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Beveled Hollow Cylinders
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| Jet Propulsion Lab, CIT Engineering Memorandum 314-523 |
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This, a 4th in a series of memos on the effects of local gravitational fields on the STEP proof masses, looks at whether high order cancellation of the forces and torques is possible by beveling the currently intended hollow cylinders. [1] showed that the effects of an external test mass could be expressed in terms of series expansions, involving a set of shape coefficients ki, i =0,1,2,..., depending only on the proof mass (PM) shape, and a set of functions of the disturbing mass location [2] next showed that the differential acceleration always cancelled at order zero. [1] also showed that, if the moments of inertia of a PM are equal (a "spherical" PM), then k1=0, and differential acceleration comes in only at 4th order. [2] also showed that, for "spherical" hollow cylinders, cancellation isn't possible at 4th order. In [3], the "spherical" result was extended to the more general class of axially symmetric PMs with mirror symmetry; and expressions for the shape coefficients through k5 were developed in terms of the arbitrary PM bounding curves. Here, the latter theory is applied to beveled cylinders; and the possibility of cancellation at 4th order is reexamined. The potential advantages are ease of machining, and straightforward (if tedious) integrations. To anticipate the final result, k2=0 can be achieved by strong beveling of the outer surface.
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