Sanjeev Bedi

Surface swept by a toroidal cutter during 5-axis machining

This paper presents a method of determining the shape of the surface swept by a tool that follows a 5-axis tool path for machining curved surfaces. The method consists of discretising the tool into pseudo-inserts and identifying imprint points using a modified principle of silhouettes. An imprint point exists for each pseudo-insert and the piecewise linear curve connecting them forms an imprint curve for one tool position. A collection of imprint curves is joined to approximate the swept surface. This method is simple to implement and executes rapidly. The method has been verified by comparing predicted results of a 3-axis tool path with analytical results and predicted results of a 5-axis tool path with measurements of a part made with the same tool path.

Tool path planning for five-axis machining using the principal axis method

A study of the effect of feed direction on five-axis tool paths generated using local surface properties for tool orientation and positioning is presented in this paper. The principal axis method for five-axis machining defines the placement of the cutting tool at a single point on the workpiece surface and assumes that a preferred feed direction will be maintained. This preferred direction may not represent a practical choice for tool path planning. In this work, numerical simulations are used to evaluate tool paths with different feed directions. Numerical simulations are then verified experimentally by machining two example surfaces. The results show that both gouging and the effective cutter profile will dictate the optimal choice of feed direction.

Flank milling with flat end milling cutters

One situation encountered in industry is that two curves on the machined surface are known, such as the top and bottom profiles of a blade. The shape of the surface is not known and is to be determined by a tool sliding along the generating rails. In this paper, we give a detailed mathematical understanding of flank milling with flat end cutters, which we then use to develop a method for milling with such a cutter. This method slides the cutter along two rails, keeping the cutter tangent to both curves at every parameter value. Examples are given to illustrate the method, along with simulations and error analysis.

Multi-point tool positioning strategy for 5-axis machining of sculptured surfaces

Multi-point machining (MPM) is a tool positioning technique used for finish machining of sculptured surfaces. In this technique the desired surface is generated at more than one point on the tool. The concept and viability of MPM was developed by the current authors in previous works. However, the method used to generate the multi-point tool positions was slow and labor intensive. The objective of this paper is to present efficient algorithms to generate multi-point tool positions. A basic multi-point algorithm is presented based on some assumptions about the curvature characteristics of the surface underneath the tool. This basic algorithm is adequate for simple surfaces but will fail for more complex surfaces typical of industrial applications. Accordingly, tool position adjustment algorithms are developed that combine the basic algorithm with non-linear optimization to achieve multi-point tool positions on these more complex surfaces.

Triple tangent flank milling of ruled surfaces

This paper presents a positioning strategy for flank milling ruled surfaces. It is a modification of a positioning method developed by Bedi et al. [Comput Aided Des 35 (2003) 293]. A cylindrical cutting tool is initially positioned tangential to the two boundary curves on a ruled surface. Optimization is used to move these tangential points to different curves on the ruled surface to reduce the error. A second optimization step is used to additionally make the tool tangent to a rule line, further reducing the error and resulting in a tool position, where the tool is positioned tangential to two guiding rails and one rule line. The resulting surface has 88% less under cutting than the method of Bedi et al. q 2004 Elsevier Ltd. All rights reserved.

Rolling ball method for 5-axis surface machining

Curvature matching for 5-axis surface machining has been plagued by the complexity of the task. As a result the current tool positioning strategies are likewise computationally complicated. Gouging the surface has been the main concern and has presented the greatest difficulty in the algorithms. Some of the methods perform exhaustive searches of the surface to avoid gouging while others incrementally adjust the tool orientation until gouges are no longer detected. In this paper a new positioning strategy is presented that is simple to implement and is not difficult to compute. The rolling ball method rolls a variable radius ball along the tool path and positions the cutting tool to cut the rolling ball. A small region of the balls surface is used to approximate a small region of the surface being machined. The radius of each ball is computed by checking a grid of points in the area of the surface that the tool casts a shadow for each tool position. A pseudo-radius is computed for each grid point and the most appropriate radius is selected to be the rolling balls radius. The selection process follows a hierarchy of surface profiles ranging from convex to concave. Convex, concave, and saddle (mixed) surface regions are all computed in a similar fashion and there are no special cases for which the positioning strategy must be changed to compute a tool position. Local gouge checking is automatically built-in to the positioning computations so that the typical iterative strategy of checking for gouging, then incrementally tilting the tool until no gouges are detected is eliminated. The method is robust and simple to implement and it only requires surface coordinates and surface normals. A simulation of the method and a cutting test were performed and are presented in this document.

Arc-intersect method for 5-axis tool positioning

A new method for 5-axis CNC tool positioning is presented in this paper that improves upon a previous tool positioning strategy named the rolling ball method (RBM), which was developed by the present authors [Gray P, Bedi F, Ismail S. Rolling ball method for 5-axis surface machining. Comput Aided Des 2003;35(4):347-57]. The special property of the RBM is that it computes tool positions by considering the area beneath the tool that the tool will be positioned to cut instead of using surface curvatures computed at a single point on the surface. This enables the RBM to generate gouge-free tool positions without secondary iterative gouge-check and correction algorithms. However, the RBM generates conservative tilt angles in order to guarantee gouge-free tool positions. The new arc-intersect method (AIM) presented in this paper improves upon the RBM by directly positioning the tool to contact the surface and thereby eliminates the conservative nature of the RBM to give optimal tool positions. Like the RBM, the AIM is an area-based method that generates gouge-free tool positions without the use of iterative gouge-check and correction algorithms. The implementation described in this paper uses triangulated surfaces and the computers graphics hardware to assist in the tool position calculations. However, the method can be applied to any surface representation since it only uses surface coordinates and surface normals for computation. A section of a stamping die was machined to demonstrate the AIM and to show the improvement over the RBM and for comparison with 3-axis ballnose machining. The results showed that the AIM was 1.33 times faster than the RBM and that the AIM, with single direction parallel tool passes, was 1.62 times faster than a zig-zag pattern 3-axis ballnose tool path for the same feed rate, cusp height and tool diameter. The workpieces were measured with a CMM and the data were compared to the CAD model to show no gouging occurred and to check the cusp heights.

Implementation of the principal-axis method for machining of complex surfaces

In this paper a new strategy for 5-axis machining of complex surfaces is presented. The method uses curvature alignment and matching between the design surface and the cutting tool to improve surface finish and reduce machining time. The method is implemented on two configurations of 5-axis machines, and used to machine a test surface. The results of the tests show a considerable improvement over conventional 3-axis machining.

Principal Curvature Alignment Technique for Machining Complex Surfaces

Machining complex three dimensional surfaces is a challenging task. This paper presents two methods of machining these surfaces on a 4 and 5 axis machine, using a toroidal shaped cutter. The methods propose to align the principal axis of curvature of the machining surface with that of the machined surface in order to increase the volume of material removed. The increase in material removal at a point reduces the scallop height. Thus, fewer passes are required to achieve the same surface finish.

Comparison between multi-point and other 5-axis tool positioning strategies

Abstract A method of generating sculptured surfaces at multiple points of contact between the tool and the workpiece was developed and proven viable by the current authors in previous work. They denoted this finish machining method, “Multi Point Machining”, or simply MPM. This paper compares MPM with two other 5-axis tool positioning strategies; namely: the inclined tool, and the principal axis method. It is also compared with 3-axis ball nose machining. Comparisons are conducted using computer simulations and experimental cutting tests. Results obtained show that MPM produced scallop heights that are much smaller than those produced by the other tool positioning strategies.