Ralph M. Richard

Derived moment rotation curves for double framing angles

Abstract Tension and compression force-deformation data obtained from laboratory tests of angle segments are used to generate moment-rotation curves for bolted double framing angle connections. These force-deformation and moment-rotation curves are analytically described by a four parameter formula which provides the basis for the analytical connection model. This connection model consists of a rigid bar and nonlinear springs representing the angle segments in either tension or compression. Design curves giving the four parameters of the moment-rotation curves are generated. These parameters are primarily a function of the angle thickness, gage length of the angle legs in flexure and the number of bolts in the connection. Comparison of these derived moment-rotation curves are made with published results of full scale tests.

Flexure Mounts For High-Resolution Optical Elements

Flexures are passive mechanical-structural devices used to isolate optical elements from the mechanical and thermal effects of the structural support system in such a way that these effects on optical instrument quality are minimized. Mechanical effects include gravity, and inertial and vibratory loadings, as well as possible stresses resulting from assembly errors. Thermal effects include both steady-state and transient environments. For example, if an optical device, with a mirror or lens having a coefficient of thermal expansion orders of magnitude less than that of the material of the support structure (e.g., steel or aluminum), is assembled at a given temperature but operates in a thermally different environment, the optical quality of the instrument may degrade very significantly unless the mirror or lens is isolated from the thermal strain of the support structure. Normally, the mechanical precision of the mount is much less than the precision of the optical surface of the element. If the optical element is rigidly clamped to the mount, this lack of precision in the mount may distort the optical element, and degrade the optical quality of the element.

Interference fit equations for lens cell design using elastomeric lens mountings

Optical designs often consist of lenses that are mounted in a common lens barrel. For lenses having diameters greater than 20 cm and subject to large temperature differentials and/or shock loading, standard metal retainer ring mountings may not be acceptable. An alternate method for mounting these lenses is to mount each individual lens in its own subcell using an adhesive and then to use an interference or press fit to mount these subcells in the lens barrel. When mounting lenses in this manner, it is necessary to evaluate the stress induced in the glass and the residual difference in the optical path. A closed-form analytical derivation was made for a simple lens mount that relates the allowable magnitude of the interference fit to the stress in the glass. This theoretcal expression was then modified using finite element models for use with complex lens designs. Moreover, since lens mountings may require the use of relatively thick layers of flexible elastomer to mount the lenses in their individual cells to prevent large thermal and/or mechanical stresses, the equation for determining the decentration of lenses mounted in circumferential flexible elastomers is also derived. The theoretical expression was used to verify finite element models that then may be used for more complex mounts.

Steel frame analysis with flexible joints exhibiting a strain-softening behavior

Abstract Local buckling of beam and/or connection elements is a source of softening in the moment-rotation behavior in certain connections. This effect can significantly reduce the maximum load-carrying capacity of steel structures. In this study, an elastic-plastic plane frame analysis which includes the effect of nonlinear connection behavior is presented to predict the ultimate load-carrying capacity of steel frames. The structural model comprises members which are assumed to behave elastically with nonlinear connection moment-rotation behavior. The main objective of this study is to investigate the effect of connections which exhibit strain-softening behavior on the ultimate strength and stability of flexible frames. Numerical studies of frames made using the developed computer program are presented. Observations regarding the effects of flexible connections on the strength and deflection of steel framed structures are discussed. The proposed analyses procedure using flexible joints modeled by the Richard function were found to be simple and accurate which compared to elastic-perfectly plastic models.

Slit diaphragm flexures for optomechanics

The slit diaphragm is a useful type of flexure for producing small rotations or translations. This type of flexure is easily fabricated using modern technique such as electro-discharge machining, and provides a convenient solution for certain types of precision motion problems. There are two types of slit diaphragms used in optomechanics: a two axis gimbal for rotation and a linear flexure for translation. Closed form solutions are discussed for determining rotational and radial stiffness of the two axis gimbal slit diaphragm flexure. Similar equations are given for finding the linear and radial stiffness of the linear translation slit diaphragm flexure. A design example of a focus mechanism employing a pair of linear translation slit diaphragm flexures is discussed.

Roller chain supports for large optics

Henry Draper described the use of flexible bands to minimize optical surface deflection of mirrors mounted in the optical axis horizontal position in 1864. Despite this historical background the theoretical basis for horizontal band support was not developed until quite recently. Use of finite element analysis has led to a better understanding of the performance of horizontal band supports. Analytical modeling of horizontal band supports has resulted in improvements in design. In particular the use of roller chains as a horizontal support significantly reduces the deflection of an axis horizontal large mirror. Providing that certain design precautions discussed in this paper are taken roller chains provide a relatively simple and low cost support. A number of successful roller chain supports for optics from 0. 68 m to 1 . 8 m in diameter have been built based on the results of the above analytical models. 2.

Optimum Shapes For Lightweighted Mirrors

Two types of monolithic lightweight mirrors with arched backs are discussed: the center-supported single arch and the ring-supported double arch. The theoretical deformations of a 20-in.-diameter double arch mirror are compared with the actual deformations. A mirror of this size weighs about 50% less than an equivalent conventional mirror. The double arch design may be scaled up to 144 in. where the mirror weighs less than 40% of the eauivalent conventional mirror. Further weight savings are possible due to the reduced size and simplicity of the support required by the double arch mirror design.

Optimum mirror shapes and supports for light weight mirrors subjected to self-weight

A parametric design study of light weight mirror shapes with various support conditions was performed utilizing the finite element program NASTRAN. Improvements in the mirror performance were made based on the following design criteria: (1) minimization of the optical surface wavefront variations, (2) minimization of the self-weight directly related to cost of manufacturing, and (3) optimal location of support points. A pre-processor to automatically generate a finite element model for each mirror geometry was developed in order to obtain the structural deformations systematically. Additionally, a post-processor, which prepares an input data file for FRINGE (an optical computer code) was developed for generating the optical deflections that lead to the surface wavefront variations. Procedures and modeling techniques to achieve the optimum (the lightest and stiffest mirror shape due to self-weight) are addressed.

Analysis of elastomer lens mountings

The equation for determining the decentering of lenses mounted in a circumferential flexible elastomer is derived. A closed form analytical solution was derived for a circular lens mounted in an elastomer to describe this deflection. The theoretical expression was used to verify finite element models which then may be used for more complex mounts. Proper modeling such as element type and aspect ratios are addressed as well as applications of the method for various mounting applications.

Optical performance of bimetallic mirrors under thermal environment

Evaluation of the optical performances of bimetallic mirrors with various substrate shapes was conducted using the finite element analysis program, SDRC-IDEAS. In these analyses, two different plating materials, nickel and aluminum were considered for an aluminum and a beryllium mirror substrate. Thermal environment used in this study is a unit thermal soak. Surface errors, individual aberration terms, such as piston, tilts, focus and other aberrations were obtained by the program PCFRINGE. It was found that the optical performances of bimetallic mirrors depend on the polating material, plating thickness, and the mirror substrate shapes materials. The optimum plating thickness combinations were determined based on plating material and mirror substrate with temperature difference. The results were compared with the optical surface errors and the corrected surface errors. The results indicate that there does not exist a definitive common rule for the optimum, but a detailed analysis such as presented herein is generally needed to design bimetallic mirrors in a thermal environment.