141 Appendix D. Deformation Corrections Whenever two materials are forced into contact there is an elastic deformation. For gauge block comparators the contact is between a spherical probe and the flat gauge block surface. The following formula, from a CSIRO Technical Note [D1] has been found to be identical to the earlier NBS nomographs [D2]. The nomographs were developed to avoid the cumbersome calculations needed for deformation corrections. However, microcomputers have made the formula easier to use than nomographs, and we therefore give only the deformation formula. (D.1) α is the deformation in millimeters P is the force in NEWTONS, D is the diameter of the probe in MILLIMETERS, V i is a number characteristic of the probe or block material from the table below: Material V (10 -8 ) Steel 139 Chrome Carbide 86 Tungsten Carbide 40 Ceramic 139 Diamond 43 Example 1: A steel gauge block is measured with a two point probe system each with a spherical diamond contact of 6 mm diameter. The top force is 1 N and the bottom force is 1/3 N. Top Contact: D = 6 mm F = 1 N V 1 = 139 x 10 -8 steel block V 2 = 43 x 10 -8 diamond sphere α = 2.231 * (1) 2/3 * (139 x 10 -8 + 43 x 10 -8 ) 2/3 * (6) -1/3 (D.2) D ) V + V ( P 2.231 3 1 - 3 2 21 3 2 ≈α 142 = 0.000181 mm = 0.181 µm Bottom Contact: D = 6 mm F = 1/3 N V 1 = 139 x 10 -8 steel block V 2 = 43 x 10 -8 diamond sphere α = 2.231 * (1/3) 2/3 * (139 x 10 -8 + 43 x 10 -8 ) 2/3 * (6) -1/3 (D.3) = 0.000087 mm = 0.087 µm Thus the total deformation is 0.00027 mm or 0.27 µm. Example 2: Same apparatus but measuring a chrome carbide gauge block: Top Contact: D = 6 mm F = 1 N V 1 = 86 x 10 -8 chrome carbide block V 2 = 43 x 10 -8 diamond sphere α = 2.231 * (1) 2/3 * (86 x 10 -8 + 43 x 10 -8 ) 2/3 * (6) -1/3 (D.4) = 0.000145 mm = 0.145 µm Bottom Contact: D = 6 mm F = 1/3 N V 1 = 86 x 10 -8 chrome carbide block V 2 = 43 x 10 -8 diamond sphere α = 2.231 * (1/3) 2/3 * (86 x 10 -8 + 43 x 10 -8 ) 2/3 * (6) -1/3 (D.5) = 0.000070 mm = 0.070 µm Thus the total deformation is 0.00022 mm or 0.22 µm. 143 If we were to use a steel master block to calibrate a chrome carbide block under the above conditions we see that the penetration correction for steel and chrome carbide blocks differ substantially. The total length correction of the calibrated block is given by: L u = M u - M s + L s + (α s - α u ) (D.6) where L u is the calibrated length of the unknown block, M u is the measured value of the unknown block, M s is the measured value of the reference standard, and α s and α u are penetration corrections of the standard and unknown respectively, and α s -α u =0.05 µm (2.0 µin). REFERENCES [D1] Puttock, M.J. and E.G. Thwaite, "Elastic Compression of Spheres and Cylinders at Point and Line Contact," Natoinal Standards Laboratory Technical Paper No. 25, CSIRO, 1969. [D2] Beers, J.S. and J.E. Taylor. "Contact deformation in Gauge Block Comparisons," NBS Technical Note 962, 1978. . materials are forced into contact there is an elastic deformation. For gauge block comparators the contact is between a spherical probe and the flat gauge block surface. The following formula, from. the calibrated block is given by: L u = M u - M s + L s + (α s - α u ) (D.6) where L u is the calibrated length of the unknown block, M u is the measured value of the unknown block, . steel master block to calibrate a chrome carbide block under the above conditions we see that the penetration correction for steel and chrome carbide blocks differ substantially. The total length