On the relationship of natural frequency, damping, and feedforward acceleration with transient vibrations of track-seek control

The relationship between natural frequency, damping, the waveform of a feedforward acceleration input, and the transient vibrations of track-seek control is derived theoretically and a target for vibration design of the head actuator of a hard disk drive (HDD) is discussed from the viewpoint of the transient vibrations. When the acceleration feedforward input of the track-seek control is expressed as a polynomial function of time, the transient response of a single degree of freedom system is solved by applying integral by parts to the Duhamel’s integral repeatedly. The results show the transient vibrations are generated at the initial and terminal times of the input and their amplitude depends on the lowest orders of non-zero derivatives of the polynomial. They also show that increasing the damping ratio effectively reduces the transient vibrations for fourth and sixth order polynomials but not for fifth and seventh order polynomials. The results were confirmed by performing a continuous time simulation and analyzing the shock response spectrum. Also discussed is the relationship between the transient vibrations and the seek time and track pitch, which are key parameters associated with the data access time and the HDD capacity. This relationship indicated the requirements needed for vibration design of the head actuator to increase HDD performance and capacity.