Tawfique Hasan

Zhipei Sun

Pingheng Tan

Daniel Popa

Emmanuel Flahaut

Edmund J R Kelleher

Francesco Bonaccorso

Fengqiu Wang

Zhe Jiang

Felice Torrisi

Giulia Privitera

Valeria Nicolosi

Andrea C Ferrari

Double-Wall Carbon Nanotubes for Wide-Band, Ultrafast Pulse Generation

Keywords: double-wall carbon nanotubes, polymer composites, saturable absorber, ultrafast laser

We demonstrate wide-band ultrafast optical pulse generation at 1, 1.5, and 2 μm using a single-polymer composite saturable absorber based on double-wall carbon nanotubes (DWNTs). The freestanding optical quality polymer composite is prepared from nanotubes dispersed in water with poly(vinyl alcohol) as the host matrix. The composite is then integrated into ytterbium-, erbium-, and thulium-doped fiber laser cavities. Using this single DWNTÀpolymer composite, we achieve 4.85 ps, 532 fs, and 1.6 ps mode-locked pulses at 1066, 1559, and 1883 nm, respectively, highlighting the potential of DWNTs for wide-band ultrafast photonics.

M

aterials with nonlinear optical properties are of critical importance for a diverse range of photonic applications, [START_REF] O'mahony | Future Optical Networks[END_REF] such as optical regeneration, 2À4 switching, [START_REF] Leclerc | Optical Regeneration at 40 Gb/s and Beyond[END_REF][START_REF] Hirano | Gbit/s RZ All-Optical Discrimination Using Refined Saturable Absorber Optical Gate[END_REF][START_REF] Jin | Detailed Design and Characterization of All-Optical Switches Based on InAs/GaAs Quantum Dots in a Vertical Cavity[END_REF] modulation, [START_REF] Guina | Saturable Absorber Intensity Modulator[END_REF][START_REF] Arecchi | A Crossed-Beam Optical Gate with a Saturable Absorber[END_REF] sampling, [START_REF] Land | STM Investigation of Single Layer Graphite Structures Produced on Pt(111) by Hydrocarbon Decomposition[END_REF][START_REF] Reid | All-Optical Sampling and Spectrographic Pulse Measurement Using Cross-Absorption Modulation in Multiple-Quantum-Well Devices[END_REF] and noise suppression. [START_REF] Clarke | 80-Gb/s OTDM System Analysis of a Vertical Microcavity-Based Saturable Absorber for the Enhancement of Pulse Pedestal Suppression[END_REF] In this field, one of the most sought-after applications involves generation of ultrafast laser pulses. [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF][START_REF] Okhotnikov | Ultra-fast Fibre Laser Systems Based on SESAM Technology: New Horizons and Applications[END_REF] Indeed, laser sources producing nano-to sub-picosecond optical pulses are a major component in the product portfolio of leading laser manufacturers. [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF] Many of the relevant applications, ranging from basic scientific research to materials processing, from eye surgery to printed circuit board manufacturing, from metrology to trimming of electronic components (e.g., resistors and capacitors) currently employ laser sources utilizing a mode-locking technique based on a nonlinear optical material, called saturable absorber (SA). These SAs, when placed in a laser cavity, modify the laser continuouswave output into a train of ultrashort optical pulses. [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF] The key requirements for such nonlinear optical materials are fast response time, large nonlinearity, broad wavelength range, low optical loss, high power handling, low cost, and ease of integration into an optical system. [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF] Currently, the dominant commercial SA technology is based on semiconductor saturable absorber mirrors (SESAMs). [START_REF] Keller | Passively Modelocked Surface-Emitting Semiconductor Lasers[END_REF] However, these typically have limited operation bandwidths (a few tens of nanometers [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF][START_REF] Okhotnikov | Ultra-fast Fibre Laser Systems Based on SESAM Technology: New Horizons and Applications[END_REF] ) and require complex fabrication and packaging. [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF] A simpler and cost-effective alternative relies on using single-wall carbon nanotubes (SWNTs) 15À28 or graphene. 15,28À40 While wide-band operation in SWNT-based devices can be achieved using a distribution of tube diameters, [START_REF] Hasan | NanotubeÀPolymer Composites for Ultrafast Photonics[END_REF][START_REF] Wang | Wideband-Tuneable, Nanotube Mode-Locked, Fibre Laser[END_REF][START_REF] Martinez | Nanotube and Graphene Saturable Absorbers for Fibre Lasers[END_REF][START_REF] Kivistö | Carbon Nanotube Films for Ultrafast Broadband Technology[END_REF][START_REF] Hasan | Molecular-and Nano-Tubes[END_REF] this is an intrinsic property of graphene, due to the gapless linear dispersion of Dirac electrons. [START_REF] Sun | Wideband Tunable, Near Transform-Limited, Graphene-Mode-Locked[END_REF][START_REF] Hasan | Molecular-and Nano-Tubes[END_REF][START_REF] Bonaccorso | Graphene Photonics and Optoelectronics[END_REF] In general, a good SA should have a high (e.g., ∼10% for fiber lasers [START_REF] Okhotnikov | Ultra-fast Fibre Laser Systems Based on SESAM Technology: New Horizons and Applications[END_REF] ) modulation depth (the absorption change between high and low intensity optical irradiation). [START_REF] Keller | Recent Developments in Compact Ultrafast Lasers[END_REF][START_REF] Hasan | Molecular-and Nano-Tubes[END_REF] However, for a pristine single-layer graphene device, the optical absorption is relatively low (∼2.3%), making it unsuitable for fiber lasers where large optical absorption and modulation depth are typically needed. [START_REF] Okhotnikov | Ultra-fast Fibre Laser Systems Based on SESAM Technology: New Horizons and Applications[END_REF] For a given optical absorption, high modulation depth can be typically achieved by minimizing the nonsaturable losses (the optical loss of SAs at high irradiation intensity). [START_REF] Boyd | Nonlinear Optics[END_REF] For SWNT-based SAs, nanotube bundles and aggregations mostly contribute to these. The most widely employed approach to avoid excessive nonsaturable losses is debundling the SWNTs via solution processing techniques and embedding them into polymer matrices. [START_REF] Hasan | Molecular-and Nano-Tubes[END_REF] Indeed, this strategy, coupled with matching the SWNT absorption peak with the operation wavelength, is followed in the majority of the SWNT-based photonic devices, [START_REF] Hasan | NanotubeÀPolymer Composites for Ultrafast Photonics[END_REF][START_REF] Sun | Ultrafast Lasers Mode-Locked by Nanotubes and Graphene[END_REF][START_REF] Hasan | Molecular-and Nano-Tubes[END_REF] giving a typical nonsaturable loss of ∼50% of total linear absorption. [START_REF] Hasan | NanotubeÀPolymer Composites for Ultrafast Photonics[END_REF][START_REF] Hasan | Molecular-and Nano-Tubes[END_REF] However, when using a wide range of tube diameters to achieve a "wide-band" SWNT SA, the high loading of SWNTs required in the devices results in instability of nanotube dispersion during the composite preparation, leading to aggregation and, therefore, high nonsaturable absorption losses and small modulation depth.

