Zeng-qiang LI，Dong YU，Tao SUN（Harbin Institute of Technology，Harbin 150001，China）

Research status of the vibration assisted machining（VAM）technology

Zeng-qiang LI*，Dong YU，Tao SUN
（Harbin Institute of Technology，Harbin 150001，China）

With the constantly development of precision and ultra-precision machining technology，the vibration assisted machining（VAM）technology applied to the precision and ultra-precision machining has become an inevitable trend.This paper combines the domestic and foreign researchers’achievements and introduces the basic principle of ultrasonic vibration assisted cutting technology.Finally，the advantages and research status of the ultrasonic vibration assisted cutting technology is summarized at the end of paper.

Vibration assisted cutting，Ultrasonic assisted cutting，Precision and ultra-precision machining

Hydromechatronics Engineering

http：//jdy.qks.cqut.edu.cn

E-mail：jdygcyw@126.com

1 Brief introduction

Turning is a machining process that uses the cutting tool’s sharp edge to remove the surface thin layer，then a cylindrical surface is formed.This technology has been used in cutting various types of metal materials for centuries.With the development of science and technology，the demands for advanced cutting technology handling difficult machining problems are increased at the same time［1］.There are great benefits and potential in ultra-precise machining of steel with single crystal diamond cutter.But the diamond is usually limited to process thenon-ferrous metals，some of the crystals and ductile materials，the adsorption between carbon（diamond）and iron（workpiece）will lead to excessive wear of the cutting tool［2］.The invention of the ultrasonic vibration cutting technology provides a solution for the above-mentionedproblems. The ultrasonic vibration cutting technology is proposed by the Japanese scholar Kumabe Junichiro in the 1950s.Ultrasonic vibration cutting overlaps regular ultrasonic vibration on the cutting tool or workpiece，and makes the tool or workpiece vibrate periodically. It is a new technology which combines the ordinary and ultrasonic cutting technologies［3］.

With the constantly development and mature of precision and ultra-precision processing technology，the vibration assisted cutting technology applied to the precision and ultra-precision machining has become an inevitable trend.After studied for many years，numerous domestic and foreign experts found that ultrasonic vibration cutting has significant advantages as compared with ordinary cutting，such as smaller cutting force，better surface quality and longer tool life. Therefore，the development of ultrasonic vibration cutting technology has attracted the attention of scientists all over the world.

Japan is the first country to study ultrasonic machining technology.In terms of the research depth and width or the practical application effects，Japan is the leader in this field.In Japan，the research on vibration cutting and ultrasonic grinding has become considerably intensive in the 1970s.There were two of the most authoritative and most representative scholars. One is Shimakawa Jungxianat Chuo University，another is Kumabe Junichiro at Utsunomiya University，who put forward the theory of vibration cutting system in 1956 and published a number of papers.He is the first expert successfully applying the vibration cutting theory to turning，planning，milling，drilling，boring，reaming，broaching，grinding，screw thread machining，gear machining，polishing，honing，stretching，squeezing and other processing fields，and all of these had promoted the worldwide researches and popularization of ultrasonic vibration cutting.The ultrasonic elliptical vibration cutting technology was put forward by Japanese scholar in the 1990s.The basic principle is based on the traditional ultrasonic vibration cutting. It adds a simple harmonic vibration toward the direction of chip flow.Two orthogonal simple harmonic vibration make the cutting tool’s motion into an elliptic trajectory，thus it could realize the elliptical vibration cutting on workpiece.

At the end of 1950s and early 1960s，the former Soviet Union began to study ultrasonic vibration cutting and published many valuable papers.The ultrasonic vibration cutting was applied to the practical processing of ultrasonic turning，grinding，finishing and composite processing，and it achieved considerable economic benefits.A discussion held in the former Soviet Union in 1973，confirmed the economic effects and practical values of ultrasonic machining，which promoted the popularization of this new technology in this country.America started the research on the ultrasonic vibration cutting since 1960s.However，the quality of the designed and manufactured acoustic vibration system，transducer and generator is disillusionary due to the immature ultrasonic machining technology.In the middle of the 1970s，American begun to use the ultrasonic drilling center hole，finishing machining，grinding and welding.Other countries like German，Britain，Singapore and South Korea have also made abundant researches on the ultrasonic vibration’s machining mechanism and industrial application，and published many valuable papers.

