A review of fly cutting applied to surface generation in ultra-precision machining

Author’s Accepted Manuscript A review of fly cutting applied to surface generation in ultra-precision machining S.J. Zhang, S. To, Z.W. Zhu, G.Q. Zhang

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To appear in: International Journal of Machine Tools and Manufacture Received date: 28 July 2015 Revised date: 28 December 2015 Accepted date: 5 January 2016 Cite this article as: S.J. Zhang, S. To, Z.W. Zhu and G.Q. Zhang, A review of fly cutting applied to surface generation in ultra-precision machining, International Journal of Machine Tools and Manufacture, http://dx.doi.org/10.1016/j.ijmachtools.2016.01.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A review of fly cutting applied to surface generation in ultra-precision machining S.J. Zhanga, b, S. Tob, *, Z.W. Zhub, G.Q. Zhangb aResearch

Institute of Mechanical Manufacturing Engineering, School of Mechatronics

Engineering, Nanchang University, Nanchang, Jiangxi, PR China. bState

Key Laboratory of Ultra-precision Machining Technology, Department of Industrial and

Systems Engineering, The Hong Kong Polytechnic University, Hong Kong. *

E-mail: [email protected], Tel: +852-2766-6587, Fax: +852-2764-7657

Abstract Fly cutting in ultra-precision machining (UPM), termed ultra-precision fly cutting (UPFC), is an intermittent cutting process in which a diamond tool is mounted with a spindle to intermittently cut a workpiece. The process offers the high flexibility necessary for fabricating freeform, micro/nano-structural surfaces, as well as hybrid structural surfaces with sub-micrometric form error and nanometric surface roughness, and its constant cutting velocity provides uniform high surface quality. However, in addition to its low machining efficiency, UPFC’s intermittent cutting process results in distinctive surface generation mechanisms, covering intermittent tool-workpiece relative motion, tool geometry imprinted into a machined surface, and surface material separation and deformation. General factors, such as cutting conditions, tool geometry, material factors (material property change, material swelling and recovery, and material separation mechanism), kinematic and dynamic errors, assembling errors, cutting strategies, tool path, and workpiece geometry, are individual to UPFC and universal in UPM. Accordingly, this paper focuses on the current investigation of fly cutting applied into surface generation in UPM. Conclusions are reached and the challenges and opportunities for further studies are discussed. Keywords: Fly cutting, Surface generation, Ultra-precision fly cutting, Ultra-precision raster milling, Ultra-precision machining

1. Introduction Ultra-precision machining (UPM) is a mechanical material removal manufacturing process that involves ultra-precision diamond turning (UPDT), ultra-precision raster milling (UPRM) / fly cutting (UPFC), ultra-precision grinding (UPG), and ultra-precision polishing (UPP). The achievable form accuracy and surface roughness is one sub-micrometer and several nanometers, respectively [1, 2]. In UPM, excellent diamond tools and ultra-precise machines are combined together for the fabrication of such high quality surfaces. Single crystal diamond is the ideal material for UPM as it has a sub-micrometric tool contour geometry and a nanometric cutting tool edge. In addition, it has many outstanding properties, such as super hardness, high thermal conductivity, a nanometric tool edge, and high wear resistance with low friction [3]. Machine-tool performance determines form error and surface roughness. In UPM, natural granite, polymer concrete or aged cast iron with high stiffness and damping properties are adopted in order to minimize or eliminate vibration and deformation effects on surface generation [4, 5]. And, high internal damping [4], aero-/hydro-static slides with low friction [5],

laser position feedback with nanometric resolution [6], high thermal stability [7], and nanometric tool positioning [8] have been applied to satisfy the critical demands of UPM. Nowadays, UPM machine tools with nanometric resolution are commercially available. Typical workpiece materials for UPM are diamond turnable materials such as aluminum alloys, copper alloys, electroless nickel-phosphor plating, and plastics [9-11]. Nowadays, due to the ever-growing demands for specialized products, it is expanded to cut diamond non-turnable materials such as silicon [12] and steel [13]. However, rapid diamond tool wear is still a deterministic drawback. Miniaturization, specialization, and functionalization have promoted the UPM applications into the fields of optics, medicine, biotechnology, electronics, and communications. [14]. Currently, UPM is the fastest and most reliable mainstream technique to cost-efficiently shape high quality complex surfaces. Significantly, UPFC developed from UPDT is highly flexible and therefore suitable for the special fabrication of freeform and structural surfaces, such as v-grooves and pyramids, with uniform surface quality. It is obviously different from UPDT in surface generation mechanisms due to its fly cutting mechanism. Distinctively, in UPFC a diamond tool is mounted with a spindle to cut a workpiece. It also provides the capability of high quality surfaces with sub-micrometric form error and nanometric surface roughness. This paper surveys the current investigation into fly cutting in UPM (i.e. UPFC) and its applications with a focus on surface generation. Previous key research findings are reported along with related discussions. Challenges and opportunities faced by academia and industry in UPFC are elaborated for future studies with some key conclusions.

