracy Of Measuring And All The Harmonics Of Roundness Were Analyzed; The Strategy And The Algorithm For Optimizing The Parameters Of The Measuring System Were Proposed; The Dist

Results The Maximum Error Of Measuring The Harmonics Of Roundness Was Reduced By 67% In Comparison With That By The Traditional Three-point Method.

Conclusion 　 The Accuracy Of Roundness Measured By The Improved Three-point Method Gets A Distinct Improvement.

Course of of Three-point Method; Roundness; Spindle Motion Error; Error Separation of Key Words 　 Dr. 　 colleges and universities nods fund of special scientific research to aid financially a task to rise at 3 o'clock law [1] measure precision, forefathers pour into tremendous energy, but its study mostly be confined to considered how to avoid from maths only the harmonic of the law added authority function ω at 3 o'clock (the 3 harmonic that cause restrain K)=1+a2e-jk φ 2+a3e-jk φ [2 ～ 4] , and ignored measure the error effect to measuring precision.

Document [5] although notice afore-mentioned issues, but fail the impact that thorough analysis measures head reading and fixed position error and circularity to measure an error.

Author focal point analyses the reading that measure a head and fixed position error to measure the effect of precision to circularity, the optimizes method and harmonic to measure an error transmission law that studies a system, with rising further the law measured precision at 3 o'clock.

1 the law measured principle and precision analysis at 3 o'clock 1.

1 the law measured a principle to pursue at 3 o'clock 1 the law measured law principle at 3 o'clock at 3 o'clock the principle is shown 1 times like the graph.

Working circumferential on decorate 3 Pi that measure a head, the included angle of they and Y axis is 1=0) of φ I(φ , working circularity is R(θ N) , the X of error of shafting radial motion, y is X(θ N) to heft, y(θ N) , the output that measures a head each is among them 0 reading that Ri is the Pi that measure a head; θ N is sampling dot, θ N=2n π / N, n=0, 1, ... , n-1.

Tectonic and linear equation writes down the Fourier coefficient that sets S0(θ N) to be Fk and Gk, for N) of detached X(θ , y(θ N) and R(θ N) , make 1=0 of α 1= β , decide A2 from this, a3.

Via proper commutation, each the Fourier coefficient of harmonic is circularity to get workpiece circularity from this among them Km is harmonic the superlative degree second.

By equation (1) can get error of shafting radial motion.

1.

The 2 main errors that the law measured systematic precision to analyse an influence to measure round precision at 3 o'clock have: ① measures a 1n of reading error δ 3 times, δ 2n, δ 3n, it affects Fk, gk; ② measures δ of brilliance position error (φ 2) , δ (φ 3) , it affects α K, β K.

By type (4) is gotten 1.

2.

The influence of the 1 reading error that measure a head to measuring precision the effect that right now oversight measures brilliance position error, the variance that sets 3 reading error that measure a head all is σ 2, all be worth the relation with variance by random variable [6] , ak, what a reading error measures to introduce for the variance of Bk is circumferential the circularity that P nods measures an error to be among them.

Criterion 1.

2.

2 measure the effect of brilliance position error to measuring precision right now, be like the influence of oversight reading error, the phasic error that is 　 to get K second harmonic by Tan φ K=Ak/Bk by the amplitude of K second harmonic is opposite error is set, qk is to express to measure head reading and part position error reachs his to circularity the main index that each harmonic measures precision to affect size.

Apparent, measure the effect of brilliance position error to measuring an outcome to reduce the reading error that measure a head to reach, should make Qk as far as possible small.

The computer emulates make clear: Circularity measures an error to basically be caused by the reading error that measure a head, position error affects part lesser, measure precision prep above when what measure brilliance place when 1 ′ , the measurement that place of the position error that measure a head introduces the error is negligible.

2 the law measured systematic parameter at 3 o'clock optimizing optimized purpose is to choose a group of first-rate to measure brilliance place, make measure head reading and part the effect that each to circularity harmonic measures precision is position error the smallest.

Optimize what the process is function of a many target to optimize decision-making problem.

Measure brilliance position error to be opposite to reduce the reading error that measure a head to reach the influence of the precision that measure a circle, to given class second Km, beg φ 2, φ 3, the maximum that makes the Qk of each all harmonic medium is the smallest.

The target function character that forms with Qk is complex, have a lot of local and dinky values, commonly used odd peak function searchs actor method to cannot get overall situation optimal value, and use enumerate method [5, 7] the search is time-consuming very long.

For this, the author is based on thought of Monte Carlo random experiment, mode of referenced simplex finds actor method [7] , wove random mode searchs algorithmic program of the method.

Its method is as follows: ① is inside the plane that decides by place of Imax of φ of ＜ of I of φ of φ Imin ＜ produce a random experiment to nod φ (0) ; ② with initiative dot φ (0) is a center, make region of one hollow circle for radius with A1 and A2, in this hollow circle presses even distributinging generation inside the country random variable searchs 5 ～ 10 times, if do not succeed, search reversely, beg a new feature φ (1) , make F(φ (φ of 1)) ＜ F((0)) ; ③ undertakes mode finds actor, φ of your φ =2 (1)- φ (0) , the φ that be like F() ＜ F(φ (1)) , state mode finds actor success, change measure to ② , it is a center with new feature, continue to search better place; ④ is like F(φ ) ＞ F(φ (1)) , state mode finds actor failure, φ to φ (1) is contractive, till F(φ ) ＜ F(φ (till 1)) , repeat measure ② ; ⑤ returns ① , repeat afore-mentioned tests 2000 ～ 5000, compare each test result, choose optimal result, get overall situation in order to ensure best dot.

