Introduction

Synthetic fine-grained EDM graphite materials offer considerable technological and economic advantages not only as electrode materials in electrical discharge machining, but are also increasingly used in the aerostatic bearing of dynamic systems, where they enable the fulfilment of the highest accuracy requirements. Isostatically pressed fine-grained graphite is particularly suitable for this purpose because of its inherent porosity and the resulting permeability. At bearing gap heights of h_g < 10 μm, these properties enable compressed air to be distributed uniformly across the entire bearing surface A_b, resulting in a considerably more homogeneous pressure profile than that achieved with nozzle-based air bearings. In addition, air bearings made of fine‑grained graphite exhibit enhanced emergency-running characteristics due to the thermal stability and excellent tribological properties of this carbon modification. Typical applications of aerostatic air bearings include metrology systems for the smooth and precise movement of measuring equipment, deflection compensation of pressure rolls in the paper industry and the contactless support of main spindles in high-precision and ultra-precision machine tools. In the contactless support of main spindles, total radial error motion of ΔE_rm < 5 nm and stable process behaviour at rotational speeds of n ≥ 100,000 RPM can be achieved [1, 2]. The load capacity c_l and stiffness s of air-bearing systems are largely determined by the manufacturing accuracy a_m, since only closely toleranced bearing gap heights h_g and geometrically accurate bearing surfaces A_b ensure a homogeneous pressure profile and stable air flow behaviour. The load capacity c_l increases disproportionately as the bearing gap height h_g decreases [3].

The machining of graphite with conventional cutting materials, such as coated or uncoated cemented carbide and polycrystalline diamond (PCD), is characterized by high mechanically and thermochemically induced tool wear and therefore reduced tool life T. Increasing cutting-edge wear and the comparatively large cutting-edge radii of r_β > 1 μm lead to an increase in passive forces F_p. These forces F_p promote material disruption, including local crack formation and the breakout of graphite particles, at the machined surface and within the underlying subsurface structure, as well as the smearing and closure of the open porosity. Consequently, the arithmetic mean height Sa, deviations in form accuracy Δa_f, material breakouts and compression effects within the near‑surface layers increase measurably, thereby impairing the permeability and ultimately the functionality of the aerostatic bearing. To address these challenges in the precision machining of fine-grained graphite materials, the use of single crystal diamond (SCD) tools represents a promising approach. In addition to their high hardness H and thermal conductivity λ, these tools are characterized by cutting-edge radii of r_β ≤ 50 nm, which enable precisely controlled material cutting mechanisms. This allow geometric chip-formation parameters in the low single-digit nanometer range to be adjusted [4]. For the process-reliable and low-wear manufacturing of aerostatic bearing components made of fine-grained graphite, both conventional and ultrasonic-assisted ultra‑precision turning with SCD tools are therefore subject of current research. Initial investigations indicate that resonance-based ultrasonic excitation of the diamond tool enables larger chip-formation parameters to be realized while simultaneously reducing surface roughness parameters. Ultrasonic-assisted ultra-precision turning therefore shows considerable potential for the application-oriented manufacturing of fine-grained graphite components in an industrial context. The investigations conducted for this purpose and the resulting findings are presented below.

The machining of graphite with conventional cutting materials, such as coated or uncoated cemented carbide and polycrystalline diamond (PCD), is characterized by high mechanically and thermochemically induced tool wear and therefore reduced tool life T. Increasing cutting-edge wear and the comparatively large cutting-edge radii of r_β > 1 μm lead to an increase in passive forces F_p. These forces F_p promote material disruption, including local crack formation and the breakout of graphite particles, at the machined surface and within the underlying subsurface structure, as well as the smearing and closure of the open porosity. Consequently, the arithmetic mean height Sa, deviations in form accuracy Δa_f, material breakouts and compression effects within the near‑surface layers increase measurably, thereby impairing the permeability and ultimately the functionality of the aerostatic bearing. To address these challenges in the precision machining of fine-grained graphite materials, the use of single crystal diamond (SCD) tools represents a promising approach. In addition to their high hardness H and thermal conductivity λ, these tools are characterized by cutting-edge radii of r_β ≤ 50 nm, which enable precisely controlled material cutting mechanisms. This allow geometric chip-formation parameters in the low single-digit nanometer range to be adjusted [4]. For the process-reliable and low-wear manufacturing of aerostatic bearing components made of fine-grained graphite, both conventional and ultrasonic-assisted ultra‑precision turning with SCD tools are therefore subject of current research. Initial investigations indicate that resonance-based ultrasonic excitation of the diamond tool enables larger chip-formation parameters to be realized while simultaneously reducing surface roughness parameters. Ultrasonic-assisted ultra-precision turning therefore shows considerable potential for the application-oriented manufacturing of fine-grained graphite components in an industrial context. The investigations conducted for this purpose and the resulting findings are presented below.

