A geometric modeling and five-axis machining algorithm for centrifugal impellers

Erik L J Bohez

Abstract

Unlike in three-axis machining, in five-axis machining the flexibility in tool orientation in space is extremely high. To obtain the full advantage of five-axis machining, the computer-aided manufacturing (CAM) system must have similar flexibility in tool orientation. Unfortunately, most CAM systems that support five-axis machining do not provide the required flexibility.

A centrifugal impeller is a perfect example of a part that can be efficiently designed and manufactured with the help of a computer. Machining these types of complex shapes requires a CAM system with a high degree of flexibility in tool orientation.

The use of programming languages is one of the best methods for eliminating the drawbacks of existing CAD/CAM systems and to obtain the flexibility required. This paper explains how flexibility is obtained using interactive geometric modeling and a programming language provided by a CAD/CAM system to access the geometry. Keywords: Five-Axis Machining, Ruled Surface, Impellers, Undercuts, CAM

1. Introduction

Design, modeling, and manufacturing of an impeller is composed of three separate yet equally important requirements. The first requirement is that the impeller provides an acceptable distribution of the relative velocity on both pressure and suction surfaces of the blade to minimize the possibility of flow separation and the accompanying loss in performance. In addition, the selected blade shape must be such that it can be manufactured accurately and economically on a CNC machining center. Finally, the blade should be designed to keep the stress at a safe level, eliminating the possibility of excessive distortion or fracture during operation.

Use of a CAD/CAM system is one of the best solutions to accomplish these requirements. It is questionable, however, whether such a blade can be produced with existing CAD/CAM systems because most do not have all the required functionality. Surface gouging, machining efficiency, and surface finish are the key factors in obtaining an error-free impeller. The main objective of this study is to analyze how a CAD/CAM system can be used to achieve the geometrical and technological advantages of five-axis machining.

2. Existing Research Results and Previous Works

Klewais describes five-axis milling of complex surfaces.1 The paper presents the important theories of machining from a practical point of view. A comparison of the flat end mill with the ballnose end mill puts forward numerous advantages that most manufacturing engineers have rarely applied in practice.

Marciniak discussed that the machining time of sculptured surface face milling on five-axis milling machines can be reduced if the tool trajectory is fitted to the surface shape.2 The most important conclusion of this study is, once the designer obtains more control of the tool, the results could be used to improve the quality of the surface and the efficiency of the machining process. This conclusion also justifies the present approach in which the rulings of the impeller blade are matched to the tool geometry, resulting in increased efficiency.

Lee and Chang discussed the problems in generating cutter points for machining a generic cavity with both roughing and finishing.3 The algorithms presented can determine the machining procedures, select the cutter for both roughing and finishing, identify the feasible cutting region within which the cutter center can move, and plan the cutter path within the feasible region.

Bohez suggested a method to model and manufacture an impeller on a four-axis machine.4 In this approach, a simplified geometric model based on canonical representation, that is, ellipses and circles, is used. A method was developed to manufacture the approximated inducer geometry with a four-axis CNC milling machine.

Smith and Merryweather showed how analytic surfaces can be used to define the blades of an impeller of a centrifugal compressor.5

Cho, Jun, and Yang conclude that machining of sculptured surfaces using a five-axis CNC machine is very effective but confined to convex or large concave surfaces.6 The present paper proves that complex “double-curved” surfaces can also very efficiently and accurately be machined with enough attention to the interference between tool and surfaces.

Kruth et al. describe a method to use the five-axis peripheral milling module of a CAD/CAM system to generate the CL file for wire EDM machines, and the postprocessing required for this method.7 The attractiveness of their method lies in the unique combination with the five-axis milling module of a high-end CAD/CAM system.

Loney and Ozsoy describe the development of an interactive surface modeler and toolpath generator based on the APT part programming language.8 In APT, the geometry of the part forms the first part of the APT source code. It requires much experience to write this part of the APT source code with a text editor. Many efforts in the late 1970s and 80s were directed at providing an interactive graphical front end to generate the geometry description. Today, in the middle of the 90s, interactive geometric modeling is mature, but interactive toolpath generation is still in many cases problematic due to lack of understanding of the requirements of the NC machine and the unavailability of some interactive functions for NC.

Bobrow discusses an algorithm to calculate a toolpath based on a CSG solid modeler with a limited number of primitives (no parametric surface bounded primitives).9 The NC programmer selects the part, drive, and check surface. The algorithm then determines a feasible toolpath by secting the part surface with an infinite planar surface and finding the portions that lie on the part. A stepping algorithm along this curve determines a three-axis toolpath. Gouging is also checked. The proposed method is an improvement on APT toolpath generation.

Boyd gives a classification of five-axis machining in positioning and surface-contouring applications.10 The five-axis contouring application is extremely complex and requires advanced CAD/CAM systems and postprocessors. The five-axis positioning application has enormous potential because of the reduction in setup time and the fact that this application does not need CAD/CAM systems.

