For a sub-micro ultra-precision turning machine using airsprings as vibration isolation elements, a 5 FOG mathematical model is established, activation f acted on the machine bed is as the input, the output are vertical displacement y1, oscillating φ1, ψ1 around the horizontal axle x and z of the machine bed, vertical displacement y2 of the main spindle box, and vertical displacement y3 of the slider. The equations for vibration system of 5 FOG are solved. The results indicate, when actuation force f ≠ 0, the outputs of all 5 FOG are increasing with the increasing of f. when activation f = 0, the outputs of all 5 FOG tend to zero. Assuming f include the vibration of machine base and an external force, when external force is equal to that of the vibration of machine base, then f = 0. The vibration of 5 FOG can be effectively isolated, so electromagnetic actuators as an external force, also as active vibration isolation elements can be used in the isolation system. Three electro-magnetic actuators arranging as triangle act as an external force, the quantity is equal to that of the base vibration, and the phase reverse. In fact ultra-precision turning machine is a complicated mechanism system and in the machining process, the headstock and horizontal-slider are in the movement, that is to say, the center of mass of the ultra-precision machine is changeable. Impossible is f = 0 for a practical control. In order to get a effective vibration isolation, fuzzy controller is used. The synthetic experiments have been done for the 5 FOG vibration system of the ultra-precision turning machine. The result of three actuations experiment that has been done in y direction indicates that the vibration of y direction, and oscillating φ1, ψ2 around the horizontal axle x and z of the machine bed are to be controlled. A work-piece of aluminum alloy has been machined using the sub-micro ultra-precision turning machine with the active vibration isolation elements, and without the active vibration isolation elements, AFM microscope graphs show the surface roughness of the work-piece machined by the former better as by the latter.

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