## Abstract

This article is written as a tribute to Professor Frederick Fongsun Ling 1927–2014. Single-point diamond machining, a subset of a broader class of processes characterized as ultraprecision machining, is used for the creation of surfaces and components with nanometer scale surface roughnesses, and submicrometer scale geometrical form accuracies. Its initial development centered mainly on the machining of optics for energy and defense related needs. Today, diamond machining has broad applications that include the manufacture of precision freeform optics for defense and commercial applications, the structuring of surfaces for functional performance, and the creation of molds used for the replication of a broad range of components in plastic or glass. The present work focuses on a brief review of the technology. First addressed is the state of current understanding of the mechanics that govern the process including the resulting forces, energies and the size effect, forces when cutting single crystals, and resulting cutting temperatures. Efforts to model the process are then described. The workpiece material response when cutting ductile and brittle materials is also included. Then the present state of the art in machine tools, diamond tools and tool development, various cutting configurations used, and some examples of diamond machined surfaces and components are presented. A discussion on the measurement of surface topography, geometrical form, and subsurface damage of diamond machined surfaces is also included.

## 1 Introduction

Cutting processes performed with single crystal diamond tools, commonly referred to as single-point diamond machining or simply diamond machining, have emerged as an important class of cutting processes for the creation of surfaces with low surface roughness and high form accuracy. The processes can be considered a subset of a broader class of processes characterized as ultraprecision machining processes. Today, diamond turning and diamond milling can achieve surface roughnesses, Sa, of 1–10 nm depending on the machining processes parameters and the workpiece material, and peak-to-valley form accuracies of 0.1–1 µm depending on the workpiece size and shape [1]. Single-point diamond machining is performed on an extreme accuracy, high stiffness machine tool that typically has hydrostatic slides and an aerostatic or hydrostatic spindle. The slide positions are measured by linear encoders. A specially prepared single crystal diamond tool is used, and machining is performed under carefully controlled temperature and vibration conditions. The process is routinely used to machine ductile materials such as aluminum, copper, and electroless nickel, as well as brittle materials such as germanium, silicon, zinc sulfide, and potassium dihydrogen phosphate (KDP). Current diamond machined components include individual diffractive or reflective optics, as well as metal molds used for the mass production of a variety of replicated optics produced by injection or compression molding, or hot isothermal pressing of glass. In recent years, the machining processes have been used for the creation of flat or axisymmetric surfaces and have also become an enabling technology for creating freeform and structured surfaces as well.

The technology had its historical origins in the early 1900s, however accelerated in the 1960s with work performed, principally at the U.S. national laboratories, for energy and defense related needs. In the early 1960s at the Y-12 facility in Oak Ridge, single-point diamond turning was first performed using single crystal diamond microtome knives [2]. In the 1970s and 1980s, further development of the machining technology continued at other U.S. national laboratories and defense contractors. Early pioneering work at Lawrence Livermore National Laboratory resulted in some of the most advanced diamond turning machines of that period. This includes the development of Diamond Turning Machine Number 3 (DTM 3) [3], the Large Optics Diamond Turning Machine (LODTM) [4], and the Precision Engineering Research Lathe (PERL) [5]. At that time, machine tool development was also underway at the Cranfield Unit for Precision Engineering (CUPE) in the UK which designed and built a vertical axis diamond turning machine [6]. Examples of some initial applications of diamond turning were for the manufacture of infrared reflective optics [2], annular resonator optics [4], and X-ray telescope mirrors [6].

This paper focuses on a brief review of the technology for cutting with diamond tools. No attempt has been made to be all inclusive. We first address the current understanding of the mechanics that govern the process including the resulting forces, energies and the size effect, forces when cutting single crystals, and resulting cutting temperatures. Efforts to model the process are then discussed. The workpiece material response when cutting ductile and brittle materials is also included. Then, we present the state of the art in machine tools, diamond tools and tool development, various cutting configurations used, and some examples of diamond machined surfaces and components. A section on the measurement of topography, form, and subsurface damage is also included.

## 2 Process Mechanics

### 2.1 Forces and Energies.

For conventional orthogonal cutting, the principal regions of energy dissipation which result from chip formation are shearing in the shear zone (I.a, the primary shear zone), and sliding of the chip along the rake face of the tool (I.b, the secondary shear zone), as shown in Fig. 1 [7]. An additional region of energy dissipation may exist due to sliding at the tool–workpiece interface due to tool flank wear or workpiece elastic recovery (II). When the tool has a negative rake angle, or when the depth of cut (uncut chip thickness for orthogonal cutting) is on the order of the tool edge radius, presenting the workpiece with an “effective” negative rake angle, a third contribution to energy dissipation due to plowing (III) results.

Fig. 1
Fig. 1
Close modal

The seminal experiments of Backer et al. [8] were the first to show that specific cutting energy increases with a decrease in the scale of the deformation zone, and this behavior was termed the “size effect.” They performed experiments on turning, micromilling, and grinding and found that the ratio of thrust force to cutting force increases with decrease in depth of cut. In the pioneering work of Nakayama and Tamura [9], it was recognized that additional zones of energy dissipation, not operative when cutting at conventional depths of cut, may take on more importance when the depth of cut is very small. They attributed the increase in energy dissipated to an extension of the shear zone below the workpiece surface. They considered this dissipated energy as one source of the “size effect.” It was also recognized that the effective rake angle of the cutting tool at depths of cut comparable with the tool edge radius also was a contributor to the size effect. In some of the first experiments that measured forces when cutting with diamond tools, Furukawa and Moronuki [10] and Moriwaki and Okuda [11] found that the size effect dominated the force system when machining at submicrometer depths of cut. Since the time these first experiments were performed, it has been well documented in the literature that there is a change in cutting mechanics that occurs when the tool edge radius (edge geometry) becomes on the order of the depth of cut. The effect of plowing becomes important and the specific cutting energy increases with decrease in depth of cut. The process can be thought of as transitioning from a cutting dominant process to a plowing/sliding dominant process as depth of cut decreases [12].

