Research On Spatial Error Models And Optimal Measurement Areas Of Flexible Coordinate Measuring Machine

The flexible coordinate measuring machine (FCMM) with high technology content is mainly composed of high-precision mechanical structure , circle optical grating encoder and multifunction software. It is an intensive and high technology product. But the FCMM is definitely restricted in application in real life , because one of the main reasons is that its precision isn't in accordance with practicle application demands. The FCMM is a kind of multistep, tandemtype and polar coordinate measurement system with more error sources. So a quantity of key technology problems must be solved in order to achieve superior FCMM measurement precision.When a workpiece is measured by FCMM, the things are : the measurement errors of the same point are not the same when the FCMM'postures are diverse; the magnitudes of errors are different but regular when different points are measured on the workpiece. The first thing above is researched by functional network basic theory ,and thus the spatial measurement point error model is build. The support vector regression theory is used to solve the second problem, then the spatial error distribution model is build also. Furthermore, optimal measurement area in the measurement space is discused. Main reasearch contents are as follows:(1)FCMM spatial measurement point error model build by functional network basic theory Three kernel content including topological structure , basis function , learning algorithm are studied in the functional network theory .Using the functional network theory to design the FCMM five-layer topological structure , present the concept of matrix neuron basis function and discuss several kinds of solving algorithm. Finally, the FCMM spatial measurement point error model is build. The error model's validity is verified by simulation and expariment. It breaks through the idea of error modeling based on measurement model from the D-H method using error separation technique. The new method of error model is discussed in another point of view.(2)FCMM measuring space solved by Monte Carlo method The Monte Carlo method is a kind of numerical value way , but it is different from traditional numerical methods. It solves mathematical problems with random sampling. This method isn't impressed by limit state , nonlinearity and other factors. And it isn't restricted by the number of FCMM degrees of freedom. So it brings forth a kind of new visual angle on solving measuring space. Research on the FCMM measuring space contributes to further verifying whether the design of the FCMM geometric dimentions accord with requests and also study on the FCMM optimal working area.(3)FCMM spatial error distribution model build by support vector regression theory The input is a three-dimensional coordinate and the output is a value of measurement error in the FCMM spatial error distribution model. The purpose of modeling is for further study on optimal working area. This is different from that of spatial measure point error modeling. The support vector regression(SVR)algorithm and the advantages and disadvantages of various kernel functions are researched. v-SVM and RBF kernel function are choosed to build the FCMM spatial error distribution model. And the the specific steps of the algorithm are given.(4)FCMM optimal working area and its existance studiedThe research on the FCMM optimal working area is based on the achievement of measurement space and spatial distribution model , which uses the theory of optimal planning. Use the convex analysis method to verify the existence of optimal measuring area , discuss the optimal working area based on single point measurement and spatial distance measurement , and give the corresponding mathematical model.(5)Experimental studies on the error- related model of the FCMM carried outThe undetermined parameters from the spatial measurement point error model based on functional networks and the spatial error distribution model on SVR are all identified by experiments.Use a tailor-made standard quartz gauge to identify the spatial measurement point error model parameters , and utilize a cone socket to calibrate the spatial error distribution model parameters in the experiments.Then the two models are tested , and the results show that: the measurement error from the error model on functional networks is less then which based on D-H matrix ; the spatial error distribution model on SVR can better fit the original test points. Finally, the mathematical models from the optimal working area based on single point measurement and spatial distance measurement are solved. Their results can guide actual measureing operation, and thus high precision measurement is realized with lower precision measuring machines.