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Ball-type automatic balancers can effectively reduce the vibrations of optical disk drives due to the inherent imbalance of the disk. Although the ball-type automatic balancer used in practice consists of several balls moving along a circular orbit, few studies have investigated the dynamic characteristics of ball-type balancers with more than two balls. The aim of this paper is to study the dynamic characteristics of a three-ball automatic balancer. Emphasis is put on the effects of the number of balls on the stability of the perfect balancing positions--the equilibrium positions where the disk is perfectly balanced. A theoretical model of an optical disk drive packed with a three-ball automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange's equations. Closed-form formulas for the equilibrium positions are presented. The stability of the perfect balancing positions is checked with the variations for a pair of design parameters. Stable regions of the perfect balancing positions in the parameter plane of a three-ball balancer are identified and compared with those of a two-ball balancer. [DOI: 10.1115/1.2948415]

The traditional ball-type automatic balancer consisting of several balls moving on a circular orbit is widely used in the optical disk drive industry for vibration reduction. Under proper working conditions, the balls can counterbalance the imbalance of a disk by positioning to appropriate angles relative to the mass center of the disk. This particular equilibrium position is referred to as the perfect balancing position. The proper working conditions are closely related to the stability of the perfect balancing position, which, in turn, depends on the parameters of the system, such as rotational speed, imbalance ratio, and damping ratios. To achieve perfect balancing, the system parameters must lie in the stable region of the perfect balancing position in the parameter space. An automatic balancer with a wider stable region can tolerate a larger amount of variations in the system parameters and hence is more robust. In this study, we propose a modified ball-type balancer composed of several ball-rod-spring units. In each unit, the ball can slide along the rod while the rod rotates freely about the spindle. The ball's displacement along the rod is restrained by a radial spring. The additional degree of freedom in the radial direction could broaden the stable region of the perfect balancing position. To understand the fundamental properties of the modified balancer, we studied the dynamic characteristics of a modified balancer with one ball-rod-spring unit. Specifically, we built a theoretical model for an optical disk drive packed with the modified balancer, and investigated how equilibrium positions and the associated stability are related to primary system parameters and the effects of the stiffness of the radial spring on the stable region of the perfect balancing position. Numerical results indicate that the ball-rod-spring balancer may possess a larger stable region of the perfect balancing position compared to the traditional fixed-orbit balancer. [DOI: 10.1115/1.2748462]

Under proper working conditions, a ball-type automatic balancer can effectively reduce the imbalance vibrations of an optical disk drive. The proper working conditions can be determined by a stability analysis of the equilibrium states of the nonlinear system formed by the rotating disk, balancer, and suspension system. Several attempts have been made to study the stability of the equilibrium states numerically in some finite regions of the relevant parameter space. This paper in contrast analytically investigates the stability characteristics of the equilibrium states. A theoretical model of an optical disk drive packed with an automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange's equations and closed-form formulas for the equilibrium positions are presented. Finally, general guidelines on the stability of the equilibrium states are proposed. [DOI: 10.1115/1.2149398] Keywords: automatic balancer, stability, vibration, optical disk

Optimization is an efficient tool for developing designs of slider air bearings that meet the strict performance demands of current hard disk drives. Previous studies in this field concentrated on determining the optimal size and shape of the air-bearing surface for a specified initial design. The resulting optimal design has the same topology as that of the initial design. Therefore, the performance of the final optimal solution depends strongly on the initial design, which is chosen either intuitively or inspired by already existing designs. In this study, a topology optimization method is developed for determining the optimal slider configuration. First, the air-bearing surface is discretized by a uniform mesh. The optimization consists in determining whether the material contained in each element should be removed or not. Then, a genetic algorithm is employed for the determination of the optimal solution from the possible candidates. An example is presented to demonstrate the effectiveness of the proposed approach. The resulting optimal design has a topology different from those of the initial designs and possesses improved performance. [DOI: 10.1115/1.1631016]

Equations of rigid-body mechanics provide a means to predict the post-collision behavior without recourse to highly complex, detailed analysis of deformations during contact. Before the prediction can be completed, the coefficient of restitution, which relates the rebound velocity to the incident velocity, must be estimated properly. The coefficient of restitution depends on the surface topography in addition to the material properties and incident velocity. Recent investigations showed that surface topography can be characterized properly by fractal models. This paper proposes a normal contact model for a fractal surface in contact with a rigid smooth half-space. The fractal surface is constructed based on the Cantor set and composed of elastic-perfectly plastic material. Asymptotic continuous expressions for the load-displacement relations during loading and unloading are derived. Based on these results, we study the effects of surface roughness, material properties and incident velocity on the coefficient of restitution. [DOI: 10.1115/1.1574063]