2. Principles and applications of UPFC Although UPFC is developed with fly cutting from UPDT, it is distinctive from UPDT. Firstly, in UPFC the diamond tool rotates with a spindle to remove surface material, i.e. fly cutting, whereas in UPDT a workpiece is mounted with a spindle. Secondly, in UPFC the cutting velocity is constant, whereas in UPDT the cutting velocity changes with the cutting radius distance between tool tip and spindle axis. Thirdly, in UPFC material removal is intermittent, i.e. intermittent cutting, whereas in UPDT it is commonly continuous. Thus, the cutting efficiency of UPFC is lower than that of UPDT. Regarding surface quality, inconsistent cutting velocity with respect to spindle speed leads to cutting quality inconsistency in UPDT [15]. Secondly, the larger the cutting radius distance in UPDT is, the higher tracking bandwidth is required, which causes tracking bandwidth limitations that induce surface distortions and deterioration [16, 17]. Finally, as the sampling number determines the cutting linearization error, azimuth sampling conflicts take place from the outside to the turning center in UPDT [15, 18, 19]. Fortunately, UPFC does not have the aforementioned disadvantages associated with UPDT, but is capable of deterministically generating a surface of uniform quality with nanometric surface roughness and sub-micrometric form error. However, due to its intermittent cutting process, it is limited by poor cutting efficiency. Therefore, UPFC is more suitable for fabricating special surfaces. Generally, UPFC includes two cutting types. Fig. 1 shows the setup of diamond tools fixed with a spindle. One type, where the tool direction is parallel to the spindle axis, as shown in Fig. 1(a), is termed end-UPFC, i.e. end fly cutting [20]. The other type, where the tool is mounted with the spindle along the radial direction, as shown in Fig. 1(b), is termed radial-UPFC (UPRM) [21]. Additionally, the spindle can be set up horizontally or vertically. Table 1 shows UPFC classifications.

Tool direction

Spindle

Tool direction

Spindle

Spindle

Tool

(b)

Tool fixture

Spindle

Tool fixture

(a)

Tool

Figure 1. UPFC: (a) End-UPFC with the tool setup along the spindle axis, and (b) Radial-UPFC (UPRM) with the tool setup along the spindle radial direction Table 1. UPFC classification UPFC 1

Spindle Vertical axis

2 3

Horizontal axis

4

Diamond tools End [22-24] Radial [13, 21] End [20, 25, 26] Radial [27]

End-UPFC was originally used to fabricate large flat surfaces with a uniform surface quality. Early, it was designed to fabricate a large flat surface. Montesanti et al. [22] developed a diamond fly cutting machine that could accommodate a 100 kg workpiece with a 490 mm × 490 mm surface. Chen et al. [23, 24] also proposed an ultra-precision diamond fly cutting machine for producing a large KDP crystal flat surface at half metric scale. However, recently the fly cutting technique has been implented into UPM with a slow/fast tool servo to fabricate hybrid structural surfaces, such as micro-nano-structural freeform surfaces. The novel method has been adopted and developed fully by To et al. [20, 25, 26], combining a fast/slow tool servo with end-fly cutting in UPM, named an end-fly-cutting-servo system, to generate hierarchical micro-nano-structures [20]. Fig. 2 shows micro/nano-structures and a freeform surface with nano-structures, which provides a very promising method for the generation of hierarchical structures. UPRM can be employed to produce large flat surfaces, relatively large freeform surfaces, v-grooves, with uniform surface quality. Brinksmeier et al. [13] carried out diamond milling of a steel workpiece to obtain flat surfaces. Fang and Liu [27] used UPRM to fabricate micro-structures, such as micro channels, gratings, and prisms. Kong et al. [28] obtained F-theta lens insert for the replication of optical lenses. Wu et al. [29] used fly cutting technology to fabricate a micro optical waveguide mold that has a trapezoidal cross-section of 65 μm top width × 38 μm bottom width × 56 μm height.

(b)

(a)

(c)

Figure 2. Hybrid structural surfaces with (a) the configuration of the proposed novel end-fly-cutting-servo system in UPM: (b) micro-aspheric array with nano-pyramids, and (c) F-theta freeform surface with nano-pyramids [20] Table 2. General factors influencing surface generation, individual in UPFC and universal in UPM Cutting conditions Tool geometry Process factors

Cutting strategy

Step distance; Swing distance Nose radius; Edge radius; Rake angle; Clearance angle Horizontal cutting; Vertical cutting Up-cutting mode; Down-cutting mode

Tool path Tool wear

Crater wear; Flank wear; Fracture wear; Chipping

Kinematic error

Spindle; Slide; Positioning; Structure

Assembling error

Spindle; Slide; Table

Environmental conditions

Extra environment; Cutting heat

Dynamic Machine-tool vibration factors

Cutting speed; Feed rate; Depth of cut

Spindle vibration; Chatter vibration; Slide vibration; Table vibration; Tool tip vibration; Tool hold vibration

Material-induced vibration; Chip-formation-induced vibration; Dynamic error

Material

Material swelling and recovery; Material pile-up, burr, and defect; Non-uniformity

factors

Anisotropy; Chip formation; Surface separation; Material property change

3. Surface generation in UPFC UPFC, typical in UPM, is capable of fabricating special structural components with sub-micrometric form error and nanometric surface roughness. Thus, many factors are individual

in UPFC and universal in UPM that directly and indirectly affect surface generation. Significantly, through an optimum selection of the factors, good surface quality is achievable. The general factors include machine tools, cutting conditions, tool geometry, material property, chip formation, surface separation, tool wear, vibration, environmental conditions, heat deformation, and tool path, as summarized in Table 2. Essentially, due to the intermittent cutting mechanism in UPFC surface generation is governed by its distinctive mechanisms, mainly involving intermittent tool-workpiece relative motion, tool geometry reproduced on a machined surface, surface material separation with pile-up, burr and defect, and material swelling and recovery with deformation, as shown in Fig. 3.

