**1. Introduction**

With the rapid growth of science and technology, precision components are increasingly in demand in various fields such as aerospace, biomedical engineering, optics, surface engineering and energy. These components not only require tight tolerances and high-quality surface finishes but also require the use of difficult-to-cut materials like high-temperature alloys and hard-brittle materials owing to the physical, mechanical, optical and electronic properties [1]. It is because of the difficultto-cut characteristics, the precision machining of these materials has always been a challenge. For traditional machining methods, there are always some disadvantages, such as high cutting temperature and cutting force, severe tool wear, low efficiency and poor surface quality. To improve the manufacturing quality, tool life and machining efficiency, let the machining cost down, elliptical vibration-assisted machining (EVAM) was proposed. In ultraprecision machining, especially the structured surface with micro-nano features, it requires exceptionally fine and repeatable motions, which makes the piezoelectric actuator a popular candidate for EVAM.

In EVAM, the elliptical vibration cutting (EVC) is a typical method for turning. It has been validated that EVC can improve the machinability of difficult-to-cut materials [2–4]. Meanwhile, the lower cutting force, longer tool life and better machining quality were obtained. In EVC, the vibration of cutting tool or workpiece is usually motivated by external excitation. For elliptical vibration cutting, the locus of cutting tool or workpiece is an ellipse due to the deliberate modulation of vibration devices. According to the principle of vibration, vibration devices can be divided into two types: resonant vibration and non-resonant vibration. For resonant type EVC vibrator, usually consists of an ultrasonic generator, a transducer and an ultrasonic vibration horn. The working frequency is generally above 20 kHz. There are two design schemes for the structure configuration, i.e. patch and sandwich. For the patch type EVC vibrator, two sets of piezoelectric plates are attached to the outer wall of the resonant rod to achieve the same or different modes of resonance. What's more, the Langevin-type transducer is usually adopted in the sandwich-type EVC vibrator. The vibrator can be achieved by adding two or more sets of piezoelectric rings to the resonant rod or coupling two Langevin-type transducers. The ellipse locus of cutting tool can be obtained through the same or different modes coupling in different directions with the nearly same vibration frequency. The working frequency is the resonance frequency. Additionally, the fixed working frequency and vibration parameters, poor dynamic accuracy and open-loop control, heat generation problems are the limitation problems for the resonant vibrator.

For non-resonant type EVC vibrator, usually consists of piezoelectric actuators and a compliant mechanism with deliberate design. Compared with the resonant vibration, the non-resonant type EVC vibrator provides much higher flexibility due to the elastic deformation of compliant mechanism. The vibration parameters like amplitude and frequency are easy to be controlled. The micro-nano motion resulting from elastic deformation of flexure hinge can guarantee the modulation ability and accuracy, which makes it more suitable for the manufacturing of micro-nano structured surfaces.

Generally, compared with workpiece vibration, tool vibration is more popular due to the ease of implementation. In fact, the modulation capability of tools plays a very important role in manufacturing for different materials and structure features. However, the tool modulation capability mainly depends on the performance of the vibrator. Obviously, the non-resonant type EVC vibrator has more advantages than the resonant type EVC vibrator. Up to now, there are many different types of non-resonant EVC vibrators were developed for vibration machining. Therefore, this chapter mainly focuses on the non-resonant type EVC vibrator, aiming to review the working principle of piezoelectric tool actuator, compliant mechanism design, static modeling, kinematic and dynamic modeling, structure optimization and offline testing.