Properties of Graphite and Process-Technological Fundamentals of Ultrasonic-Assisted Ultra-Precision Machining

In an ideal graphite crystal, graphene layers, also referred to as basal planes, are stacked in an A‑B‑A‑order, while the carbon atoms within each plane form a two-dimensional hexagonal lattice structure, see. Fig. 1.

Strong covalent sp²-hybridised carbon bonds act within the basal planes, whereas the individual planes are bounded only through comparatively weak Van der Waals forces. This results in a significant difference in bond energies of ΔBE ≤ ∼75/1. Consequently, the mechanical properties exhibit high anisotropy, particularly with regard to the shear modulus G_S, which increases the tendency of displacement mechanisms between the basal planes. Crack-based and brittle‑fracture-based cutting mechanisms therefore dominate during machining. In synthetic fine‑grained graphite materials, the layered graphite crystallites are statistically randomly oriented and agglomerated into larger particles. Together with the binder and pore regions, they form a heterogeneous polycrystalline microstructure that leads to locally varying and therefore uncontrolled crack propagation under the action of shear stresses τ [5].

The fundamental cutting mechanisms in the conventional macro- and micromachining of graphite materials have already been investigated comprehensively in the current state of the art [6, 7, 8]. Stress-based crack initiation and crack propagation beneath the nominal depth of cut a_p have been identified as the predominant cutting mechanisms [9]. Previous conventional ultra-precision turning experiments have additionally demonstrated significant interdependencies of the rake angle γ₀ and the depth of cut a_p on crack formation and on the direction of crack propagation during formation of the cutting plane [10, 11]. The characteristic cutting behaviour in conventional ultra‑precision turning is illustrated in Fig. 2 (a) ‑ Fig. 2 (d).

The process-technological advantages of ultrasonic assistance in precision machining of brittle materials, including graphite, are widely known and already established in various areas of industrial manufacturing [12, 13]. However, due to the fundamentally different tool engagement conditions, the knowledge gained in these applications cannot be transferred directly to the ultra‑precision turning of fine-grained graphite using SCD tools. In particular, the effects of conventional and ultrasonic-specific process parameters and their interdependencies on the cutting mechanisms have not yet been sufficiently investigated for this application.

For the experimental effect analysis, the resonance-based ultrasonic tool system UTS2 by Edmund Optics son‑X GmbH, Aachen, Germany, was used. The resonant vibration of the ultrasonic tool system causes the active cutting-edge section to follow a cyclic elliptical tool path, see. Fig. 2 (e) ‑ Fig. 2 (h). Superimposing this tool motion on the rotation of the workpiece generates an oscillating relative motion. The relative cutting speed v_c,rel results from the rotational cutting speed of the workpiece v_c,rot and the oscillation speed of the tool v_c,os. If the rotational cutting speed v_c,rot is lower than the maximum oscillation speed v_c,os in cutting direction, the tool and workpiece are periodically separated. Owing to this kinematic condition, the effective rake angle γ_0,eff and the local strain rate ε̇ vary during the cyclic tool engagement, directly influencing the duration, magnitude and direction of the induced stresses σ [14].

The investigations presented below are based on the hypothesis that the periodic and impulse energy input during ultrasonic-assisted ultra-precision turning of fine-grained graphite causes a local concentration of shear stresses τ within the cutting zone. This is expected to reduce the crack inclination angle α_c and enable a more horizontal crack propagation parallel to the cutting direction.

The horizontal crack length l_c and the propagation direction of the resulting cracks can therefore be controlled indirectly through the process parameters and the applied energy input. Consequently, the overall objective of the parameter study is the target-oriented analysis of ultrasonic-assisted ultra-precision turning process of fine-grained graphite materials. For this purpose, the main effects and interdependencies of the conventional process parameters under superimposed tool oscillation are initially investigated, together with the correlations between characteristic process parameters and the formation of the surface topography. A more detailed analysis of the effects of ultrasonic-specific process parameters will be the subject of future research.