In China，research on ultrasonic machining began at the end of the 1950s，but the research of the ultrasonic generator，transducer，acoustic vibration system cools down quickly due to the lack of reasonable organization and sustaining researches.In the 1970s，Harbin Institute of Technology has applied the ultrasonic turning to the airborne aluminum slender axis，and achieved excellent cutting effects，which still lacks enough summaries and studies in-depth［4］. Until the late 1990s，because of the urgent demands of vibration cutting technology from national defense，aerospace and other fields，ultrasonic vibration cutting technology became the research hot topic ofChinese scholars again.In this period，the Beihang University achieved a series of technological breakthroughs.At present，China has made lots of valuable achievements in the machining of materials difficult to cut or difficult to break and remove chip［5］.

2 Advantages of VAM

2.1 Reducing the cutting force

Experimental data in various literatures show that，with the same parameter，the cutting force in vibration assisted machining will be obviously lower than that in conventional machining［6-12］.

Ma etal.used conventional method，one-dimensional VAM（traditional vibration cutting）method and two-dimensional VAM（elliptical vibration cutting）method respectively to machine aluminum workpiece and compare the magnitude of the cutting force.As shown in Fig.1，the average thrust forces drop to 20% of the conventional machining value for 1D VAM，and to 2%for 2D VAM［6］.Ming etal.from Singapore Nanyang Technology University used conventional and the 1D VAM turning method for turning 304 stainless steel and studied the changes of average cutting force as processing distance increased with a polycrystalline diamond（PCD）tool，as shown in Fig.2.This figure shows that the average cutting force under 1D VAM is much lower than the force in conventional machining. With the increase of cutting distance，the average cutting force in conventional processing conditions gets increased significantly，while the rise of average cutting force in 1D VAM is much slower［7］.

Fig.1 Average thrust force comparison for conventionaI cutting，1D VAM and 2D VAM for carbide tooI in aIuminum workpiece，f=18.66 kHz

Muhammad etal.compared the magnitude of the cutting forces in ultrasonic vibration assisted turning（UAT）and conventional turning（CT）by turning titanium alloys，and discussed the change of average cutting force when the cutting speed gets changed. Their results also demonstrate that the application of ultrasonic vibration cutting could reduce the average cutting forces significantly［8］.

Fig.2 Average tooI forces comparison between conventionaI machining and 1D VAM.PCD tooI and 304 stainIess steeI workpiece.f=40 kHz

2.2 Extending the tool life

Many papers have mentioned that the use of VAM system could significantly extend the tool life［7，13-14］.Masahiko etal.used conventional cutting（CC）and ultrasonic cutting（UC）processing method respectively to machine the workpiece of quenched chromemolybdenum steel SCM435（40HRC）.Fig.3 present the relationship between the workpiece cutting number N and the flank wear width VB，as well as the shape of the workpiece in the figure［13］.As a result，in conventional cutting，flank wear width will get increased quickly，which will increase much slower in ultrasonic cutting.Dong etal.also obtained a relationship curve of the surface roughness and cutting distance while turning ferrous metal 1Cr18Ni9Ti with single crystal diamond tool，as shown in Fig.4［14］. With the increase of cutting distance，the increase of surface roughness（Ra）will be much slower in ultrasonic vibration turning，which indicates that the tool life in ultrasonic vibration turning could be much longer.

Fig.3 ReIationship between the workpiece cutting number N and the fIank wear width VB（workpiece：SCM435（40HRC），tooI：K10，f：21 kHz）

Fig.4 Roughness comparison between CT and UAT（workpiece：SCM435，tooI：K10）

Fig.5 and Fig.6 are the SEM pictures of PCD tool after cutting for 300 m distance by conventional cutting and VAM，respectively.As shown in Fig.5，in the case of traditional cutting，besides the wear occurred on the rake face，there is more obvious wear occurred on the flank which is in contact with workpiece.In the case of VAM，tool wear is much smaller［7］.

Fig.5 SEMof a worn-out tooI in conventionaI cutting at a cutting distance of 300 m

Fig.6 SEM of a worn-out tooI in vibration cutting at a cutting distance of 300 m

2.3 Achieving better surface quality

The use of vibration assisted machining could achieve better surface finish than traditional processing［7，8，14-24］.Table 1 summarizes some research data about the surface roughness obtained by traditional cutting and 1D or 2D vibration assisted machining. The results are mixed but the roughness will be decreased by approximately 40%with 1D VAM and 95%for 2D VAM.These examples illustrate that VAM could achieve substantial improvements in surface finish as compared to conventional machining over a broad range of tool types，work materials，and depths of cut.

Fig.7 shows the roundness of machined Inconel 718 workpiece by ultrasonic assisted cutting and traditional cutting，a considerable improvement is obtained for roundness of machined workpieces by UAT method［9］.Masahiko used UAT and CT method respectively tomachine the workpiece of clover shape，and obtained their roundness graphs［13］.The roundness in UAT is 2.5 μm，as compared with the 36.8 μm in CT，the form accuracy could be improved greatly.The application of ultrasonic vibration cutting method can not only obtain better surface finish，but also effectively improve the surface shape accuracy，so as to promote the workpiece’s surface quality.

