Proceeings of the Worl Congress on Engineering 00 Vol III The Analysis an Complementarity of Abbe Principle Application Limite in Coorinate Measurement Fei Yetai, Shang Ping, Chen Xiaohuai, Huang Qiangxian an Yu Lianong Abstract The accuracy requirements of coorinate measuring technology are increasingly high. The effectiveness an applicability of the Abbe principle is severely limite uner this case. The first-orer errors are not completely eliminate even if the equipment layout meats the Abbe principle, thus they will impact the accuracy of measurement results greatly. Error correction has also lost its original effect to the micro nanometer measurement. In this paper, the analysis an complementarity of Abbe principle application limite in coorinate measurement is given; new approaches an instrument structure programs are propose to reuce the first-orer measurement error arising from inevitable instrument structure an manufacturing errors. Inex Terms Coorinate Measurement, Abbe Principle, Limitation analysis, Complementarity. I. INTROUCTION There are many factors that woul lea to measurement errors, mainly from the errors of measuring instrument itself which are generate in the process of esign, manufacture, assemble an ajustment. So the reasonable instrument structure is the important reasons affecting the measurement accuracy []. For the coorinate measurements, the layout of the measure objects, measurement stanars an the working table is the key. Germany's E. Abbe lecture at the University at Jena mentioning the esign principles of measuring instrument. The principle was publishe in 890, an promulgate through the various eitions of Czapski s theory of optical instruments after Abbe []. He thought the stanar length (stanar line) shoul be collinear with the line of the measure length (measure line) in the length measurement process. Measurement errors ue to guie movement characteristics which have quaratic relationship with the angular motion are the small secon-orer errors. They can be ignore for low-precision measuring instruments []. However, because it is often ifficult to meat the Abbe principle ue to space constraints of the instrument structure, they have the first-orer measurement errors which have linear relationship with the angular motion. Fig. shows a one-imensional measurement system which violates the Abbe principle. As can be seen from the figure, Abbe arm S exists between the stanar scale an measure line. Measuring frame generates inclination angle for the straightness eviation of the lea rail movement. Proucing a measurement error: S L Fig.. A one-imensional measurement system which violates the Abbe principle Manuscript receive March, 00. This work was supporte by National High Technology Research an evelopment Program of China uner Grant No. 008AA009. Fei Yetai is with the School of Instrumentation an Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui, China(e-mail: ytfei@hfut.eu.cn). Shang Ping is with the School of Instrumentation an Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui, China(phone: 6709060; fax:055-908; e-mail: shangping090@yahoo.com.cn). Chen Xiaohuai is with the School of Instrumentation an Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui, China(e-mail: xhchenhf@6.com). ISN: 978-988-80-8-9 L S tan S () As the progressing of the technology, the machining centers at home an abroa are eveloping towar precision an ultra-precision irection. The accuracy requirements of coorinate measuring technology are increasingly high. The effectiveness an applicability of the Abbe principle is severely limite uner this case. The analyses of Abbe principle limite in high-precision coorinate measurement are given in this paper. The first-orer errors are not
Proceeings of the Worl Congress on Engineering 00 Vol III completely eliminate even if the equipment layout meats the Abbe principle, an the existent secon-orer errors are not small, thus they will impact the accuracy of measurement results greatly. Error correction techniques are effectively use for reucing the first-orer errors over the years. ut about the micro nanometer measurement, error correction has also lost its original effect. Therefore, we must explore new ways to reuce the measurement error arising from inevitable instrument structure an manufacturing errors. II. THE EXISTENCE ANALYSIS OF THE FIRST-ORER MEASUREMENT ERROR IN ONE-IMENSIONAL MEASUREMENT One-imensional measurement system structure is compose mainly by rail, working table, workpiece, scale an probe. Lea rail is ivie into sliing rail an rolling rail, etc. []. ue to the movement of sliing an rolling rail type one-imensional measurement system in vertical an horizontal irection are ifferent. The analyses are mae respectively in the following. A. The Existence Analysis of The First-orer Measurement Error in The Vertical irection The architecture iagram of sliing rail type (the rolling rail type) one-imensional measurement system in the vertical irection is shown in Fig.. The workpiece is fixe on the working table. Measure line is collinear with the stanar scale in the contact