Determine the control default gears and vibration function of machined metal carbide tool rotation and gain a better understanding of the mechanism of generation of machined surfaces, and their relationships with the variation and this work aims to geometry of mechanical parts. Indeed, in the study of the equations were used to show the status of the vibration surface and simulated using the mathematical relationships, then the implementation of the neural network system with two hidden layers prediction, two inputs and two outputs to have the neural mode. This allows modeling of the default control gear despite the complexity of the signature of the machining operation. In addition, research is the study of the variation of the mechanical geometry of the parts obtained by removing material with cutting tools, taking into account the function of the geometric and kinematic parameters of the cutting operation and the factor vibration. To achieve our goal, and on the basis that there is a close relationship between the state of the machined theoretically and experimentally the dimensional quality mechanical parts area, we developed a model of default control gears by a network theory can reproduce virtually topography of a surface obtained by a turning operation.