Since the arrival of NC (Numerical Control), machining of curved surfaces has been a challenging task due to the increasing demands on precision and productivity. The motion commands such as the NC part program are realized by a sequence of very small step movements along the machine axes. In general, this step movement is on the order of micrometers and it means the machine resolution. CNC (Computerized Numerical Control) interpolators process the motion commands in order to generate the reference commands for the driving of the CNC machine tools.
Nowadays most CAD (Computer-Aided Design) systems provide the tools for defining 2D and 3D sculptured surfaces. In contrast, CNC machines basically support only the functions of straight line and circular interpolations. Thus the curve/surface has to be machined as a collection of linear or circular segments within the specified tolerance requirements. There are several problems with this process. The only solution to this problem in the past is either to make the segments longer by making the tolerance value large, sacrificing the accuracy of the part, or to slow down the feedrate, reducing the productivity of the machine.
This thesis presents the real-time 3D interpolators for CNC machine tools in reference-pulse technique. To achieve the basic motions of 3D straight lines and circular arcs, linear and circular interpolation algorithms are proposed. And for the machining of 3D free-form surfaces, NURBS interpolation algorithm is designed.
In 3D space, the line or circle is not expressed as an implicit function, it is only defined as the intersection of two surfaces. A 3D line can be defined as the intersection of two planes, and a 3D circle can be defined as the intersection of a plane and the surface of a sphere. Based on these intersection criteria, interpolation algorithms are designed to follow intersection curves in searching for the minimum path error strategy.
To obtain other 3D curves including free-form curves, 3D NURBS interpolation algorithm is proposed. Based on the searching for minimum path error strategy, a high-precision 3D NURBS interpolation is achieved. From this, the post processing to generate the large segmented part program is no longer required, and many of the problems associated with processing linear or circular segments are eliminated.
Real-Time 3D interpolator for the machining of straight lines, circular arcs and free-form curves is developed in software based on the presented interpolation algorithm. And this interpolator is implemented in the framework of a 3-axis PC-NC milling machine.
The simulations of the proposed 3D interpolation algorithms have shown that the interpolation error does not exceed the machine tool resolution with reasonable machining speed for most of today’s manufacturing systems. And the implementations on the PC-NC milling machine proved the effectiveness of the presented 3D interpolator for the high-precision machining of all kinds of 3D surfaces. It is expected that presented real-time 3D interpolator can be applied to the CNC systems for the high-precision machining.
