Modeling the surface swept by a generalized cutter for NC verification

Chung, Young-Sook; Park, Jung W.; Shin, Hayong; Choi, Byoung Kyu

doi:10.1016/s0010-4485(97)00033-x

Cited by 82 publications

(28 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The term swept surface (or swept volume) is often used to refer to the region defined as the union of the instances of a rigid body that executes a general spatial motion -such surfaces are of great importance in modeling material removal in CNC machining, collision avoidance in robotics, and related fields [2,3,5,6,26,27,36,37]. A closely related concept is the generalized cylinder (or cone) that has seen widespread application as a basic shape primitive in computer vision and biomedical applications [1,7,20,28,29,30,32].…”

Section: Rational Swept Surfacesmentioning

confidence: 99%

Rational swept surface constructions based on differential and integral sweep curve properties

Farouki

Nittler

2015

Computer Aided Geometric Design

View full text Add to dashboard Cite

A swept surface is generated from a profile curve and a sweep curve by employing the latter to define a continuous family of transformations of the former. By using polynomial or rational curves, and specifying the homogeneous coordinates of the swept surface as bilinear forms in the profile and sweep curve homogeneous coordinates, the outcome is guaranteed to be a rational surface compatible with the prevailing data types of CAD systems. However, this approach does not accommodate many geometrically intuitive sweep operations based on differential or integral properties of the sweep curve -such as the parametric speed, tangent, normal, curvature, arc length, and offset curves -since they do not ordinarily have a rational dependence on the curve parameter. The use of Pythagorean-hodograph (PH) sweep curves surmounts this limitation, and thus makes possible a much richer spectrum of rational swept surface types. A number of representative examples are used to illustrate the diversity of these novel swept surface forms -including the oriented-translation sweep, offset-translation sweep, generalized conical sweep, and oriented-involute sweep. In many cases of practical interest, these forms also have rational offset surfaces. Considerations related to the automated CNC machining of these surfaces, using only their high-level procedural definitions, are also briefly discussed.

show abstract

Section: Rational Swept Surfacesmentioning

confidence: 99%

Rational swept surface constructions based on differential and integral sweep curve properties

Farouki

Nittler

2015

Computer Aided Geometric Design

View full text Add to dashboard Cite

show abstract

“…This technique, although very slow, has been proven to be very accurate when compared with actual cutting tests [4].…”

Section: Simulation Of Machining a Turbine Bladementioning

confidence: 99%

“…Chung, Park, Shin and Choi [4] also found the generating curve on the tool at different cutter locations. The authors developed analytical expressions of that curve for different tools.…”

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Generation of swept volumes of toroidal endmills in five-axis motion using space curves

Roth

Bedi

Ismail

1999

Proceedings of the Fifth ACM Symposium on Solid Modeling and Applications

View full text Add to dashboard Cite

Accurate prediction of the swept volume of a cutting tool is essential in NC verification algorithms for detecting deficiencies in a proposed tool path, such as gouging, undercutting and interference. This paper explores a new technique for generating the swept volume of a toroidal endmill, and analyzes the results obtained for two test cases. For a given tool location along a path, a curve on the cutting surface of the tool is identified that rs:presents the imprint of the tool on the machined surface. This curve will be designated a space curve as it is defined in 3D spa.ce. The method relies on forward difference information obtained from a G-code or cutter location data file in order to compute the space curves. Once several su.ccessive space curves have been identified, a facetted surface model of the footprint of the tool along a pass may be readily calculated and compared with the design surface. The method has b,een verified for two test cases: a) 5-axis tool path on a hemispherical cavity and b) a 5-axis tool path on the complex surface of a turbine blade. Results from the new method are compared with the slow, but dependable my-casting technique. It is concluded that the new technique offers al fast and accurate method of verifying multi-axis tool paths. In the future, it is hoped that the simulation can be extended to all cutter shapes, and not be limited to toroidal cutters.

show abstract

“…Then in Section 3, we extend this work to elliptic cylinders, giving examples in Section 4. 2 Grazing Curves and Swept Surfaces Chung, Park, Shin and Choi [4] present a method for determining the surface swept by a generalized APT cutter for 3-axis machining. The generalization of Chung et al's method to 5-axis machining is non-trivial.…”

Section: Introductionmentioning

confidence: 99%

The swept surface of an elliptic cylinder

Mann

Bedi

Roth

2001

Proceedings of the Sixth ACM Symposium on Solid Modeling and Applications

View full text Add to dashboard Cite

In this paper, we present a method for computing a piecewise linear approximation to the surface swept by a moving, rotating elliptic cylinder. Our method is a generalization of the imprint point method we developed for computing points on a surface of revolution. The method is based on on identifying grazing points on the surface of revolution at a sequence of positions, and for each position connecting the grazing points with a piecewise linear curve. A collection of grazing curves is joined to approximate the swept surface and stitched into a solid model. Previously this method has been tested on cylinders, toruses, and cones.This work extends the imprint point method to compute the swept surface generated by a general closed surface. The method is demonstrated by translating and rotating an elliptic cylinder along a spline curve. The application of this method is in interference detection of moving machinery such as robots. It is anticipated that a robot would be modeled as a collection of components enclosed in elliptic cylinders, cones, toruses and spheres. Our method can be used to generate the swept volume of these enclosing objects, and used for interference detection and avoidance.1 Introduction Swept surface are frequently needed in many engineering applications. Swept volumes are important for determining interference free trajectories for robots and for generation of gouge free tool paths. The existing methods rely on SEDE [1] or envelop theory [2,3]. Implementation of these techniques results in simultaneous solution non-linear equations which can be tedious to generalize and time consuming to compute.A new method was presented for the creation of swept surfaces swept by surfaces of revolution. This method is similar to envelop theory, but uses some surface properties to speed up the calculation. The idea is based on the observation that when a solid cylinder translates it sweeps a surfaces made up of straight lines. To find points on the straight lines, the cylinder can be imagined to be made of a stack of disks and each disk translates in the same direction. Then the grazing point on one disk on the surface at a particular tool position can be identified by taking a cross product of the normal to the disk with the direction of motion. This basic idea can be extended to a cylinder executing simultaneous translation and rotation, although in this case the grazing curves are not straight lines but curves on the cylinder. The cross product method works for tori and spheres; a more general method can be applied to find grazing curves on an arbitrary surface of revolution, which we review in the next section.In this paper, we further extend the method to determine the surfaces swept by straight and twisted elliptic cylinders (Figures 4 and 5). The concept can be generalized to convex closed surfaces, but examples in this paper will be limited to the elliptic case.In the next section, we will review grazing curves and our earlier work on computing the surface swept by an APT cutter (i.e., a surf...

show abstract

Modeling the surface swept by a generalized cutter for NC verification

Cited by 82 publications

References 7 publications

Rational swept surface constructions based on differential and integral sweep curve properties

Rational swept surface constructions based on differential and integral sweep curve properties

Generation of swept volumes of toroidal endmills in five-axis motion using space curves

The swept surface of an elliptic cylinder

Contact Info

Product

Resources

About