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5-Axis Machining of Sculptured Surfaces

5-Axis Machining of Sculptured Surfaces

Hong Ji

A report prepared for the IE616
Computer Integrated Manufacturing
Instructor: Dr. Y.S. Lee
November 13, 1995

The report presents surveys on different topics on sculptured surface machining. It covers cutter path generation, calculation of cusp height in 5-axis machining and consideration of cutting force. The purpose of this report is to study the state of art and the current difficulties in free form surface machining, and also try to propose methods to solve some of the problems. This report emphasizes on the techniques of 5-axis machining with a flat end mill.

1.0 Introduction

In the 1990s, the role of numerical machining is not just to improve machining accuracy, but also to shorten the product realization cycle, and to compensate for the diminishing of the skilled workforce. High accuracy and high efficiency are both important in the NC machining.

This report will address following subjects in the 5-axis machining. How to generate cutter-contact path to give a minimum machining time (or a maximum width of a machined strip). How to generate CL data from CC data. How to optimizing cutting conditions.

2.0 Terminologies in 5-Axis Machining

In this section, some terminologies used in the paper are introduced.

The surface of the raw stock to be machined is called the raw-stock surface, and the final smooth surface to be produced is called the part surface. A mathematical description of the part surface is called the surface data r(u,v).

A point on the part surface at which the cutter is planned to make contact is called the cutter-contact point C. A series of cutter-contact points may form a cutter-contact path. The distance between a pair of adjacent cutter-contact paths is called the path interval d.

In Figure 1, the face-milling cutter is contacting with the part surface r(u,v) at a cutter-contact point C. It is convenient to define an orthogonal coordinate frame at C. The unit vector in the diraction of the cutter feed motion is called a cutter-feed vector f, and a unit tangent vector perpendicular to f is called a surface-tangent vector t. A unit normal vector n is defined as n=fxt. Thus, the three unit vectors f, t, n and position c define an orthogonal coordinate frame.

Figure 1. Cutter location and coordination frame.

Figure 2. Cutter orientation angles and orthogonal views

The cutter location in Figure 1 is called a zero location in which the bottom of the face-milling cutter is seated on the f-t plane making a point contact with the t-n plane at c.

If the shank of the cutter is tilted to the direction of f (i.e rotated around t) while maintaining the point contact at c, as shown in Figured 2a. The rotation angle is called tilted angle α.

If the cutter in a zero location is rotated around the normal vector n, while still maintaining the point contact at c, the resulting cutter location becomes the one shown in Figure 2b. The second rotation angle is called the yaw angle .

These two angles completely define the orientation of the cutter. Figure 2c shows the three orthogonal views of the cutter with both the tilt and yaw angles α, being positive ( can be negative). In this general cutter location, the bottom face of the cutter appears as an ellipse in each of the orthogonal views.

3.0 Input Data

There are two kinds of input data that we are trying to deal with. The first one is the regular CAD data. The sculptured surface is defined by NURB patches or Bezier patches. The second one is cloud-of-points data. This kind of data comes from a laser scanner or a CMM.

For the second kind data, one method to generate toolpath is to construct a surface description from the cloud-of-points data. Then the toolpath is generated from the surface description. [ ] have done some work. But the transition surface features (S-type, double S-type and C-type) they deal with are fairly simple. The actual product shape from reverse engineering or other sources may be much more complex.

To develop a general algorithm to generate surface description from cloud-of-points data might be very difficult. It may also require the coordination from the measurement department. [Kavwabe 1980] presented an overall procedure for obtaining a composite Bezier surface model from 3D coordination measuring data.

4.0 Cutter Contact Path Generation

The automatic generation of cutter paths is regarded as one of the keys to the integration of CAD and CAM. In this report, we concentrate on cutter paths generation for sculptured surface in 5-axis machining. Readers who are interested in cutter path generation for other features, such as pocket, may refer to [Marshall and Griffiths 1994].