It is not only the size of the tool edge radius that affects the cutting and thrust forces but also the shape of the cutting edge. What starts out to be a true radius for a new tool can become an elongated profile with a wear flat on the flank face of the cutting tool. Edge radii of single crystal diamond tools have been reported to be between tens of nanometers [13] to several hundred nanometers [7]. Accurate characterization of the diamond tool edge geometry has been shown to be challenging due to its size, however various methods have been developed [1416]. In a study on the effect of tool edge geometry on energy dissipation in orthogonal diamond flycutting of Te-Cu, cutting and thrust forces were measured for new and worn tools. Figures 2 and 3 show the significant effect tool geometry has on the force system when the tool edge geometry is on the order of the uncut chip thickness. Figure 4 shows that as the uncut chip thickness is decreased there is a rotation of the resultant force vector toward the workpiece surface normal [12].

Fig. 2
Fig. 2
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Fig. 3
Fig. 3
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Fig. 4
Fig. 4
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Studies of the forces resulting from the diamond machining of single crystal materials have also been performed. Moriwaki et al. [13] studied the orthogonal diamond flycutting of single crystal Cu at nominal depths of cut from 3 µm down to 10 nm. They found that when the depth of cut was greater than 1 µm the cutting force varied with crystallographic direction of the workpiece. Below 1 µm, the workpiece crystallographic direction had no effect on the chip formation process or the resulting forces. Burnishing of the near surface by the cutting tool and the resulting amorphous-like damage layer was implicated as the cause. Yuan et al. [17] investigated the effect of crystallographic orientation on the cutting forces in the diamond cutting of single crystal Cu and Al with a 5 µm depth of cut. They found that crystallographic direction had a significant effect on the resulting cutting forces, and that the measured variation in cutting force compared well with analytical results from a microplasticity model. Similar studies investigating the variation of cutting force with crystallographic direction have also been reported for diamond machining Cu [18] and KDP [19] single crystals.

In one of the first experimental investigations of the resulting temperatures in diamond cutting, Iwata et al. [20] measured both the cutting temperature and workpiece temperature when diamond flycutting oxygen-free Cu (OFC) with both a single crystal diamond tool and a sintered diamond tool. They used the Cu workpiece and a constantan wire as a dynamic thermocouple to measure the cutting temperature. They found that when cutting with a small depth of cut and feedrate, the sharpness of the cutting edge and the grain size of the sintered diamond had a large effect on the cutting temperature. When diamond face turning an Al alloy, Moriwaki et al. [21] found that the tool shank temperature rise can reach up to 10 °C. The temperature rise of the workpiece was found to be much lower than that of the tool. For high-speed quasi-orthogonal diamond cutting of OFC Cu, Moriwaki et al. [22] found that the workpiece temperature at the cutting zone, as measured by a dynamic thermocouple, could reach 270 °C above the average workpiece temperature when cutting with a 1 µm depth of cut at 4.3 m/s. Ueda et al. [23] used a two-color pyrometer to measure the tool temperature on the rake face when diamond cutting Cu and Al. For a 10 µm depth of cut, they found maximum rake face temperatures of 190 °C for Al and 220 °C for Cu. In a study on ultraprecision raster milling of Al 6061, Wang et al. [24] proposed a new method to quantify heat generation by cutting. They used the time-precipitates-temperature characteristics of Al 6061 alloy to quantify the temperature of the workpiece.

There has been a substantial amount of interest in modeling the ultraprecision machining process. Models have been put forth that are based on molecular dynamics (MD) simulations, finite element analyses, and analytical approaches. Atomic scale cutting or nanometric cutting has been investigated by MD approaches. In early work, Ikawa et al. [25] developed an atomistic model that investigated the chip formation process and the effect of tool edge radius on the minimum thickness of cut when cutting Cu and Al with a diamond tool. They found that while the minimum thickness of cut is dependent on the tool–workpiece interaction, it is much more dependent on the tool edge radius. They concluded that the minimum thickness of cut may be on the order of one-tenth of the tool edge radius. In a similar study [26], it was found that the cutting mechanism depends on the crystallographic orientation of the workpiece and the interatomic potential between the tool and workpiece materials. Using a MD simulation, Komanduri et al. [27] further investigated the crystal orientation and the cutting direction when cutting single crystal Al. Molecular dynamics simulations were also used to investigate the material removal mechanisms in the nanometric cutting of a metallic glass [28], the effect of the tool edge radius in the nanometric cutting of single crystal Si [29,30] and the effects of surface structured diamond tools on the cutting of single crystal Si [31].

A variety of studies focused on finite element analysis of the diamond cutting process have been reported. In early work, as part of the “Chip Science” program at Lawrence Livermore National Laboratory, Donaldson et al. [32] studied the chip formation process in diamond cutting using the finite element program NIKE2D. Moriwaki et al. [21] used three-dimensional finite element models to predict the effect of the heat generated in the diamond turning of Al and Cu on machining accuracy. Using a two-dimensional model, Ueda et al. [23] predicted maximum temperatures on the tool rake face when diamond cutting pure Al and Cu. Finite element modeling has also been used to predict both temperature and stress fields in the orthogonal diamond cutting of Cu [22,33]. Brinksmeier et al. [34] used the FEM software package DEFORM to investigate temperatures and effective stress and strain distributions in the cutting zone for the high-speed orthogonal diamond cutting of oxygen-free high thermal conductivity (OFHC) Cu. Crystal plasticity finite element models have also been used to study cutting force and shear angle variations in the diamond cutting of single crystal Al [35] and to investigate the grain boundary steps that result when diamond cutting polycrystalline Cu [36]. The finite element modeling of brittle materials has also been pursued. Zhang et al. [37] investigated the effect of tool rake angle in the diamond turning of a KDP crystal by using a hybrid model that combines finite elements and smoothed particle hydrodynamics. Modeling efforts that rely on analytical approaches have also been reported. Kim and Kim [38,39] developed a round edge cutting model that takes into account the cutting edge radius and the elastic recovery that occurs behind the tool. The cutting and thrust forces and resulting specific cutting energy were calculated for the orthogonal diamond cutting of Cu and compared with experimental results from the literature [7,11]. Another analytical model that considers the cutting edge radius and elastic recovery at the tool flank face was that proposed by Kwon et al. [40]. A fluid dynamics approach was used to predict the cutting and thrust forces in the orthogonal cutting of Cu which were then compared with experimental results from the literature [7,11].

