This invention relates generally to numeric controlled machining of parts and more particularly to a method for flank milling of ruled surfaces.
Creation of machining instructions for flank milling of ruled surface components is perceived to be a simple task. However, practical limitations such as finite cutter thickness, surface description, and milling machine shortcomings yield results that compromise final dimensions and surface quality.
Twisted ruled surfaces commonly found in aerodynamic designs are characterized by the difference in blade angle between corresponding hub and shroud contour points. These surfaces can be seriously undercut during flank milling if the alignment of the cutting tool simply follows the desired line-element rulings. The resulting blade thinning may exceed profile tolerances and cause vibration or structural problems.
Standard flank milling practice is to place the cutting tool tangent to the blade surface and normal to the hub and shroud endpoints of a particular line element. However, if the surface normal at the hub differs from that at the shroud, a cutter skewed to make contact at these two tangencies results in a surface undercut causing reduced blade thickness. This undercut is greatest near the mid-streamline of the blade since by design no error exists at the hub and shroud contours.
A useful analogy is to visualize a string (the line element) connecting two points at different positions on the surface of a cylinder (the cutting tool). If the string were merely laid across the surface of the cylinder, it would form a curve segment like a spiral. However, if the string is forced to follow a straight line, it must necessarily intrude into the surface of the cylinder. The amount of this intrusion represents the undercut.
In this model, the undercut error is proportional to the offset from the blade surface to the tool centerline (tool radius and taper) and the direction of this offset (blade angles at the hub and shroud). Surprisingly, the error is not directly related to the size of the blade, but, because tool sizes are often selected and maximized to fit a particular part size, an indirect relation exists. For a cylindrical cutting tool, the error may be approximated as: EQU .epsilon.=r(1-cos(.theta./2))
where r is the tool radius and .theta. is the difference in blade angle. The error may be split across the line element, but the total cannot be reduced further with this approach. For conical cutting tools, the formulation is similar. PG,4
Because undercut is related to the twist in the blade surface, errors are largest in areas of the inducer section of a compressor. Other classes of turbomachinery, including radial-inflow turbines, experience undercut less often because they are designed with little or no twist between the hub and shroud contours.
Many techniques are currently employed in an attempt to deal with the problem of undercut. Of course, the most common solution is to do nothing. For many designs, the degree of undercut is small enough to avoid exceeding profile tolerances.
In some software packages, multiple passes are used to create sets of "mini-ruled surfaces." Undercut is reduced, but a wavy surface results. If enough multiple passes are taken, it becomes a point-milling solution. No undercut exists because very little of the cutting tool makes contact with the surface. However, this technique sacrifices machining time efficiency and the superior surface finish that can result from effective flank milling.
To balance machining time and reduce undercut, a moderate number of passes may be used to minimize undercut, followed by manual hand finishing to achieve smooth blade surfaces. Like so many compromises, however, the balanced approach optimizes neither the machining time nor the part quality.
Another solution is to select two rails (streamlines) for computation along the line element and let the cutting tool pivot along these rails to locations with reduced undercut. Common rail selections are hub and shroud contours, or 20% and 80% streamlines. This method retains the benefits of flank milling but generally requires trial and error and is cumbersome. Although undercut reduction is possible, an optimal solution is not assured.
One approach tried by the present inventors extends the trial and error method found in CAD/CAM systems to algorithmically determine the ideal rail extent and cutting tool tilt angle that minimize surface error. The rail extent and tilt vary smoothly as the tool proceeds around the entire blade surface. As rail extent and tilt values change, the surface formed by the swept cutting tool also changes. At its simplest, reorienting the line elements on a ruled surface geometry creates a different blade surface. Similarly, changing the cutting tool orientation in flank milling produces a different surface envelope. A better approach to reducing and optimizing machine performance is described below.
Machining instructions and machined components can be enhanced by using additional constraints in the mathematical formulations. Concepts such as surface analysis, blueprint tolerances, and understanding machine tool motion, when integrated with standard methods produce parts with desirable characteristics.
The foregoing illustrates limitations known to exist in present methods for flank milling of ruled surfaces. Thus, it is apparent that it would be advantageous to provide an alternative directed to overcoming one or more of the limitations set forth above. Accordingly, a suitable alternative is provided including features more fully disclosed hereinafter.
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