TabIe1 Improvement in surface roughness achieved through use of VAM

Fig.7 Roundness profiIes of InconeI 718 specimens machined with UAT and CT（workpiece：SCM435，tooI：K10）

Fig.8 Comparison of the roundness profiIe between CT and incIined UAT

3 Vibration assisted machining system

According to different output forms of the vibration，vibration assisted machining system can be divided into one dimensional vibration assisted machining（1D VAM）system and two dimensional vibration assisted machining（2D VAM）system.In 1D VAM system，tool nose trace is straight line.In 2D VAM system，the trace is 2D curve，in which the most typical kind is ellipse.

3.1 1D VAM system

In 1D VAM system，there is a low-amplitude and high-frequency displacement movement overlapped on the tool’s cutting motion.Under appropriate cutting speed，vibration amplitude and frequency，tool and workpiece could contact and separate periodically，so as to reduce the average cutting force and obtain better surface quality.Tool life，especially the life of diamond tool for cutting nonferrous metal，will be extended significantly due to the use of VAM system.

It is essential for the transition from the conventional process to a process with an intermitted tool-work piece contact，that the maximum oscillation speed is greater than the constant workpiece speed（as shown in Fig.9 between point 2 and 3）.Only on this condition，the tool could separate itself from the chip during the vibration（point 2，relative speed vrel=0）.The contact occurs again（point 4）during the upward motion after the vibration direction changes at the bottom point（point 3）.Therefore，the effective contact time between workpiece and cutting edgecould be reduced. The improvement on cutting process dynamicshas a great influence on the ultra-precision machining for critical materials such as steel or glass.The intermittent contact will improve the cooling condition of tool. Accordingly，the effective contact time between the part and the cutting edge will be reduced significantly by the high frequency excitation of the tool.Since each chemical reaction needs a starting time，the time，in which the chemical reactions，oxidations and diffusion reactions cause the wear will be significantly reduced.Hence from this point of view，the higher frequency should improve the overall process quality［25］.The experiments conducted by Heselhaus［26］and Klocke［27］show that once the processing frequency increased from 40 kHz to 60 kHz，the surface roughness and tool life could be improved markedly.

Fig.9 Kinematic modeI for uItrasonic assisted diamond turning with a Iinear osciIIation［25］

1D VAM can be divided into resonant 1D systems and non-resonant 1D systems.In the case of resonant 1D system，which is the most common 1D VAM system，the system works at resonant frequency.Fig.10 shows a typical 1D VAM system.Ultrasonic transducer with a piezoelectric or magnetostrictive actuator is used to generate high-frequency and low-amplitude reciprocation motion.The cutting tool is attached at the end of the horn，aligned so that the rake face is normal to the vibrating direction.

Fig.10 TypicaI 1D VAM system

One of the major advantages of ultrasonic assisted turning（UAT）is the reduction of average cutting forces.A set of advanced ultrasonic assisted cutting device Agostino designed by Maurotto etal.confirmed this point.A universal lathe was adequately modified to accommodate an ultrasonic cutting head with flexibility of switching between conventional and ultrasonic cutting regimes during a single turning operation.Fig. 11 shows a schematic of the cutting head，demonstrating its various parts that make up the ultrasonic cutting assembly.The assembly was fixed to the cross slide of the lathe by a specially designed tool-post attachment（Fig.12）.Necessary precautions were taken to ensure the stiffness of the entire system at all fixed point.They have proved that the utilization of a similar device could reduce the cutting force by 60% while machining Inconel 718，with the help of finite element simulation method［28］.Then they optimized the stiffness of the overall system，the ability to reduce the cutting force has reached 70%.And when the device is used to the practical machining process，the result showed a substantial improvement on the surface quality［29］.

Fig.11 Schematic of uItrasonic cutting assembIy

Fig.12 UItrasonic cutting assembIy［29］

Riaz Muhammad etal.at Loughborough University carried out a research on ultrasonic vibration cutting of α+β titanium alloy，in order to study the machinability，chip shape，cutting force，temperature in the cutting area and surface roughness of both traditional and ultrasonic vibration turning.A customized Harrison 300 lathe was used to carry out both CT and UAT，as shown in Fig.13.As a result，UAT shows improvement of machinability with reduced nominal cutting forces，surface roughness of the machined workpiece and generation of shorter chips as compared to the conventional machining conditions［30-31］.