4.1 Related Work Up to now, many approaches have been proposed for cutter path generation. Generally, they can be classified into three catalogs.

The first kind of method is isocurve. The approach exploits the parametric representation, and generates isocurves that are uniformly distributed across the parametric domain. The method is not optimal if the surface mapping into Euclidean space is not isometric. However, [Elber and Cohen 1994] proposed and adaptive isocurve extraction method. It eliminates most of the redundancy that occurs when equally spaced complete isocurves are used as a toolpath, while retaining all the advantageous properties of isocurve toolpaths.

The second kind of method is iso-planar. The cutter paths are formed by intersecting the surfaces with parallel planes equally spaced in Euclidean space. Because the distance between parallel planes (cutter path interval) are constant and the same, the method has weakness when a surface has a very steep slop. [Huang and Olive 1992] solved this problem by varying tool path interval (cutter path interval) according to the given cusp height and the local surface curvature.

In the above two approaches, the cutter paths are generated based on the worst-case cusp height. The cusp height varies along the tool path, but the maximum value is less than the permissible "h". So some portions of the part may be very smooth, while some portions may be rough.

The third kind of method is iso-cusp-height. [Suresh and Yang 1994] proposed the techniques to keep cusp height constant along all the tool path, This leads to significant reduction in the size of CL data. So the machining time is significantly reduced.

However, [Suresh and Yang 1994]'s work was based on 3-axis machining. In 5-axis machining, the situation and calculation will be much more complicate and difficult.

4.2 Proposed Approaches Here we propose two approaches to generate the cutter path for free form surface machining.

4.2.1 Iso-Cusp-Height Approach

In this approach, the basic idea is similar to that of [Suresh and Yang 1994]. However, we developed an algorithm which is suitable for 5-axis machining. We will introduce the general algorithm here, and then introduce the cusp height calculation in 5-axis machining in section 4.

To achieve the goal of reduction in the size of CL data file and machining time, this approach tries to maximize the cutter path interval by maintaining a constant cusp height. This is analogous to maximizing the forward-step by maintaining a constant tolerance.

We first introduce the two important conceptions in iso-cusp-height machining.

a. Parallel Point.

Let an existing tool path be given by P(u(t), v(t)). At a point P, determine the allowable cutter path interval "d" (for an allowable cusp height "h"). The parallel point P* is then defined as the point on the surface along the geodesic path perpendicular to the path P(u(t), v(t)), that is at a distance of "d" from the original point P.

b. Parallel path.

A parallel path is the continuous curve that joins all the parallel points of a tool path. Obviously, from definition, the cusp height between the original tool path and its parallel path is a constant.

[Suresh and Yang 1994] gave a detail algorithm for the evaluation of parallel point in 3-axis machining. However, in 5-axis machining, the evaluation of the parallel point is much more complicate. We have not derive the detail solution. Here, we state the problem and the general approach.

Let an existing tool path be given by P(u(t), v(t)). At a point P on this path, the cutter location is (P, α, ). We are trying to find its parallel point P* and the cutter location at P*, (P*, α*, *),

The P* has to satisfy the following conditions:

1. P* should lie on the path perpendicular to the path P(u(t),v(t)).

2. The cusp height between P and P* should be equal to the allowable "h".

In other words, we are trying to find the parallel point P* and cutter location (P*,α*, *) which can maximize the path interval under a given cusp height h.

4.2.2 Iso-curvature Approach.

Similar to iso-parametric approach, here we use the iso curvature curve at cutter path. When the distance between two adjacent iso curvature curve is too far. We can insert one iso-curvature curve between them. The insertion is similar to that of [Elber and Cohen 1994]'s.

The benefit of this approach is that we can utilize the flexibility of 5-axis machining by changing the orientation of the cutter to fit the local surface shape in order to maximize the width of machined strip [Lee and Ji 1995]. And when the cutter moves along the iso-curvature path, the orientation of the cutter do not need to change too much.

