Practical Study Of The Optimal Measurement Area Of The Articulated Arm Coordinate Measuring Machine

The articulated arm coordinate measuring machine(AACMM)has the advantages of large measuring range,convenient portability and high measuring efficiency compared with the orthogonal coordinate measuring machine.However,due to the series mechanical structure,the measurement error is transmitted and accumulated,which leads to low measurement accuracy,the accuracy can not meet the needs of some practical projects and limits applications.Therefore,promotion of measurement accuracy is an important issue in front of us.It has been found that the optimal measurement area where the measurement error is smallest exists in the measurement space of AACMM.If a part is measured in optimal measurement area,a better measurement accuracy can be achieved.Based on circular sensor error,this paper focuses on this issue to find and determine the optimal measurement area and to make the error of given easy-to-use area smaller.Based on the measurement model of the AACMM,the error model of the measuring machine was established in regard to the circular sensor error.Using the combination method of photoelectric autocollimator and metal prism calibrated circular encoder error.The eccentric error model of the circular encoder was built and used to modify the error component caused by the installation eccentricity in the calibration data.Three order Fourier series was used to fit the error curve,and the error characteristic curves of the 6 circular encoders was obtained.Using the method of Monte Carlo simulated the measurement space of the measuring machine.By using the Newton iteration method to inversely solve the measurement equation of the measuring machine,multi angle joint angles combinations of a single point was obtained and imported into the measurement error model and the single point error distribution was obtained.Through designing reasonable layout of sampling points and promotion method,thousands of groups of joint angles of a large number of sampling points are obtained and imported into error model of measuring machine.The error distribution of a large number of sampling points in the measurement space was analyzed.In order to get specific location of the optimal measurement area,the measuring space was cut into a series of small areas with equal interval.A mathematical model was established to calculate the maximum measurement error in each region.The improved ant colony optimization(ACO)algorithm was used to solve the model.The maximum measurement error of each small cube region was determined.By contrast,the area where the maximum measurement error is smallest is the best measurement area.Based on the analysis of the influence of the angle between the circular sensor zero position and joint zero position(initial installation angle)on the measuring error and the spatial error distribution,using the particle swarm optimization(PSO)algorithm determined the combination of the six initial installation angles which makes the error of given easy-to-use area smaller.The optimal measurement area and practical area were verified.The simulation results showed that the method to solve the optimal measurement area and the practical method were effective.The research results can be used to guide the practical measurement and measuring machine assembly to achieve the practical purpose of the optimal measurement area.