Kim and Chu provide a quantitative analysis of the selection of the optimal toolnose radius in fiveaxis end mill machining.11 This optimizes the total machining time.

3. Geometric Modeling of an Impeller

The machining of an impeller blade surface is difficult because of the extreme local curvature of the blade surface. A tool with point contact only would require too much time to machine the impeller. On the other hand, to maintain the required surface finish a secondary operation such as polishing is required. A more appropriate machining method is one in which the cutter has a line contact, and hence a large cutting rate and improved surface quality are obtained. For machining considerations, a blade shape consisting of straight-line elements on both surfaces is preferred.l2 With this in mind, a geometric model has been developed based on canonical representations in curvilinear coordinates.

An impeller is composed of two regions (Figure 1). The first region, where the fluid particles are bent from axial to radial, is called the inducer. The most important role of the inducer is to reduce the tangential velocity component of the relative velocity in an axial direction and obtain a first compression of the gas. The second part, where the flow is radial, is called the impeller. In this zone, the energy of the gas is increased by the centrifugal force field. It is common to refer to the complete rotor (inducer + impeller) as the impeller.

About 10 variables are used to model an impeller (Figure 2). These are: hub curve, shroud curve, hub surface, shroud surface, meridional section, camber surface, suction surface, pressure surface, and angles alpha and Beta. Hub curve and shroud curve are used to define the hub surface and shroud surface, which are surfaces of revolution. The section formed by the hub curve and shroud curve is called the meridional section, which forms a plane passing through the axis of rotation. The next entity, known as the camber surface, is used to describe the threedimensional blade; in other words, it is the mean surface of the blade. Angle alpha is the angle, at a given point M of the camber surface, that a streamline (or isoparametric line) makes with the axis of rotation (Z axis). Angle Beta, which is referred to as the camber angle, is the relative angle between the meridional section and the camber surface. The next two entities are used to prescribe the blade suction and pressure surfaces and are spaced equal orthogonal distance on either side of the camber surface to give the required thickness distribution; they are offset surfaces from the camber surface.

3.1 Geometric Modeling Based on Canonical Forms

3.1.1 Meridional Surface

To accept a particular meridional surface, the distribution of alpha along the hub and shroud curve as well as the meridional section itself is examined. To obtain a smooth distribution of blade aerodynamic loading and to avoid early boundary-layer separation, the alpha distribution should be smooth. In general practice, alpha at the inlet and outlet are made equal to 0 and 90deg with the axis of rotation, respectively. Thus, to obtain an acceptable meridional section, the hub curve and shroud curve are considered to be elliptical (Figure 3). The hub surface and shroud surface are obtained by revolving the hub and tip ellipse about the axis of rotation.

3.1.2 Program to Determine Initial Geometry

An optimization program13 is used to obtain the initial impeller geometry. The output of the initial one-dimensional flow analysis is used as input for the optimization program. The minimum value for the hub radius, the ratio of the hub radius to tip radius at the impeller inlet, the ratio of outlet tip width to outlet radius, and the axial length are input. The cross section is completely defined after optimizing the flow. The program also calculates the point where the boundary layer separates, using the Jet-Wake model developed by Dean.l4

The output provides data relevant to a number of meridional ellipses. Out of these meridional ellipses, only the hub and shroud ellipses are taken into consideration for geometric modeling; this is a simplification so that the blade surfaces can be formed using ruled surfaces. By taking the intermediate ellipses into account a more accurate geometrical model could be obtained, but blade surfaces would not be ruled, making machining more difficult and creating a bending moment on the blades that in many highspeed impellers (100,000 RPM) is to be avoided.

3.1.3 Camber Surface

In the modeling approach, elliptical camber curve functions are defined on the hub and shroud surface to obtain the distribution of the camber angle along the meridional section. The boundary layer load for a circular camber line is higher in the beginning than at the end of the inducer section. This is beneficial because in the beginning of the circular camber curve the boundary layer is much more stable and the influence of coriolis force is small. For a circle, however, there is a very high initial load. Experiments proved that the best results are obtained with an elliptical camber line with the ratio of large axis to small axis equal to 2.15,16 In this study, the camber lines are defined in such a way that they are elliptical, and parameters of the ellipse are obtained from the program output.13

3.1.4 Camber Surface Based on Canonical Forms

The impeller blade can be divided into two regions. The camber surface is defined for each of these regions separately and is based on the program output.13 The output defines different meridional ellipses along with the camber angle at the inlet and at the flow separation section in the inducer region. But for simplification only the hub and shroud meridional ellipses are used to obtain the camber surface. Consider the hub meridional ellipse in the inducer region (see Figure 3). At point X, flow separation is taking place. Y is the point on the hub ellipse at the inlet. Z is the point on hub camber line at the hub inlet. O is the origin of the curvilinear coordinate system defined on the hub surface. U and V are the curvilinear coordinates at any point on the hub surface. Based on the curvilinear coordinate system, and considering the camber lines are elliptical, the equation of the camber line on the hub surface can be written as follows (see Figure 3):

This is the equation of an ellipse with the center in a point (EQ) with the axis parallel to U and V, where P, Q, A, and B are constants. It should be clear that the above equation represents an ellipse in a curvilinear coordinate system and that the curve in Cartesian coordinates is complex. gamma is defined as the ratio of ellipse axes.