Surface generation mechanisms Intermittent tool-workpiece relative motion General factors

Swelling and recovery Surface deformation Surface separation

Surface generation

Defect, burr, pile-up

Tool geometry Figure 3. Surface generation mechanisms

3.1 Surface generation modeling In cutting, surface topography is produced by the transaction between tool and workpiece. It is mainly governed by tool-workpiece relative motion, material deformation, and material separation with tool geometry and material property changes [2]. It reflects the kinematic and dynamic process and the material removal mechanisms in cutting. Fig. 4 shows a diamond-turned flat surface and a raster milled flat surface. In Fig. 4 (a), the turned flat surface is formed by the spiral tool path, while inn Fig. 4 (b) the raster milled flat surface is produced by intermittent scallop-like tool marks.

(a)

(b)

Figure 4. Surface topographies in (a) UPDT and (b) UPRM In Fig. 4, surface topographies in UPM are featured by tool mark, material swelling, vibration-/motion-error-induced waviness, material pile-up, and surface defect. The general factors influencing surface generation involve machine tool, environmental conditions, cutting

conditions, tool geometry, material factors, chip formation, tool wear, vibration, and tool path. [2]. In UPFC, cutting modes and cutting strategies falls into the general factors [30]. Input layer Static and dynamic characteristics of machine, metrology settings

Static and dynamic characteristics of machine, metrology settings

Output layer Machine tool model, diamond cutting tools, workpiece material, workpiece geometry

Recommended cutting strategy Optimum cutting conditions System performance

Model-based simulation system Freeform tool path simulator

Feed rate Workpiece geometry Spindle speed Tool-workpiece vibration Metrology information Material information

Surface topography simulation Module

Tool path simulator

Simulation results

Optimization module

Surface quality

Tool path simulator

Range of feed rate Range of spindle speed Range of depth of cut

Surface topography model

Range of vibration frequency Range of vibration amplitude

Surface topography

Roughness values

3D surface topography

Output

Spiral cut Raster cut

model Linear cut

Range of tool nose radius

Output Tool interference condition 3D tool locus

Cutting performance

Performance characteristics diagram

Optimum cutting strategy

Optimum surface quality

Optimum cutting conditions

Figure 5. The model-based surface generation system in UPRM [32] The surface generation technique is a powerful tool for (1) understanding surface generation mechanisms, (2) predicting surface generation, and (3) optimizing cutting conditions [2]. In UPFC, some research work has involved surface generation simulation by mathematical models, determined by the tool-workpiece geometrical relationship. The general surface generation model is a pure geometrical model [21, 31, 32]. In this model, the assumption is that the surface material will be cut rigidly. Cheung et al. [32] proposed a model-based surface generation system, which includes tool path generation, surface generation, and surface generation optimization. Fig. 5 shows their model-based surface generation system in UPRM. Further, they [21] developed a powerful surface generation model, which could be used to simulate surface topography, and predict surface form error. The flow chart of surface generation is shown in Fig. 6. However, the model was based on the assumption that the surface material was removed rigidly. Cheng et al. [31, 33] proposed a pure geometrical model to optimize machining conditions (tool tip geometry, spindle speed, depth of cut, feed rate, swing distance, and step distance) and cutting strategies (horizontal cutting and vertical cutting) and predict surface roughness in UPRM.

Fig. 7 presents the flow chart for surface generation optimization based on the geometrical relationship between tool and workpiece. Kong [34] established various surface roughness models to predict and optimize surface generation considering cutting mechanics and cutting strategies. In addition, Kong and Cheung [35] presented an integrated kinematics error model to analyze form error in UPRM of optical freeform surfaces to study motion errors and its effects on surface generation. In this model, the kinematic machine motion errors were taken into account fully with their effects on freeform surface generation. Input layer Workpiece dimensions Machining parameters Segment of axis in use Simulation system Compensation of swing distance and tool nose radius Ideal tool path generation Over-cutting detection model Slide moving error model Factual tool path generation 3D surface generation

Output layer Graphical display of form errors Parameters for 3D form errors Others Figure 6. Flow chart of the model-based simulation system in UPRM [21] Wang [30] built a three-dimensional holistic kinematic model for surface generation, in which cutting strategies had been taken into account. Wang and co-researchers [36] later developed a more complex model to predict and optimize surface generation. In this model, the tool path was considered thoroughly. Zhang et al. [37-39] developed a geometrical model to study the effect of tool wear on surface generation, which represents the relationship between worn tool geometry and surface topography, and makes it possible to monitor diamond tool wear. Zhang and To [40, 41] developed a dynamic model, integrated with a spindle vibration model, to study the effect of spindle vibration on surface topography. Sun et al. [42] developed a machining performance forecasting method integrated with cutting simulation, machine tool dynamic performance simulation, and a control system, considering the interaction between manufacturing process and machine tool. Chen et al. [43-47] established a surface generation model with machine tool dynamics. Based on the model, a novel machine tool design method bridged the gap between machine tool performance and surface topography by optimizing machine tool dynamics to improve its strength and stiffness.

