Access of the tool to the complex surfaces of the workpiece.

Minciu, Constantin ; Sebe, Andrei ; Catrina, Dumitru 等

Abstract: The problem of collision between cutting tool and the work piece when milling complex surfaces is the machining of "deep" zones or "concave details". Contour milling is a particular case of medial machining and it is enough to study the problem of tool access for this case only. The models used to define the tool access result from various transformations of a given work piece model are the following: equidistant surface (or offset for simpler surfaces), convex hull (zones where the curvature of the medial cutting tool is zero) and medial surfaces.

Key words: contour milling, medial surfaces, offset, visibility, orientation, tool.

1. INTRODUCTION

The access of a tool to a point of the work piece model is determined by the dimension of the cutting tool shape (local condition). In figure 1, b, point A cannot be reached by the tool, but the points B, C and D can. In case the tool diameter increases it could be possible the points B and C would not be reached, but the point D will remain accessible. Consequently, points on the convex hull are accessible whatever dimension, shape dimension and shape orientation the cutting tool has.

Geometrically, the machining phases could be inversed with the same result. Thus, the surface can be manufactured in an infinite number of modes. Medial machining is only one of the means to determine the sequence of reaching different points of one work piece surface.

One zone of the work piece surface can be reached with a tool if the following conditions are fulfilled simultaneously:

1. Surface to be manufactured can be orientated, so that the cutting tool can have access (orientation condition);

2. Cutting tool finds room in the target point (local condition);

3. Contact point between the tool and work piece surface is visible (visibility condition);

4. Tool is long enough to reach target point (length condition).

Depending on the machining mode the accessibility may be discrete (3+2 axes) or continuous (5 axes).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

2. DISCRETE VARIABLE ORIENTATION

2.1. Actual approaches of the access by discrete orientation One approach of this problem is based on orientation maps and own circles. Thus, every point of the surface has a visibility cone [Tang et al, 1992]. The tool can approach the surface starting from an infinite distance. Intersection of the unit sphere with a visibility cone having its point in the centre of the sphere is a visibility map (Gaussian Map). Moving a point of a Gaussian Map with up to 90[degrees] on the unit sphere a cone up to a hemisphere will be generated. The visibility cone of the surface represents the intersection of all these cones. Its image on the unit sphere is the visibility map [Tang et al, 1992].

On a machine tool with 3 axes the tool "sees" maximum one hemisphere of the visibility map. The fourth axis, which would allow the work piece rotation, can be represented on the unit sphere as a large circle or eigen circle. Association of the visibility map (3 axes) with the own circle (fourth axis) defines the machining in 4 axes. In order to define the orientation in 5 axes one can use the case of the fourth axis. The fifth axis is perpendicular to the fourth axis. On a sphere, these two axes form a band, named eigen band. Because always inside the own band there will be at least one own circle, the problem can be reduced to the previous case (4 axes).

Each point of the visibility map represents an orientation of the tool, with which the whole surface can be manufactured. In order to minimize the number of holds and detachments of the work piece is necessary to determine the own circle which intersects as many own maps as possible. Even if the complexity of these calculations is reduced, the implementation of the presented algorithm is extremely laborious and it is valid only in case of relatively simple surfaces. On the other hand, this algorithm can be successfully used to determine orientation in the holder, which can dramatically limit the accessibility to the work piece's surfaces.

Another approach of the access problem [Elber, 1997] (fig. 2) is based on the fact that in 3 axes machining the visibility problem reduces to the problem of the hidden lines of the offset surface. This is a classic processing used in visualization but it is valid only in 3 axes.

2.2. Medial machining with discrete orientation In this case the first fixed parameter is orientation. Thus, the specific models of the phase can be obtained by extrusion of the work piece model, along the tool axis directions. The aim is to determine minimum number of work piece orientations for maximum machining of the work piece surface. There are points where visibility of the concave detail is continuous (main directions) and zones where it is discontinuous. The access problem with discrete orientation is reduced to determine the main directions, along which each concave detail can be maximally machined. In medial machining work piece manufacturing is the machining of the concave details, because the other surfaces are situated on the convex hull. The main directions are zones of convergence of the field lines starting from the concave details of the surface. If the test point of visibility is modified, one can observe the points along the medial axes have maximum visibility (fig. 3).