Fig.13 Setup for UAT at Loughborough University

Gan etal.applied the ultrasonic assisted technique to the turning of glass.Fig.14 shows the ultrasonic vibration system and workpiece mounted on an Optimum 2400 ultra-precision lathe system.Glass workpiece was clamped on the spindle，and the ultrasonic vibration system is fixed by a dedicated fixture.Cutting tool vibrates in the vertical direction under the action of ultrasonic vibration system.A dynamometer was used to measure the cutting force in the process of cutting.With ultrasonic vibration overlapped on the SCD tool，plastic processing of the fused silica could be realized even at a 2 μm depth of cut，which shows that the use of ultrasound assisted cutting technology can achieve fascinating results in the turning of glass materials［32］.Razavi etal.applied the UAT to oblique turning，and analyzed the kinematical and dynamical performance of oblique ultrasonic assisted turning（oblique UAT），traditional oblique turning is included in their study to make a comparison［33-34］.

Fig.14 UItrasonic vibration system and workpiece on Optimum 2400［32］

Bending stiffness in 1D VAM must be large enough to prevent lateral oscillation，which will cause tool deviation from the ideal linear path that could allow the tool to hit the workpiece when it is withdrew from the uncut material face，it results in impact damage on the cutting surface，and affects the surface quality and chipping of the tool on the flank side of the cutting edge.To prevent possible contact，some researchers operate 1D systems with the tool vibration direction inclined at an angle to the work upfeed motion，as shown in Fig.15.Masahiko conducted a series of experiments to prove that this method could finish machining stably［13］.The proposed method could effectively prevent the generation of debris from cutting edgein the processing of hard materials，and obtain favorable surface quality in continuous orintermittent mode.

Fig.15 1D system with the tooI vibration direction incIined to the upfeed motion

Ultrasonic generators are high Q resonant systems. Interrupted cutting is a repetitive，non-linear and impulsive-type load which will lead to the possibility of several amplitude regimes where the system could operate.The result can be instabilities in the tool motion which will adversely affect the surface roughness. Babitsky etal.［35-36］developed an auto-resonant control scheme which uses the feedback of the ultrasonic generator’s position and velocity to dynamically establish and maintain a resonant frequency optimum for the specific machining circumstances.Application of this scheme could result in a 50%improvement in surface finish when turning macro-scale Inconel components as compared to the operation without auto resonant control［37］.

Fig.16 demonstrates an experimental set-up of an ultrasonically assisted cutting tool used in this work. The ultrasonic transducer consists of piezoceramic rings clamped into a package together with a metallic waveguide（concentrator）.A cutting tip is fixed in the tool holder which is installed at the thin end of the concentrator，the transducer is fixed through its housing at the machine tool vertical slide and workpiece is clamped by a three jaw spindle chuck and could be rotated universally by a lathe drive.When the highfrequency electric impulses from an electronic amplifier feed the input of the piezo transducer，it begins to vibrate due to the piezoelectric effect.The vibration excites the longitudinal waves in the concentrator and vibration of the cutting tip.In this case（as shown in Fig.17），the amplified signal obtained from the performance sensor is fed to the transducer directly by means of a positive feedback，which provides instant control of the mechatronic system［38］.

Fig.16 ExperimentaI set-up of UAT［38］

Fig.17 Schematic of autoresonant uItrasonic system

Chinese universities and research institutes has explored the 1D VAM technique for decades.In the 1980s，Guangxi University，Nanjing film machinery factory and Nanjing cutting tool factory jointly developed China＇s first ultrasonic vibration cutting system CZQ-250A，as shown in Fig.18.

Fig.18 CZQ-250A uItrasonic vibration cutting system

Chen etal.applied ultrasonic vibration to the turning of thin-wall parts to reduce the deformation，and developed the height adjustment mechanism for vibration cutting system.Thecomparative data of ultrasonic cutting and conventional cutting shown that the ultrasonic cutting could effectively improve the processing quality in thin-wall parts’turning.Fig.19 shows the longitudinal vibration cutting device with a tools-tip height adjustment mechanism，through which the fine adjustment of tools-tip height could be realized by two meshed rotation sleeve［15］.

Fig.19 LongitudinaI vibration cutting device with a tooIs-tip height adjustment mechanism

According to the machining characteristics of magnesium alloy，researchers at North University of China designed a longitudinal ultrasonic turning device for turning magnesium alloy materials based on the parameters of C620-1 lathe，as shown in Fig.20.The ultrasonic vibration system comprises an ultrasonic generator，a sandwich piezoelectric ceramic transducer and a horn.Cutting tool is bolted at the end of the horn，and the ultrasonic vibration system is fixed on the worktable by a dedicated fixture.The turning experiments demonstrate that UAT can improve the machining precision and surface quality of magnesium alloy workpiece as compared to CT，and it could solve the spontaneous combustion and thermal deformation of magnesium alloy materials in machining process［39］.