### 2.2 Material Response.

The response of the workpiece material when cutting with diamond tools strongly depends on the material being cut, the process parameters, and the tool geometry. For ductile polycrystalline materials, such as Al or Cu, the material response depends on the depth of cut relative to the tool edge radius. Moriwaki and Okuda [11] put forth two conceptual models for orthogonal cutting a polycrystalline material at large and small depths of cut, as shown in Fig. 5. When the depth of cut is large relative to the edge radius of the tool, the cutting process is dominated by the response of each individual grain and its relative orientation to the cutting direction. As shown in Fig. 5(a), the resulting surface topography can exhibit steps caused by the elastic recovery of each grain after the tool has passed. Typically, the ratio of the cutting to thrust force is greater than one. When the depth of cut approaches the size of the edge radius of the tool, the workpiece material is subjected to a large effective negative rake angle that results in plowing and sliding, leaving an amorphous-like layer on the surface. As a result, the machined surface appears burnished and there is no evidence of the elastic response of each individual grain, as shown in Fig. 5(b). This is consistent with the transition from a cutting dominant to a sliding/plowing dominant process discussed above [12] and the pioneering studies of Syn et al. [41] on the diamond cutting of electroless Ni. In this case, the ratio of the cutting to thrust force is less than one and is consistent with the direction of the resultant force vector acting at the surface, as shown in Fig. 4 [15]. An example of a surface cut at a depth of cut that is large relative to the tool edge radius is shown in Fig. 6. Shown is an atomic force microscope image of the surface of diamond turned OFHC Cu where the elastic response of the individual grains can be seen [42]. For ductile single crystal materials, the material response again depends on the orientation of the crystal to the cutting direction. Moriwaki et al. [13] found a material response when diamond cutting single crystal Cu similar to that for cutting polycrystalline materials. At depths of cut greater than 1 µm, the chip formation process was dependent on crystallographic orientation of the workpiece. At depths of cut below 0.1 µm, crystallographic orientation of the workpiece was not significant and the workpiece response consisted of an amorphous-like layer being formed at the surface caused by burnishing. The material response when diamond cutting brittle materials has also been extensively investigated. Early studies on the diamond cutting of brittle materials [43] have been aimed at identifying the mechanisms of material removal at depths of cut where there is the appearance of ductile cutting of an otherwise brittle material. These studies are based on a three dimensional facing operation with a round nose diamond tool where cutting is interrupted and the resulting shoulder, which exhibits a range of depths of cut from the nominal depth to zero depth of cut at the base of the shoulder, is examined. A clear transition, the so-called “ductile-brittle transition,” from a low roughness region at the base of the shoulder to one that is clearly pitted at the top is observed. The transition point along the shoulder, or critical depth, is seen to vary with feed rate, workpiece crystallographic orientation, tool rake angle, and lubricant. Plunge cutting using a round nose diamond tool and a linearly increasing depth of cut has also been used to examine the transition from a minimum roughness region to a fractured one [44]. Diamond cutting of brittle materials is typically performed with negative rake angle tools. Both depth of cut and tool rake angle have been shown to have a significant effect on the resulting forces and the surfaces produced [45].

Fig. 5
Fig. 5
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Fig. 6
Fig. 6
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Several excellent review papers, which include some of the aspects of the process mechanics of cutting with diamond tools, can be found in the literature [1,4648].

## 3 Present State of Cutting Technology

There is a continuing drive toward miniaturization in a number of industries including the semiconductor, optoelectronic, and medical industries that is stimulated by requirements that include enhanced functionality, performance and reliability, increased energy efficiency, a cleaner environment, improved healthcare, and reduced costs. New “micro” and “nano” manufacturing processes, e.g., diamond machining or ultraprecision cutting processes, coupled with the development of new advanced materials, and new machines will pave the way for new emerging products [49]. Despite many qualified technologies that have been established for the manufacture of precision parts and microstructured surfaces in the field of MEMS and energy assisted processes, mechanical processes such as diamond machining play a significant role for the generation of microstructured surfaces and precision parts [50].

### 3.1 Machine Tools.

Ultraprecision machine tools with a sophisticated, dedicated, and demanding design are one of the major prerequisites for performing ultraprecision machining. The fundamental bases for precision design and mechanical accuracy were described by Moore [51] in his classic text. The historical evolution of ultraprecision equipment and machine tools, and in general, the discipline of precision engineering has been put forth by Evans [2,52]. Recently, Preuss [53] described the techniques involved in diamond machining from a production engineering perspective. Masuzawa [54] described the two conditions that should be met when considering a range of micromachining processes, namely, unit removal and equipment precision. When considering the design of ultraprecision machine tools, the stringent requirements that must be met are (1) thermal stability, (2) precision spindle bearings and linear guides, and (3) high resolution of linear and rotary motions [48]. Specific features of such dedicated machine tools therefore include a compact size, enclosures for temperature controlled air circulation, hydrostatic air bearings and guide ways or hydrostatic oil bearings with low friction [55], special motors and specific encoders for nanometric tool positioning, and high thermal stability [56].

The machinability of the workpiece material factors into the overall performance of the ultraprecision machine tool. Typical materials that can be diamond machined are aluminum and copper alloys, electroless nickel-phosphor plating and polymers. As diamond machining technology developed, it was observed that hard and brittle materials could also be successfully machined including both single crystal and polycrystalline materials such as silicon [57] and germanium [58]. Even steel, which exhibits chemical instability wear with diamond [59], has shown the possibility to be machined with diamond tools [60,61], although tool wear is still a limitation.

