The objective of this study is to develop an equation of motion which accurately describes the motion of the flywheel of a mass-flywheel acceleration integrator. The initial problem is to write an accurate equation of motion for a coasting flywheel supported with radial ball bearings. Viscous and Coulomb frictional terms are included in this equation of motion. Experimental evaluation of these friction¬al terms reveals discrepancies in this mathematical model of ball bearing friction. Consequently, a single frictional term is included in the equation of motion. The results are very consistent and the equations are much more straightforward. The torque loss, due to friction in radial ball bearings, is a function of the radial load raised to the 2.34 power and the coefficient of friction is a function of radial load. From the results of the coasting flywheel analysis, an equation of motion is developed to describe the motion of the flywheel when coupled with an acceleration sensing mass by a precision gear train. Agreement between predicted and observed flywheel motion is good for both the accelerated and coasting system.
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