Good SAs should also have a low value of saturation intensity, [START_REF] Zitter | Saturated Optical Absorption through Band Filling in Semiconductors[END_REF] I sat . This is defined as the optical intensity required to reduce the SA absorption coefficient to half of the initial value, considering zero nonsaturable absorption losses. [START_REF] Boyd | Nonlinear Optics[END_REF] In graphene, I sat is estimated to be in the range of a few tens [START_REF] Popa | Sub 200 fs Pulse Generation from a Graphene Mode-Locked Fiber Laser[END_REF][START_REF] Cho | High-Quality, Large-Area Monolayer Graphene for Efficient Bulk Laser Mode-Locking near 1.25μm[END_REF][START_REF] Xing | The Physics of Ultrafast Saturable Absorption in Graphene[END_REF] of MW/cm 2 . For SWNTs, I sat is in the range of ∼30 GW/cm 2 in aqueous dispersions. [START_REF] Kamaraju | Double Walled Carbon Nanotubes as Ultrafast Optical Switches[END_REF] For multiwall nanotubes (MWNTs) with ∼40 nm outer diameter, I sat is >100 GW/cm 2 in aqueous dispersions. [START_REF] Elim | Ultrafast Absorptive and Refractive Nonlinearities in Multiwalled Carbon Nanotube Films[END_REF][START_REF] Lim | Electronic and Optical Properties of Nitrogen-Doped Multiwalled Carbon Nanotubes[END_REF] Therefore, when compared with SWNTs and graphene, MWNTs require higher irradiation intensity to reach absorption saturation. [START_REF] Elim | Ultrafast Absorptive and Refractive Nonlinearities in Multiwalled Carbon Nanotube Films[END_REF][START_REF] Lim | Electronic and Optical Properties of Nitrogen-Doped Multiwalled Carbon Nanotubes[END_REF] This is why, except for only a handful of reports, [START_REF] Zhang | Passive Mode-Locked Nd:YVO 4 Laser Using a Multiwalled Carbon Nanotube Saturable Absorber[END_REF] MWNTs have not been traditionally considered as SAs for passive mode-locking.