1. Ultrasonic-Assisted Machining of Fine-Grained Graphite
   1. Experimental Setup and Procedure

The ultrasonic-assisted ultra-precision turning experiments were conducted on the five-axis ultra-precision machining center Nanotech 350 FG by Moore Nanotechnology Systems, LLC, Swanzey, USA. The vibration was generated using the ultrasonic tool system UTS2 by Edmund Optics son‑X GmbH, Aachen, Germany, which was installed on the B-axis of the machine tool. The sonotrode of the ultrasonic tool system oscillates at resonance with a constant oscillation frequency f_os ≤ 103 kHz. In previous investigations, maximum amplitudes of û ≤ 1.1 µm were proved to be suitable for the machining process [11]. The tool-specific amplitudes û were determined prior to processing using the laser vibrometer OFV 503 by Polytec GmbH, Waldbronn, Germany. The SCD tools with corner radii of r_ε ≤ 800 µm were supplied by Gruppe Matzdorf GmbH, Nuremberg, Germany. The specimen material used was fine‑grained graphite EDM AF5 by Novotec GmbH, Chemnitz, Germany, with an average grain size of g_s ≤ 1 µm. The specimens were characterized by a diameter of d_sp = 50 mm and a height of h_sp = 10 mm. The cooling of the SCD tool and the removal of chip particles from the cutting zone were achieved using a focused jet of pressurized air without the use of cutting fluid.

To generate isolated tool engagement conditions, annular test surfaces with a defined width l_ts were pre-turned on the front side of the specimens. For economic reasons, these contours were initially rough-machined using the uncoated cemented carbide inserts DCGT11T308 FN HU7315‑1 by Hoffmann SE, Munich, Germany. Since the circumferential length l_tc, and therefore the length of cut l_c, of the annular test surfaces decreases with the ring diameter d_r and consequently varies between the individual radial positions, the test surface widths l_ts were individually designed as a function of the respective feed f to provide a constant length of cut l_c,const = 100 m. This ensured the direct comparability of the results. The test surfaces were subsequently conventionally turned in several finishing process cycles using a depth of cut a_p = 10 µm, which is suitable for ultra‑precision machining. For this purpose, a SCD tool with a corner radius r_ε ≤ 3,000 µm by Contour Fine Tooling B.V., Valkenswaard, the Netherlands, was used. This preparation step intended to remove potential subsurface damages caused by the comparatively large cutting-edge radii of the cemented carbide tools of r_β,cc ≤ 6.75 µm and the correlated increase in material loading due to the resulting passive forces F_p. Optical surface roughness measurements of the annular test surfaces were conducted using the 3D‑laser scanning microscope (LSM) VK‑X3000 by Keyence Deutschland GmbH, Frankfurt am Main, Germany.

Additionally, the scanning electron microscope (SEM) LEO 1455VP by Carl Zeiss AG, Jena, Germany, was used for the optical analysis of the manufactured surface topographies. The investigated parameter ranges for turning fine-grained graphite with SCD tools were based on previous preliminary experiments, in which relevant process parameters and variables as well as achievable surface qualities were fundamentally classified [10, 11]. In this context, the rake angle γ₀ = 0°, the fine-grained graphite EDM AF5 and amplitudes of û ≤ 1 µm proved to be suitable for the subsequent investigations. The main experiments conducted in this work comprised 15 experimental runs following a Box–Behnken design of experiment (DoE), which enables the analysis of parameter effects and interdependencies with a reduced number of experiments n_exp. Fig. 3 shows the annular test surfaces on the fine-grained graphite specimen, the experimental setup and the investigated parameter ranges. The rotational speed v_rot programmed for each test surface corresponds to the specified constant rotational cutting speed v_c,rot.

Results and Discussion

The subsequent investigations focused on a detailed analysis of the conventional process parameters feed f, depth of cut a_p and rotational cutting speed v_c,rot with regard to the achievable arithmetic mean height Sa. This surface parameter has a significant influence on the minimum achievable bearing gap height l_g,min and therefore on the load capacity c_l of aerostatic bearing systems. The main effects identified within the investigations are presented in Fig. 4.

