Measurement Theory Research On Surface Profile Of High-precision Small Spherical Cap

High-precision spherical component has been widely used in the fields of precision engineering, national defense, aerospace, and so on, in the process of modernization, with the rapid development of economy and society. Especially, it often need to be processed as small spherical cap with low ratio between height and length of the chord(small spherical cap for short). The layout and optimization of datum, the improvement of optimization algorithm and the identification of error law are studied and researched, analyzing the surface characteristics and fitting requirement of the spherical cap synthetically. The mainly emphasized above are the priority in this thesis. The research content is summarized as follows.1) Research in the layout of surface profile and its optimization analysis. Through the description in existing layout and optimization methods regarding the data points, scheme research status in the above mentioned could be clear, the extent and scope of application could be understand as well. Through the comparison in measuring points, an incremental step sampling method combining the circumferential and radial path layout patterns is proposed based on both the morphology of spherical surface profile and current methods. According to the requirement in measuring accuracy, stability and efficiency, both the abnormal and common noise points are eliminated using orthogonal wavelet signal analysis method, which could improve the acquisition accuracy of measuring data points.2) The research and analysis of the fitting optimization algorithm. The fitting assessment in spherical component, and both the initial spherical center and diameter will be positioned by adding the spherical coordinates in least square method. The rationality and validity has been verified through two revised methods, one is segmentation optimization algorithm which is synthesizing both the least square method and half step approaching ideal point principle, and the other is spherical coordinates optimization algorithm, which is aiming at approaching the fitting position based on the minimum zone criterion and matrix transformation theory.3) Research in the error law. The concept of error identification, residual measurement error analysis and the establishment of an error identification model are presented in this thesis, through both the parameters of spherical geometry error, system error, detection system pre-travel error, non repetitive error and the contact form of the measurement probe to tested spherical cap.4) Simulation experiment. The data optimum processing application effect of biorthogonal wavelet can be verified based on examples in Matlab simulation environment. the validation, which the proposed optimization algorithm could effectively reach high precision in fitting evaluation, can be achieved through analyzing segmentation optimization algorithm, spherical coordinates optimization algorithm and comparing the simulation results to the related literatures. The conclusion can be drawn that both the two revised algorithms have advancement in convergence rate and stability.