Abstract: This paper studies the dynamics of cutting system, has advanced a new cutting transitive fuction analyzed the error of cutting depth (simply residual error) and its amplitude-frequency, directed the formulas with which the static stiffness and the ratio can be designed for controlling the error. Theory and- tests have shown: the optimum damping ratio ξod is able to restrain the vibration-error existing most often in the cutting system and to improve distinctly the cutting quality. The paper has also proved the marked difference between the cutting o system and general mechanical system, and made clear concepts in the tranditional theory. The compensating tormula for static residual error has also-given in this paper.