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surfaces are clean and free of "burrs." (The blocks and the comparator anvil are cleaned and "stoned" lightly prior to all Process II measurements).

The nature of the "practical" surface in the interface between the block surface and mating platen is altered by the presence of a "wringing" fluid. For a given measurement, the film thickness in the interface, whatever it might be, is included in the initial assignment of a length value by an interferometric process. The variability of a collection of repeated measurements reflects in part the variability of this film thickness. The development of micro-scratches in the surface of the block by virtue of the sliding action necessary to make the "wring" indicates that, at least part of the time, there is an interpenetration of the two surfaces similar to the previous argument. Eventually, surfaces deteriorate to the point that they will no longer "wring." While there is a possibility that some of the damage may occur because of the abrasive action of foreign material on the surfaces, this suggests that for minimum or "zero" film thickness, the "practical" surface between the block and the platen is essentially the same as the practical surface between the block and the comparator anvil.

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The maximum "film thickness" is largely a matter of operator "feel" at the time of making the "wring." As a consequence of this added variability, the position of the gage block on the comparator anvil may well be more reproducible than its position as "wrung" on a platen. The standard deviations of the two processes tend to support this conclusion. ("Wringing film thickness" is discussed further in section 7.4.) The practice, after cleaning and "stoning" the long blocks, is to "wring" to a quartz flat and judge the quality of the "wring" by its appearance as viewed through the flat. If all is

immediately "wrung" to the appropriate platen.

Because of the operations necessary to obtain a highly reflective surface, figure 15 may be more representative of the block surface profile. In Process I measurements, light waves are reflected from such a surface. Typical gage block interferograms are shown in figure 16 [18]. The presence of surface scratches is evident in most of the interferograms, but the surface from which the light appears to come is not in coincidence with the "practical" surface of the gaging face.

In the case of reflected light, the location of the "virtual" surface is thought to be a function of the roughness of the surface and reaction of the light with the surface molecules. In the first case, interference occurs over a large area so that, with the exception of the edges of the fringe, the detailed surface profile is not revealed. It is sometimes assumed that the reflection plane is located about midway between the peaks and the valleys. In the second case, in the process of absorbing and reradiating the incident light beams, the phase relation between the incident and reflected ray may be changed. The net result of the two effects, which are inseparable, is a "virtual" reflecting surface which cannot be in coincidence with the "practical" surface.

In the Process I measurements, the "reflecting virtual" surfaces are located at both the gaging face and the platen face. As long as the separation between the "virtual" surface and the "practical" surface on both of these faces is nearly the same, the separation between the two "virtual" surfaces is essentially the same as the separation between the two "practical" surfaces. Defining S(g) as the separation between the "virtual" surface and the "practical" surface of the gaging face, and S (p) as a like separation at the platen face, one is concerned as to the significance of [S(g) - S(p)] relative to the precision of the measurement process, for various combinations of blocks and platens. Early studies on short gage blocks under 4 in, reported in reference [19], utilized the "slave block" technique. Later studies used short blocks of various manufacture and two steel platens with different surface finishes. In both cases there was no evidence to indicate that S(g) # S(p). In the Process I measurements of long gage blocks, the platens used are made from the same type of material and have the same surface finish as the blocks. It is assumed that S (g) S(p). (This is not the case when the results from a steel platen are compared with the results from a quartz platen [20].)

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The "virtual" surface in the Process II measurements is in the interface between the surface of the contact probe and the deformed gaging surface of the block, as shown in appendix 4. Defining the separation between this surface and the "practical" surface of the block as penetration, one is concerned with the difference in penetration, B, from block

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to block. Factors which determine the magnitude of the penetration are the geometry and physical characteristics of the contacting probe, the geometry and physical characteristics of the block surface, and the contact force. In the transfer of the length of one block to another, as long as both blocks respond in a similar manner to a fixed force on a given probe, ẞ is essentially zero, and the difference in separation between the "virtual" surfaces of the blocks and the reference plane of the comparator is very nearly the same as the difference in separation between the "practical" surfaces of the blocks and the reference plane.

