ASME B89.4.21.1:2020 pdf free download – Environmental Effects on Coordinate Measuring Machine Measurements
3.2 Differential Thermal Expansion
Considering the thermal expansion of all materials, the dimensional measurement process is illustrated in Figure 3.2-1. Both the measuring scale and the workpiece are expanding (or contracting), each according to the temperature and its own coefficient of expansion. A measurement on the workpiece that is not corrected for thermal expansion will be the length of the workpiece as indicated on the scale. This is the length of the workpiece at 20°C plus the difference between the expansion of the workpiece and the scale. Thus, when discussing thermal effects in dimensional metrology, differ- ential expansion must be considered.
3.3 The Metrology Loop: A Three-Element System in Coordinate Metrology
A more sophisticated view of the measurement process in a varying thermal environment involves analyzing dimen- sional measurement instruments using the three-element concept of length measurement; this is comprised of a master gage, a comparator, and a workpiece and represents a generalization of the differential expansion concept of para. 3.2. The prototypical example is a gage block comparator; however, for coordinate metrology, the situation is more complex. The master gage for a CMM is the calibrated scales affixed to each coordinate axis, and the comparator represents the entire machine structure including workpiece fixturing. The three elements form a loop, known as the metrology loop, which is the path from the CMM probe tip through the machine structure to the scale reading, to the point where the scale is fixed to the machine structure, through the machine structure to the CMM table, through the fixturing to the workpiece, and to the measurement point on the workpiece. Since coordinate metrology involves the calculation of one set of coordinate points relative to another set of coordinates (e.g., a feature relative to a datum), each set of coordinates involves the metrology loop. There are two general measure- ment scenarios to be considered, as follows:
(a) If all of the coordinates are measured in quick succession so that thermal expansions and distortions of the metrology loop do not change during the measurement, then the thermal effects in the loop are static to all coordinates, and dynamic thermal effects, e.g., thermal drift, can be neglected when evaluating the dimensional measurement uncer- tainty.
(b) For measurements that involve long measurement times or a significant change in temperature, thermal expan- sions and distortions of the metrology loop may evolve and hence the measurement coordinates become increasingly shifted relative to their coordinate system and to each other. In this case, thermal drift within the metrology loop is significant. Frequently reestablishing the workpiece coordinate system can partially mitigate this effect, but a careful analysis of the thermal behavior of the metrology loop is needed to evaluate the impact of thermally induced measure- ment uncertainty; see para. 3.6 for more information on thermal drift.