A second-order LuGre friction model is presented which can be viewed as an extension of the well known LuGre friction model. This model is based on a dynamic extension, which can be seen as an extra dynamic to capture some kind of periodic motion produced by the bristles in motion. The additional dynamic can be viewed as an internal disturbance due to the vibration associated with the use of motors. Our model can capture the friction phenomena of the original LuGre friction model and presents two new behaviors, one is the multi-loop behavior in the hysteresis curve when velocity is varied during unidirectional motion, and the other, in the presliding motion curve of friction force versus displacement in the spring regime, where two jumps appear.