In addition to the machinability of the workpiece material, the performance of the machine tool itself governs achievable form accuracy and surface roughness. Therefore, natural granite, polymer concrete, and other materials with high stiffness and damping properties are used to minimize vibration and deformation effects during surface generation [51,62]. Additionally, spindle performance and dynamics must be analyzed and optimized to reduce imbalance-induced vibrations, so as to minimize the required balancing effort, enhance the performance, or achieve automation [6365]. When compared with conventional machining, typical diamond machining processes are limited with respect to flexibility and economic efficiency. To overcome these shortcomings, new machine tool-based approaches for high-performance ultraprecision machining are being developed. These include the application of high-speed spindles, and faster and more precise balancing procedures [66]. For all ultraprecision machining processes, accurate workpiece clamping is vital for high surface quality and shape conformity. Clamping includes workpiece centering and alignment, as well as precision balancing; the latter being of highest importance when large, heavy workpieces or off-axis parts are machined in order to avoid process-induced vibrations [67]. In addition, monitoring of ultraprecision machining processes with techniques such as acoustic emission has been shown to provide addition in situ feedback of unwanted shifts in the process [68].

### 3.2 Diamond Tools.

The most commonly used tool material for ultraprecision machining is single crystal diamond which exhibits several unique properties especially well-suited for extreme precision cutting including high hardness, high thermal conductivity, high wear resistance, and low friction [69]. Equally important is the capability of single crystal diamond to be lapped and polished to achieve sharp and precise cutting edges with radii down to a few tens of nanometers. There are two basic types of single crystal diamond tools used in diamond machining, viz., (1) radius tools with a circular or elliptic nose (depending on the rake angle and the shape of the clearance face) for turning and milling applications and (2) v-shaped tools, mainly used in prism cutting, as shown in Fig. 7 [53]. In addition to lapping and polishing to obtain the needed geometry of the diamond tool, focused ion beam machining has also been used to prepare the diamond tool edge [70].

Fig. 7
Fig. 7
Close modal

Alignment of the diamond tool is essential for both diamond turning and diamond milling. Tools must be precisely aligned with respect to the coordinate axes of the workpiece and the machine tool. Deviations can lead to significant aberrations in the geometry of the machined part. To determine the tool radius and the exact tool position within the machine tool coordinates, tool alignment is performed manually, through tool set stations, with on-machine camera systems or with the machining of witness samples [67].

Despite the high hardness of diamond, single crystal diamond tools show signs of wear when machining all materials. Types of wear that have been observed include abrasive wear, adhesive wear, microfracture, cleavage, and chemical wear. The relative importance of each type of wear depends on the workpiece material and cutting conditions. Uddin et al. [71] found that in the diamond turning of {111} silicon, abrasive wear and adhesive wear were the dominant tool wear types with some chemical wear also taking place. Yoshino et al. [72] found that in creating v-grooves in quartz glass with diamond tools, abrasive wear was the dominant tool wear type with some adhesive wear also taking place. In the raster milling of copper, Yin et al. [73] found that microfracture was the dominant tool wear type because of the impact of the tool and workpiece. Chemical wear associated with machining ferrous materials has long been recognized. Chemical wear consists of diffusion of carbon atoms from the diamond into the workpiece, and to graphitization of the diamond. It has been found to be associated with the number of unpaired d-shell electrons [59]. In the diamond turning of 3Cr2NiMo steel, Zou et al. [74] observed graphitization of the rake face of the tool and diffusion of carbon into the workpiece. To reduce the graphitization of the tool during machining of commercially pure titanium and the titanium alloy Ti-6Al-4V, Zareena and Veldhuis [75] coated the tool with perfluoropolyether (PFPE). To measure the wear of tools, Evans et al. [76] proposed making plunge cuts in a reference material periodically while machining the part. The plunge cut is then measured with a scanning white light interferometer and compared with a plunge cut made with the new tool. To directly measure the tool edge geometry, Lucca and Seo [15] demonstrated the use of scanning probe microscopy (SPM) (see Sec. 4). It is well known that the wear of diamond is anisotropic. In one of the first works to quantify this effect, Wilks and Wilks [77] measured the material removal rate (MRR) of diamond when lapped or ground. Different crystallographic planes were examined as were different directions. Figure 8 shows a summary of the results where the MRR is a relative value normalized to lapping or grinding on the (100) plane in the [011] cutting direction. Note there is a two order of magnitude difference in the material removal rate for the (100) plane, [011] direction compared with the (110) plane, [001] direction.

Fig. 8
Fig. 8
Close modal

### 3.3 Cutting Configurations

#### 3.3.1 Diamond Turning.

In diamond turning, the cutting motion is generated by the rotation of the workpiece, while the tool is moved relative to the surface. In contrast to conventional machining, diamond turning does not require complex tool geometries, and as a result, the cutting kinematics is straightforward [53]. In addition to the generation of continuous surfaces, diamond turning can also be used to manufacture optical structures by either replicating the geometry of the diamond tool into the surface, or by modulation of the infeed depth. In the most basic setup, only two controlled axes (for generating the feed and infeed motion) and a spindle are necessary for the generation of rotationally symmetric structures, e.g., Fresnel lenses [78]. A typical diamond turned surface of OFHC Cu, as measured by white light interferometry, is shown in Fig. 9. The surface roughness is 9.2 nm Sa with a PV of 175.4 nm. In addition to the 10 µm feed marks, the steps produced by the elastic response of the individual grains can also clearly be seen, as discussed in Sec. 2.2.

Fig. 9
Fig. 9
Close modal

#### 3.3.2 Diamond Milling.

Diamond milling is one of the most flexible and efficient processes in ultraprecision machining. Unlike in diamond turning, the tool rotates while the workpiece is moved by a comparably slow translational or rotational motion defined by a numerically controlled path to achieve a constant cutting velocity. A wide range of optical quality geometries can be produced, and complex, continuous shapes or structured surfaces can be generated. Diamond milling processes are classified as either face milling or peripheral milling. In face milling, the tool rotates perpendicularly to the workpiece surface, while in peripheral milling, the rotational axis of the tool is parallel to the surface to be machined [67]. These diamond milling geometries are shown in Fig. 10. Diamond milling has been successfully used in the generation of functional surfaces. Typical shapes of diamond tools used for the structuring of functional surfaces by diamond milling are shown in Fig. 11 [79]. As a result of the development of multi-axis ultraprecision machine tools, raster milling emerged as one method for milling freeform surfaces. In the process, the cutting tool is moved along “raster lines,” either parallel to or perpendicular to the cut plane. The surface is then generated raster line by raster line [53]. A comparison of flat surfaces produced by diamond turning and by raster milling is shown in Fig. 12 [80]. The diamond turned surface shows the spiral path of the cutting tool, whereas the raster milling surface shows the scallops created on the surface as a result of the intermittent cutting process. Flycutting is the simplest diamond milling operation, where the flycutter moves in a straight line, and the process is mainly used for the face milling of flats or peripheral milling of profiles and prism arrays [53]. Diamond flycutting is typically performed with a single cutting edge, and as a result exhibits low machining efficiency. In recent work, a tool setting mechanism based on a thermo-mechanical actuator was designed and built to incorporate multiple cutting edges in such diamond milling operations [81].