For the investigated feeds in the range of 0.15 μm ≤ f ≤ 0.35 μm, low arithmetic mean heights in the range of 0.150 μm ≤ Sa ≤ 0.152 μm were determined at both the lowest and the highest factor levels. The analysis showed that, in particular, a feed of f = 0.15 μm in combination with the minimum and maximum factor levels of the depth of cut a_p resulted in reduced arithmetic mean heights Sa. The results indicate an interdependency between the feed f and the depth of cut a_p, as the influence of the feed f on the arithmetic mean height Sa depends on the respective depth of cut a_p and exhibits both decreasing and non-uniform trends. A further interdependency was observed between the feed f and the rotational cutting speed v_c,rot. At the low feed of f = 0.15 μm, the arithmetic mean height Sa initially decreased and subsequently increased. At the highest feed of f = 0.35 μm, it increased continuously with higher rotational cutting speed v_c,rot. This suggests lateral crack propagation orthogonal to the cutting direction, which appears to be directional especially at reduced feed f.

At the minimum depth of cut a_p = 1.75 μm, arithmetic mean heights of Sa ≤ 0.146 μm were achieved, whereas values of Sa ≤ 0.133 μm were measured at the maximum depth of cut of a_p = 6.25 μm. The highest depth of cut a_p at which reduced arithmetic mean heights Sa were achieved was therefore at least Δ a_p ≥ 25.75 % above the critical depth of cut a_p,krit determined for the conventional ultra-precision turning process [11]. The results also highlight an interdependency between the depth of cut a_p and the rotational cutting speed v_c,rot, as the influence of the rotational cutting speed v_c,rot on the arithmetic mean height Sa varies in magnitude depending on the selected depth of cut a_p. This result indicates a significant increase in the critical depth of cut a_p,krit due to ultrasonic assistance and therefore enables the potential for increasing the applicable material removal rate Q_W. Based on these findings, it was assumed that a parametric reduction of the maximum undeformed chip thickness h_max, combined with an increase in the ratio of depth of cut to feed a_p/f, enables the achievement of reduced arithmetic mean heights Sa. In regard to the effect analysis, the relevant geometric chip-formation parameters, the ratio of depth of cut to feed a_p/f and the maximum undeformed chip thickness h_max and their dependency on the arithmetic mean height Sa are examined in greater detail.

The investigated rotational cutting speeds were in a range of 2 m/min ≤ v_c,rot ≤ 4 m/min. The lowest arithmetic mean height Sa were achieved at the center point v_c,rot = 3 m/min, with all measured arithmetic mean heights remaining below Sa ≤ 0.148 μm. In accordance with the formulated hypothesis, the rotational cutting speed range was selected with the primary objective of generating high oscillation‑based shear velocities v_s and impulse energies E_im. The high ratio between the tool oscillation speed of v_os ≤ 43.3 m/min and the rotational cutting speed in the range of 2 m/min ≤ v_c,rot ≤ 4 m/min resulted in pronounced intermittent tool engagement, with contact durations in the range of 12.5 % ≤ t_c ≤ 17.9 %. The periodic separation of the SCD tool and the workpiece actively reduced the contact time t_c and therefore the thermal load on the tool cutting-edge, thereby preventing wear-related interference with the parameter effects analyzed and on the targeted variables.

For the geometric classification of the investigated process configurations, the dimensionless ratio of depth of cut to feed a_p/f was additionally evaluated for the rotational cutting speeds in the range of 2 m/min ≤ v_c,rot ≤ 4 m/min. This key parameter indicates whether the underlying tool engagement is dominated by the depth of cut a_p or the feed f, thereby enabling the direction of the induced stresses σ and the resulting crack propagation within the fine-grained graphite to be assessed, as shown in Fig. 5. The lowest arithmetic mean heights Sa occurred at high ratios in the range of 17.9 ≤ a_p/f ≤ 41.7, although the wide scatter prevented the identification of a clear monotonic relation. Nevertheless, the results demonstrate that a depth of cut a_p = 6.25 μm, combined with feeds of f = 0.15 μm and f = 0.35 μm at a rotational cutting speed of v_c,rot = 3.0 m/min, resulted in suitable cutting conditions.