All the models mentioned above are geometrical models only. Wang et al. [30, 48] firstly built up a surface generation model considering material swelling and recovery. The swelling and recovery material distorted surface topography. Although their model used material factors, the material factors are not taken into consideration fully. To a certain extent, it takes an impact upon surface generation through material swelling and recovery [30], material pile-up [41]/ burr formation [27], material effects [48, 49] etc. The material factors were only studied experimentally, but the theoretical relationship between surface generation and material factors was not clearly discussed. More efforts should be carried out to study surface generation mechanisms considering material factors. Fig. 8 shows the development for a surface generation model from pure geometrical models, then to dynamic models, finally to integrated models.

Define minimum surface roughness criterion

Cutting parameters (i.e. range and interval) V, f. r, R, ε, F, d

Workpiece dimensions

Cutting strategies

Construct an array of cutting conditions being considered

Calculate the surface roughness parameters (i.e. Rq and Rt) for all cutting conditions being considered

Calculate the approximate machining time for all the cutting conditions being considered

Critical ranges for each cutting parameters as reference

Search the appropriate cutting conditions as the minimum surface roughness criterions

A series of performance characteristics diagrams

Search the appropriate cutting conditions as the minimum machining time, and the minimum surface roughness conditions

Suggested optimal cutting conditions

Recommended cutting strategy

Figure 7. Flow chart of surface generation optimization in UPRM [31]

Pure geometric model +Cutting conditions +Tool geometry

Dynamic model

Integrated model

+Relative vibration

+Material factors

Figure 8. Development of surface generation in modeling [2]

3.2 Machine tool An UPFC machine is a high stiffness and damping system. Its kinematic and dynamic characteristics are the important factors affecting such a high quality surface with nanometric surface roughness and sub-micrometric form error. Montesanti et al. [22, 50] adopted

high-loop-stiffness and high-resolution measurement and control to design a vertical-axis diamond fly cutting machine for producing flat half-meter scale optics. It reached up to a flatness of 0.1 μm and a roughness of 10 nm. Liang et al. [43] analyzed the kinematic chain and configuration of machine tools to optimize an UPFC machine design under much higher requirements for surface roughness and flatness. Functional requirement analysis

Conceptual design Kinematic chain analysis

Configuration analysis

Component design

Integrated dynamic design modal Mechanical structure

Electrical equipment

Control system

Simulation model

Interference factor ……

Spindle runout

Pressure fluctuation

Ground vibration

Cutting force

[M] [C] [K]

FE modal

Mathematical model

Predicted surface

No

Judgment Yes Prototype

Figure 9. Framework of machine tool design for the functional requirements of workpiece [43] Mechanical system Components Servo system Control system Electronic system

A

B

System A

C

Machining performance Surface topography Servo performance

B C

Figure 10. Mechanical design: analytical modeling [23] and finite element modeling [51, 52] In addition, Liang et al. and Chen et al. [51, 52] designed and optimized an UPFC machine for machining a large KDP crystal surface by analyzing its kinematic and dynamic performances to improve its strength and stiffness using finite element modeling and modal testing. For surface waviness induced by machine tool dynamic characteristics, a control method was proposed. Fig.

9 illustrates the design approach of machine tool based on the functional requirement of workpiece. Moreover, Liang et al. [23] proposed a mechanical structure-based design method for UPFC. The method took full account of the effect of dynamic performance of the mechanical control system on surface generation to optimize the hydrostatic slide and the air-spindle structure. Fig. 10 shows the mechanical design method to analyze the effect of kinematics and dynamics on surface generation using analytical modeling and finite element modeling. Chen et al. [44] used a two-round design method for machine tool design termed “design-simulation-experiment-simulation-redesign-experiment” strategy. It comprises a machine tool structure design, machine tool optimization based on machined surfaces, and simulation models (finite element model, dynamic model and mathematical model) to improve machine tool performances. The main factors for all specifications were determined by the method. In addition, Sun et al. [45] proposed an error budget method for designing and characterizing machine tools taking into account the kinematic and dynamic errors of machine tools and its effect on surface generation. The errors cover spindle motion error, slide motion error, machine-tool-structure induced error, and environment-vibration induced error.

Before

After

MS

RMSG

MS

RMSG

Figure 11. Finite element modeling of dynamics of machine tool and its effects on the measured surfaces and their corresponding the root mean square gradient after and before optimized (MS: measured surface topography; RMSG: root mean square gradient) [46] Chen et al. [46] increased dynamic stiffness to reduce its effects on the root mean square gradient, considering that the root mean square gradient was a key parameter for KH 2PO4 crystal of low frequency wave-front influencing the focusing performance in the inertial confinement, which results from the dynamic performance of the machine tool. Fig. 11 shows the dynamic performance of a machine tool analyzed by finite element modeling and its effects on the