Fig. 10
Fig. 10
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Fig. 11
Fig. 11
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Fig. 12
Fig. 12
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#### 3.3.3 Slow Slide and Fast Tool Servo Diamond Machining.

Servo machining is used to significantly extend the flexibility of diamond turning. By modulating the cutting depth dynamically according to the radial and angular position of the surface to be machined, surfaces and structures beyond those with rotational symmetry can be realized in a turning process. Depending on the frequency of the modulation and the device used, these processes are referred to as Slow Slide Servo (SSS) diamond turning (usually using the machine slides) or Fast Tool Servo (FTS) diamond turning. Slow Slide and Fast Tool Servo machining are the most commonly used methods for generating non-rotationally symmetric optical surfaces. Fast Tool Servos have been developed in various configurations depending on the intended purpose. For example, Lu and Trumper [82] developed an ultra-fast tool servo device which was used for the diamond turning of contoured surfaces. A long-range tool servo was developed [83] to extend the stroke of the tool displacement by using a voice coil driven actuator based on a flexure mechanism equipped with a laser interferometer feedback system. A two degree of freedom fast tool servo was developed for the diamond turning of freeform surfaces [84]. A nano-fast tool servo (nFTS) was specifically developed for the diamond turning of diffractive microstructures [85], and the influence of different workpiece material properties on process forces, burr and chip formation, and surface finish was examined. It was found that burr and chip formation were predominantly influenced by the machining strategy. The same nFTS device was used to generate submicron optical structures (diffractive optical elements) for ultraviolet applications [86]. Figure 13 shows a white light interferometric image of a holographic structure that was diamond turned into a copper-nickel-zinc surface using the nFTS. A piezo-actuated dual-axial fast tool servo (DA-FTS) was developed for the diamond turning of micro-structured surfaces into single crystal silicon. By combining the concepts of fast/slow tool servo and fly cutting, hierarchical micro-nanostructures were deterministically generated. In the process, a complex shaped primary surface was generated by cutting, and a secondary nanostructure by residual tool marks through actively controlling the tool loci [87].

Fig. 13
Fig. 13
Close modal

#### 3.3.4 Ultrasonic Assisted Machining.

Moriwaki and Shamoto [88] were the first to introduce the use of ultrasonic vibration to a single crystal diamond tool in their seminal investigation of the diamond turning of stainless steel. It is well accepted that excessive chemical wear occurs to a single crystal diamond tool when machining ferrous materials (see Sec. 3.2). In their study, Moriwaki and Shamoto applied a 40 kHz vibration to the single crystal diamond tool in the cutting direction. It was found that an optical quality surface of the stainless steel workpiece could be produced with a surface roughness Rmax of 0.026 µm. A similar study by the same research group was performed on the ultraprecision machining of glass with a single crystal diamond tool, where again the ultrasonic vibration was applied in the cutting direction [89]. Several years later, based on the same concept, Shamoto and Moriwaki [90] introduced ultrasonic elliptical vibration cutting. An elliptical motion (in a plane including both the cutting and thrust directions) was applied to a high speed steel tool to cut OFHC copper, first in a scanning electron microscope [90], and then on a ultraprecision lathe [91]. Using the elliptical motion, a surface roughness Rmax of 0.02 µm on the OFHC copper was obtained. Figure 14 shows the overall cutting geometry used. The technique has also been applied to milling, with the development of an elliptical vibration milling machine [92]. Since its introduction, elliptical vibration machining has been extensively studied and its application has broadened beyond the cutting of steel. It has also been applied to the cutting of difficult-to-machine materials, such as tungsten carbide. Zhang et al. [93] have used elliptical vibration cutting using a single crystal diamond tool for the creation of micro textured grooves in tungsten carbide. Microphotographs of the micro textured grooves and the surface profiles along the cutting direction are shown in Fig. 15.

Fig. 14
Fig. 14
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Fig. 15
Fig. 15
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### 3.4 Examples of Surfaces and Components Produced.

The generation of freeform surfaces, i.e., surfaces without rotational symmetry, has received much attention. With the emergence of multi-axis machine tools, deterministic diamond milling processes using at least three numerically controlled axes, operating either in Cartesian or polar coordinates, have been used to create a variety of optical surfaces with applications particular to modern telescopes and their instrumentation [94]. A comprehensive review on the current applications of freeform optics and current research topics including their manufacture and measurement has been put forth [95].

A SSS diamond turning technique was introduced which enables the machining of deep aspheric surfaces in a fast and economic way and provides an alternative to ball-end milling. In the machining technique, the servo motion is executed in two directions, parallel and perpendicular to the rotational axis [96]. Figure 16 shows an elliptic half shell that was machined using slow slide servo diamond turning.