measurement, so it is in line with the Abbe principle. When the working table moves towar the otte position in the measurement, the working table rotates in the vertical plane ue to the errors of rail. The rotating center is O. Then, the measurement error reflecte on the stanar scale is: L tan () s The istance between the rotating center an the stanar scale line is the first-orer error arm. The working table s angular motion error of the sliing rail type one-imensional measurement system is etermine by the rail straightness. The locus of the instantaneous rotating center is a straight line. The working table s angular motion error of the rolling rail type one-imensional measurement system is etermine by the rounness of balls, the straightness of the moving rail s upper surface an the statical rail s lower surface three factors ue to the unique structure of rolling rail. The working table s rotating center O of each location is instantaneous in the vertical plane. They are connecte into an irregular curve shown in Fig. (b), so the first-orer error arm is also instantaneous. Light beam is usually aime at the ege of the workpiece s silhouette in the non-contact measurement. There is the Abbe arm s between the measure line an the extension line of the stanar scale for ifferent workpiece s imension. That is to say, there not only has the first-orer measurement error but also the Abbe error in the non-contact measurement system.. The Existence Analysis of The First-orer Measurement Error in The Horizontal irection There is also the first-orer measurement error of the one-imensional measurement system in horizontal irection. The architecture iagram of sliing rail type one-imensional measurement system in the horizontal irection is shown in Fig..The straightness of the two rails an the rounness of balls ecie that the working table has angular motion error in the horizontal plane. The locus of instantaneous rotating center is an irregular curve shown in Fig.. When the working table moves from location A to in the measurement, the working table rotates, the rotating center is P. When the straightness of the two rails L θ (a) Sliing rail type O s L θ (b) Rolling rail type Fig.. The architecture iagram of one-imensional measurement system in the vertical irection. Contact probe. Not-contact acquiring light beam ~. The locus of instantaneous rotating center O ISN: 978-988-80-8-9
Proceeings of the Worl Congress on Engineering 00 Vol III an the rounness of balls are exactly the same, the rotating center P is on the stanar scale line, the first-orer error platform. The upper structure moves on the lower structure by the river formatting X axis movement; while the lower A P θ L L Fig..The architecture iagram of rolling rail type one-imensional measurement system in the horizontal irection arm is zero. That is to say, the first-orer measurement error is zero. ut this is almost impossible. When the instantaneous rotating center P eviates from the stanar scale line, the measurement error is: L tan. The first-orer measurement error of sliing rail type one-imensional measurement system in the horizontal irection is the same with the rolling rail type. Not to repeat here. From the above analysis we can see that one-imensional measurement system has first-orer measurement error L in the vertical an horizontal irection. The first-orer measurement error L 5nm, when the rotation angle ", the first-orer error arm 5 m m. This shows that even the measurement systems are in line with the Abbe principle, they can not completely eliminate the impact of the first-orer measurement error. Table Ⅰ shows a few examples of the first-orer measurement errors prouce by ifferent parameters. Uner normal circumstances, the first-orer error arm will be larger thanmm, an then the first-orer measurement error will be more than 5nm at least. This is not allowe for nano-precision measurement. structure moves on the base of rail by the river formatting Y axis movement. Two one-imensional systems are stacke into the two-imensional positioning platform in this structure actually. Measure line is collinear with the line of the stanar scale, so it is in line with the Abbe principle. Iniviually, X, Y imension in the horizontal an vertical plane both have the first-orer measurement errors resulting from the first-orer error arm as the one-imensional measurement system. In aition, we can see the istance H between the lower rail an the measure line is greater because of this stacke structure from the architecture iagram in Fig.5. That means the first-orer error arm may be longer, the first-orer measurement error cause by the straightness of the rail an the rounness of balls will be significant from the () anⅠ. For example, H is usually 0mm, if 0.5 -, then the resulting first-orer measurement error will reaches 5nm - 50nm. The impact of the first-orer measurement error can not be allowe for precision two-imensional measurement system. Error correction techniques can be use to reuce the impact of them for the two-imensional measurement systems which have stable structure. III. THE EXISTENCE ANALYSIS OF THE FIRST-ORER MEASUREMENT ERROR IN TWO-IMENSIONAL MEASUREMENT Most of the traitional two-imensional positioning platforms are stacke structure as shown in Fig.. Stacke structure is compose of two-layer rails an measurement TALEⅠ. EXAMPLE OF THE FIRST-ORER MEASUREMENT ERROR PROUCE Y RAIL MOTION ERROR (mm) L(nm) 0. 5 0 5 θ( ) Y 0.5.5 5 0 5 0 5 50 75 00 50 00 50 00 75 50 5 00 X Fig.. The moel of stacke structure two-imensional measurement system IV. THE FIRST-ORER MEASUREMENT ERROR CORRECTION EFFECT ANALYSIS ISN: 978-988-80-8-9
