Mathematical Programming Method Of Hausdorff Distance Calculation And Its Application In NC Machining Of Impellers

Distance computation between geometric objects is one of the most frequently used geometric operations in engineering. Among many different distance measures, the Euclidean minimum distance and the Hausdorff distance have attracted considerable research attention of many geometrical researchers. This work is keen to research the quick and stable methods to compute the Hausdorff distance and minimum Hausdorff distance between continuous geometry objects, and then to apply them to high-performance precision machining for impeller tunnel. Thus with it to solve the key problems such as the reasonable segmenting of the tunnel, confirming the tool orientation and size during rough plunge machining, as well as planning the tool positions in the finish machining of blade. The presented models are verified by actual machining processes, and the processing efficiency and the processing cost are compared with the traditional machining. Numerical simulation and experimental study are carried out to investigate the effect of machining precision on the aerodynamic performance of centrifugal compressor.A coarse-to-fine two-step model to computing the one-side Hausdorff distance between planar curves is proposed which simplifies the computing process to solve different constraint equations for many kinds of special cases. Base on this modal, the mathematical programming model and solving method for computing the minimum Hausdorff distance between planar curves under the similarity transformation and the optimization model and solving method of exact solution near characteristic point are investigated. The model based on the minimization of the one-sided Hausdorff distance is applied to the evaluation of roundness error, and the comparison with the traditional evaluation method is made.In order to make the machined tunnel surface of semi-open impeller after plunge milling as close as possible to its designed surface for the fixed-axis plunge rough machining, the solving model and method for finding the maximum inscribed general cylindrical surface of the tunnel is proposed. In order to further improve the processing efficiency for the parts with tunnels, to choose the sizes of the cutters and the cutter axes orientation reasonably, the method of segmental machining according to the width of the tunnel is proposed. The tool path generating method for the fixed-axis plunge milling in a given region is studied. Aiming at the flank milling of the impeller blade which is undevelopable ruled surface, the tool positioning optimization models based on the minimizing distance norms between mapping curve and the designed surface are developed. The mapping curve is a typical one that can be used to express the closeness between the tool surface and the designed surface. Two individual tool positioning methods of cylindrical cutter and conical cutter for flank milling ruled surface are investigated based on the least squares approximation and the best uniform approximation respectively. The sizes and patterns of the geometrical residual errors on the designed surface are numerically simulated. The estimation errors based on the individual tool positions and the real errors are compared which validate the effectiveness of the proposed methods.In order to verify the validity of the rough machining and finish machining models and methods of the impeller proposed in this paper, firstly, a principle cutting test of nylon material is conducted on a five-axis machining centre. Secondly, rough and finish machining tests are also conducted on the FV520B stainless steel which is a commonly used material in the impeller. Furthermore, comparative studies of processing efficiency and cost are conducted among the rough machining methods of five-axis flank milling, three-axis high-speed milling and the fixed axis plunge milling proposed in this paper.At the end of the dissertation, the numerical simulation and the performance experiment are conducted to study the effect of the residual riblets of impeller's hub surface on aerodynamic performance of centrifugal compressors. The drag reduction mechanism of the riblets left on the hub surface, the relationship between the spacing and size of the riblets and the aerodynamic performance of the compressor is discussed, which provide a reference for the making of the impeller machining precision reasonably.In this work, the quick and stable computing methods for the Hausdorff distance between geometric objects are the key points. And then, the approximation problems between curves or surfaces in engineering can be solved which will provide technical support for the high-performance precision machining of impeller. Numerical simulation and experimental study are also carried out to investigate the effect of machining precision of the impeller on the aerodynamic performance of whole machine. It is wished to find a solving stragegy and method that can unify the design method, the processing method, the machining precision and the performance in a unified framework.