Fig. 16
Fig. 16
Close modal

Lens arrays, retroreflectors, and Fresnel lenses are important optical elements, and their efficient fabrication is required. Several processes have been developed to make components with these optical elements feasible. For the manufacture of non-rotationally symmetric freeform optics such as lens arrays, a four-axis single-point diamond machining process was developed as an alternative to slow tool servo, fast tool servo, and three-axis micromilling [97]. The technique is capable of rapidly fabricating arrays of lenses in a fully automated process. Retroreflection is an important optical feature for safety applications, communications, and measurement equipment. For the generation of miniature retroreflecting triple mirrors, in particular full-cube retroreflectors, the Diamond Micro Chiseling (DMC) process was developed [78]. Figure 17 shows scanning electron microscopy (SEM) micrographs of cube corner arrays produced by the diamond micro chiseling process. Fresnel lenses for optoelectronics and photonic devices have evolved into arrays of individual elements with improved performance and capabilities. These polygonal Fresnel lens arrays are not rotationally symmetric and are usually manufactured by expensive lithography techniques or multiple mold assembly. An automated four-axis ultraprecision machining technique for manufacturing an array of hexagonal Fresnel lenses was developed. In the method, similar to that of a Guilloche machine, a diamond tool moves as a fixed point on a circle rolling inside a fixed circle [98]. Figure 18 shows images of a hexagonal Fresnel lens array machined using the technique. The diamond milling of a chalcogenide glass for use in thermal imaging optics has been demonstrated [99]. Figure 19 shows a thermal landscape imaging aspheric lens with integrated mounting features which was diamond milled. A sample thermal image is also shown.

Fig. 17
Fig. 17
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Fig. 18
Fig. 18
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Fig. 19
Fig. 19
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## 4 Characterization of Machined Surfaces

Due to the achievable nanometer level surface roughnesses and peak-to-valley form accuracies down to 0.1 µm, the characterization of diamond machined surfaces presents a difficult task. In addition to the measurement of topography and form, near surface changes to the material, subsurface damage, may be important as well. Numerous methods of surface characterization have been developed, only a sampling of common methods will be given below. For convenience, the methods are divided into two categories: surface topography and form, and subsurface damage.

### 4.1 Measurement of Surface Topography and Form.

The measurement of the surface topography is often the primary means of assessing a workpiece. There are a variety of methods to measure the surface topography; a few common methods will be given here. The methods were chosen to provide a range of measurement volumes from nanometers to meters. After a brief description of the methods, some example uses of the methods will be presented. Some examples of freeform surfaces will also be given. Freeform surfaces have attracted much attention especially in the optics field where the use of a freeform lens can reduce the number of traditional lenses needed in a given application. Freeform surfaces have no axis of symmetry. These surfaces present unique challenges in quantifying the surface topography and form.

Scanning probe microscopy (SPM) is a broad class of related techniques based on the work of Binnig and Rhorer [100] and Binnig et al. [101]. SPM for the measurement of surface topography is often performed in intermittent contact mode although constant contact mode is also used. In either case, a small probe attached to the end of a flexible cantilever is used. The cantilever deflects as the probe contacts the surface and this deflection of the cantilever is measured. The amount the cantilever deflects is held constant by adjusting the height of the workpiece or the cantilever. The measurement of the surface is performed by raster scanning over the surface and making a measurement at discrete points during the scanning.

Typical SPM systems have a resolution of a few nanometers in the x- and y-directions and sub-nanometer in the vertical, z-direction. Typical maximum scan sizes are around 100 μm in the x- and y-directions and less than 10 μm in the z-direction. The time required for one scan is in the range of 3–20 min with the longer times required for the collection of more data points. The workpiece needs no special preparation for scanning probe microscopy.

After the development of SPM for topography, the technique has been extended to measure other properties of the near surface. These include magnetic field strength (scanning magnetic force microscopy), capacitance (scanning capacitance microscopy), resistance (scanning resistance microscopy), etc.

White light interferometry is an optical measurement technique based on the constructive and destructive interference of light. The system is often incorporated with an optical microscope. Light reflected from the workpiece surface is combined with light reflected from a reference flat producing interference which provides a means to measure the workpiece surface.

Typical white light interferometry systems have a resolution of around 100 nm in the x- and y-directions and sub-nanometer in the vertical, z-direction. Typical maximum image sizes are around a millimeter in the x-, y-, and z-directions. The time required to capture an image ranges from a few seconds to around 1 min depending on the measurement height in the z-direction. There is no special preparation required for the workpiece surface, however it must be somewhat reflective.

Whereas the above mentioned techniques are principally used in the measurement of surface roughness, a coordinate measuring machine (CMM) is used in the determination of geometrical form. The most common configuration for a CMM is the gantry type also called the bridge type. The system is composed of a bed upon which the gantry moves in one direction, either the x- or y-direction. On the gantry is a cross member on which an arm-like structure can move which provides the second axis of motion. At the end of the arm is a probe that can be moved in the vertical direction to establish the location of the surface. There are a variety of probes available, typically either mechanical or optical. The probe is moved in a user-defined pattern from point to point and the location of the probe’s x-, y-, and z-coordinates is recorded. An image of the surface is made from the discrete data points collected.

Most typical CMM systems have a measurement volume of around one meter in the x-, y-, and z-directions, however the maximum z-height is often less than in the x- and y-directions. The resolution of the system is typically around 1 μm in all the directions. The time required to measure a workpiece depends on the number of data points being collected but can range from minutes to hours. There is no special preparation required for the workpiece to use this method. Figure 20 shows the measurement of a parabolic segment of a mirror using CMM with the probe in the front of the image.