Proceeings of the Worl Congress on Engineering 00 Vol III 5 H The emergence of error compensation technology makes the accuracy of coorinate measurement systems guarantee. The first-orer measurement error cause by the rail straightness can be amene by software after measuring the rotation angle an the first-orer error arm base on the above analysis. ut the effectiveness of this technology is limite. It is not applicable in the high-precision measurements, particularly in nano an sub-nano precision measurement. The limit error of L in () is as follows: f f L If the accuracy requirements of the measurement are L 0 nm,, 0 mm, accoring to the error of etecting instrument is / 0 of the error of etecte instrument an the principle of equal error istribution, the allowable errors calculate respectively are: 0.5mm 0.05 Fig.5. The architecture iagram of rolling rail type two-imensional measurement system If L 0 nm, then 0.5 mm, 0.05 The current instruments are very ifficult to achieve such a high-precision measurement of the rotation angle an the first-orer error arm; In aition, the complex law of the first-orer error arm s instantaneous change ue to the instantaneous center is ifficult to grasp. So it is ifficult to meet the requirements through on-line real-time etection to error correction for the high-precision coorinate measuring systems. V. THE COMPLEMENTARITY OF AE PRINCINPLE Abbe principle has great limitations or oes not have universal applicability on high-precision measuring systems accoring to the above analysis. The parallel structures which are multi-abbe principle have been aopte in the moern wie range measurement system. That is inconsistent with the Abbe principle. However, the measurement system structure shown in Fig.6 is often mistakenly consiere to meet the Abbe principle ue to the stanar line using the laser as a stanar is collinear with the measure line. ut in fact the angular motion error of the rail will lea to significant first-orer measurement errors, therefore it o not meet the Abbe principle. So the Abbe principle nees to be complemente new concept. The new concept of the Abbe principle shoul be: the. () Fig.6. Schematic iagram of the common measurement system. Workpiece. Probe. Reflecting prism. Measuring light beam 5. Laser 6. Peestal 7. Rail stanar length (stanar line) shoul be place in extension line of the measure length (measure line), while the stanar quantity an measure quantity or stanar quantity an the targeting reaing system of the measure quantity must be settle on the same mobile station or evice. This new content will make Abbe principle more scientific, rigorous an complete. The measurement system structure base on this concept will have the characteristics of the same line an the same station. That is to say, the significant first-orer measurement errors an small secon-orer errors ue to angular motion error o not exist for having this "ouble same (S) "feature. The measurement systems an structures which are compliance with the new concept of the Abbe principle strictly will achieve the ability of high-precision measurement. In the traitional measurement systems, the requirement of "the same line" an "the same station" can be easily achieve for grauate scales use as measurement stanars. ut in most of the moern measurement systems, wavelength is use as measurement stanars, the light sources are fixe an can not be move. Therefore the requirement of "the same station" can not be achieve, that is to say, they o not meet the Abbe principle. VI. APPROACH TO REUCING THE FIRST-ORER MEASUREMENT ERROR A. Using Two-imensional Coplane Structure an Layout The rotation angle of working table an the first-orer error arm are the main parameters etermining one-imensional measurement error. Thus we can reuce the error through these two aspects. The rotation angle error cause by the rail straightness an the balls rounness only can be reuce through improving the quality of processing an assembly; the first-orer error arm can be reuce through esigning the new structure an layout of the measurement system. It is the main way to reuce the first-orer measurement errors effectively base on the structural principle. In view of the above, coplane structure two-imensional measurement system shown in Fig.7 is propose. The oriente surface of the X, Y two-imensional movement rail is coincient with the measurement surface of working table. The first-orer measurement errors ue to not coincie can be eliminate base on this coplane orientation [5]. The measure parts are fixe on the surface of working table in the measurement. The Abbe error of the small workpiece cause by the height ifference can be ignore for small thickness. ut the Abbe errors can not be 7 6 ISN: 978-988-80-8-9
