Using curvature bounds towards collision free 5-axis tool-paths
Graphical abstract
Introduction
Computer numerical control (CNC) machining, is a widely used form of subtractive manufacturing. In CNC machining, a target model, usually expressed as a set of boundary surfaces, is manufactured from some initial model (stock) by removing excess material using a machining tool. In this paper, we present methods that can be adapted to any convex machining tool, and use two types of tools as examples: Definition 1.1 A ball-end tool has a cylindrical shank, that ends in a tip: a hemisphere of the same radius. A flat-end tool is made of a cylindrical shank, with the bottom disc of the cylinder being the tip.
An important aspect of CNC machining, is the generation of collision free (valid) tool-paths. Collision (or gouging) free tool-paths are those in which the tool does not remove material that should remain as part of the target model. Generating collision free tool-paths is especially challenging in 5-axis machining, where both the tool position and orientation change along the tool-path. Collisions can be divided into two main types:
- 1.
Local, in which the tip of the tool gouges the target model (or the CNC machine, etc).
- 2.
Global, when the shank of the tool gouges the target model (or the CNC machine, etc).
In this paper, we show how bounds, computed for the normal curvatures of a given model surface, can be used to generate collision free 5-axis tool-paths for convex tools. The main contributions of this paper are:
- 1.
A method to generate tight bounds for the normal curvatures of a whole surface.
- 2.
A method to generate globally verified valid 5-axis tool-paths for convex tools.
- 3.
A collision avoidance strategy that enables global optimizations of the tool-path, without compromising its validity.
The rest of the paper is organized as follows: in Section 2, we discuss some of the relevant previous work. We lay down the theoretical background for bounding the normal curvature values of a surface in Section 3. Section 4 presents how we apply these normal curvature bounds in an algorithm that generates a globally collision free tool-path, for a flat-end or a ball-end tool. We present our experimental results, which include simulations validating our approach in Section 5. We mention some avenues for future research in Section 6, and conclude in Section 7.
Section snippets
Previous work
The concepts introduced in this work relate to local collisions in CNC machining, and so in this section we focus on other research efforts that deal with local collision avoidance. A more thorough (but not very recent) review of CNC machining research, in general, can be found in [1].
Perhaps the greatest challenge in local collision avoidance stems from the fact that the tool has to make contact with the target model as part of the machining process. This means collision avoidance algorithms
Calculation of normal curvature bounds
Given a polynomial or rational regular C2 surface its normal surface and its unit normal surface we recall the following terms of the first and second fundamental forms (following [11] or similar):
The principal curvatures at a point would be the roots of the following quadratic equation for the variable κ, evaluated at (u0, v0):
Collision avoidance in 5-axis machining
Let be our our target model, with a closed boundary that is expressed as a set of regular C2 surfaces, . Further, let be a subdivision of the boundary surfaces of into smaller sub-surfaces. We wish to generate a collision free 5-axis tool-path for moving a given tool T along a given cutter contact (CC) curve C(t), t ∈ [t0, t1], on .
To generate a locally as well as globally collision free 5-axis tool-path we use a configuration space (or C-space) based method. For more
Experimental results
We implemented the algorithm described in Section 4 as a C/C++ single threaded program. All tests ran on an Intel i7-4770 3.4 GHz windows 7 machine. To validate our results, using CNC simulations, we use the machining Verifier Application by ModuleWorks (https://www.moduleworks.com).
Throughout the following experiments, we use a tool with a unit (1) radius, regardless of type. For the normal curvature bounds calculation the maximum number of recursions is set to 8, and the accuracy value is set
Future work
One additional feature that can be added to the calculation presented in Section 3, for bounds on principal curvature values, is the computation of bounds on the principal curvature directions as well. Once the intervals for the principal curvatures are known, bounds on the principal curvature directions can also be calculated using interval arithmetic. The bounds for the two principal curvature directions will take the form of two cones, with perpendicular axes, that will encompass all
Conclusion
Bounding surface positions using the control mesh, and surface normals using normal cones, are both well known procedures. In this paper, we add to these, a procedure to bound the (normal) curvature values of a surface. In the context of machining, normal curvature bounds allow the second order behavior of a surface to be conservatively approximated by that of the tool, without resorting to point sampling. The methods presented in this work show that collision free tool-paths can be generated
Acknowledgements
This research was supported in part with funding from the Defense Advanced Research Projects Agency (DARPA), under contract HR0011-17-2-0028. The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.
References (25)
- et al.
Recent development in CNC machining of freeform surfaces: a state-of-the-art review
Comput. Aided Des.
(2010) - et al.
Precise gouging-free tool orientations for 5-axis CNC machining
Comput. Aided Des.
(2015) - et al.
Tool path planning for five-axis machining using the principal axis method
Int. J. Mach. Tools Manuf
(1997) - et al.
Rolling ball method for 5-axis surface machining
Comput. Aided Des.
(2003) - et al.
Arc-intersect method for 5-axis tool positioning
Comput. Aided Des.
(2005) - et al.
Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining
Comput. Aided Des.
(2017) - et al.
Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution
Comput. Aided Des.
(2016) - et al.
Multi-point tool positioning strategy for 5-axis mashining of sculptured surfaces
Comput Aided Geom Des
(2000) - et al.
Loop detection in surface patch intersections
Comput Aided Geom Des
(1988) - et al.
Pyramids that bound surface patches
Graph. Models Image Process.
(1996)