Anlysis And Compensation Of Abbe Error In The Laser Heterodyne Straightness Interferometer

In the modern manufacturing of precision machines and instruments, straightness has animportant position and role in the mechanical precision because it is one of themajor geometrical elements in characterizing the shape of the parts. The method of measuringstraightness based on laser heterodyne interferometer has been widely used for its characteristicsof high accuracy, high SNR and strong anti-interference. However, its measuring precision isseriously influenced by the Abbe error in the actual measurement process. This thesis issupported by the National Natural Science Foundation of China (Grant No.51375461). In orderto reduce or eliminate the influence of Abbe error in the laser heterodyne straightnessinterferometer, the analysis and compensation method of Abbe error is studied. Therefore, themeasuring accuracy of straightness and its position can be improved. Meanwhile, a measuringmethod of multi-degrees of freedom (DOF) based on this system is proposed.This thesis comprehensively analyzes the present research status at home and abroad on thelaser straightness measurement and determination and compensation method of Abbe error. Theprinciple of measuring straightness and its position simultaneously based on laser heterodyneinterferometry is introduced and the cause of Abbe error in this system is analyzed. The opticallayout of the laser heterodyne straightness interferometer system with error compensation andsimultaneous measurement of multi-DOF error parameters is designed. The mathematical modelof detecting Abbe error is established. Using the method of ray tracing and geometry, themapping relationship between the light spot positions on the detectors and the multi-DOF errorparameters is analyzed and the expressions of simultaneous measurement of six degrees offreedom in the proposed system is obtained. Then the influence of the measured stage’s rotationerrors on the measurement of straightness and its position is analyzed, meanwhile the method ofAbbe error compensation is proposed. Lastly, the signal processing system including the laserheterodyne interference signal processing and the Abbe error detection signal processing isdesigned and the software is programmed using the Visual Basic language.In order to verify the feasibility of the proposed straightness interferometer system forsimultaneous measurement of six DOF parameters and the proposed compensation of the verticalstraightness error and its position, an experimental setup was constructed and some experimentswere conducted as follows:(1) Measurement and comparison experiments of single parameterincluding yaw error, pitch error, roll error and horizontal straightness error. The results are listed as follows: the maximum deviation of pitch error between the proposed system and the anglemeasuring kit of Renishaw interferometer is1.586arcsec while the standard deviation is0.568arcsec. The maximum deviation of yaw error between the proposed system and the anglemeasuring kit of Renishaw interferometer is0.842arcsec while the standard deviation is0.352arcsec. The maximum deviation of roll error between the proposed system and WL11level is2.692arcsec while the standard deviation is1.080arcsec. The maximum deviation of horizontalstraightness error between the proposed system and the Renishaw straightness interferometer is1.869μm while the standard deviation is0.735μm. These results demonstrate the effectivenessand high accuracy of the proposed system in measuring the multi degrees of freedom.(2) Theexperiments of Abbe error compensation including measuring and compensation experiments ofthe measured stage’s vertical straightness and its position. The results are listed as follows: themaximum deviation of vertical straightness error between the proposed system and Renishawstraightness interferometer with the straightness retro-reflector fixed before compensation is26.311μm while the standard deviation is9.767μm. After compensation, the maximum deviationis2.075μm and the standard deviation is0.935μm. The maximum deviation of displacementbetween the proposed system and PI stage before compensation is10.229μm while the standarddeviation is3.669μm. After compensation, the maximum deviation is0.712μm and the standarddeviation is0.331μm. These results verify the good effectiveness of the Abbe error compensationmethod proposed by this thesis and its higher accuracy in measuring straightness and its position.(3) In order to verify the repeatability of simultaneously measuring six degrees of freedomparameters and error compensation of the proposed system, three repeatable experiments wereconducted and the results are listed as follows: the standard deviations of yaw are2.50arcsec,2.23arcsec,2.34arcse, respectively. The standard deviations of pitch in three experiments are9.00arcsec,9.33arcsec,9.16arcsec, respectively. The standard deviations of roll are3.39arcsec,3.44arcsec,3.29arcsec, respectively. The standard deviations of horizontal straightness are2.02μm,2.27μm,2.64μm, respectively. The standard deviations of vertical straightness are2.52μm,2.43μm,2.64μm, respectively. The standard deviations of displacement are0.33μm,0.29μm,0.29μm, respectively. These results show that the proposed system has goodrepeatability.