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Commercially available long gage blocks are made from through-hardening steel, such as Type W-1 tool steel or Type 52100 steel. Blocks made from such steels, when properly heat-treated, sufficiently hard for resistance to wear, can be polished to obtain a suitable surface finish, and exhibit a high degree of stability with time [21]. The physical properties of these materials are very nearly the same. One would expect the penetration of a given comparator probe on any pair of steel blocks to be about the same so that ẞ would be very nearly zero. The closure studies between the Process I and Process II measurements, dis

cussed in section 6, verify that ẞ is not large relative to the precision of the process. It is assumed that B = 0, therefore the small variation in penetration across the surface of the block, and from block to block, is a component of the process variability. This assumption is not true when transferring the value from a steel block to a block made from grossly different material. Gage blocks of nominal length 4 in, and under are commercially available in cervit, chrome-carbide, tungsten-carbide, as well as steel, therefore a detailed discussion of B is included in reference [20].

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rather than one provides a means for monitoring one with reference to the other and also provides a collection of "repeated" measurements which, in turn, reflects the long term performance of the process. Accepting the NBS (.) blocks as one group of "knowns," the task is to establish suitable values for a second set (the NBS (..) blocks) with the "new" interferometric process. In order to do this, the continuity of the results from the historical interferometric measurements and the "new" interferometric process must be demonstrated.

For one group of reference blocks, the NBS (.) group, table 10 compares the predicted historical values discussed in section 4.3 with the values established by the "new" interferometric process. (Process I) discussed in section 5.2. With one exception, the area of doubt associated with the historical predicted value encompasses the new process value. For the 8 (.), the uncertainty bands overlap. Within the precision of both processes, continuity appears to be preserved. As an additional check on the continuity of the two processes, table 11 compares the historical values established for the USN blocks with values for selected blocks established by the "new" process. Again, for the blocks which were measured by the new process, the difference between the two sets of values is less than the uncertainty of the historical value. On the basis of this evidence, it was concluded that the change from one process to the other did not affect the continuity of the measurements.

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TABLE 12

NBS (..) Reference Standards with Reference to NBS (.)
(Mechanical Comparison with Restraint for Solution on Value for NBS (.) Only)

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NBS(.) and (..) Accepted Values, Sums and Differences, November 22, 1972

Y Values-Nov. 22, 1972

Δ Ave n

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S,σ (μ in)

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s.d. of old process (figure 5) s.d from differences (figure 8) s. d. of new Process I

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etry but which had no previous history of values assigned by the "old" process. By virtue of the closure between the two processes discussed above, the average values from the "new" process (see table 7) were accepted as the tentative values for the NBS (..) blocks. Intercomparison measurements with reference to the NBS (.) blocks, summarized in table 12, were made to verify closure between the transfer values relative to the NBS ( . ) assigned values, and the tentative interferometric values. With the exception of the 20 in blocks, the agreement is remarkably close. The discrepancy at the 20 in level is considered acceptable in

view of the small number of measurements available for the assignment of values to both the 20(.) and the 20(..) blocks.

With additional measurement data available, the accepted values for the individual blocks, the sums and difference for the pairs, and the process uncertainty in use in September 1972, are shown in table 13. The estimated uncertainty tabulated in table 13 is 3(V2) σ, where σ is from the "fitted" line on figure 17. The points plotted in figure 17 are the computed standard deviation of the collections of values for each of the (.) and (..) blocks and the appropriate USN blocks. The dash-dot line, σ=0.635, is the original estimate established in figure 8. The dashed line is the estimated process standard deviation for the "old" process established in figure 5.

6.2. Predicted Values (Process I)

Partly as a practical expedient, and partly because it was thought that the relatively small rates of change would not be apparent over the short time span associated with "new" process measurements, changes with time have not been considered up to now. Under the assumption that the length of all of the blocks change with time, the average value is not the best estimate of current or future values. It is necessary to predict appropriate values for individual blocks, sums and differences, together with appropriate uncertainties, over some reasonable time interval. Because closure is an important criteria for judgment, it is necessary to have realistic estimates of uncertainty for the predicted values. This and the following two sections are devoted to establishing and verifying realistic rates of change.

In the case of the NBS (.) blocks, with a long history of measurement, significant rates of change

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