Fig. 20
Fig. 20
Close modal

Surface topography can be used to understand the material response to the cutting process, aid in identifying problems with the machining center, verify models of surface generation by the cutting process or aid in the development of novel machining processes. Owen et al. [58] used SPM to investigate the effects of feed rate on the workpiece surface during the flycutting of (111) Ge with a rounded nose single crystal diamond tool. The SPM images showed that for feed rates less than 3 μm/rev, there was little or no pitting of the surface. For larger feed rates, the quantity and extent of surface pitting was found to increase with the feed rate. Zhang et al. [102] used white light interferometry to investigate the lamellar chip formation in the ultraprecision machining of single crystal copper, single crystal silicon, hydrogen implanted silicon, and a copper nickel alloy. They found that the spacing of the peaks on the chips was consistent with vibrations in the workpiece. Lee and Cheung [103] also considered workpiece-induced vibrations and developed a model for its effects on the surface topography of ultraprecision machined singled crystal aluminum. The workpiece surfaces were examined by white light interferometry. Their model was able to predict the surface topography and roughness of the machined workpieces. Two groups [104,105] developed models for the prediction of surface roughness in ultraprecision raster milling. In both cases, white light interferometry was used to measure the surface topography. The model of Zhang and To [104] was a 2D model and that of Wang et al. [105] was 3D. In both cases, the measured roughness values were in agreement with those predicted by the model. Zhang et al. [106] used white light interferometry combined with a fast Fourier transform (FFT) of the surface profile to investigate ultraprecision machined ZnAl. Using FFT, they identified contributions of vibration and grain size to the overall measured surface profile. Li et al. [107] used white light interferometry in the development of a technique that used a slow tool server with a diamond turning machine to produce freeform optics. Two patterns were made in aluminum (Al 6082): a sinusoidal surface profile and a microlens array. Surface roughness values of less than 10 nm were obtained for both surfaces. Whereas quantifying workpiece surfaces that have an axis of symmetry is well established [108], techniques for quantifying freeform surfaces are still evolving. Jiang et al. [109] suggest a two-stage technique for the evaluation of smooth freeform surfaces. A reference surface to which the measured results will be compared must be provided from a source such as a CAD model. The first stage of the technique roughly determines the location and orientation of the fitting surface and the second stage refines and improves the fitting. In the first stage, a structured neighborhood reference technique is used [110]. In the second stage, a Levenberg–Marquardt technique with a combination of Gauss–Newton and gradient descent methods is used. Figure 21 shows an example of a measurement of a worn knee replacement. The measured surface is shown by the lines and data points; the model is shown by the solid surface. An example of the measurement of a structured surface has been shown by Xu et al. [111] where scanning white light interferometry and optical methods were used to measure a structured spherical surface, a convex spherical blazed grating for a freeform spectrometer.

Fig. 21
Fig. 21
Close modal

### 4.2 Assessment of Subsurface Damage.

Subsurface damage is a broad term that includes any change in the surface layer characteristics caused by processing. Subsurface damage may include lattice disorder for single crystals, changes in dislocation density, hardness, residual stress, phase changes, voids, cracks, etc. There are a variety of techniques to assess the near subsurface damage, a few will be listed below. After a brief description of the techniques, examples of uses will be given.

Transmission electron microscopy (TEM) is a well-established technique that can provide direct observation of the atomic spacing. Combined with selective area diffraction it can also provide the structure of the workpiece material. Sub-nanometer resolution can be obtained. TEM requires extensive sample preparation to make the workpiece electron transparent. TEM can be considered a direct technique since the atomic spacing is observed. Because of the expense and time required for TEM, indirect techniques are often used. In an indirect technique, something about the subsurface damage is inferred from the measured value.

Nanoindentation can be used to measure the elastic modulus and hardness at very small depths of penetration. Nanoindentation uses a hard indenter, usually diamond, which is applied to the workpiece with a user-defined loading and unloading pattern. This pattern can be either in terms of the force applied or the depth of penetration. Throughout the loading–unloading cycle, the depth of penetration and force on the indenter is measured. Analysis of the unloading portion of the force versus depth curve can give the elastic modulus and hardness of the workpiece.

Rutherford backscattering spectrometry under channeling conditions (RBS-c) can be used to identify lattice disorder as a function of depth from the surface. In RBS-c a high energy, typically MeV, ion beam is directed toward a crystal that is aligned with the incident beam. The energy and quantity of backscattered ions is analyzed to obtain a measure of the lattice disorder.

Kunz et al. [112] used cross-sectional TEM to investigate single-point diamond turned (100) Si. The depth of cut varied from 1.27 μm to 50.4 μm and the workpiece was machined in the <100> and <110> directions. The TEM images showed slip along the {111} slip planes, as well as dislocation loops. The depth of slip planes extended from about 0.25 to 2.5 μm below the machined surface. Dislocation loops were not observed for the workpiece machined in the <100> direction with a depth of cut below 25.4 μm. Otherwise the dislocation loops extended from about 1 to 3 μm. Lucca et al. [113,114] used RBS-c to investigate (0001) CdS that had been ultraprecision machined in the <10$1¯$0> and <11$2¯$0> directions. The depth of cut was varied from 0.1 to 10 μm. There was greater lattice disorder at the higher depths of cut and when machining along the <10$1¯$0> direction. The relative disorder of the crystalline structure was nearly amorphous in the first 50 nm from the surface and undisturbed at depths of about 400 nm for machining along the <10$1¯$0> direction. In a study of a Zn-Al-Cu alloy, Dong et al. [115] used nanoindentation to investigate phase changes of the material. Raster milling of a 76% Zn–22% Al–2% Cu (wt%) workpiece was performed with tools that had minimal wear, moderate wear, and severe wear. Nanoindentation was performed to obtain the hardness over a depth range of approximately 20 nm to 5000 nm. They found that the near surface had a higher hardness than the bulk material. The extent of the increased hardness varied from 100 nm for the moderately worn tool to 350 nm for the severely worn tool. The variation was attributed to phase changes of the material that were measured by X-ray diffraction.

## 5 Conclusions

A brief review of the technology for cutting with diamond tools has been presented. The technology had its historical origins in the early 1900s, however accelerated in the 1960s when it was mainly developed for the machining of optics for energy and defense related needs. Today, diamond machining has broad applications that include the manufacture of precision freeform optics for defense and commercial applications, the structuring of surfaces for functional performance, and the creation of molds used for the replication of a broad range of components in plastic or glass.

The process mechanics when cutting with diamond tools at small depths of cut is significantly different than the mechanics which govern conventional machining processes. As the depth of cut approaches the dimension of the tool edge radius, the material encounters an effective negative rake angle. Here, the effect of plowing becomes important and the specific cutting energy increases with decrease in depth of cut. The process can be thought of as transitioning from a cutting dominant process to a plowing/sliding dominant process as depth of cut decreases. Accompanying this increase in specific cutting energy is a rotation of the resultant force vector toward the workpiece surface normal. When cutting single crystal materials, it is observed that the crystallographic direction relative to the cutting direction has a significant effect on the resulting cutting forces. In addition to the study of cutting forces and energies that result in the diamond cutting process, investigations of the cutting temperatures have also been undertaken. It is found that while the total dissipated energy in diamond cutting is small compared with conventional machining, the resulting cutting temperatures could be substantial. There has been significant interest in modeling of the process, and studies using analytical approaches, finite element modeling, and molecular dynamics modeling have been reported.