Then Eq. (1) can be written as follows:

P, Q, and B are unknowns that can be evaluated by means of boundary conditions at the hub inlet and flow separation sections.

3.1.5 Camber Line Equation for Impeller Zone

The zone where the flow is completely radial is called the impeller zone. Generally, from the flow separation point onward, gas flow is completely radial (Beta = 0). Therefore, in this region the camber line coincides with an isoparametric line. This gives the equation of the camber line as v = constant-in this case, v = 0. If the flow is not completely radial, the camber curve of the impeller region may follow any other shape, a similar procedure (as inducer region) being required for the impeller region. The complete camber line of the hub surface is obtained by joining the above curves using a cubic spline curve or B-spline curve with appropriate degree. By repeating the same procedure for the shroud surface and tip ellipse, the camber line of the shroud surface is defined. A ruled surface is fitted between the hub camber line and shroud camber line to obtain the camber surface.

3.1.6 Blade Suction and Pressure Surfaces

The camber surface and the given normal blade thickness along the hub and shroud contour determine the suction and pressure surface of the blade. The blade suction and pressure surfaces are formed by ruled surfaces placed at an equal distance on either side of the camber surface to give the required thickness distribution (see Figure 4). The surface normals at point A and B are created, and appropriate points that reflect the required thickness distribution on these surface normals are selected. Selected points are joined by a cubic spline curve. Likewise, the suction and pressure surface curves of the shroud and hub surfaces are obtained. Ruled surfaces are created between corresponding curves, obtaining the suction surface and pressure surface.

To obtain the correct thickness distribution all over the blade, the suction surface and the pressure surfaces should be created as offset surfaces that are placed on either side of the camber surfaces at an equal distance. Indeed, these newly defined offset surfaces are not ruled surfaces. Therefore, the use of peripheral milling is questionable. For the case considered, this maximum deviation was -0.065 mm (too thin).

3.1. 7 Profile for Blade Leading and Trailing Edges

It is usual to have a rounded edge or elliptical edge along the inlet of the blade to obtain a better flow in this region. These edges can be represented by two additional ruled surfaces connecting the suction and pressure surfaces at the inlet and outlet. Circular leading/trailing edge curves are obtained by filleting. These fillet curves are the generating curves of the ruled surface (Figure 1).

4. Manufacturing of an Impeller

4.1 Machining Technique Considerations

Generally, the blade surface is machined using swarf milling, which provides a line contact between the tool and the workpiece. The periphery of the tool perfectly touches the workpiece geometry. Hence, very high surface quality in the direction of feed and the direction perpendicular to the feed is obtained.

The machining technique to remove material between blades mainly depends on the shape of the space between two blades. This is especially true when there exists a radial tilt at the inlet or an axial tilt at the outlet. Head milling with a flat end mill, with appropriate lead angle, is highly recommended in this case because of technological and geometrical advantages of using a flat end mill.1,11,17,18 The lead angle should be as small as possible so that no undercuts appear on the hub surface. Machining of the impeller blade consists of four machining operations: suction surface machining, pressure surface machining, leading-edge surface machining, and trailing-edge surface machining. Machining these surfaces sequentially improves the surface quality as well as the efficiency of the machining process. It reduces the number of admissions and exits to two, hence reducing nonproductive machining time. The sequence of the toolpath should be such that the leading-edge surface machining is taking place between the other surfaces being machined, making use of the stiffness of the material that has to be removed. Therefore, all the blade surfaces should be machined prior to hub surface machining. Machining of the blade surfaces should start from the trailing edge, proceeding to the suction surface and leading-edge surface, and ending up at the pressure surface, as shown in Figure 5.

4.2 Tooling Consideration

Ballnose mills rather than flat end mills are often used for machining curved surfaces because ballnose mills are easier to position in relation to curved surfaces and generate simple machining programs. The cutting speed is not the same at every point of the ballnose cutter-at the center of the ball it is zero, which creates very poor cutting conditions requiring many more passes across the surface to generate the same surface finish as that produced with a flat end mill (point contact instead of line contact).17

The profile of an end mill can be made to match that of a curved surface by inclining it correctly to the surface normal. As an end mill is inclined to the surface normal, an elliptical profile is generated and the effective radius of curvature, r^sub eff^, on the cutter axis is given by the following:

where R is the cutter radius and Delta is the cutter inclination. Thus, the effective radius of curvature of an end mill varies from infinite to R as 0

5. Toolpath Generation Using the Unigraphics II CAD/CAM System19

5.1 Blade Surface Machining

The sequential surface machining option is used because it provides the highest flexibility in tool axis orientation. Individual portions of the toolpath are generated by moving a tool along a pair of intersecting surfaces until the motion is stopped by the third surface. The drive surface guides the tool through space as it cuts along the part surface. The motion continues until the tool reaches the check surface. An important advantage of this method is that different feed rates can be specified while generating the toolpath to compensate for cutter load variation along the segments. This reduces the risk of cutter deflection or sinking in corners.