Fig.20 Schematic of uItrasonic turning device suitabIe for turning magnesium aIIoy materiaIs

Song analyzed the cutting mechanism and cutting force in 1D VAM，and carried out the design and simulation analysis of ultrasonic vibration assisted turning device in stainless steel machining.The researcher emphasized the importance of the booster structure，and designed a stepped booster and a conical booster，as shown in Fig.21，with finite element analysis software［40］.

Fig.21 Structure

There are few examples of non-resonant 1D VAM systems.Han etal.made a system in which the tool was mounted to a flexure driven by a piezoelectric actuator.A sinusoidal voltage signal applied to the piezo stack caused it to expand and contract along its length.This actuator motion was amplified by the flexure to produce an amplitude of 10 μm at ultrasonic frequencies.Fig.22 shows the structure of the integrated cutting tool consisting mainly of an error compensation actuator and an ultrasonic vibration actuator.The error compensation actuator could provide micro-displacement for error compensation，while the ultrasonic vibration actuator is utilized to generate ultrasonic vibration so as to achieve ultrasonic vibration cutting.Moreover，the ultrasonic vibration actuator is directly placed at the cutter tip.Compared with other designs，in which the actuator is not placed at the tip and the ultrasonic energy is transmitted to the tip only via a coupling system，the current design can simplify the tool structure and improve the efficiency of energy transformation.This device had obtained good roundness and surface quality in the cutting experiments［41］.Cuttino and Overcash developed a non-resonant 1D VAM system which can be operated over a wide range of ultrasonic frequencies.Multiple actuators are used to achieve high frequencies.The activation sequence is phased so that individual actuators operate at an acceptable frequency lower than the tool vibration frequency［42］.

Fig.22 Construction of an integrated cutting tooI［42］

3.2 2D VAM system

The advantages of ultrasonic vibration turning includes the small cutting force，low temperature，improvement of the surface quality and position accuracy.But in the conventional ultrasonic vibration cutting（1D VAM）process，if the tool and the workpiece are separated，the friction and impact could occur between the flank and machined surface，and it will not only damage the surface quality of the machined surface，but also make the tool work under pressure.Especially in ultra-precision machining，where the hard and brittle material tool like SCD tool or PCD tool is generally used，the tool will be damaged fast under tensile stress，which will seriously affect the tool life and machining quality and limit the application of ultrasonic vibration cutting technology in the field of ultra-precision machining.In the 1990s，Japanese researchers put forward that the flaking problems in ultrasonic vibration cutting tools could be solved by using ultrasonic elliptical vibration cutting technology，which could successfully apply the ultrasonic elliptical vibration cutting technology into the field of ultra-precision machining［43-45］.

Elliptical vibration cutting system is a typical 2D VAM system，so the elliptical vibration cutting is used as an example here to introduce the work principles of the 2DVAM.As shown in Fig.23，it is a schematic diagram of the elliptical vibration cutting.

While the elliptic vibration velocity is greater than the cutting speed in the cutting direction，the cutting tool can contact with or separate from the part along the elliptical vibration path as shown in Fig.23（a），F(xiàn)ig.23（b）shows the moment the tool is ready to contact the workpiece and begin to cut.At this moment，the cutting tool and chip are still separated. Fig.23（c）is the process of real cutting.Fig.23（d）shows the finish moment of cutting，it represents the difference between elliptical vibration cutting and conventional cutting，as the tool moves away from the parts along the elliptical trajectory.As compared with the traditional vibration cutting，the direction of the friction force between the rake face of the cutting tool and chip is reversed，which is good for the chip flow and reduces the cutting force.While the tool separated from the part completely，it will move to the starting position of the next circle.Fig.23 shows a cutting cycle of ultrasonic elliptical vibration cutting，in each cycle，the toolturns the part intermittently along an elliptical trajectory［1］.

Fig.23 Schematic diagram of the eIIipticaI vibration cutting system［1］

In this method，the workpiece is fed at a nominal cutting speed，while the elliptical mode vibration is applied to the cutting edge.As the maximum vibration speed is set to be higher than the cutting speed，the tool is separated from the chip in each cycle of the vibration.The cutting takes place after reentering of the cutting edge into the workpiece，and the chip is mainly pulled up and formed while the tool moves upward in the chip flow direction.The tool moves down without cutting while it is separated from the chip.Thus，the frictional direction is mainly reversed and the reversed friction could cause the average frictional force to be less than zero virtually.The virtual lubrication effect of the elliptical vibration cutting increases the shear angle significantly and consequently reduces the cutting force［46］.