measured surfaces and their corresponding root mean square gradient after and before optimization. Chen et al. [47] also proposed a new machine tool design method based on surface generation simulation. The model quantitatively analyzes the effect of straightness, dynamic stiffness, and frequency of machine tool on surface topography. Overall, the system-loop stiffness, dynamics, and control are fully considered to improve the machine tool performances to guarantee the machined surface quality by increasing the machine-tool strength and stiffness and by optimizing the machine-tool design structure. Kong and Cheung [35] built an integrated kinematics error model, considering the machine kinematic motion errors in UPRM. The model was used to predict the effects of the machine kinematic motion errors on freeform surface errors. It shows that form error majorly originated from the machine kinematic motion errors, i.e. slide errors [21, 28]. Chen et al. [53] found that in flat fly cutting of a KDP crystal the spatial position during each cutting path caused a convex surface, which was reduced by a novel adjusting mechanism. It was designed to adjust the axis of the spindle and the workpiece slightly forward to the slide, rather than being completely vertical. Zhang et al. [54] discussed the spindle inclination error in UPRM and developed a novel spindle inclination error identification and compensation method to establish the relationship between the spindle-tilting angle and the tool mark direction. This method is efficient for calibrating the spindle-tilting angle and for reducing the machining error. Although machine tool kinematic motion errors in UPFC have been fully studied, machine dynamic motion errors have not fully been discussed in depth and little relevant research has been reported. Moreover, assembling errors for machine tools have not been studied sufficiently with regard to their effects on surface generation in UPFC, especially multi-axis UPRM. Much research work should be carried out on the effects of dynamic motion errors and assembling errors on surface generation not only in UPFC but also in all UPM. 3.3 Machining conditions In UPFC, cutting strategies, tool path, and kinematic motion errors are crucial to the form accuracy of freeform surfaces, and cutting conditions, tool geometry, cutting strategies and tool wear are the key factors influencing surface generation [28]. Table 2 shows the general factors influencing surface generation, individual in UPFC and universal in UPM. Cheng et al. [31, 33] conducted a theoretical and experimental investigation into surface generation in UPRM and developed a surface generation model to optimize cutting conditions in order to improve surface quality. They also discussed in depth the effects of machining conditions (tool tip geometry, spindle speed, depth of cut, feed rate, swing distance, and step distance) and cutting strategies (horizontal cutting and vertical cutting) on surface roughness. Kong et al. [28, 34] conducted an experimental and theoretical investigation into the effects of various factors on surface generation in UPRM. They found that cutting conditions, tool geometry, tool wear, and cutting strategy had a major effect on surface roughness, while cutting strategies, tool path, and slide error had a significant impact upon form accuracy with slide errors. In Kong’s thesis [34], different models were developed to predict and optimize surface generation. A model-based simulation system with a tool-path-generation model was developed to predict and optimize form generation, taking into account cutting mechanisms, tool path, and cutting process. In the tool-path-generation model, the errors are compensated for the tool nose radius and swing distance, and the tool path is produced under surface residual error

requirements. Wang [30] theoretically and experimentally studied the effect of cutting strategy with tool path on surface generation in UPRM. In addition, the cutting strategy optimization methodologies and quality-optimal and time-optimal strategies optimizing cutting parameters and tool path were established to achieve ultra-precision freeform surfaces in an efficient way. It was found that shift length, tool interference, and tool path affected surface generation. Shift length means the relative distance among adjacent cuttings / tool marks. Tool interference means that some areas left ideally by the previous cuttings are removed by the preceding cuttings. Furthermore, Wang et al. [36] developed a new integrated optimization method for cutting parameters and tool path with surface-roughness-prediction models for machining time in UPRM. The method optimized feed rate, path interval, shift length, and entry distance with tool path for the best surface quality in a given machining time. The method is well supported by the experimental results. Fig. 12 shows that when it is 0.5, the surface roughness is minimal.

Figure 12. Effect of the entry distance (shift length) on surface roughness under horizontal cutting in UPRM [36] Overall, the current models are capable of predicting surface generation and optimize machining conditions to improve surface quality and reduce machining time. However, the influence of workpiece surface geometry on surface generation has been ignored. For machining of freeform surfaces under constant machining conditions, surface curvature variations will results in non-uniform material pile-up that forms a non-uniform surface quality. Hence, modulating machining conditions can be used to improve surface quality or guarantee uniform surface quality. 3.4 Material factors Material factors cover material swelling and recovery, material pile-up/bur formation, and

material effects, all of which affect tool life, machining accuracy, and surface quality, whilst material properties are influenced by the cutting processes. Some scholars have paid attention to material removal mechanisms in UPFC. To et al. [55] reported that UPRM induced microstructural changes and phase decomposition at the milled surface of Zn-Al alloy. With increasing depth of cut, microstructural changes and phase decomposition accelerated and further increased depth of cut might induce structural recoveries. The deformation surface depth was about 400 nm. Zhu et al. [56] further found that UPRM caused plastic deformation and consequently induced phase decomposition at a surface layer with a thickness of about 250 nm.

(a)

(c)

(b)

Figure 13. Material-induced surface roughness under the machining conditions (depth of cut of 3 μm, spindle speed of 2000 rpm, feed rate of 300 mm/min, step distance of 30μm, tool nose radius of 2.453 mm, swing distance of 38.23, rake angle of 0o, and flank angle of 12.5o, horizontal cutting, up-cutting mode, and coolant-on): (a) copper, (b) Al6061, and (d) albronze [48]

(a)

(b)

Figure 14. Workpiece material effect on burr formation: (a) brass and (b) copper at cutting speed of 350 m min-1, undeformed chip thickness of 10 μm, and 80 nm edge radius of a diamond [27] Wang et al. [57] found the cutting-induced heating effect in UPRM based on the study of the time–temperature-dependent precipitation of Al 6061. UPRM resulted in the phase precipitation of Al6061 and the cutting temperature at a raster-milled surface was over 500°C. Furthermore, Wang [30] and Wang et al. [48, 49] theoretically and experimentally studied the effect of workpiece materials on surface roughness in UPRM. It was found that elastic recovery affected surface finish. Albronze had the greatest effects on surface quality due to its hardness and fast elastic recovery, and the machining of copper produced the lowest surface roughness, when the feed rate was less than 300 mm/min. The cutting-induced precipitation at the milled surface of Al6061 produced imperfections that degraded surface quality. Fig. 13 clearly shows the effects of different materials on surface topographies under the following machining conditions: depth of