5.2 Hub Surface Machining

The simplest way of machining the hub surface is rotating the toolpath generated for machining the suction or pressure surface about the axis of rotation. This way of machining is preferable when a ballnose mill is used. Three major problems are encountered while machining in this way. First, toolpath rotation must be limited; otherwise, the tool may interfere with the next blade surface. This drawback can be avoided by first rotating the suction surface toolpath in increments until just before interference with the next blade. The remaining material can be further removed by rotating the pressure surface toolpath in increments. Another difficulty is that even though the tool is spherical or flat, the number of passes must be increased to avoid the presence of ribs. The third problem is bad cutting geometry because the toolpath that is used for hub surface machining is created during blade surface machining, not based on the hub surface geometry (see Figure 6).

5.3 Test Machining

Trial machining of the impeller was performed on an epoxy-based workpiece of 160 mm diameter and 120 mm length on a five-axis MAHO 600E machine. A cylindrical flat end mill of 3/8 in. (9.525 mm) diameter was used. The tool axis was chosen parallel to the drive surface. The toolpath generated for suction and pressure surfaces was rotated about the axis of rotation (see Figure 7) for machining the hub surface. Each of these rotations had to be confined to 8deg because a rotation beyond 8deg causes the tool to interfere with the next blade at the inlet.

5.4 Limitations and Observations of the Approach

After test machining of the blade, it was noted that the blade shape is completely distorted from the expected shape of the blade by undercuts (max. -0.8 mm). Further investigation revealed the existence of overcuts also.

In machining the hub surface, the geometry of the tool does not match with the hub surface. This drawback results in very poor cutting geometry and surface finish as well as a greater number of passes necessary to maintain a given scallop height.

The material has to be removed step by step along the blade height so that hub offset surfaces are required as part surfaces. This creates air cutting leading to inefficient machining.

5.5 Analysis of the Unigraphics II Toolpath

A ruled surface is defined by two space curves and a straight line sliding over these two reference curves. The blade surface is defined as a ruled surface in which the reference curves are the shroud curve and hub curve. These two reference curves are neither parallel nor straight, but twisted. Consider the isoparametric line AB on a blade surface that has to be machined (see Figure 8). The surface normals at points A and B are not parallel. The side of the tool should exactly touch the isoparametric line AB to obtain the exact surface. To accomplish this requirement at each point of the line AB, the tool must be offset at a distance that is equal to the tool radius along the surface normal. The line that passes through these points is the correct tool axis orientation. Unfortunately, these points form a curve instead of a straight line, so the tool axis that is a straight line can never completely coincide with this curve.

The manufacturing module of the Unigraphics II CAD/CAM system defines the option “Parallel to Drive Surface” such that the side of the tool is parallel to the surface rulings of the drive surface. In ruled surface machining with the option of tool axis parallel to drive surface, the CL data is determined by orienting the tool tangent to the “first” reference curve and maintaining the tool axis parallel to surface rulings. The tool is made tangent at point B, and the tool axis is parallel to line AB. This way of selection of the tool axis orientation creates undercuts along the tool contact line. Figure 7 shows the undercut created while machining a ruled surface generated by two straight edges on two parallel planes. The maximum undercut is equal to R(1 cos theta), where R is the tool radius and theta is the angle between surface normal at each end of the isoparametric line. Figure 8 shows the undercut while machining with Unigraphics II with curved edges on arbitrary planes. It is difficult to define a mathematical formula that reflects the accurate maximum undercut because it depends on the curvature and the angle between the planes. But the maximum deviation is a function of the tool radius R and angle theta. Larger undercuts can be observed where the angle theta is large. The magnitude of the undercut is almost the same as R(1 – cos theta).

Undercuts can be reduced by using cutters with a smaller diameter or by reducing the angle theta. The use of a small diameter is often difficult or not possible because it creates stability problems, especially in peripheral milling. The most sensible solution is to change the relative position of the tool. The Unigraphics CAM module doesn’t support this kind of alternative, which is further discussed in Section 6.

6. New Toolpath Generation Algorithm

Section 6 explains the drawbacks and limitations encountered in machining an impeller with the Unigraphics II CAD/CAM system. Most of these problems cannot be solved with the system; the designer can use only the options that are built into it. In five-axis machining, the tool can be located anywhere in the space in an arbitrary orientation. To take full advantage of five-axis machining, the CAM system must have extremely high flexibility in tool orientation compared to three-axis machining. Theoretically, the CAM system should have the same flexibility as five-axis machining. Unfortunately, most of the CAM systems available on the market today are mainly built for three-axis machining.

