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A new freeform surface generation method for the difficult-to-cut materials is proposed in this paper. Fast tool servo and slow slide servo diamond turning are the main generation technologies for freeform surfaces, whereas they cannot machine the freeform surfaces of difficult-to-cut materials very effectively. On the other hand, elliptical vibration cutting has demonstrated its excellent performance in material processing, especially for the difficult-to-cut materials. Nevertheless, it is unable to generate the freeform surfaces very successfully. Therefore, this paper proposes the double-frequency elliptical vibration cutting method for the freeform surface diamond machining on the difficult-to-cut materials, which provides the high-frequency elliptical vibration to improve the machinability in material removal and the low-frequency reciprocating movements for the freeform surface profile generation. The relative movements …