Spiral tool paths for high-speed machining of 2D pockets with or without islands

We describe new methods for the construction of spiral tool paths for high-speed machining. In the simplest case, our method takes a polygon as input and a number δ>0 and returns a spiral starting at a central point in the polygon, going around towards the boundary while morphing to the shape of the polygon. The spiral consists of linear segments and circular arcs, it is G1 continuous, it has no self-intersections, and the distance from each point on the spiral to each of the neighboring revolutions is at most δ. Our method has the advantage over previously described methods that it is easily adjustable to the case where there is an island in the polygon to be avoided by the spiral. In that case, the spiral starts at the island and morphs the island to the outer boundary of the polygon. It is shown how to apply that method to make significantly shorter spirals in some polygons with no islands than what is obtained by conventional spiral tool paths. Finally, we show how to make a spiral in a polygon with multiple islands by connecting the islands into one island. Keywords: Spiral-like path, Medial axis, Smoothing, High-speed machinin

Spiral Complete Coverage Path Planning Based on Conformal Slit Mapping in Multi-connected Domains

Generating a smooth and shorter spiral complete coverage path in a multi-connected domain is an important research area in robotic cavity machining. Traditional spiral path planning methods in multi-connected domains involve a subregion division procedure; a deformed spiral path is incorporated within each subregion, and these paths within the subregions are interconnected with bridges. In intricate domains with abundant voids and irregular boundaries, the added subregion boundaries increase the path avoidance requirements. This results in excessive bridging and necessitates longer uneven-density spirals to achieve complete subregion coverage. Considering that conformal slit mapping can transform multi-connected regions into regular disks or annuluses without subregion division, this paper presents a novel spiral complete coverage path planning method by conformal slit mapping. Firstly, a slit mapping calculation technique is proposed for segmented cubic spline boundaries with corners. Then, a spiral path spacing control method is developed based on the maximum inscribed circle radius between adjacent conformal slit mapping iso-parameters. Lastly, the spiral path is derived by offsetting iso-parameters. The complexity and applicability of the proposed method are comprehensively analyzed across various boundary scenarios. Meanwhile, two cavities milling experiments are conducted to compare the new method with conventional spiral complete coverage path methods. The comparation indicate that the new path meets the requirement for complete coverage in cavity machining while reducing path length and machining time by 12.70% and 12.34%, respectively.Comment: This article has not been formally published yet and may undergo minor content change

Spiral Toolpaths for High-Speed Machining of 2D Pockets with or without Islands

We describe new methods for the construction of spiral toolpaths for high-speed machining. In the simplest case, our method takes a polygon as input and a number $\delta>0$ and returns a spiral starting at a central point in the polygon, going around towards the boundary while morphing to the shape of the polygon. The spiral consists of linear segments and circular arcs, it is $G^1$ continuous, it has no self-intersections, and the distance from each point on the spiral to each of the neighboring revolutions is at most $\delta$. Our method has the advantage over previously described methods that it is easily adjustable to the case where there is an island in the polygon to be avoided by the spiral. In that case, the spiral starts at the island and morphs the island to the outer boundary of the polygon. It is shown how to apply that method to make significantly shorter spirals in polygons with no islands. Finally, we show how to make a spiral in a polygon with multiple islands by connecting the islands into one island.Comment: 22 pages, 13 figure

Toolpath algorithm for free form irregular contoured walls / surfaces with internal deflecting connections.

This paper presents a toolpath generation method to efficiently machine free form irregular contoured walls / surfaces (FIWS) containing internal deflecting connections (IDC’s). The toolpath generation method is based on a series of identifications and calculations, where initially a ‘Main Computable Zone (MCZ)’ in the Machinable Areas (Ma’s) of FIWS is identified based on the Tool track dimensions (Td). Then the MCZ’s are divided into Split Computable Zones (SCZ’s) and Split Computable Zones for Internal Connections (SCZI’s) which are subsequently sub divided as ‘Categorized Computable Zones’ (CCZ) with simple-medium-high complexity. The identification of CCZ’s is based on the 10 different types of FIWS representations developed for this study. From the CCZ’s categorization of complexity, they are further split into smaller ‘Machinable Zones (MZ’s)’ using a 4-step algorithm. In the algorithm, the first step calculates a common plane (CP) to cut the steep areas in the CCZ’s where the tool cannot have full access for machining. Once the CP is identified, the second step is to extend it by moving them along the CCZ’s and calculate the necessary ‘Machinable Zones (MZ’s)’ in the next stage. This is done by finding the intersection of CP with the FIWS through a point to point / line plane intersection concept. After this step, the MZ’s are re-iterated by including the open and closed surface criteria and is analyzed for the IDC’s to be combined in the fourth stage. This is achieved by adding up the IDC’s with the existing MZ’s computed by the algorithm. At every stage, the algorithm considers tool collision avoidance and tool rubbing in the CCZ’s and MZ’s . This is by an automatic computation based on the height to fixture clearance for safer neck length which avoids collision and rubbings in the final toolpaths. Finally, a combined tool path is generated for all the MZ’s and has been verified / tested for a sample part and impeller containing similar shapes using UG NX / STEP –NC software