The use of a programming language is one of the best methods in obtaining the flexibility required for five-axis machining. This section explains how this flexibility is obtained using the Graphics Interactive Programming (GRIP) language for machining an impeller. The most important feature of this approach is that the CAM module of the Unigraphics II CAD/CAM system is not used, and a new algorithm is proposed and implemented using GRIP (or CAD module only).

6.1 Blade Surface Machining

The theory explained below is based on a cylindrical end mill. A similar explanation is valid for a tapered tool. Figure 7 shows that the maximum undercut is equal to R(1 – cos theta), and no undercut is observed along the first reference curve, but maximum undercut occurs along the other edge (Figure 8). It was explained above that changing the relative position of tool and surface is the solution to reduce the undercut. Now consider Figure 10 in which the tool is made tangent to the ruled surface at point P on the respective isoparametric line, along with the option tool axis parallel to the drive surface. Point P is defined such that the angle between the surface normal at point P and the surface normals at each end of the isoparametric are the same.

When machining ruled surfaces in which the reference curves are neither parallel nor straight and lie on arbitrary planes (as in impeller blade machining), there may be a very small deviation between the actual maximum undercut and theoretical maximum undercut obtained from the above equations. The maximum undercut depends on various factors, such as the angle between the planes of the reference curve, curvature of both reference curves, and so on. The deviation can be neglected because generally it should be expressed in terms of thousandths or tenthousandths of a millimeter, which cannot be maintained when machining in an open environment (in the test case, it is about .003 mm). The minimum distance between the tool axis and the surface that has to be machined is measured. The tool radius is subtracted from this value to obtain the existing undercut. If it is required to maintain a very high precision, an iterative procedure can be used until the tool axis lies within the specified tolerances. An initial guess for the iteration is obtained from the expressions explained. Based on this algorithm, the CL data can be generated to machine the blade surface eliminating undercuts on the blade surface, but there may be some unremoved material along the middle area of the blade surface.

In practice, material around the blade is removed step by step. It was explained how the orientation of the tool axis is obtained on the blade surface. Instead of using the same tool axis pattern for all the tool passes, different tool axis patterns are generated by varying the first reference curve of the surface that has to be machined to avoid the overcut appearing on the middle area of the blade surface. A number of isoparametric lines, depending on the number of tool passes, are created on the surface that has to be machined, as shown in Figure 12. Instead of taking the first reference curve and the second reference curve of the surface that has to be machined for the tool axis creation, the second reference curve and the first isoparametric line (a) are used. In this way, angle Theta becomes very small, providing a very small overcut between these curves. For the second pass, the second reference curve and the isoparametric line (b) are used. Now no undercuts or overcuts are shown along the second reference curve and the isoparametric line (b). Theoretically, there should be some unremoved material between these two curves, but most of the material is machined away by the previous pass. The same procedure is repeated for isoparametric lines c, dX e, f, …. The CL data that are obtained in this way provide an almost identical surface to the modeled ruled surface. By increasing the number of passes, a very high accuracy can be obtained. Theoretically, if the number of passes tends to infinity, machined surface and modeled surface coincide.

The modeled surface is not the actual surface that is needed. Consider the analysis made on the geometric model in Section 3.1.2. It is shown that there is a deviation between the modeled surface and the actual surface. It is noted that the thickness of the middle area along the blade is less than expected (see Section 3.1.6). When machining, there is overcut in the same area so this excess material compensates for the material shortage in the middle area of the blade.

The maximum deviation between the actual surface and the modeled surface is .065 mm at the leading edge of the surface. The deviation between the actual surface and the machined surface using the CL data generated by the new machining algorithm gives no deviation along the hub edge and shroud edge, but maximum deviation occurs at the middle of the blade (.06 mm). The undercut is confined to .005 mm. Average deviation is about .06 mm. The overcut at the middle of the blade can be further reduced by using a number of tool passes. The values presented here correspond to a single pass (.06 mm).

6.1.1 CL Data Generation Module for Blade Surface Machining

This module uses a cylindrical flat end mill in generating the CL data for blade surface machining. The same module can be used when a cylindrical bullnose end mill is used. When a tapered mill is used, some part of this module should be altered according to the geometry of the tool.

Machining of an impeller blade consists of four main machining operations, namely, trailing-edge surface machining, pressure surface machining, leadingedge surface machining, and suction surface machining. A number of isoparametric lines along the blade height are created on each of these surfaces. Generally, about 100 isoparametric lines on each surface are sufficient to obtain an accurate surface finish.