5.0 Calculation of Cusp Height in 5-Axis Machining

The calculation of cusp height is the essential part in the maximizing cutter path interval.

[Suresh and Yang 1994] presented a method suitable for 3-axis machining. [Choi 1993] proposed an approach for 5-axis machining. However, [Choi 1993]'s approach was under the condition that the cutter has the same orientation (i.e. the same α, ) at the two adjacent cutter contact points.

Another shortcoming of [Choi 1993]'s approach is using the tangent plane to approximate the local surface in calculation.

Here, we propose a modified approach to calculate cusp height in 5-axis machining. And we use the geodesic curve, which starts at the given point on a tool path and in a direction perpendicular to that tool path, to calculate the local radius of curvature.

Given two cutter locations (P, α, ) and (P*, α*, *), the calculation of the cusp height in 5-axis machining involves following steps:

1. Project the cutter at two locations to the t-n plane at point P. We get two ellipses from the cutter bottoms. The mathematic expressions for the ellipses are introduced by [Lee and Ji 1995]. The shape of the ellipse is determined by cutter radius and cutter orientation at a certain cutter contact point.

2. Calculation the intersection point between the two lower half ellipse. If no intersection point can be found, calculate the intersection point between the lower half ellipse at a cutter location and the side of the cutter at the other location.

3. Calculate the distance between the intersection point and the surface.

The distance is the cusp height.

6.0 Generation of CL path from CC path

The CL data for given CC data is a function of the cutter position, the cutter orientation and the cutter shape. We will first consider the end milling cutter, and then the fillet milling cutter.

(1) End Milling Cutter

In order to get the CL data, we need first, in the local surface coordination system, rotate the cutter center under given α and , and then transfer the cutter center from local surface coordination system to the global surface coordination system.

(2)Fillet Milling Cutter

For the fillet cutter, we need first to decide where is the CC point on the cutter. So we can define the position of the cutter center in the local surface coordination when the cutter is at its zero position. Then we rotate the cutter center under given α and . And then transfer the cutter center from local surface coordination system to the global surface coordination.

7.0 Consideration of Cutting Force.

After the calculation of cutter path, the cutter can travel along the path to machine the surface.

At this stage, in order to improve the machining accuracy and shorten machining time, we need to determine the proper spindle speed and feed rate, and also to detect the tool wear and breakage.

[Gaide 1995] have done some work on tool wear development. They found the tool wear development follows a certain pattern with three phases: initial wear, stable wear and catastrophic failure. In the initial phase, the flank wear only affects the coating. With increasing cutting length, the stable wear phase begins when coating chipping starts in small area at the chamfer and adjacent parts of the flank. After some cutting length under stable wear, the cutting edge suddenly becomes unstable and significant chipping appears along the flank face. Under these conditions, catastrophic failure of the edge eventually occurs.

[Gaide 1995] also proposed an adaptive milling strategy. The strategy is to maintain the maximum cutting speed within a specific target range by adapting the spindle speed. In addition, the maximum chip thickness is also maintained with a target range by adapting the feed rate.

[Yazar 1994] also did some work on feed rate optimization based on cutting force calculations. But their work was based on 3-axis milling.

[Ko, 1995] proposed a method on on-line monitoring of tool breakage in face milling by using a self-organized neural network.

8.0 Simulation

After the generation of cutter path and the choose of the proper machining parameters, we may simulate the machining process on computer before the actual machining. We can also verify the cutter path and detect interference between cutter and workpiece during simulation.

Up to now, many work have been done on 3-axis machining simulation by Z-buffer techniques. However, due to the complexity of 5-axis machining, more research work on simulation are expected. We will work on this area, but have not thought out a good methodology.

9.0 Conclusion

In this report, we have a survery on the 5-axis machining of sculptured surface. We reviewed the previous work, and also proposed some new approaches. In the future, we need to implement the proposed approaches.

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