Applying Fractional Calculus Method to Evaluation of Damping in Testing Apparatus of Hard Drive Systems

Fractional Calculus Method is increasingly recognized as central to the interpretation and solution of nonlinear differential equation which is included time power domain [1]. Some of the authors have been engaging in the development of an nanometer positioning actuator (Hereinafter referred to as “Nano-Motion Actuator or N.M.A.”.) which is used for a spin-stand. The spin-stand is a testing apparatus for the hard disk drive system in computer hardware [2]. The N.M.A. needs a large working displacement range over 10 micrometers and its primary resonance frequency should be kept at as high a frequency domain as possible. Moreover, positioning resolution of the N.M.A. is required to be less than 0.5 nanometers (10⁻⁹ meters). A new damping mechanism which consists of visco-elastic material has recently been developed for the N.M.A. to improve vibration response characteristics [3]. However, the damping mechanism causes a new vibration problem and the characteristic of the visco-elastic material needs to be clarified. A response spectrum of the N.M.A. is examined by applying a sinusoidal sweep test. Fractional Calculus Differential Equation is introduced for curve fitting of the response spectrum of the N.M.A. Finally, the calculated results are compared with the experimental results, and both agree.