ASME B89.4.21.1 pdf free download

ASME B89.4.21.1 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 processis illustrated in Figure 3.2-1.Both the measuring scale and the workpiece are expanding (or contracting), each according to the temperature and itsown coefficient of expansion.A measurement on the workpiece that is not corrected for thermal expansion will be thelength of the workpiece as indicated on the scale.This is the length of the workpiece at 20C plus the difference betweenthe 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 mastergage, a comparator, and a workpiece and represents a generalization of the differentialexpansion concept of para.3.2.Theprototypical example is a gage block comparator; however,for coordinate metrology, the situation is more complex.Themaster gage for a CMM is the calibrated scales affixed to each coordinate axis, and the comparator represents the entiremachine structure including workpiece fixturing:The three elements form a loop, known as the metrology loop, which isthe path from the CMM probetip through the machinestructure to the scale reading,to the point where the scale is ixed tothe machine structure, through the machine structure to theCMM table,through the fixturing to the workpiece, and to themeasurement point on the workpiece.
Since coordinate metrology involves the calculation of oneset of coordinate points relative to another set of coordinates(eg. a feature relative to a datum), ach set of coordinates involves the metrology loop.There are two general measure-ment scenarios to be considered, as follows:
(a) lf all of the coordinates are measured in quick succession so that thermal expansions and distortions of themetrology 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 increasinglyshifted relative to their coordinate system and to each other. In this case, thermal drift within the metrology loop issignificant. Frequently reestablishing the workpiece coordinate system can partially mitigate this effect, but a carefulanalysis 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.
3.4 Bimetallic and Gradient Bending
3.4.1 Bimaterial Effects.Materials thermally expand proportionally to their coefficient of thermal expansion (CTE)values. If a workpiece or CMM is composed of materials with different CTEs or of a material with a nonuniform CTE,geometrical distortions may occur as the ambient temperature varies.In the case of CMMs, the CMM manufacturer mayprovide either mechanical or software means of mitigating or compensating for these expansions.In the case of work-pieces, a nonuniformCTE will generally result in bending due to the different coefficients of expansion at different pointsin the structure.
While this effect can occur when materials with explicitly different CTEs are present, it is less clear for materials withnominally the same CTE.However,even for a single material, the CTE can vary for many reasons, including the following:(a) stresses induced during the material’s fabrication from rolling or forging
(b) metallurgical variations in castings due to nonuniform rates of cooling (many finished metals start outas castingsfrom ingots and can also exhibit these variations)
(c) hardening of surfaces (either by flame or electrically), due to the metallurgical changes that provide the hardness3.4.2 Gradients.Spatial temperature gradients in CMM components may cause bending.In particular, beams bend ifheat inputs or time constants at opposite faces are unequal.Joints between beams are a particularproblem due to unevenwall thicknesses. Generally, gradient and bimaterial effects cause changes in machine squareness. The squarenesschanges are caused by thermal distortion of the joints between structural members and by distortion in themovable carriages that interconnect the machine guideways. There is an additional thermal error caused by distortionof the structure between the primary guideway (the guideway that is fixed relative to the workpiece) and the workpiecemounting point. Workpiece distortion causes movement of the workpiece measurement points.These movements mustbe determined relative to the point on the workpiece that is fixed relative to the machine.
Scales are a major factor in machine response to the thermal environment.The nature of the effect depends on howthescales are mounted. The following three methods are in general use:
(a) If the scale is fixed to the machine structure at one point and floats at all other points, then scale expansion isdetermined from scale temperature and the scale’s coefficient of expansion.Laser scales fallinto this class; the coefficientof expansion is determined from the air index of refraction.
(b) lf the scale is rigidly fixed to the machine structure at all points, then scale expansion is determined from thestructure’s temperature and coefficient of expansion.Scales that are fixed at both ends, e.g., stretched-tape scales, are inthis class.
(c) lf scale expansion is partially constrained by the structure,e.g,by means of a layer of elastomer between the scaleand structure,then a more complicated situation occurs.Ifthe scale and structure have differentcoefficients ofexpansion,then shear forces set up in the elastomer affect scale expansion.The shear forces, and consequently the scale expansion,vary along the scale length.