Proceeings of the Worl Congress on Engineering 00 Vol III x X Y O θ Fig.7. The moel of coplane structure two-imensional measurement system. X axis slie. Y axis slie. Working slie platform. Working table ignore for a certain high workpiece. Two solutions are propose in this case. One is the measurement surface of working table can be esigne below the coplane position, then select the gaskets of appropriate thickness accoring to the measure height to ensure that the measure surface an the rail-oriente surface coincie; Another approach is the measurement surface of working table can be esigne into Z-isplacement component, but its isplacement control accuracy is unemaning, the coincience egree of the measure surface an the rail-oriente surface just be controlle less than 0.5mm. For example, there is the first-orer error arm 0.5m m ue to not coincie of the two rail-oriente surfaces an movement rotating angle of the working table ", the impact of resulting error L tan.50nm is very small an coul be ignore for two-imensional measurement platform, an the rail with this precision is easy to processe. The first-orer measurement error cause by straightness error in the rail s vertical plane close to zero as the coincience egree of two surfaces can be controlle smaller in actual processing an assembly. Then the higher precision measurements can be achieve.. The locus of Working Table s instantaneous rotating center moeling an correction principles About the two-imensional measurement systems in line with coplane structure, the instantaneous rotating center of the working table exists ue to the rail straightness, which resulting in the first-orer measurement error exists. Instant center locus equation of working table is erive by the metho of separating instant center in any position. The first-orer measurement error of the working table s any measurement points cause by the rail straightness can be calculate by the equation, then it can be amene by the software. There are calculation errors of the first-orer measurement arm because that the geometrical center of the working table is acte as the rotating center in traitional methos of separation an amenments. Now the problem is solve through the metho above [6]. Calculating schematic of the working table s instant center is shown in Fig.8. Assume that one point is taken in working table, it moves to the point when the working table rotating relate the instantaneous rotating center O ue to the impact of rail straightness error. The position Fig.8. Calculating schematic of the working table s instant center errors of are the coorinate ifferentials of point an point respectively in X, Y irection. Assume that the coorinates of the measure point are ( X, Y ), an then the coorinates of point can be obtaine by the coorinate transform matrix following. X X O cos sinx X O Y Y O sin cos Y Y O The coorinate errors are the ifferentials of ( X, Y ) an ( X, Y ). In aition to high-precision micro-nano three-imensional measurement system, fining new methos an esigning new structures are neee to achieve the measurement requirements. The author has propose a novel architecture esign principle for three-imensional measurement system, which can reuce the first-orer measurement errors effectively. It will be further iscusse in the author's publishe. VII. CONCLUSION From the above analysis of one-imensional an two-imensional measurement system, the first-orer measurement error always exists for the traitional layout of the measurement system even meet the Abbe principle, it has a great impact on measuring accuracy of the precision measurement system, an it is ifficult to compensate. Therefore, this paper presents a new layout, mechanical structure an solutions to reuce the errors. Two-imensional coplane layout an the software compensation metho are taken in the two-imensional measurement system, so the impacts on the measurement accuracy cause by the first-orer measurement errors are reuce. The analysis is significant for reucing the measurement error of coorinate measuring system. y () ISN: 978-988-80-8-9
Proceeings of the Worl Congress on Engineering 00 Vol III REFERENCES [] Y. T. Fei, Error theory an ata processing. Machine Press, China, 00, pp.. [] C. Evans, Precision engineering: an evolutionary view. Cranfiel Press, 989. [] W. K. Shi, X. F. Yu, etection technology. China Machine Press, 000, pp.. [] Z.. Pu,. G. Wang, Measurement an control instrument esign. China Machine Press, 00, pp. 6. [5] W. L. Wang, Y. T. Fei, an K. C. Fan, Investigation of nanometer XY positioning stage, Proceeings of the st IEEE International Conference on Nano / Micro Engineere an Molecular Systems, Jan. 006, Zhuhai, China, pp. 0. [6] H. T. Yang, Y. T. Fei, an X. H. Chen, The high precision error separating principle an technique of the guie strip of nanometer measuring machine s working table, Journal of Shanghai Jiaotong University, vol. 0, No., ec. 006, pp. 066-069. ISN: 978-988-80-8-9