INTRODUCTION TO THE COORDINATE SYSTEM
All machines are equipped with the basic traveling components, which move in relation to one another as well as in perpendicular directions. CNC turning centers are equipped with a turret and tool carrier, which travels along two axes (Figures 1-8 and 1-9).
Note that in the following drawings of lathes, the cutting tool and turret is located on the positive side of spindle centerline. This is a common design of modern CNC turning centers. For visualization purposes, in this book the cutting tool will be shown upright. In reality, it is mounted with the insert facing down and the spindle is rotated clockwise for cutting.
Note: the direction of spindle rotation in turning—clockwise (CW) or counterclockwise (CCW)—is determined by looking from the headstock towards the tailstock and tool orientation.
Machining centers are milling machines equipped with a traversing worktable or column, which travels along two axes, and a spindle with a driven tool that travels along a third axis (Figure 1-10).
All axes of machines are oriented in an orthogonal coordinate system (each axis is perpendicular to the other), for example, the Cartesian coordinate system or right-hand rule system (Figure 1-11).
Figure 1-8 Turning Center Axes Courtesy Kennametal
Figure 1-9 Two-Axis Turning Center Courtesy MAZAK Corporation
Figure 1-10 Three-Axis Machining Center Courtesy MAZAK Corporation
Figure 1-11 Right-Hand Rule
The Right-Hand Rule System
In discussing the X, Y, and Z axes, the right-hand rule establishes the orientation and the description of tool motions along a positive or negative direction for each axis. This rule is recognized worldwide and is the standard for which axis identification was established.
Use Figure 1-11 to help you visualize this concept. For the vertical representation, the palm of your right hand is laid out flat in front, face up, the thumb will point in the positive X direction. The forefinger will be pointing the positive Y direction. Now fold over the little finger and the ring finger and allow the middle finger to point up. This forms the third axis, Z, and points in the Z positive direction. The point where all three of these axes intersect is called the origin or zero point. When looking at any vertical milling machine, you can apply this rule. For the horizontal mill, the same steps described above could be applied if you were lying on your back.
Visualize a grid on a sheet of graph paper with each segment of the grid having a specific value. Now place two solid lines through the exact center of the grid and perpendicular to each other. By doing this, you have constructed a simple, two-dimensional coordinate system. Carry the thought a little further and add a third imaginary line. This line passes through the same center point as the first two lines but is vertical; that is, it rises above and below the sheet on which the grid is placed. This additional line, which is called the Z-axis, represents the third axis in the three-dimensional coordinate system.
Two-Dimensional Coordinate System
A two-dimensional coordinate system, such as the one used on a lathe, uses the X and Z axes for measurement. The X-axis runs perpendicular to the workpiece and the Z-axis is parallel with the spindle centerline. When working on the lathe, we are working with a workpiece that has only two dimensions, the diameter and the length. On engineering drawings or blueprints, the front view generally shows the features that define the finished shape of the part for turning. In order to see how to apply this type of coordinate system, study Figures 1-12, 1-13, and 1-14.
Figure 1-12 Two-Dimensional Coordinate System
Figure 1-13 Part Drawing Overlaid on 2D Coordinate System
Figure 1-14 Two-Dimensional Turned Part Drawing
Think of the cylindrical work piece as if it were flat or as shown in the top view of the part blueprint. Next, visualize the coordinate system superimposed over the engineering drawing or blueprint of the workpiece, aligning the X-axis with the centerline of the diameter shown. Then align the Z-axis with the end of the part, which will be used as an origin or zero-point. In most cases, the finished part surface nearest the spindle face will represent this Z-axis datum and the centerline will represent the X-axis. Where the two axes intersect is the origin or zero point. By laying out this “grid,” we now can apply the coordinate system and define where the points are located to enable programmed creation of the geometry from the blueprint. Another point to consider on a lathe is that the cutting takes place on only one side of the part or the radius because the part rotates and is symmetrical about the centerline. In order to apply the coordinate system in this case, all we need is the basic contour features of one-half of the part (on one side of the diameter); the other half is a mirror image. When given this program coordinate information, the lathe will automatically produce the mirror image.
Three-Dimensional Coordinate System
Although the mill uses a three-dimensional coordinate system, the same concept (using the top view of the engineering drawing or blueprint) can be used with rectangular workpieces. As with the lathe, the Z-axis is related to the spindle. However, in the case of the three-dimensional rectangular workpiece, the origin or zero-point must be defined differently. In the example shown in Figure 1-15, the lower left-hand corner of the workpiece is chosen as the zero-point for defining movements using the coordinate system. The thickness of the part is the third dimension or Z-axis. When selecting a zero-point for the Z-axis of a particular part, it is common to use the top surface.
Figure 1-15 Three-Dimensional Coordinate System
The Polar Coordinate System
If a circle is drawn on a piece of graph paper so that the center of the circle is at the intersection of two lines and the edges of the circle are tangent to any line on the paper. This will help in