Consider an isoparametric line on the surface that has to be machined. The angle between the surface normals at each end of the isoparametric line is measured (Theta). The surface normal vectors at each end of the isoparametric line are obtained. The inverse cosine of the dot product of these two vectors provides the angle between the surface normals. Point P is found on the isoparametric line using an iterative procedure. For an initial guess, point P is assumed to be at the midpoint of the isoparametric line. The angle between the surface normal at P and the surface normal at one end of the isoparametric line is measured; depending on the magnitude of the angle, point P is moved upward or downward incrementally along the isoparametric line. The iteration is continued until the angle between the surface normal at P and the surface normal at an end of the isoparametric line is equal to Theta/2 or within the specified limits. At the end of the iteration, a point at a distance equal to R/(cos theta/2) from P along the surface normal at the point P is located. A line is drawn parallel to the isoparametric line through the defined point. At the end of this procedure, the optimized line element that corresponds to the tool axis that eliminates undercuts and minimizes overcuts is completely defined. The iterative procedure to find point P can be omitted by taking the midpoint instead of the exact location. This approximation gives nearly the same improvement in the undercut. The iterative procedure allows evaluation of this difference.

Once the straight line corresponding to the tool axis is obtained, the cross section of the tool tip is formed at the midpoint of the isoparametric line such that the tool axis coincides with the straight line. In the case of the cylindrical flat end mill, the cross section is a circle (see Figure 13). The cross section is projected on the hub surface along the tool axis, and the minimum distance between the cross section and the projected entity is measured. To obtain the CL data point coordinates, the cross section is translated a distance equal to the minimum distance between the cross section and the projected entity along the line toward the hub surface. The center of the newly defined cross section provides the coordinates of the CL data point eliminating undercuts on hub surface. The procedure is repeated for all the isoparametric lines on each surface of the blade. The coordinate of the center of the newly defined cross section and the i, j, k components of the unit vector along the optimized line element are sent to the output data file.

If the tool is tapered, the line element should be created in such a way that the angle between the isoparametric line and the line element is equal to the taper angle of the tool. The tool tip cross section is created at the midpoint of the isoparametric line, and the same procedure discussed above is carried out to obtain CL data. If the tool is a ballnose mill, the tool tip cross section created at the midpoint of the isoparametric line should be a hemisphere, and the same procedure is carried out to obtain the CL data.

6.1.2 Machining the Blade Step by Step

When actual cutting is done, the tool should be moved into the material step by step. This can be accomplished by using the isoparametric line elements created on the blade surfaces. The length of the lines is measured. Lines that are longer than a specified length (length – feed) are identified. These lines are machined first. Next the line elements that are longer than (length – 2*feed) are identified and machined. This procedure is repeated until the complete blade is machined. To avoid hub surface undercut, the method discussed in Section 6.1.1 should be used in the final pass. This CL data provides an efficient cutting process eliminating air cutting.

6.2 Algorithm to Machine the Hub Surface

6.2.1 Interaction Geometry Between Tool and Hub Surface

The CL data generation for the hub surface machining consists of two phases. In the first phase, the geometry of the hub surface is redefined to identify the boundaries along which the tool can be driven safely without interfering with the blade surface. In the second phase, the identified surface area is machined with the positive lead angle toward the tool movement.

At best, the tool trajectory should be selected in such a way that the tool is always driven along a surface isoparametric line. Consider isoparametric line AB on the hub surface in Figure 14. C is a hub surface point that lies on the isoparametric line AB. By maintaining a positive lead angle gamma, the CL data that corresponds to point C should be evaluated. The surface normal vector at point C is Q, and the tangent vector to the isoparametric line at point C in the direction of the tool movement is P. The cross product of vectors P and Q gives the vector R, which is perpendicular to the plane that contains P and R=P X Q.

By means of the position vector at point C, the surface normal vector at point C, vector S, which makes an angle ty with the surface normal at point C toward the tool movement direction, is obtained. The vectors P, Q, S lie in the same plane. The cross product of vector R, S defines a vector T perpendicular to the plane containing vectors R and S. T = R X S. For a cylindrical flat end mill, point D is selected on the vector T in such a way that the magnitude of CD is equal to the tool radius. In the case of a tapered end mill, the magnitude of CD should be equal to the radius of the tool tip.

The coordinates of point D and the unit vector along the vector S reflect the CL data corresponding to point C. With this CL data, the tool makes a positive lead angle gamma with the surface normal at point C, eliminating undercuts on hub surface and providing the geometrical and technological advantages associated with flat end mills while machining.

6.2.2 Redefinition Module of the Hub Surface

Consider the two consecutive blades shown in Figure 15. A number of isoparametric spline curves are created on the hub surface in the area that has to be machined between the blades. About 50 points are selected on each of these splines, starting from the trailing edge. The first point of the first spline is selected. The tool axis is created as a line element at the selected point according to the theory explained in Section 6.2.1. The distance between the tool axis line element and the closest blade surface is measured. If the distance is less than the tool radius, the first point on spline 2 is selected. The tool axis is created at the selected point. The distance between the tool axis line element and the closest blade surface is measured. This procedure is repeated until the distance between the tool axis line element and the blade surface is greater than the tool radius. This eliminates the undercut of the blades.