According to the vibration frequency，2D VAM system can be divided into resonant system and non-resonance system.Resonant 2D VAM system generates a circular or elliptical tool path at resonant frequency. According to the excitation amount，2D VAM system can be divided into single excitation 2DVAM system and double excitation 2D VAM system.

3.2.1 Single excitation 2D VAM system

Brinksmeier and Glabe built a simple resonant 2DVAMsystem by mounting the center of mass of the diamondtoolawayfromthecenterlineofa 1Dultrasonic system like those described in Section 3.1.The off-center mass of the tool caused bending vibration of the supporting structure in the depth-ofcut direction.This motion combined with the horizontal vibration to produce an elliptical tool path.A 40 kHz，700 W ultrasonic generator and an air-cooled piezoelectric converter was used to stimulate the tool. The diamond tool was fixed＇off axis＇to the face side of the transducer.Due to the displacement of the tool mass the tool vibrates elliptically.Using a counterweight，the elliptical motion could be controlled within a certain range.By carefully monitoring and adjusting the tool oscillation，tool wear could be reduced by a factor of 10 and surface roughness could be improved. Using optimized cutting conditions，the cutting distance on steel could be increased up to 1 500 m while the roughness of the machined surface was still acceptable［47］.

Fig.24 Structure of the transducer［48］

Li and Zhang used the similar concept，and replaced the ultrasonic transducer and booster with a specially shaped beam，on which the cutting tool is mounted off-center，as shown in Fig.24［48］.A discshaped piezoelectric actuator at the base of the beam is driven at ultrasonic frequency of 20 kHz.The beam is specially designed to convert the small-amplitude longitudinal vibration of the piezoelectric element into combined longitudinal and bending vibration，then to create an elliptical tool path.The vibration cutting method reduced the thrust force generated in the machining process and improved the surface quality，as compared to conventional cutting.Roughness of Ra 0.08 μm was obtained with this device，in the turning of LY12 material.Researchers at Beihang University also developed a set of single driven ultrasonic elliptical vibration turning system based on the similar principles，and conducted a series of experiments on ultrasonic elliptical vibration cutting with PCD tool，in which favorable processing quality was achieved［49］.

Domestic universities and research institutes have also conducted quite much work，and obtainedquite fascinating results.Researchers from Beihang University and Henan University of Technology put forward the structure of a new single excitation elliptical vibration cutting system，the system architecture is shown in Fig.25.It uses a 1/2 wavelength sandwich piezoelectric transducer to generate ultrasonic vibration，and the tool part is a half-wavelength stepped horn with rectangular cross section.It cuts transverse chutes at a certain angle and a certain position at the large end（or the small end）of the horn.The cutting tool is mounted at the small end.Under the transducer’s excitation，the stepped horn generates longitudinal vibration.While the natural frequency of the longitudinal vibration and the resonance frequency of the transducer are the same or close enough，the whole vibration system will achieve resonance.Since the grooved width chute is tiny，its effects on the structural parameters of the overall system can be ignored.After working out the transverse chute，the entire horn is divided into three parts：the left part of the chute，the right part of the chute and the chute itself.The chute connects the left part and the right part，as shown in Figure 3-25.Experiments show that when the chute and the horn are designed in an appropriate way，the small end of the horn will generate an elliptical vibration. After installation of the tool，the tool tip will make elliptical motion，which makes the elliptical vibration cutting on the workpiece possible.Driven by a single longitudinal excitation，switch from single longitudinal vibrations to longitudinal-bending composite vibrations can be achieved.It is possible to make the bending vibration’s natural frequency and the longitudinal vibration’close with a phase difference existed in the two vibration，which finally achieves the elliptical vibration at the small end of the stepped horn［50］.

Fig.25 Schematic diagram of the LongitudinaI-bending eIIipticaI vibration cutting system

Researchers at Southeast University have proposed a new two-dimensional ultrasonic vibration cutting system，namely piezoelectric ultrasonic vibration cutting system.Fig.26 is the schematic of the system，which is mainly composed of an ultrasonic generator，matching circuit，cascading piezoelectric crystal，resonant tool holder，supporting and adjusting mechanism and tool.After the generator output ultrasonic signal，it will enable cascade crystals generate ultrasonic mechanical telescopic，then drive the resonant vibration of the cutter bar directly and realize the ultrasonic vibration.The characteristics of this device includes less energy transmission links，less energy leakage，high electromechanical conversion efficiency，simple structure，small volume，and convenient operation［51］.Zhao Ji etal.studied the ultrasonic horn and bending vibration cutter as a whole system，developed an ultrasonic vibration cutting system with a 1/4 wavelength horn，as shown in Fig.27［52］.

