Opto-Mechanical Systems Design, Volume 1, 4th Edition

DESIGN EXAMPLE 11.6 PEAK TENSILE STRESS IN A LENS WITH TANGENTIAL MECHANICAL INTERFACES

Consider the same biconvex germanium lens as in the preceding example. It has the following dimensions: D_G = 3.100 in. (78.745 mm), R₁ = 18.000 in. (457.200 mm), and R₂ = 72.000 in. (1828.800 mm). The lens is mounted in a 6061 aluminum cell with tangential interfaces at y_C = 1.500 in. (38.100 mm) on both surfaces. What peak tensile contact stress is developed at each interface if the axial preload is 20.000 lb (88.964 N)?

From Table 3.10,

$\begin{array}{c}{E}_G=1.504\times {10}^7\text{lb/in}{\text{.}}^2\left(1.037\times {10}^5\text{MPa}\right)\\ {\nu }_G=0.278\end{array}$

From Table 3.12,

$\begin{array}{c}{E}_M=9.900\times {10}^6\text{lb/in}{\text{.}}^2\left(6.820\times {10}^4\text{MPa}\right)\\ {\nu }_M=0.332\end{array}$

By definition, the linear preload is

$p=\frac{20.000}{\left(2\text{π}\right)\left(1.500\right)}=2.122\text{lb/in}\text{.}\left(0.372\text{N}/\text{mm}\right)$

From Equation ...