Research On Measurement And Evaluation Technologies Of Space Quadric Surface Profile Error And Position

Quadric surface is used widely in various fields of modern engineering and research because of its special geometrical or physical propertis. Quadric surface measurement and evaluation technology recieves more attention, including quadric surface profile error evaluation and the caculation on the position and orientation of spacial quadric surface. The profile error and the position and orientation of quadric surface component are closely related to their geometrical or physical propertis. For example, profile error of satellite antenna and the spacial position and orientation is closely related with the performance of the antenna in the study of space research. In order to evaluate quadric surface profile error accurately, as parabolic antennna, and calculate its position and orientation, the following related technologies is studied.The definition of sphericity, conicity, ellipsoid, paraboloid and hyperboloid profile error is established for the study of the evaluation of quadric surface. The definitions are based on the current international and national standards, the definition of the shape tolerance and quadric surface profile error, the definition of flatness, cylindricity error. The model of quadric surface profile error evaluation in any position and orientation based on the minimal zone principle or based on least squares principle is established for the quadric surface measurement and evaluation in the engineering. In order to improve the efficiency and accuracy of the calculation, a method for categorizing the quadric surface based on three coordinates measurement data, a fomula for calculating the initial value of the model and the constrain condition of quadric surface type in the model are proposed. Finally, the existence of optimal solution of the model is analyzed.In order to solve the measurement and evaluation model of spacial quadric surface in any position and orientation, angle subdivision approach algorithm combined with improved particle swarm optimization(IPSO) is proposed. The normal deviation from measurement point to spacial quadric surface is calculated by angle subdivision approach algorithm, and the objective function of the model is constructed according to the profile error definition. A reasonable grid recurrence formula and two hypotheses are proposed. The grid recurrence formula is based on two hypotheses which are angle subdivision approach algorithm preconditions. PSO improved by the idea of optimized analytical method is proposed to solve the optimization in the error evaluation model according to the characteristics of the objective function. The convergence of the algorithm and the time complexity of the algorithm are discussed.The calculation for the spacial quadric surface profile error evaluation model is simplified based on their geometrical propertis, and the initial value formula of the simplified model is proposed. In the experiment, the model of spacial quadric surface profile error evaluation in any position and orientation based on the minimal zone principle or based on least squares principle, the simplified model of the minimal zone quadric surface profile error evaluation, the commercial software, Spatial Analyzer(SA) are adopted and compared each other. It is proved the models complete quadric profile error evaluation effectively and the simplified model is more efficient.The definition of the position and orientation of quadric surface based on the minimal zone principle or based on the least squares principle is established according to the current international and national standards and previous research, the corresponding calculating model and the initial value formula are proposed too. According to the concept of surface profile error in the study of parabolic antenna performance, the calculation models of the quadric surface position and orientation based on normal root mean square(RMS) error and axial RMS are proposed. In the experiment, the calculation models of the quadric surface position and orientation are validated.A direct radius compensation method for quadric surface at arbitrary position in space with using coordinate measuring machining(CMM) is proposed based on the spacial quadric surface profile error evaluation model. In order to verify the effect of the methods, the experiment on a parabolic antenna is carried out. In the experiment, arm type three coordinates measuring instrument, FARO arm standard edition, is adopted to measure the parabolic antenna reflector in any position and orientation. The results show that the quadric surface profile error evaluation models and the corresponding simplified model, the calculation models of quadric surface position and orientation, angle subdivision approximating algorithm and direct radius compensation method can complete the quadric surface measurement and evaluation effectively.