The dependability of afore-mentioned methods and algorithmic error can make an on-the-spot investigation through two kinds of ways: The opposite error that ① takes the result that find actor is less than 10-31 to end criterion; ② excel document [5] medium result.

Graph 2 gave out Km is the 20 Qk that fall with the 160 optimal angle when and optimal angle, can see each harmonic measured the way at 3 o'clock from this the transmission rule of the error.

The Qk below the optimal angle of author plan cipher out is worth, not only the Qk(below the optimal point of view that apparent excel defines by traditional method sees graph 2b and graph 2d) , and apparent excel document [5] (2a seeing a picture and graph 2c) .

The experiment makes clear, take the accretion of Km as place, the Qk of each corresponding harmonic greatens.

When using the definite system below some Km to measure the harmonic that is more than this harmonic upper limit, because the error delivers coefficient very big, minor reading error can make circularity measures an outcome generation is larger lack fidelity.

Because this is correct,estimation needs the optimal horn place that measure a harmonic upper limit and measures a head certainly with this crucial.

(A) optimizes methodological result (B) optimizes methodological result (C) optimizes methodological result (result of D) traditional method pursues 2 the law measured an optimal horn position and circularity at 3 o'clock each harmonic measures an error to transfer a system 3 measure brilliance position to measure an error to reach the sensitivity that measure a head abhorrent corrective and actual in measuring, considering: ① measures brilliance position existence to measure error Δ φ 2, Δ φ 3; The sensitivity that ② measures a head 3 times is abhorrent, the specific value that establishs them is P3 of ∶ of 1 ∶ P2.

Criterion circularity and the postulate with shafting detached error should are apparent, by the A2 that 1=0 of α 1= β reachs, a3 cannot assure to go up type holds water.

This brings about: ① circularity and shafting error cannot depart thoroughly, rudimental shafting moves error plan enters circularity in; The circularity that ② computation reachs each Fourier coefficient is magnified by false ground, cause bigger measurement error.

When the postulate that departs when contented error, 1=0 of α 1= β , right now, the humorous amplitude of S0(θ N) is worth C21=F21+G21=0.

When φ 2, 3 have φ when the error, ＞ of ｜ C1 ｜ 0.

Can be opposite accordingly φ 2, the immediate measured value of 3 undertakes φ optimize in order to determine its true value.

The method is: When φ 2, when 3 change of φ , a2, a3 changes subsequently, the value of C1 also changes subsequently, if decrescent of ｜ C1 ｜ , show φ 2, 3 hasten of φ are bordering on its true value.

Namely: Beg φ 2, φ 3, 2 ≤ of φ of φ 2min ≤ φ 2max, 3 ≤ of φ of φ 3min ≤ φ 3max, make ｜ C1(φ 2, φ 3) ｜ is the smallest.

Among them, φ Imin, φ Imax by measure limits of error to decide directly.

Use the method of direct search, can get φ 2, φ the true value of 3.

The experiment makes clear: Through optimizing, can make the numerical value of ｜ C1 ｜ is reduced apparently, raised φ effectively 2, φ the measurement of 3 precision.

Watch 1 gave out 5 times to differ measure those who list S0(θ N) to optimize a result, apparent, optimize a result to have better repeatability precision.

Watch 1 measure brilliance span φ 2, φ of 3 optimize a result initiative value measured value optimizes value average variance ° of 12345 φ 2/() 112.

45112.

49112.

45112.

47112.

49112.

47112.

480.

° of 014 φ 3/() 230.

23229.

91229.

89229.

90229.

86229.

88229.

890.

｜ of 018 ｜ C1 / the φ 2=84 that 10-63521891957126410189844 test result and analysis use some document to recommend respectively.

24 ° , φ 3=168.

The point of view that give is optimized to find a place for when Km=160 is being taken in 78 ° and article measure a head, the standard component that is 110mm to a diameter undertakes metrical, measure so that result photograph compares with Talyrond circularity appearance, see a table 2.

Watch 2 measure a result to compare methodological round 　 to spend harmonic error each bits more circumferential measure an error to all be worth / μ M improves rate / % σ / μ M improves rate / % maximum / μ M improves rate / % maximum / μ M improves rate / % circularity appearance 1.

253 　 0.

050 traditions at 3 o'clock law 1.

292 　 0.

035 　 0.

072 　 0.

250 optimize at 3 o'clock law 1.

282260.

026260.

024670.

16036 　 result makes clear: ① is traditional at 3 o'clock because the law is certain class second the error delivers coefficient Qk bigger, reading error is magnified greatly, there is error of apparent Gao Cixie wave in making measure an outcome thereby (2d seeing a picture and graph 3a) .

The law measured ② tradition the disperse rate of value of circularity and each harmonic is more greatly at 3 o'clock, only group measured value and circularity appearance are measured so that the value differs bigger, must take average ability many rounds to get more accurate result.

③ optimizes what law circularity and each harmonic was worth at 3 o'clock to measure uncertainty to be reduced apparently, especially Gao Cixie wave measures an error to be reduced apparently (3b) seeing a picture.

(A) is traditional at 3 o'clock law result (B) is optimized the law measured a result to pursue at 3 o'clock 3 circularity and each harmonic amplitude measures an error CNC Milling