Fig.26 Schematic of the piezoeIectric uItrasonic vibration cutting system

Fig.27 UItrasonic vibration cutting system with a 1/4 waveIength horn

Zhang Xiong designed a similar single excitation longitudinal-bending composite elliptical vibration cutting system with transverse chute，and compared the turning performance of 2D vibration turning，conventional turning and 1D vibration turning.Through the experiment，it can be found that cutting force in 2D vibration turning is the smallest compared with 1D vibration turning and conventional turning，under the same turning parameters.Besides in three kinds of turning mode，the surface quality in 2D ultrasonic vibration turning is the best［17］.

3.2.2 Double excitation 2D VAM system

Moriwaki and Shamoto developed the resonant 2D VAM system as shown in Fig.28.Piezoelectric actuators attached to the side faces of the beam structure are activated in opposed pairs to induce bending in the up feed and vertical directions at the third resonant frequency.A phase difference exists between the two pairs of actuators.The beam is supported at its nodal points.Bending vibration of the beam ends amplifies the motion induced by the piezo strips.The diamond tool is mounted on the end of the beam and the combination of the two bending vibrations at right angles make it move in an elliptical path.This system has been used at discrete frequencies in the range 20-40 kHz.Vibration amplitudes are selected depending on the specific workpiece material and application［16，46，53］.In their experiments，the resonant 2D VAM reduced the chip thickness and cutting force significantly as compared with conventional cutting and 1D VAM，and obtained good shape accuracy and surface roughness（Rmax 0.02 μm）.

Fig.28 Resonant 2DVAMsystembyShamoto and Moriwaki

In the above design，the modal frequencies of the two vibration directions are very close to one another. This permits energy transfer back and forth between the two modes，or“crosstalk”，causing the tool path to become distorted.A corrective feedback system was developed that uses piezoelectric strain gauges to sense the beam position and compensates for crosstalk by dynamically changing the voltage signal to the driving actuators.As a result，form accuracy when turning a stainless steel mirror was improved from 2 μm without the control to 200 nm with the control system activated.The system is shown in Fig.29.The vibrator has 4 large piezoelectric plates as actuators and 2 small plates as sensors.It is vibrated in the cutting direction in the third resonant mode by applying sinusoidal voltage to the upper and lower actuators with a phase shift of 180 degrees.It is also vibrated in the normal direction to the cutting direction and the vibrator axis by exciting the front and back actuators.The diamond tool tip is set at the end of the vibrator and vibrated elliptically by resonating the vibrator in the both directions with some phase shift.The two directional vibrations are detected by two sensors respectively［54］.

Fig.29 UItrasonic eIIipticaI vibrator deveIoped

Wang Yue designed an ultrasonic elliptical vibration system，of which the elliptical path is composed of two orthogonal ultrasonic vibration with a certain phase difference.The structure includes of two orthogonalhorn，named horn-1 and horn-2，as shown in Fig.30. Two horns are connected by bolts，the cutting tool is bounded on the small end of the horn-2.When the sinusoidal voltage signals overlapped on the end of the horn shave a certain phase difference，the horns will stretch out and draw back periodically，so that an elliptical vibration path is formed on the tool［1］.

Fig.30 UItrasonic eIIipticaI vibration device

Wang Guilin etal.developed a new type of highfrequency（147.5 kHz）elliptical vibration transducer，as shown in Fig.31，according to the two-path vibrational principle.For the transducer，a longitudinal and a transverse ultrasonic vibration are used to complete the synthesis of the elliptical vibration.Their experiments shows that the high-frequency ultrasonic elliptical vibration cutting can be carried out at a high cutting speed，which greatly improves the work efficiency，on the premise of ensuring the surface roughness［55］.

Fig.31 Structure of high-frequency eIIipticaI vibration transducer

Similar to the 1D VAM system，there are non-resonance 2D VAM systems.In non-resonant 2D VAM systems，sinusoidal voltage signals are applied to piezoelectric actuators causing them to extend and contract but at a frequency below the first natural frequency of the system.The linear motion of the piezo stacks is converted into elliptical tool motion by a mechanical linkage.Fig.32 shows a non-resonant 2D VAM system created at Pusan National University.A micro-drilling machine tool composed of a xy table and a z-axis column is equipped with a tool two PZT actuators are located perpendicularly each other in the tool vibrator so that two-dimensional vibrational tool path is created. If a sine wave generated from a function generator is input to a two-phase signal generator，two sinusoidal signals with phase difference φ corresponding to a required tool pattern are output.The two-phase signals are amplified enough to actuate PZT actuators by a two-channel signal amplifier［56］.