Analytical and experimental study of feed rate in high-speed milling

In the context of high-speed milling (HSM), during the machining process dynamic machine response has to be identified. To achieve this, we have to calculate the feed rate evolution in linear and circular interpolation according to dynamic performance of machine. In addition to that, actual trajectory for transition passages between two interpolations must be estimated with take into account of specific machining tolerances. This article proposes a model of machine tool behavior for a tool path with linear and circular interpolations and machining cycle time prediction. The method involves subdividing the trajectories into elementary geometries according to the type of interpolation (circular or linear). At points where different trajectories meet, there is often a discontinuity in curvature or in tangency, which decreases the feed rate. At the points of discontinuity in tangency, a fillet radius is inserted. In this article, the influence of the geometry for elementary trajectories was determined. Then, the value of the fillet radius between linear and circular contours in different combinations was modeled. An industrial application was carried out in order to validate models and to determine the influence of feed rate evolution on the machining cycle time

Feed rate modeling in circular–circular interpolation discontinuity for high-speed milling

In this paper, a modeling approach is presented in order to evaluate feed rate during a circular interpolation in high-speed milling. The developed model depends on the type of discontinuity and the kinematic performance of the machine tool. To begin with, a feed rate modeling for circular interpolation with continuity in tangency is developed. After, the discontinuity in tangency between two circular interpolations is replaced by discontinuity in curvature by adding a fillet which is in relation to the functional tolerance ε imposed in the part design. An experimental study has been carried out to validate the models

Contour parallel milling tool path generation for arbitrary pocket shape using a fast marching method

Contour parallel tool paths are among the most widely used tool paths for planer milling operations. A number of exact as well as approximate methods are available for offsetting a closed boundary in order to generate a contour parallel tool path; however, the applicability of various offsetting methods is restricted because of limitations in dealing with pocket geometry with and without islands, the high computational costs, and numerical errors. Generation of cusps, segmentation of rarefied corners, and self-intersection during the offsetting operations and finding a unique offsetting solution for pocket with islands are among the associated problems in contour tool path generation. Most of methods are inherently incapable of dealing with such problems and use complex computational routines to identify and rectify these problems. Also, these rectifying techniques are heavily dependent on the type of geometry, and hence, the application of these techniques for arbitrary boundary conditions is limited and prone to errors. In this paper, a new mathematical method for generation of contour parallel tool paths is proposed which is inherently capable of dealing with the aforementioned problems. The method is based on a boundary value formulation of the offsetting problem and a fast marching method based solution for tool path generation. This method handles the topological changes during offsetting naturally and deals with the generation of discontinuities in the slopes by including an "entropy condition” in its numerical implementation. The appropriate modifications are carried out to achieve higher accuracy for milling operations. A number of examples are presented, and computational issues are discussed for tool path generatio

Contour parallel milling tool path generation for arbitrary pocket shape using a fast marching method

Contour parallel tool paths are among the most widely used tool paths for planer milling operations. A number of exact as well as approximate methods are available for offsetting a closed boundary in order to generate a contour parallel tool path; however, the applicability of various offsetting methods is restricted because of limitations in dealing with pocket geometry with and without islands, the high computational costs, and numerical errors. Generation of cusps, segmentation of rarefied corners, and self-intersection during the offsetting operations and finding a unique offsetting solution for pocket with islands are among the associated problems in contour tool path generation. Most of methods are inherently incapable of dealing with such problems and use complex computational routines to identify and rectify these problems. Also, these rectifying techniques are heavily dependent on the type of geometry, and hence, the application of these techniques for arbitrary boundary conditions is limited and prone to errors. In this paper, a new mathematical method for generation of contour parallel tool paths is proposed which is inherently capable of dealing with the aforementioned problems. The method is based on a boundary value formulation of the offsetting problem and a fast marching method based solution for tool path generation. This method handles the topological changes during offsetting naturally and deals with the generation of discontinuities in the slopes by including an "entropy condition" in its numerical implementation. The appropriate modifications are carried out to achieve higher accuracy for milling operations. A number of examples are presented, and computational issues are discussed for tool path generation