cut of 3 μm, spindle speed of 2000 rpm, feed rate of 300 mm/min, step distance of 30 μm, tool nose radius of 2.453 mm, swing distance of 38.23 mm, rake angle of 0o, and flank angle of 12.5o, horizontal cutting, up-cutting mode, and coolant on. In fly cutting, due to cut-in / cut-out burrs form along feature edges, which are the main negative influence on surface quality in micro cutting. There are many factors influencing burr formation, such as cutting speed, undeformed chip thickness, tool sharpness, tool feed mode, workpiece edge geometry, and workpiece material properties [27]. Fig. 14 shows the effect of workpiece materials copper and brass on material burrs. Fang et al. [27, 58, 59] carried out a theoretical and experimental study of burr formation in UPRM. They found that exit-burrs could be reduced less than 25 nm in height through the selection of optimal cutting parameters (cutting speed of 400 m/min and feed rate of 20 μm/rev.). The parameters were obtained by experimental cutting tests and theoretical analysis. Undeformed chip thickness and tool sharpness were the most important factors. Cutting speed did not seem to reduce burr size. The larger the tool edge radius was and the more ductile the workpiece, the larger the burr size. The sharper the tool was, the smaller the tool edge angle, and the bigger the edge angle of workpiece (the angle between workpiece edge and cutting direction), the smaller the burr size. Jacob et al. [60] employed fly cutting to study ductile-brittle transition and critical depth of cut of 6H-silicon carbide. They found that the transition depth was about 70 nm, and the thrust cutting forces increased with the increase of depth of cut while the main cutting force did not. It is an efficient method to observe the ductile-brittle transition and critical depth of cut on cut surfaces of brittle materials. Peng et al. [61] studied critical ductile-brittle transition depth of cut in fly cutting. Using small feed rates and large negative rake angles, the ductile removal area was much larger and the surface was much smoother with fewer cracks. They also found that fly cutting was highly suitable for the ductile removal of brittle materials. Fig. 15 schematically shows the ductile-brittle

Tool

transition of brittle material in fly cutting.

Ductile removal area

Brittle removal area

Figure 15. Schematic diagram for ductile-brittle transition of brittle material in fly cutting Li et al. [24] proposed that mid-frequency waviness and subsurface crack were two fundamental factors damaging KDP crystals in UPFC, which affected the laser-induced damage threshold of KDP. Smaller feed rate and depth of cut improved the KDP threshold. Sun et al. [45] reported surface damage in the machined surface of KDP crystals after fly cutting. They owed it to the spatial frequency error from dynamics and kinematics of machine tools. The surface damage would degrade product performances. Over all, some significant results have been obtained, but much theoretical work needs to be conducted on the relationship of material factors and surface generation. Material swelling and

recovery, tool mark irregularity, surface cracking, and material separation, should be taken more attention. It is important to have a comprehensive understanding of material removal mechanisms. 3.5 Cutting forces In diamond fly cutting, cutting force is an important indicator in cutting mechanisms and the selection of machining conditions, as it reflects surface characteristics, system dynamics and tool wear. In UPFC, the cutting force is periodically intermittent. Some research work has been conducted to measure cutting forces, analyze cutting force characteristics, and establish a cutting force model in UPFC. Yin et al. [62] analyzed cutting forces in UPRM to study diamond tool wear and attempted to establish the relationship between them. Cutting force is a key indicator of diamond tool wear. Zhao et al. [63] proposed a mechanistic cutting force model taking into consideration material hardness, elastic modulus, uncut chip area, tool geometry and the average value of shear angle, respectively, which well predicted the cutting force in diamond fly cutting of a microstructural surface. Jacob et al. [60] and Peng et al. [61] measured cutting forces to analyze the ductile-brittle transition of brittle materials. The thrust cutting forces increased with the increase of depth of cut, but the main cutting force did not [60]. To and Zhang [64] and Zhang [65] developed an analytical model to predict the main and thrust cutting forces in UPRM of V-grooves. They discussed the effect of machining conditions on cutting forces. It was found that the cutting forces increased with feed rate and depth of cut, which were more sensitive to larger depth of cut and higher feed rate. Furthermore, it was observed that a characteristic frequency of the measured cutting forces in UPRM was an indicator of diamond tool wear [65, 66].

Tool wear Cutting forces

Material removal

Tool geometry

Pile-up/burr/side/crack effect/etc. Material property change Swelling and recovery Surface Integrity (Surface roughness, form error, residual stress) Figure 16. Tool wear effects on surface integrity in UPDM

3.6 Tool wear In UPM, diamond is an exclusive material employed as a tool. Slight diamond tool wear will be

imprinted into an ultra-precision machined surface to further downgrade nanometric surface quality [28]. The loss of original cutting-edge accuracy and the consequent fluctuation in cutting force will degrade machining accuracy. DTW increases cutting force, which accordingly influences residual stress, material properties, chip formation, form error, and surface roughness. The relationship is presented in Fig. 16. Especially in cutting brittle materials, DTW results in an undesirable ductile-brittle transition, which further deteriorates surface quality and shortens tool life. The relationship among them is also extremely complicate, although some research attempts have been conducted to discuss the effects of DTW on surface integrity.

