**5. Conclusions**

To improve the turning performance of BMG, first, a longitudinal ultrasonic vibration turning system was designed and then relative modal and harmonic response analysis was conducted. The analyses indicated that the vibration shape of the system met the design requirements at 19th mode. Through the experimental test, it turned out that the vibration amplitude of the system can reach 12 µm, which verified the design and the simulation. Therefore, the established LUAT system can realize ultrasonic assisted turning. Then the critical turning speed was derived, which proved a key factor of the effect of ultrasonic vibration and is determined by the parameters of the turning system. Finally turning simulations in different turning speeds were conducted on Vit1 BMG described by D–P constitutive model. For this work, the following conclusions can be drawn:

1. Simulation and theoretical analysis show that there is a critical turning speed in LUAT, which is determined by the longitudinal ultrasonic device. When the turning speed is lower than the critical turning speed, the longitudinal ultrasonic vibration can effectively reduce the average cutting force and von Mises stress of BMG cutting processing;


**Author Contributions:** Conceptualization, S.S. and H.Z.; methodology, P.F.; validation, F.F.; investigation, S.S.; resources, F.F.; supervision, H.Z.; project administration, P.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Shenzhen Foundational Research Project (Subject Layout), Grant Number JCYJ20180508152128308 and Shenzhen Science and technology plan, Grant Number JSGG20180507181638381.

**Conflicts of Interest:** The authors declare no conflicts of interest.
