A vibration damping system for machining parts uses magneto rheological radial squeeze film damper technology to reduce part vibration, enhance tool lifecycles, and to improve part surface finish. In the described embodiment, the damping system includes a pair of damping cylinders affixed to a machine tool fixture, each cylinder containing a solid core concentrically situated within an internal sleeve portion of the cylinder. Rheological fluid contained within a radial space between the core and sleeve defines a radial squeeze channel for the fluid. Fluid stiffness is controlled in real time by varying an electric current to modulate a magnetic field passing through the fluid to dampen vibrations in accordance with at least one predetermined algorithm. As material is removed from the part during machining, the fluid damping characteristics are actively managed by a machine tool controller as a function of a combination of dynamically changing and predetermined algorithmic inputs.