Original image of fly-cutter rake face

Median filtering

Edge detection of

Threshold segmentation

outer contour Hough arc transform of outer-contour

Elimination of feigned wear lands

Combination

Inner-contour polynomial fitting

Auto-regressive calibration

3D topography of tool wear lands

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Figure 17. Flow chart of 3D reconstruction of diamond tool wear in UPRM [68] Some research has been carried out to study diamond tool wear and its effect on surface generation in UPFC. Yin et al. [62] conducted copper UPRM to investigate DTW characteristics using the acoustic emission technique and cutting force measurement. They found that diamond tools were particularly prone to microchipping wear. With the increase of the cutting distance, microchippings rose, acoustic emission RMS and main cutting forces became lower, and thrust cutting forces became higher. Brecher et al. [67] stated that cutting forces increased with increasing wear (rounding) of the cutting edge. Zhang [65, 66] also found that in the power

spectrum of cutting force a characteristic frequency increased with tool wear evolution in UPRM. It can be employed to detect diamond tool wear in UPRM.

(a)

Fracture 1

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Figure 18. Surface generation and cutting chips influenced by tool fracture wear and tool flank wear in UPRM of CuZn30: (a) the surface topography with a new diamond tool, (b) the surface topography with the facture worn diamond tool, (c) the fracture worn diamond tool, (d) the chip with the facture worn diamond tool, (e) the chip with the new diamond tool and (f) the chip with the flank worn diamond tool [37-39] Based on digital image processing technique, Zhang et al. [68] developed a new measurement method for diamond tool wear in UPRM. In the method, the image was captured by a CCD camera under a 100X optical system, and then an autoregressive calibration method was used automatically to calculate its 3D topographic surface, wear area, maximal wear width, average wear width, and average worn volume. Fig. 17 shows the method for 3D reconstruction of a worn diamond tool in UPRM. This method provides the possibility of in-situ measuring diamond tool wear in UPM.

Zhang et al. [37-39] established a relationship between diamond tool wear and surface generation with chip formation to quantitatively estimate diamond tool wear in UPRM of CuZn30. Fig. 18 shows the effects of fracture wear and flank wear of diamond tools on surface generation and chip formation. In Fig. 18(b), the fracture wear was imprinted on the machine surface to form ridges. However, in Fig. 18(a) for a new tool no rides were observed. Fig. 18(c) presents the SEM image of the fracture wear. In Fig. 18(d), the fracture wear left ridges on the chip. In Fig. 18(f), the flank wear shortened the chip size, less than that for a new tool in Fig. 18(e). After observing chip formation, diamond tool wear could be derived using the proposed relationship and then surface roughness could be obtained. Hence, by observing chip formation it is a possible by an on-line indirect method to detect diamond tool wear under a nanometric resolution. Furthermore, as UPFC is an intermittent cutting process, it can suppress diamond tool wear by controlling cutting contact and cooling time [69] when machining difficult-to-cutting materials. Milling is also more flexible in the fabrication of freeform surface components for molding replications [42]. Therefore, more research work should be carried out deeply to study monitoring, controlling and mechanisms of diamond tool wear thoroughly. Overall, tool wear is a process factor that deteriorates surface quality if a tool is worn severely. Tool wear affect surface generation directly and indirectly through a vicious-circle process whereby the worn tool increases cutting forces that enhance vibration in a cutting process and the vibration not only downgrades surface quality but also increases cutting temperature and cutting pressure to accelerate diamond tool wear. Therefore, more studies should be conducted on the control, suppression, and detection of diamond tool wear. 3.7 Vibration Vibration is a natural process in UPM and is a crucial factor influencing surface generation. Generally, it covers tool tip vibration, spindle vibration, slide vibration, and table vibration [1] affecting surface roughness and form accuracy. In UPFC, the vibration is a distinctive dynamic response, due to the periodical intermittent excitation of cutting forces, which produce a significant impact upon surface generation. Liang et al. [70] analyzed the effect of tool vibration on surface topography under intermittent cutting forces in UPFC. It was found that some defects on the machined surface of KDP were induced by tool-tip vibration. Some researchers [23, 42-47, 51, 52, 71] fully considered the effects of machine tool dynamics on surface generation to optimize the UPFC machine design by increasing the strength and stiffness of machine tools. Spindle vibration plays a key role in influencing surface generation in UPFC. Marsh et al. [72] first reported the fluctuation of surface profiles induced by spindle vibration in fly cutting. An et al. [73] established a dynamic model for tilting vibration of spindle and discussed its effect on surface generation in UPFC. Zhang and To [40, 41], and Zhang [74] developed a five-DOF dynamic model for spindle vibration in UPRM. The results show that axial vibration, radial vibration and coupled-tilting vibration influence surface topography. The coupled-tilting vibration in UPRM produces ribbon-stripe and irregular patterns in UPRM, as shown in Fig. 19 (a). End-UPFC forms periodical patterns, as shown in Fig. 19 (b). This is due to the distinctive dynamic responses of spindle vibration under the different excitation of cutting forces. Some great contributions have been made and some significant results have been achieved from the investigation into vibration and its effect on surface generation. In UPFC cutting forces

intermittently and periodically act on the machine tool system, which may cause a self-excited vibration, i.e. chatter vibration, and even may catastrophically deteriorate surface quality. Generally, Chatter vibration will take place when the machine-tool vibration is synchronous with the excitation of cutting forces. However, an in-depth investigation needs to be conducted into why chatter vibration has not been observed in UPM.