The concentric tube arrangement makes DWNTs an interesting class of nanomaterials, with wide-ranging potential applications, including in (opto)electronics. 52À54 Of particular interest relevant to this work, DWNTs also exhibit ultrafast carrier dynamics. [START_REF] Kamaraju | Double Walled Carbon Nanotubes as Ultrafast Optical Switches[END_REF],55À57 Kamaraju et al. [START_REF] Kamaraju | Double Walled Carbon Nanotubes as Ultrafast Optical Switches[END_REF] measured a linear limit of saturable absorption (R 0 ∼ 6.1 Â 10 3 and ∼6.4 Â 10 3 cm À1 ) and I sat (∼68 and 14 GW/cm 2 ) for aqueous dispersions and thin films of DWNTs, respectively. This is similar to the values reported for SWNT aqueous dispersions by the same authors (R 0 ∼ 5.6 Â 10 4 cm À1 and I sat ∼ 33 GW/cm 2 , respectively). [START_REF] Kamaraju | Double Walled Carbon Nanotubes as Ultrafast Optical Switches[END_REF] Thus, in terms of carrier dynamics, DWNTs are comparable to SWNTs.

Further, DWNTs can have outer and inner wall combinations with different electronic types (semiconducting, s, or metallic, m) in their structures (outer-inner: s-s, s-m, m-s, and m-m), resulting in different charge transfer behaviors between the tubes. [START_REF] Kalbac | Probing Charge Transfer between Shells of Double-Walled Carbon Nanotubes Sorted by Outer-Wall Electronic Type[END_REF] With a semiconducting outer tube for s-s and s-m combinations, optical absorption from excitonic transition energies of both the inner and outer walls is expected to contribute to the overall optical absorption of the resultant DWNT structure, making them suitable as wide-band SAs. Conversely, with metallic outer wall for the m-s and m-m combinations, the outer wall has zero band gap with wide absorption range and may create a screening effect, [START_REF] Chen | Chemically Doped Double-Walled Carbon Nanotubes: Cylindrical Molecular Capacitors[END_REF] suppressing optical absorption from the inner s-or m-nanotubes. Nevertheless, such combination may also work as an advantage for ultrafast photonic applications of DWNTs. This is because the presence of inner or outer m-nanotubes (s-m, m-s) in the same structure can increase the carrier relaxation speed of the s-nanotubes as electrons and holes can tunnel from them to their metallic counterparts. [START_REF] Hertel | Spectroscopy of Single-and Double-Wall Carbon Nanotubes in Different Environments[END_REF][START_REF] Blau | Optical Materials: Variety Pays Off for Nanotubes[END_REF] Indeed, experimental observations indicate that the relaxation times of inner nanotubes of DWNTs are comparable or shorter [START_REF] Hertel | Spectroscopy of Single-and Double-Wall Carbon Nanotubes in Different Environments[END_REF][START_REF] Hirori | Exciton Energy Transfer between the Inner and Outer Tubes in Double-Walled Carbon Nanotubes[END_REF][START_REF] Koyama | Ultrafast Energy Transfer of One-Dimensional Excitons between Carbon Nanotubes: A Femtosecond Time-Resolved Luminescence Study[END_REF] than the SWNTs of same species. For example, Nakamura et al. [START_REF] Nakamura | Third-Order Nonlinear Optical Response in Double-Walled Carbon Nanotubes[END_REF] showed that, under the same experimental conditions, the exciton decay time for (7,6) inner tubes in DWNTs is 0.65 ps, compared to 3.2 ps for a (7,6) SWNT species due to shorter exciton decay time and energy relaxation from inner to outer tubes 57 via exciton energy transfer (EET). [START_REF] Tan | Photoluminescence Spectroscopy of Carbon Nanotube Bundles: Evidence for Exciton Energy Transfer[END_REF][START_REF] Tan | Optical Properties of Nanotube Bundles by Photoluminescence Excitation and Absorption Spectroscopy[END_REF] The strong third-order