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Chapter 13:
Estimation of Mounting Stresses
Contact stress is created whenever force is applied within small areas on the surface of an optical component. This stress depends on the magnitude of the force, the shapes of both surfaces in contact, the size of the contact area between the optical and mechanical bodies (both considered to be elastic), and the pertinent mechanical properties of the contacting materials. In this chapter, we summarize a theory based on equations of Roark for estimating the magnitude of compressive contact stress for a variety of commonly used glass-to-metal interface types involving lenses, windows, mirrors, and prisms. A relationship from Timoshenko and Goodier is then applied to estimate the tensile stress accompanying this compressive stress. A “rule-of-thumb” tolerance for this tensile stress based on work published elsewhere is stated. The stress and surface deflections resulting from radially unsymmetrical application of axial clamping forces on opposite sides of rotationally symmetrical components are approximated for simple cases. The analytical models forming the bases for the stress equations given here are believed be conservative representations of real-life situations. A compressive force exerted over a small area on an optical surface causes elastic deformation, i.e., strain, of the local region and hence proportional stress within that region. If the stress exceeds the damage threshold of the optical material, failure may occur. Rigorous calculations of damage thresholds for glass-type materials are complex and rely on statistics to determine the probability of failure under specified conditions. We report key results of these studies and the basis for the generally accepted rule-of-thumb value of 1000 lb∕in. (6.9 MPa) for the tensile stress in glass that might cause damage. As a further approximation, we assume that the same tolerance applies to nonmetallic mirror materials and optical crystals. For simplicity, we refer to all optical materials as glass and all mechanical ones as metal. Stress also builds up within the mechanical members that compress the glass. This usually is compared with the yield strength of that metal (generally taken as that stress resulting in a dimensional change of two parts per thousand) to see if an adequate safety margin exists. In critical applications (such as those demanding extreme long-term stability), stress in mechanical components may be limited to the microyield stress value for the material. Since operational environmental conditions invariably are less stringent than survival conditions, damage is not a concern, but detrimental effects on performance can occur. Mounting forces then may cause optical surfaces to deform, i.e., become strained. Such deformations may affect performance. No meaningful general tolerances for surface deformations can be given since they depend on the level of performance required and the location of the surface in the system (surface deformations are less significant near an image but are more significant near a pupil). Closed form equations for estimating surface deformations, as functions of force applied to optical components, are available only for a few cases. These evaluations are best done by finite-element analysis methods. Such methods are beyond the scope of this work.
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