Cylindrical compression spring behavior has been described in the literature using an efficient analytical model. Conical compression spring behavior has a linear phase but can also have a nonlinear phase. The rate of the linear phase can easily be calculated but no analytical model exists to describe the nonlinear phase precisely. This nonlinear phase can only be determined by a discretizing algorithm. The present paper presents analytical continuous expressions of length as a function of load and load as a function of length for a constant pitch conical compression spring in the nonlinear phase. Whal’s basic cylindrical compression assumptions are adopted for these new models (Wahl, A. M., 1963, Mechanical Springs, Mc Graw-Hill, New York). The method leading to the analytical expression involves separating free and solid/ground coils, and integrating elementary deflections along the whole spring. The inverse process to obtain the spring load from its length is assimilated to solve a fourth order polynomial. Two analytical models are obtained. One to determine the length versus load curve and the other for the load versus length curve. Validation of the new conical spring models in comparison with experimental data is performed. The behavior law of a conical compression spring can now be analytically determined. This kind of formula is useful for designers who seek to avoid using tedious algorithms. Analytical models can mainly be useful in developing interactive assistance tools for conical spring design, especially where optimization methods are used.
This article presents columnar grain structures characteristic of niobium components fabricated by electron beam melting, using two different size and size distribution spherical powders produced by rapid solidification atomization. The precursor powder microstructures are characterized by equiaxed grains while the columnar grain structure in the electron beam melted (EBM)-fabricated products contain dislocation substructures ranging in density from *10 9 to 10 10 /cm 2 as observed by transmission electron microscopy. X-ray diffraction analysis illustrates the variations in orientations in both the processor powders and the fabricated components. Microindentation hardness values ranged from 0.8 GPa for the precursor powders and 1.1 and 0.92 GPa for the EBM-fabricated, solid components.
The ability to make components from copper and copper alloys via additive manufacturing is spurring a range of novel applications. Although the high thermal conductivity of copper presents challenges for direct AM processes, fully dense copper components with complex geometries have been demonstrated. Of particular interest is the ability to use AM methods to fabricate internal cooling channels and mesh structures to optimize thermal management. This article describes feasibility studies to evaluate AM processing of copper parts.
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