A rectangular stainless steel part (alpha = 9.4 mu in./in.- degree) is placed to

Question

A rectangular stainless steel part (alpha = 9.4 mu in./in.- degree) is placed to side-by-side next a gage block stack (nominally 0.875 inches wide and 2.03710 inches high, alpha = 6.4 mu in./in.- degree), and an optical flat is placed on top. The room temperature is 44 degree F. The part width measured at the room temperature is 1.250 inches. It is also determined that the gage block stack is higher than the part and when illuminated with a mercury monolight (lambda_Hg = 21.5 mu in.), 8 fringe shifts occur across the top of the gage block stack. Determine the height of the part, at the standard temperature of 68 degree F, to 1/100,000^th of an inch.

Explanation / Answer

At 44oF, the rectangular stainless steel part is shorter than the gage block stack by 8 fringes. 8 fringes = 8 wave lengths = 8 x Hg (21.5 inches) = 172 inches shorter. Thus length of the part at 44oF = 2.03710-172 inches= 2.036928 inches.

When measured at 68oF, its height will expand by (= 9.4 inches)* (68-44) * height (2.063928) = 0.000459531 inches.

Thus new height of the part at 68oF = 2.036928 +0.000459531 =2.037388 inches.

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