At the point where the distance is greater than the tool radius, the intersection point of the corresponding tool axis and the hub surface is obtained. Now the second point on the same spline is selected. The same procedure is repeated until the point with the distance between tool axis line element and blade surface is greater than the tool radius and the relevant intersection point is obtained. Likewise, a point set that maintains a safe distance from the blade surface is defined. Once one blade surface is completed, a similar procedure is applied to the other blade surface. Starting from the trailing edge, the first point of the last spline is selected, and the procedure is continued until the next safe point set is obtained. Cubic spline curves are fitted through these points. The curves as shown in Figure 16 are created on the hub surface between the defined splines. A B-spline surface is fitted through the curves obtained. This surface is identified as the safe area that can be machined without any interference with the blade surface using a flat end mill with a given lead angle and radius (Figure 16). If the user needs to maintain some clearance between the tool and the blade surface for further safety, the clearance is added to the tool radius.

6.2.3 CL Data Generation Module

A number of isoparametric splines depending on the scallop height are created on the newly defined B-spline surface. The tool axis is located as discussed in Section 6.2 on the points of each spline starting from the trailing edge and ending at the leading edge. At the leading edge, the tool changes direction of movement along with the direction of the lead angle, maintaining the same cutting conditions between tool and hub surface. This procedure is repeated until the complete hub surface is machined. At every tool orientation, coordinates of the tool tip and unit vector along the tool axis are output. Like blade surface machining, hub surface machining also should be done step by step. This can be accomplished by creating line elements normal to the hub surface.

The algorithms are programmed using the Graphic Interactive Programming language, which provides three user-friendly program modules for toolpath generation. The module outputs the x, y, z, i, j, and k values of the tool to the output data file. The outputs of these modules are converted into the format defined by the Unigraphics II CAD/CAM system by adding additional technological parameters. The final output is postprocessed for machine code generation.

6.2.4 Postprocessing the CL Data for a Five-Axis Machine

Additional problems that have to be solved are concerned with postprocessing the CL data. Many CAD/CAM systems provide a generalized postprocessor, claiming that it can handle five-axis machines; the authors’ experience has proven, however, that this is not the case. A postprocessor was developed on the personal computer for the machine used in this paper.20

The postprocessed part program is quite different from the CL file as the motions are not executed by the tool alone but generally by a combination of tool and workpiece motions. Collision danger is extremely high. Also, the toolpath is not the same as in the CL file. The transformation from the workpiece coordinate system (CL file) to machine coordinates is complex and not unique (inverse kinematics). The motion between two successive CL points is assumed to be a straight line at the time of the generation by a CAD/CAM system. On a five-axis machine, after transforming to the machine coordinates, the tool tip will not follow a straight path between two successive transformed CL points. The real toolpath will be curved (see Figure 17). This curved toolpath depends on the specific machine tool and the location of the workpiece on the machine. If this curved path is not corrected, a completely different workpiece geometry would be obtained. Therefore, more points will be inserted by the postprocessor to linearize the tool motion within the specified tolerance. Also, the rapid traverse function GO will have a positioning logic dependent on the constructor of the machine tool. To be able to verify this five-axis machining program, the G code must be verified and not the CL file.

The postprocessor will have to adjust the feedrates to obtain a feed relative to the workpiece that is optimal at the cutter contact point. The tool tip travel is much smaller than travel along the machine axis, which increases the requirements for the maximum feedrate on the machine axis.

6.2.5 Machine Tool and Cutter

The impeller was machined on a MAHO 600 E five-axis milling machine with the Phillips CNC 432 five-axis control (five-axis simultaneous). The only tool used was a flat end mill of 3/8 in. (9.525 mm) in high-speed steel. The free length of the tool was about 200 mm. The rotor had eight blades with an inlet tip Beta angle of 78deg and an outside diameter of 160 mm. The selection of the tool diameter is based on a few constraints. The maximum tool diameter is determined by the space between two consecutive blades at the inlet where the curvature of the blades is the highest (15 mm). The smaller the tool diameter the smaller the undercuts will be (see Section 5.5). If the diameter is too small, the tool may break or deflect too much during machining. Larger tool diameters will result in a smaller number of toolpaths especially for the hub machining. A small tool diameter requires higher spindle speeds, but the cutting forces are reduced. In many cases, the connection between the blade surface and the hub surface needs to be filleted to reduce mechanical stress concentration. The best solution is then to use a toroidal tool with the required radius for the blade machining. The hub machining should ideally be done with a flat end mill.

7. Conclusions

To obtain the full advantages of five-axis machining, the CAM system should be mainly built for five-axis machining and provide options for two, three, and four-axis machining.