Fig.32 Schematic of for 2-D non-resonant cutting

Fig.33 shows the operating concept of a non-reso-nant 2D VAM system developed at North Carolina State University.Sinusoidal voltage signals are supplied to the two parallel actuators.The tool holder serves as a mechanical linkage to convert the linear motion of the actuators into elliptical tool motion.Advantages of this system are its abilities to operate over a range of frequencies and for the tool path size，aspect ratio，and orientation to be varied by changing the amplitude and phase difference of the voltage signals to the actuators［57］.

Fig.33 Operating concept of a non-resonant 2D VAM system

Through the combination of the two high frequency signal，double excitation 2D VAM system can accurately control the shape and size of the ellipse，but its mechanical structure and control system is more complex compared with single excitation system.As for single excitation 2D VAM system，its electrical and mechanical structure is much simpler than double excitation structure.Both of the two types have their own advantages；the choice of them in the application should depend on the specific needs.

Besides 1D VAM systems and 2D VAM systems，3D VAM systems have been created by Japanese researchers Norikazu Suzuki and Eiji Shamoto and successfully applied into the milling processing［58-59］.

4 Products of VAM technology

UTS one，as shown in Fig.34，is a typical products of ultrasonic vibration assisted cutting system produced by son-x GmbH at Germany.In cutting process，the piezo driven ultrasonic transducer generates a linear movement of the diamond tool with a frequency of 80 kHz.The highly frequent oscillation of the tool in cutting direction leads to an intermitted contact between the diamond cutting edge and the machined material. Due to the intermitted contact，the absolute contact time for a machining operation is only about 20%of the actual processing time.Several positive effects are realized with the help of this technology，like better cooling of the tool，interception of chemical wear reactions，better tool lubrication，less friction，less forces. Altogether these effects lead to a significant reduction of the diamond tool wear which enables the machining of difficult to cut materials，such as hardened steel.

Fig.34 UTS one uItrasonic tooIing system

In 2014，the company launched a new product UTS2，as shown in Figure 4-2.UTS2’s vibration frequency reaches up to 100 kHz，and there is no limit on machining size in the cutting process.It can be used to the ultra-precision turning of materials such as hardened steel，titanium alloy，nickel alloy and glass，and surface shapes such as aspheric surface，free surface，the diffraction optical surface and microstructure，with surface roughness of Ra 3 nm and surface accuracy of 150 nm.This innovative product pushes the diamond turning technology to a new level.

Fig.35 UTS2 uItrasonic tooIing system

5 Conclusions

With the constant development and mature of precision and ultra-precision machining technology，the application of the vibration assisted machining technology to the precision and ultra-precision machining has become an inevitable trend.Ultrasonic vibration cutting has significant advantages as compared with ordi-nary cutting，such as smaller cutting force，better surface quality and longer tool life.According to different output forms of the vibration，vibration assisted machining system could be divided into one dimensional vibration assisted machining system and two dimensional vibration assisted machining system.In 2D VAM system，the trace is 2D curve，in which the most typical kind is ellipse.The flaking problems happened in 1D ultrasonic vibration cutting tools could be solved and better cutting performance is obtained by using ultrasonic elliptical vibration cutting technology.

According to the excitation amount，2D VAM system can be divided into single excitation 2D VAM system and double excitation 2D VAM system.The 2D VAM system can accurately control the shape and size of the ellipse，but its mechanical structure and control system is more complex.As for single excitation 2D VAM system，its electrical and mechanical structure is much simpler.Both of the two types have their own advantages；the selection of them in the application depends on the specific needs.

Acknowledgements

This paper is supported by Heilongjiang Province Science and Technology Research Projects（GC03A523）.

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振動(dòng)輔助切削加工技術(shù)研究現(xiàn)狀

李增強(qiáng)*，喻 棟，孫 濤
哈爾濱工業(yè)大學(xué)精密工程研究所，哈爾濱 150001

隨著精密與超精密加工技術(shù)的不斷發(fā)展和成熟，將振動(dòng)輔助切削技術(shù)應(yīng)用到精密與超精密加工中去已成為發(fā)展的一個(gè)必然趨勢。結(jié)合國內(nèi)外研究人員的研究成果，介紹了超聲振動(dòng)輔助切削技術(shù)的基本原理，綜述了超聲振動(dòng)輔助切削技術(shù)的優(yōu)勢以及研究現(xiàn)狀。

振動(dòng)輔助切削；超聲輔助切削；精密與超精密加工

10.3969/j.issn.1001-3881.2015.12.001Document code：A

TG115.6+3

4 November 2014；revised 26 February 2015；accepted 5 March 2015

*Corresponding author：Zeng-qiang LI，Professor.

E-mail：zqlee@hit.edu.cn