Tool Path Planning For Sculptured Surface Parts Machining Based On Hausdorff Distance

Sculptured surface parts are widely used in the field of aerospace,ship,automobile and other manufacturing fields.It plays an important role in the development of these industries.Plane characteristics exist in most mechanical parts,so flatness error evaluation is an important part in geometric error evaluation.Hausdorff distance provides the measurement of similarity evaluation between geometric objects,so this paper first completes the evaluation of the plane flatness error of the actual plane based on the Hausdorff distance.Tool path planning of sculptured surface involves approximation of tool envelope surface and surface to be processed.The Hausdorff distance is applied to tool path planning method,and the cutter axis and cutter location are optimized.Firstly,the related mathematical tools for building 3-D models of sculptured surface parts are introduced,including B spline curves,rotary motion groups and so on.The definition,classification and general calculation method of Hausdorff distance are introduced in detail.The basic knowledge of tool path planning method for sculptured surface parts is introduced,including the criteria for judging the quality of tool path planning,etc.Based on the calculation of Hausdorff distance between planes,this paper transforms the evaluation of the flatness error into computation of the minimum one-way Hausdorff distance from the measured plane to the reference plane in the space,and constructs a nonlinear mathematical model of the minimum one-way Hausdorff distance.The Optimization Toolbox of MATLAB is used to solve this model.The method we propose makes up for the deficiency of common used method for evaluation of the flatness error like Least Square Method and Minimum Zone Method,etc.The criterion of minimum condition is given by K-T condition,so as to ensure that the calculation result satisfies the minimum condition.Finally,this method is used in some examples to verify its effectiveness and efficiency compared with the Least Square Method and the Minimum Area Method.Then,based on the above method,the machining process of sculptured surface parts using flat end milling cutter is studied.A tool path planning method based on the minimum one-way Hausdorff distance calculation from sculptured surface to the flat end surface is proposed.A minimum one-way Hausdorff distance mathematical model is established.The optimization function in the MATLAB toolbox is used to solve the model.The tool orientation and cutter location are optimized.By calculating the related calculation examples using method proposed above,the tool path and the processing parameters are determined,and the result of the machining error calculated is compared with the calculated error using traditional tool planning method.The tool path planning method we proposed has better processing quality,and the effectiveness of the algorithm is verified.