For five-axis machining, the Unigraphics II CAD/CAM system is good not because of the CAM module of the system but because of the GRIP module. The CAM module is limited, especially in the area of peripheral milling and some options where the flat end mill is used.

The Graphic Interactive Programming Language (GRIP) is a versatile programming language. With GRIP, extremely high flexibility in tool orientation can be obtained. On the other hand, GRIP is completely based on the Unigraphics II CAD/CAM environment. Therefore, if the CAD/CAM environment is changed, it will affect all activities or developments that have been completed using the existing CAD/CAM system. To avoid this, a general-purpose language such as C, Pascal, or FORTRAN could be used, but with considerable more effort. The GRIP language is very similar to APT (Automatically Programmed Tools) to access the geometry.

The modules developed can model and produce a variety of impellers, improving accuracy, efficiency, and flexibility of the manufacturing system. The new algorithm explained in this study is valid not only for impellers but also for any similar surface machining problems.

Parametric modeling is a very good modeling tool. It saves disk space, remodeling time, and improves flexibility in modeling. This study can be considered as a case that exhibits the limitations of today’s high-end CAD/CAM systems.

In the beginning of the 1980s, CAD/CAM systems concentrated on interactive graphics and computeraided geometric modeling. Later and often still today, CAD/CAM systems concentrate on improving the user interface. Parametric modeling and feature modeling are popular, but CAM is neglected in many cases.

The main advice concerning the machine is to buy a machine with a very high maximum spindle speed (10,000 rpm or more) because this will allow use of smaller cutter diameters. Also very high feed ranges are required, especially on the rotary axis (14,000 deg/min.) to obtain an excellent surface quality. Because CNC programs are very large, it is important to buy the BTR feature on the CNC control.

Bibliography

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Erik L.J. Bohez, Asian Institute of Technology, Bangkok, Thailand S.D. Ranjith Senadhera, CML Edwards Construction Ltd., Sri Lanka Ketan Pole, Micron Group of Companies, Thailand Joost R. Duflou, Katholieke Universiteit Leuven, Belgium Tsau Tar, Wentworth Mold and Die Co. Ltd., Canada

Authors’ Biographies

Erik L.J. Bohez is an associate professor and the industrial systems engineering program faculty coordinator at the Asian Institute of Technology (Bangkok, Thailand). He teaches courses in advanced manufacturing processes, CAD/CAM, FMS, control theory, and computer control of manufacturing systems. He has 20 years of experience in industry and academia. He is a graduate of the State University of Ghent in Belgium. His research interests include holonic and fractal manufacturing, manufacturing resources planning (MRPII), modeling of FMS, simulation of metal removal processes, robust control, five-axis machining, virtual-axis machines, and adaptive control. He has been a consultant to UNIDO, UNESCO, and other international organizations. His e-mail is: bohez@ait.ac.th.

S.D. Ranjith Sena&era graduated from the mechanical engineering department of the University of Moratuwa (Sri Lanka) in 1986. He obtained his master of engineering degree from the School of Advanced Technologies at the Asian Institute of Technology in the field of industrial engineering and management. Presently he is plant and equipment manager attached to CML Edwards Construction Ltd., a leading construction company in Sri Lanka.

Ketan K. Pole, a mechanical engineer and expert in CAD/CAM and CNC machining technology, has experience of more than 15 years in various industries, including job shops and flexible manufacturing as well as mass production industries. Presently he is engaged as the operations director in the high-technology tool and die industry supporting semiconductor industries in Thailand. He has experience in five-axis CNC machining, wire EDM, die-sinking EDM, jig grinding, and sheetmetal forming. As operations director, he is responsible for engineering, production, quality assurance, and marketing. In the past, Pole has carried out assignments for the manufacturing of aerospace as well as nuclear power plant components.

J. Duflou holds master’s degrees in architectural (1985) and mechanical (1987) engineering from K.U. Leuven (Belgium). While working with private enterprises as a systems engineer, project engineer, and project manager, he has been involved in R&D and product development projects in the sectors of large-scale composites development and manufacturing and railway carriage construction. He has been employed by BN Bombardier in the context of the shuttle train development (Channel Tunnel) and has worked on a UNIDO project developing new GRP silo systems. Presently he is seconded to the Asian Institute of Technology by the Royal Belgian Government. He is an affiliated faculty member and senior research engineer. His main activities are teaching courses and conducting research related to CAD, CAD/CAM, CIM, CNC sheetmetal working, and product design. As the CIM lab manager, he supervises the computer-integrated manufacturing laboratory.

Tar Tsau, CAD/CAM manager, Wentworth Mold and Die Co. Ltd., is a post-graduate engineer in industrial engineering and management at the Asian Institute of Technology with the background of a mechanical engineering degree from Rangoon Institute of Technology. He has more than 12 years of experience in mechanical engineering, automotive plastic blow mold design, plastic container blow mold manufacture, and CAD/CAM and computer applications in moldmaking technology.

Copyright Society of Manufacturing Engineers 1997

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