[FIGURE 3 OMITTED]

Each point on the convex hull is accessible along perpendicular directions to the tangent at the convex hull in the considered point. The difference is that for each face of the convex hull could be several concave details, as the method of the field lines generate for each concave detail one field line. As a consequence, the normal directions to the convex hull are used as main directions of access (fig. 4).

[FIGURE 4 OMITTED]

3. CONTINUOUS VARIABLE ORIENTATION

In case of contour machining the work piece surface can be generated in two modes: by "gearing" between tool and work piece or by "sliding" along the work piece surface. Gearing contouring process will necessitate longer tools than sliding contouring process. Consequently, a method of determination the tool accessibility is to generate a sufficiently big number of discrete orientations as presented before, with extrusion along tool axis for each orientation. For one point on a medial machining trajectory [2] of a complex surface, the feed vector, passing through the studied point will intersect the offset surface, work piece surface and medial surface. Consequently, the angle defining the tool position without interference is limited by the values [[psi].sub.l] and [[psi].sub.r], for tangential left/right real-medial machining (fig. 5).

In case of a tool inclined with lateral angle [psi] the only requested condition is the visibility. Consequently, even if the tool has "room" in the point of the real medial trajectory, the visibility of this point could be partially or totally obstructed by the offset surface. In case the point has no visibility at all, the withdrawal of the tool must be ordered. Another solution to solve the visibility is diminishing the tool radius.

[FIGURE 5 OMITTED]

4. MEDIAL TANGENTIAL HELICOIDAL MACHINING

4.1. Normal medial tangential helicoidally machining The medial helicoidally tangential trajectory is given by two trajectories: tool centre trajectory LS1 and tool holder trajectory LS2, which are perpendicular on feed vector. This is the case of normal medial tangential helicoidally machining. 4.2. Inclined medial tangential helicoidally machining When the section plane is inclined by frontal angle [beta] (Sturz angle) to the tool axis vector, the tool can cut in good conditions because the tool tip (which has zero cutting speed) is no more implicated in cutting, but its areas with greater cutting speed. Calculation of trajectories is done similarly by solving the visibility in the plane inclined by angle [beta] for each final and intermediary position on resulted trajectories. This is an efficient machining method because it allows shorter trajectories, reduced number of approaches and withdrawals of the tool, very good surface quality, good cutting conditions for the tool, use of high speed machining, thin walls etc.

4.3. Double medial tangential helicoidally machining

When instead of using a constant angle [beta] limit values are used (with no interference), we obtain a double tangential machining because the tool tip is tangent to the work piece surface and the tool flank is tangent to the surface already machined or to be machined. In this case, instead of the offset surface related to the tool centre, another offset surface shall be used. If the tool shape is not cylindrical, but conical with abrasive areas, then in HSM conditions, the grinding of the previous machined surfaces could be obtained. It should be mentioned that this cutting machining is expected to be the most efficient ever, both from the productivity and the machined surface quality points of view.

5. CONCLUSIONS

In this paper the tool access to the complex surfaces of the work piece is defined and analyzed for contouring and medial machining. There are presented aspects related to the machine tools which allow discrete/continuous angular variable orientation. There are underlined both the cases of normal and inclined medial tangential helicoidally machining. The statements and conclusions of this paper were verified by milling the petals of a rose made of dur-aluminium.

6. REFERENCES

Catrina, D., Totu, A., Carutasu, G., Carutasu, N.& Croitoru, S. (2003). Sisteme flexibile de prelucrare prin aschiere (Flexible systems for cutting procedures), Ed. Bren, ISBN 973-648-231-6--Bucuresti, Romania.

Sebe, A.P. (2004) Cercetari privind prelucrarea suprafetelor complexe pe masini-unelte cu comanda numerica (reasearches regarding complex surfaces processing using numerical control machine-tools), PhD Thesis, POLITEHNICA University of Bucharest, Romania

Elber, G. (1997). Accessibility in 5-Axis Milling Environment, Department of Computer Science, Technion, Israel Institute of Technology.

Sebe, A.P., Minciu, C. & Catrina, D. (2004). NC Milling Of Geometrically-Complex Surfaces Using Implicit Volumes, Proceedings of the 15-th DAAAM Symposium, B. Katalinic, ISSN 1726-9679, Vienna, Austria

Tang, K., Woo, T. & Gan J. (1992). Maximum intersection of spherical polygons and workpiece orientation for 4 and 5 axis machining, Journal of Mechanical Design, september 1992, vol 114, p 477-485