(a1)

(a2)

(b1)

(b2)

Figure 19. Surface topographies in (a) UPRM [41] and (b) end-UPFC [73]: (1) simulated and (2) measured

4. Challenges and opportunities Fly cutting in UPM, termed UPFC, has been developed to fabricate special structural components with nanometric surface roughness and sub-micrometric form error due to its great flexibility. There are two types of UPFC: UPRM is used to fabricate relatively large freeform surfaces and v-grooves, while end-UPFC is employed to fabricate large flat surfaces, or periodical microstructures such as compound eyes. Additionally, UPFC provides uniform surface quality for surface generation as well as having a great potential for fabricating real micro/nano-structures or hybrid structures with slow/fast tool servo techniques. Some research, which has already been carried on such applications of UPFC, suggests that it will bring out a great significance in the future. Due to the complexity of the cutting process, many factors affect extremely high quality surfaces, some of which are individual to UPFC and some of which are universal in UPM. Although many efforts have been made to study these factors, some physical surface generation mechanisms in material removal are not fully understood, including intermittent tool-workpiece relative motion, tool geometry imprinted into the machined surface, surface material separation with pile-up, burr and defect, and material swelling and recovery with deformation. In particular,

surface material separation and deformation has not attracted much attention. Moreover, a physical surface generation model requires a comprehensive knowledge of all physical surface generation mechanisms. Therefore, the surface generation model integrated with material factors needs more attention. Furthermore, in machining of freeform surfaces under constant machining conditions, due to surface curvature variation non-uniform material pile-up will occur. Hence, modulating machining conditions is a possible method for surface generation optimization. Although vibration is intrinsic in machining, the investigation into physical mechanisms of vibration and its influence on surface generation has not been adequate. Even though chatter vibration may take place in UPFC because of the intermittent cutting process, little research has been reported on this topic. More attention should therefore be paid to studying chatter vibration. Active control is a possible method to eliminate or reduce the effect of vibration on surface generation in UPM if real-time vibration can be detected on-line. Significant advances have been made over the years in the understanding of diamond tool wear in UPM have been made over last decade years, including wear mechanisms, wear monitoring and controlling, and wear modeling. However, some mechanisms of diamond tool wear are still not fully understood, particularly in relation to improving cutting performance of diamond tools, reducing diamond tool wear, and prolonging diamond tool life. More effort should also be made to study on-line monitoring of diamond tool wear in order to enhance surface quality. Moreover, because difficult-to-cut materials causes rapid diamond tool wear, it is of great significance to develop an efficient method to control diamond tool wear and to theoretically explore its physical mechanisms.

5. Conclusions By applying fly cutting to ultra-precision machining (UPM), ultra-precision fly cutting (UPFC) has been developed, where diamond tools rotate with a spindle to remove surface material through an intermittent cutting process. Consequently, it is more flexible for the fabrication of freeform and micro/nano-structural surfaces, such as v-grooves and pyramids, but low in machining efficiency. It not only provides uniform high surface quality with sub-micrometric form error and nanometric surface roughness but also leads to different surface generation mechanisms through its distinctive fly cutting mechanism. With regard to UPFC, many studies have been undertaken with significant results. Key information concerning UPFC is summarized as follows: (1) UPFC covers two types. One is ultra-precision raster milling (UPRM), in which the diamond tool direction is parallel to the radial direction of the spindle. It can be employed to fabricate a relatively large freeform surface and v-grooves and honeycomb-shaped surface topography is formed by UPRM. The other type is end-UPFC, in which the diamond tool direction is parallel with the spindle axis. End-UPFC is generally used to fabricate large flat surfaces, or periodical microstructures. For example, it combines with slow/fast tool servo to fabricate compound eyes with uniform surface quality. The stripe-like surface topography is produced by end-UPFC. (2) Surface topography in UPFC consists of tool marks, material swelling and recovery, vibration induced waviness, machine tool motion errors, material pile-up, and material crack/surface wrinkle/fracture/defect/dimple. It is influenced by cutting conditions, tool geometry, material factors (material property change, material swelling and recovery, and material separation

mechanism), kinematic and dynamic errors of machine tool, assembling errors, cutting strategies, tool path, and tool wear. Some are individual to UPFC and some are universal in UPM due to the distinctive fly cutting mechanism, and affect surface topography through distinctive surface generation mechanisms involving intermittent tool-workpiece relative motion, tool geometry imprinted into a machined surface, and surface material separation and deformation. (3) With a focus on surface generation in UPFC, more research should focus on the kinematics and dynamics of machine tool, material separation and deformation mechanism, diamond tool wear, and vibration. In addition, it is possible that in the future UPFC will be capable of fabricating real micro/nano-structures or hybrid structures with fast tool servos / slow tool servos, and ultra-sonic vibration, which will be of great significance.

Acknowledgments The work is supported by the National Natural Science Foundation of China (Grants no. 51405217 and 51275434), the Youth Science Foundation of Jiangxi Province of China (Grant no. 20142BAB216025) and Jiangxi Educational Committee of China (Grant no. GJJ4210), and the Research Grants Council of the Hong Kong Special Administrative Region (Project no. PolyU 5263/12E).

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Grapghical abstract

Highlights

(1) Fly cutting in UPM, i.e. UPFC, applied into surface generation is surveyed. (2) UPFC causes distinctive surface generation mechanism. (3) It is highly flexible to fabricate the special structural surfaces. (4) The key issues in UPFC are drawn. (5) The challenges and opportunities with some speculations are proposed.