Computation Of The Parts Of The Surface Normal Vector Field And Evaluation Of Contour Error

The rapid measurement of surface contour error is a difficult problem in the process of free surface machining. The existing measurement methods are too long and difficult to make a comprehensive measurement and inspection for each part. From the method of estimating the contour error with the actual position and the command position, which is recorded in CNC interpolation period while machining, this paper explores a method to evaluate the contour error of the surface immediatedly after machining.Geometric relationship between tracking error and contour error is introduced and a scheme of using normal projection of tracking error to approximately represent the contour error is designed. The key point of this scheme is: how to calculate the normal vector on the surface according to the discrete 3D interpolation point of the surface. In this paper, we study three methods of calculating the normal vector of interpolation tool position, which are plane fitting method, characteristic decomposition method and cross section method.Fitting plane method is based on the given neighborhood radius to get neighborhood points of cut location point, and then fitting the points into plane using with Constrained Least Squares. The normal vector angle error of spherical, conical and cosine swept surfaces,which is between 0 and 0.3°, is 98.34%?98.28% and 97.82% respectively in this method.Characteristics of decomposition constructs covariance matrix by neighborhood points of cut location point. The minimum eigenvalue corresponding eigenvector of this matrix is the normal vector. The Normal vector angle error of spherical, conical and cosine swept surfaces,which is between 0 and 0.3°, is 97.55%?98.36% and 97.85% respectively in this method.Cross section uses cut location points to get boundary point of adjacent track of machining toolpath, and then get points in the track of cut location point, and fit the choosed points into B-spline curve to get the tangent vector and constructs normal plane of the B-spline curve. Get points on the proper interval on the trace and then fit the choosed points into B-spline curve again. Using this B-spline curve and plane intersection to fit into B-spline curve. Work out the tangent vector of direction perpendicular to the cutter location trajectory of cut location point, according to the two tangential vectors to seek the vector. The Normal vector angle error of spherical, conical and cosine swept surfaces,which is between 0 and 0.3°, is 23.84%, 99.08% and 99.82% respectively in this method.Comparing the advantages and disadvantages of the three methods. In terms of algorithm efficiency and computational precision, characteristic decomposition method whose comprehensive index is average is chosed for the evaluation of the surface contour error of the actual surface parts. The normal vector of each point is calculated from all interpolation points recorded in the machining process of the surface. The contour error is estimated by projecting the tracking error onto the normal vector and the three-dimensional chromatogram of the surface colored by the value of the contour error is obtained. Compared with the actual surface, it shows that there is a corresponding relationship between the discontinuity of the chromatogram of the contour error and the contour defects of the part, which indicates that the method is feasible.