Spindle vibration influencing form error in ultra-precision diamond machining

Ultra-precision diamond machining (UPDM) is widely used to manufacture high quality surface within sub-micrometric form error and nanometric surface roughness due to its high efficiency and low cost. However, in a complex UPDM process, many factors affect such sub-micrometric form error. Especially, spindle vibration produces a significant impact upon surface generation, not only influencing nanometric surface roughness, but also affecting sub-micrometric form error. In this study, a five-DOF dynamic model is established for spindle vibration in UPDM. The form error under spindle vibration is discussed with a surface generation model. The results show that (i) axial, radial, and coupled-tilting spindle vibration makes a great contribution to form error; (ii) the coupled-tilting frequencies are influenced by spindle speed; and (iii) the spindle vibration is reproduced at a machined surface to generate regular patterns consequently to cause form error, which is well identified with a focus on axial spindle vibration by face turning in UPDM. Its wavelength is linearly proportional to spindle speed and cutting radius distance, i.e. cutting speed. Significantly, the proposed models provide a possibility to predict surface roughness and form error under spindle vibration.