Rotor vibration due to unbalance causes a lot of problems during operation. One of the simplest ways to reduce rotor vibration is the passive balancing. Unbalanced vertical rotor is modeled by a two degrees of freedom system considering Jeffcott model assumption. A (2+n) degrees of freedom mathematical model is derived with respect to a Cartesian co-ordinate system for the unbalanced rotor with the automatic ball balancer. The model equations are expressed as state equations then solved numerically to calculate vibration amplitudes and angular positions of balancing balls. Model validation is achieved by comparing these results with a three-dimensional model. The effect of the automatic ball balancer on vibration amplitudes is explained at different speed ranges. A parametric study is done to explain the effect of the system damping coefficient on the ball balancer behaviors.