The resulting maximum undeformed chip thicknesses ranged from 9.9 nm ≤ h_max ≤ 43.7 nm and were therefore considerably smaller than the mean grain size g_s ≤ 1 μm of the EDM AF5 graphite and within the range of the cutting-edge radii of the SCD tools r_β ≤ 50 nm. No clear linear relation with the arithmetic mean height Sa was identified. However, the lowest arithmetic mean height of Sa ≤ 0.133 μm was achieved at a maximum undeformed chip thickness of h_max ≤ 18.7 nm resulting from the combination of a depth of cut a_p = 6.25 μm, a feed f = 0.15 μm and a rotational cutting speed v_c,rot = 3.0 m/min. These results demonstrate that the maximum undeformed chip thickness h_max cannot be considered in isolation, but must be evaluated in relation to its position along the active major cutting edge and the underlying engagement geometry.

Future investigations should therefore additionally consider the effective rake angle γ_eff. The results further show that a rotational cutting speed of v_c,rot = 3.0 m/min, in combination with an oscillation speed of v_c,os ≤ 43.3 m/min, results in suitable arithmetic mean heights Sa. However, the influence of substantially higher rotational cutting speeds v_c,rot on the cutting mechanisms remains unknown and needs be addressed in future investigations.

Finally, the surface topographies manufactured in the ultrasonic-assisted ultra-precision turning experiments were evaluated using SEM as well as LSM images and were compared with the results from previous investigations on conventional ultra-precision turning of EDM AF5 [10, 11]. The corresponding microscopy images are shown in Fig. 6. The test surfaces manufactured by conventional ultra‑precision turning exhibit considerably more distinct material breakouts and a more heterogeneous appearance than those manufactured with ultrasonic assistance. The surface topographies generated by ultrasonic-assisted turning are characterized by a homogeneous structure and reduced material breakout behaviour, indicating a more uniform cutting mechanism as a result of the periodically tool-workpiece separation.

The results support the assumption that stress-induced crack propagation is concentrated within a considerably smaller material region as a result of the high-frequency ultrasonic vibration. Accordingly, the periodically applied impulse energy E_in promotes horizontal crack propagation parallel to the direction of cut. The extent to which the oscillation-related amount of tool passes n_p effects the local surface topography is the subject of ongoing investigations.

Conclusions and Outlook

The objective of the investigations was to analyze the influence of conventional process parameters on the arithmetic mean height Sa and the surface topography during ultrasonic-assisted ultra‑precision turning of the fine-grained graphite EDM AF5. In particular, a feed of f = 0.15 μm, a depth of cut of a_p = 6.25 μm and a rotational cutting speed of v_c,rot = 3.0 m/min in combination with a constant oscillation frequency of f_os ≤ 103 kHz and an amplitude of û ≤ 1.1 μm, had a significant effect on the machining result. The findings indicate that a high ratio of depth of cut to feed in the range of 17.9 ≤ a_p/f ≤ 41.7 and a maximum undeformed chip thickness of h_max ≤ 18.7 nm enable preferable tool engagement conditions and suitable crack-propagation directions resulting from the induced stresses σ within the investigated process parameter range. Compared with the current state of the art, ultrasonic vibrations in ultra-precision turning process of fine-grained graphite resulted in a significant increase in the critical depth of cut of Δa_p ≥ 25.75 % compared with the conventional turning process.

In summary, ultrasonic-assisted ultra-precision turning of the fine-grained graphite material EDM AF5 resulted in more homogeneous surface topographies, reduced material breakout behaviour and therefore lower arithmetic mean heights Sa than conventional ultra-precision turning. The results therefore support the hypothesis that periodically interrupted tool engagement and impulse stress induction enable controlled crack propagation within the workpiece material.

Further investigations are required, particularly with regard to the upper process limit of the rotational cutting speed v_c,rot, the wear-relevant contact duration t_c and the related local cutting mechanisms. The determined maximum undeformed chip thicknesses h_max, which are in the range of conventional cutting-edge radii of SCD tools of r_β ≤ 50 nm, suggest that the locally effective negative rake angle γ_eff within the cutting-edge radius r_β is gaining in importance for the cutting of fine‑grained graphites for the manufacturing of aerostatic bearing components. In this context, it must be investigated which aspects of the cutting process are attributable to shearing, breaking or displacement of the material microstructures. The findings therefore provide a basis for further increasing the material removal rate Q_W and gain the industrial application potential of ultrasonic-assisted ultra-precision turning of fine-grained graphite materials using SCD‑tools.