Summary Vibration with small amplitude and low frequency usually remains in precision diamond machine tools even supported on sir mounts, and inevitably deteriorates surface roughness. Analysing an enveloping curve of feed Harks disturbed by a steady vibration, the surface roughness is estimated as the function of both the ratio of vibration amplitude to geometrical roughness, and the phase shift of the vibration to work rotation. This makes it clear that the roughness can be reduced to 20-30% of the sum of the geometrical roughness and a vibration amplitude at optimal cutting conditions. The analytical results are proved in experiment cutting Al alloy with straight and round tools. The lathe used for the experiment was oscillated at low frequency, small relative amplitude between a tool and a workplece, by the disturbance from the floor. These results show that straight tools are more effective for improving surface roughness than round ones, and provide a surface roughness within 0.01μmRnax during the vibration with 5.8Hz frequency, 0.03μmp-p relative amplitude.