The response of the workpiece material when cutting with diamond tools strongly depends on the material being cut, the process parameters and the tool geometry. For ductile polycrystalline materials, the material response depends on the depth of cut relative to the tool edge radius. When the depth of cut is large relative to the edge radius of the tool, the cutting process is dominated by the response of each individual grain and its relative orientation to the cutting direction. This results in discontinuities or steps at the surface as a result of the elastic response of the individual grains. When the depth of cut approaches the size of the tool edge radius, the workpiece material is subjected to plowing and sliding which leaves an amorphous-like layer on the surface. When cutting ductile single crystals, the response is similar. When the depth of cut is large compared with the tool edge radius, the crystallographic orientation of the crystal relative to the cutting direction dominates material response. At depths of cut comparable with the tool edge radius, the crystallographic orientation of the workpiece is not significant, and the workpiece response is the creation of an amorphous-like layer on the surface. The response of brittle materials is seen to vary with feed rate, workpiece crystallographic orientation, tool rake angle and lubricant. Studies in the literature have been focused on identifying the mechanisms of material removal at depths of cut where there is the appearance of ductile cutting of an otherwise brittle material, the so-called “ductile-brittle transition.”

The present state of cutting technology has been reviewed including considerations for machine tool development, diamond tools and their use, and the current configurations used in cutting with diamond tools. The requirements for the design of ultraprecision machine tools are seen to include thermal stability, precision spindle bearings and linear guides, and high resolution of linear and rotary motions. Specific features of such machine tools include a compact size, enclosures for temperature controlled air circulation, hydrostatic air bearings and guide ways or hydrostatic oil bearings with low friction, and motors and encoders for nanometric tool positioning. Single crystal diamond is the most common tool material used for ultraprecision machining. Its unique properties that make it especially well-suited for extreme precision cutting include high hardness, high thermal conductivity, high wear resistance, and low friction, and the capability to be lapped and polished to achieve sharp and precise cutting edges with radii down to a few tens of nanometers. A variety of wear mechanisms have been observed in cutting with diamond tools including abrasive, adhesive, and chemical instability wear. A range of studies examining diamond tool wear have been reported.

There is a range of current cutting configurations being used when cutting with diamond tools. In diamond turning, the cutting motion is generated by the rotation of the workpiece, while the tool is moved relative to the surface. Diamond milling is one of the most flexible and efficient processes in ultraprecision machining. Here, the tool rotates while the workpiece is moved by a comparably slow translational or rotational motion. Servo machining is used to extend the flexibility of diamond turning. By modulating the cutting depth dynamically according to the radial and angular position of the surface to be machined, surfaces and structures beyond those with rotational symmetry can be realized in a turning process. Ultrasonic assisted machining has been extensively developed for the machining of steel and other hard to machine materials. By applying an elliptical cutting motion to the tool, a significant reduction in diamond tool wear is observed.

The characterization of diamond machined surfaces presents a difficult task due to the nanometer scale surface roughnesses and submicrometer peak-to-valley form accuracies which can be achieved. Important characterizations of the surfaces produced are surface topography, surface geometrical form or figure, and subsurface damage. There are a range of instruments particularly well-suited for the measurement of topography including scanning probe microscopy and white light interferometry. These instruments allow for the measurement of nanometer scale surface roughness but also can measure topographical features such as structured surface geometries. Coordinate measuring machines enable form accuracies of large-scale surfaces to be mapped. Characterization tools for the measurement of subsurface damage include transmission electron microscopy, channeling RBS, and nanoindentation.

Current and emerging uses of the technology are centered on the manufacture of complex, freeform surfaces for optical elements, structured surfaces that can be used in optical applications or other applications such as surface wettability or tribological performance. Also, extensions of existing diamond machining processes such as elliptical vibration cutting to new applications such as the micro- and nano-structuring of difficult to machine materials have been demonstrated. The development of new diamond machining processes such as diamond micro chiseling and high-speed diamond machining have also been introduced.

## Tribute to Professor Frederick F. Ling

Frederick Fongsun Ling, one of the 20th century’s most prominent tribologists and a distinguished professor of mechanical engineering, died on Nov. 8, 2014, in New York City at the age of 87. He is most well-known for his rigorous applications of the principles of mechanics and mathematics used to provide basic understanding of surfaces in contact. Prof. Ling was born in Qingdao, China, on Jan. 2, 1927. After having received a B.S. degree in civil engineering from St. John’s University, Shanghai in 1947, he came to the United States where he earned a B.S. degree in mechanical engineering from Bucknell University in 1949. He continued his graduate work at Carnegie Institute of Technology earning an M.S. in 1951 and a D.Sc. in 1954, both in mechanical engineering. His initial faculty appointment was as an assistant professor of mathematics at Carnegie Institute of Technology. Two years later, he began his long, distinguished career at Rensselaer Polytechnic Institute. After retiring from Rensselaer in 1990, he served on the mechanical engineering faculties of Columbia University and the University of Texas at Austin. In the late 1960s, Prof. Ling defined the field of surface mechanics to encompass the mathematical treatment of interacting surfaces. In the Preface to his monograph “Surface Mechanics,” published in 1973, he wrote “Surface mechanics pertains to surfaces, to be sure, but it was coined also to characterize the notion that information on the surface may be obtained analytically and rigorously without the encumbrance of the entire solution.” Prof. Ling’s significant contributions to the field of tribology were recognized by his many honors and awards including membership in the National Academy of Engineering, the ASME Mayo D. Hersey Award, and Honorary Membership in ASME. Professor Ling was a modest and reserved scholar, a champion for his former students and colleagues, and as he often characterized others, a gentleperson.

## Acknowledgment

The support of the US National Science Foundation under Grant Nos. 1437232 and 1727244 and the German Research Foundation (DFG) under Grant No. RI 1108/9-1 is gratefully acknowledged.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

No data, models, or code were generated or used for this paper.

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