Ruled Surface Approximation For Free-form Surfaces And Its Applications In Five-axis Flank Milling

Five-axis NC machining provides an effective way to process complexand intractable work piece surfaces. Five-axis flank milling are receivingmore and more attention nowadays due to its high material removal rate,short manufacturing time, low tool wear rate and high quality finish surface.But five-axis flank mill also has its limitations due to its distinguishedfeatures. Current five-axis flank milling tool path planning algorithms incommercial CAM software can only deal with ruled surfaces. There is noeffective way to generate high quality five-axis flank milling tool path for anarbitrary free form surface. This is the main reason why five-axis flankmilling applications are constrained, thus the five-axis machine center cannot realize its full potential.This paper focuses on the geometrical principle and method to generatefive-axis flank milling tool path for manufacturing complex free formsurface. The technical route of this paper is to approximate the garget freeform surface with one or more ruled surfaces thus to change the problem ofgenerating flanking milling tool path for free form surfaces into the problemof generating flanking milling tool path for ruled surfaces. Approximatingan arbitrary free form surface (or a set of point cloud representing a surface)contains three steps: Find a set of discrete straight line segments (rulings) tobest fit the free form surface (or the set of point cloud); interpolate thediscrete line segments with a ruled surface and minimize the geometricalerror between ruled surface and target surface applying optimizationstrategy. The ground work of this paper is list below:1. A method to approximate a free form surface (or a set of point cloudrepresenting a surface) is proposed. The method includes strategy ofsearching in a2-D domain, strategy of advancing the searching centerand the method to fit one line segment to the target surface. And themethod is altered in the second stage to adapt different applications. Themethods can be sorted as: free ruling searching method, constrainedruling searching method and heuristic ruling searching method.2. For special surface like the meshing profile of a globoidal indexing camor a rolling worm, a searching method based on the feature of the surface is proposed. This approach is superior to the traditional ones by focus onthe work piece’s physical property.3. An assessment criterion is proposed to evaluate the surfaceflank-malleability and smoothness. A method with geometrical clarity tointerpolate the discrete line segments with a ruled surface is proposed.An optimizing strategy is proposed to minimize the geometrical errorbetween ruled surface and target surface.4. A multi passes ruled surface approximation method is proposed toprocess complex and twisted surface. The method to divide the surfaceinto regions that can ben approximate by ruled surface also consider thedifficulties that may occur during flank milling. And the strategy toapproximate these regions with ruled surfaces is proposed.The approximation methods proposed in the paper greatly expand theapplication of five-axis flank milling. The surfaces formerly thought to beun-flank-milleable can be processed by the algorithms proposed canachieved high quality tool path. The methods and algorithms proposed inthe paper are testified with a large amount of data and applied to realproduction, and the results are satisfying.