Reversal techniques in measurement: General Industry Coverage

The accuracy with which a machine tool can produce parts is determined in part by the accuracy of the motions of the machine axes. The motion in a given coordinate direction should be straight, and the motion in other coordinate directions should typically be perpendicular to that. Motion straightness and perpendicularity is checked when a machine is built, rechecked when installed and should be periodically rechecked throughout its operating life.

A granite or cast iron metrology square can be used to measure the squareness of the X and Y axes of a machine tool (Figure 1). A common size for a granite square is 12 “×12 “×3 ” (304.8mm × 304.8mm × 76.2mm), and it would weigh a little less than 50 lbs. Larger squares exist, but are difficult for a person to lift without assistance. Typical flatness tolerances for surfaces of such squares are one part in 120,000 to one part in 250,000.

All images courtesy S. Smith

Figure 1. Measuring the squareness of the X and Y motions using a precision square.

If the top of a table is flat, and that surface is aligned with the X motion of the machine, it is easy to see how the square could be used to measure the squareness of the axis motions. A dial indicator is attached to the moving element and brought into contact with the vertical edge of the square. As the Y-axis is moved, the dial indicator reading at various positions shows X-axis errors in the Y-axis motion.

Squareness is the angle between the X motion and the Y motion, but neither motion is perfect. The sides of the square are perpendicular to a high tolerance. The X side of the square is lined up with the X motion, and a dial indicator is used to measure the distance to the Y side of the square as the Y-axis is moved. The result is not a straight line, but a wavy line, because the motion is not perfect. The Y motion is interpreted as the best fit straight line through the data measured with the dial indicator. The angle between that line and the X motion is the squareness.

However, this simple measurement idea is mixed with several possible errors. For example, the square may not be sitting flat on a flat surface. Figure 2 shows a small piece of debris between the square and table, tilting the square to one side. If the vertical edge was measured in this case, it is not possible to tell whether the X and Y motions of the machine are not square to each other or whether the granite square is tilted. Perfect Y motion—perfectly perpendicular to the perfect X surface—would still look like an error in squareness, which is greatly exaggerated for clarity in the figure.