Design and Manufacturing of a Single Plane Automatic Dynamic Balancer

Residual unbalance in hand-held power tool rotors transmits undesirable vibrations to the hand of its operator. These vibrations can be effectively suppressed using a one plane automatic dynamic balancer (ADB). This balancing device consists of several balls constrained to move inside a sealed cylindrical ball-race unit partially filled with oil. One of the hand-held power tools is an angle grinder. This study introduces the design of an ADB for eliminating vibration of a grinder based on the achieved design parameters. A physical model of the system is derived for a Jeffcott rotor with an ADB. Utilizing Lagrange's method, the nonlinear equations of motion for an autonomous system in polar coordinate system is derived. Further, the equilibrium position and the linear variational equations are obtained by the perturbation method. Moreover, the dynamic stability of the system in the neighborhood of the equilibrium positions is investigated by the Routh-Hurwitz criteria. The results of the stability analysis provide the design requirements for the ADB to achieve balancing of the system. In addition, time responses are presented by the generalized-alpha method. Employing the modal analysis method the equivalent damping and stiffness coefficients are achieved. Finally, the ADB is designed and manufactured by solving the equations of motion governed on identified unbalanced grinder. To evaluate and identify the performance of the ADB, vibration levels are measured in cases of with balancer, without balancer, and are compared with a typical commercial ADB.