**1. Introduction**

Bulk metallic glass (BMG), also called amorphous alloy or liquid metal because of its topologically disordered constituent atoms, is formed by the rapid condensation of alloy. In BMG, the absence of crystal defects such as grain boundaries and dislocations brings to a series of unique properties [1]. BMG has high strength, high hardness, low thermal expansion coefficient, low density and favorable corrosion resistance, which makes it a potential new engineering material [2–5]. However, these excellent properties of BMG on the other hand would lead to poor machinability. For example, during the cutting process of BMG, the cutting force is considerately large, which can damage the cutting tools, jeopardize the surface quality and hinders their wide scale application [6–8]. Karaguzel et al. [9]

carried out the orthogonal cutting experiment of BMG, and the cutting force empirical formula of BMG is fitted by the experimental results and process parameters. Fujita et al. [10] examined cutting characteristics of BMG by tuning with different parameters, presumed a slipping-off mechanism at planes of short intervals of BMG. When cutting Zr-based BMG in low speed, there will be adiabatic shear bands and cavities in serrated chips, while in cutting with high cutting speed or small rake angle tools, there will be sparks and chip oxidation in the material [11–14]. Under ambient temperature, when BMG breaks, the local temperature of the alloy exceeds the glass transition temperature or even the melting point [15]. It is of great significance to raise new processing methods or improve the processing technology of BMG for promoting its engineering application.

Ultrasonic assisted machining has been termed as one of hybrid process that uses ultrasonic vibration during the machining action. Ultrasonic electric signal is converted into high-frequency mechanical vibration by transducer. The mechanical vibration is amplified by horn and transmitted to the end of the tool. In the turning process, the relative velocity between the tool tip and the workpiece changes due to the effect of ultrasonic vibration. Lauwers et al. [16] investigated the ultrasonic assisted grinding of ceramics, showed that the vibration resulted in more craters and lowered process force, making it feasible to increase the productivity. Pujana et al. [17] carried out ultrasonic assisted drilling experiments on titanium alloy, the results manifested that the drilling force decreases about 20%, and the it decreases with the increase of amplitude. Sui et al. [18] examined high-speed ultrasonic cutting, and the results showed that the material removal rate of high-speed ultrasonic cutting can be improved by up to 90% compared with conventional cutting. Maurotto et al. [19] applied ultrasonic longitudinal vibration to titanium alloy cutting. The average cutting force could be reduced by 70% compared with that of conventional cutting. Nath et al. [20] conducted cutting experiments on tungsten carbide by using elliptical ultrasonic vibration machining, studied the influence of tool nose radius on the surface quality, and obtained a better machining surface at 0.6-mm tool nose radius. Due to the application of longitudinal ultrasonic vibration, when the instantaneous speed of high-frequency vibration of the tool tip is greater than the cutting speed, there is contact-separation phenomenon between the tool tip and the workpiece. This kind of discontinuous contact makes the extrusion of the tool to the workpiece become high-frequency hammering, which changes the cutting force, cutting temperature, chip morphology and surface morphology of the machining surface.

A host of researches showed that ultrasonic vibration can improve the processing effect of BMG. Luo et al. [21] applied ultrasonic assisted micro-punch to BMG. The certain areas of BMG are subjected to the high frequency vibration transmitted by the punch, which leads to viscous flow. BMG gradually become soft and a series of shapes and products can be successfully fabricated in relative low pressing force. Ma et al. [22] proposed ultrasonic assisted forming for BMG processing, which not only forms BMG rapidly so that the crystallization and oxidation can effectively be avoided, but also works in a large scale range. In ultrasonic assisted punching and ultrasonic assisted forming on BMG, the cutting force and cutting temperature are effectively restrained, and the surface quality and productivity are improved. Whereas at present, there are few studies in ultrasonic assisted turning on BMG, which is subject to further investigation.

In this study, a longitudinal ultrasonic assisted turning (LUAT) system is established for processing BMG at first, and its frequency and amplitude are obtained through modal analysis and harmonic response analysis. A displacement testing experiment is performed to verify the designed system. Then the critical turning speed of the device is calculated. On this basis, the turning model of BMG is established, and the turning simulation of BMG under different turning speeds is carried out by using the LUAT device mentioned above. Finally, the influence of longitudinal ultrasonic vibration on the turning force, von Mises stress and chip forming under different turning speeds during turning BMG is discussed.