optical nonlinearity, ultrafast carrier dynamics, 48,55À57,63 and wide optical absorption [START_REF] Nakamura | Third-Order Nonlinear Optical Response in Double-Walled Carbon Nanotubes[END_REF][START_REF] Iakoubovskii | Optical Characterization of Double-Wall Carbon Nanotubes: Evidence for Inner Tube Shielding[END_REF] make DWNTs with ∼1.6À1.8 nm outer diameter very attractive for ultrafast photonic applications in the 1 to 2 μm range. With an interwall distance of ∼0.36À0.38 nm, [START_REF] Pfeiffer | Topics in Applied Physics[END_REF][START_REF] Pfeiffer | Unusual High Degree of Unperturbed Environment in the Interior of Single-Wall Carbon Nanotubes[END_REF] the diameter difference between inner and outer tubes is ∼0.7À0.8 nm. Therefore, DWNTs with 0.8À1.1 nm inner diameter have outer tubes with 1.6À1.8 nm diameter with two distinct and strong eh 22 and eh 11 s-tube absorption bands at ∼1.1 and ∼2.0 μm, [START_REF] Liu | An Atlas of Carbon Nanotube Optical Transitions[END_REF] respectively. The eh 11 from inner stubes at ∼0.8À1.1 μm are expected to be overlapped by eh 22 of the outer tubes. [START_REF] Iakoubovskii | Optical Characterization of Double-Wall Carbon Nanotubes: Evidence for Inner Tube Shielding[END_REF][START_REF] Liu | An Atlas of Carbon Nanotube Optical Transitions[END_REF] This makes DWNTs efficient SAs at ∼1 and ∼2 μm and for larger diameter tubes, potentially beyond this range. This is very attractive for biomedical and biosensing applications where significant demand exists for portable, tunable, pulsed laser sources from ∼2 to up to 10 μm. [START_REF] Ilev | Mid-Infrared Semiconductor Optoelectronics[END_REF] Similar to other nanoparticles, the aggregation phenomenon of nanotubes, especially in low viscosity dispersions, is largely governed by the diffusion process of nanotubes and nanotubeÀnanotube interactions in a certain medium. [START_REF] Sandler | Ultralow Electrical Percolation Threshold in Carbon-Nanotube-Epoxy Composites[END_REF] This is in addition to the effect of solvent properties (e.g., pH) and stabilization by dispersant (e.g., surfactants). In low viscosity dispersions, aggregation between nanotubes can therefore increase significantly with increased nanotube concentration because of more "exposed" nanotube surfaces. [START_REF] Grady | Carbon NanotubeÀPolymer Composites: Manufacture, Properties, and Applications[END_REF] The processing technique we use here involves slow evaporation of solvents from a low viscosity (1.6 mPa 3 s at 25 °C) mixture. This highlights the need for a stable dispersion to avoid large aggregation during solvent evaporation. DWNTs allow two nanotubes in a single structure, minimizing the possibility of such large (>1 μm) aggregations and bundle formation during composite fabrication and thus scattering losses while potentially offering high modulation depth at a range of wavelengths. Thus, they are potentially an attractive class of carbon nanomaterial for wide-band ultrafast pulse generation. Here, we demonstrate DWNTÀpolymer composites as wideband passive mode-lockers for ultrafast pulse generation at 1, 1.5, and 2 μm in Yb-, Er-, and Tm-doped fiber laser cavities, respectively.

RESULTS AND DISCUSSION

We use DWNTs produced by catalytic chemical vapor deposition (CCVD) of CH 4 over Mg 1Àx Co x O solid solution containing Mo oxide. [START_REF] Flahaut | Gram-Scale CCVD Synthesis of Double-Walled Carbon Nanotubes[END_REF] After CCVD, the nanotubes are oxidized in air at 570 °C for 30 min. [START_REF] Osswald | In Situ Raman Spectroscopy Study of Oxidation of Double-and Single-Wall Carbon Nanotubes[END_REF] The residual material is next washed with HCl to dissolve the metal oxides. [START_REF] Osswald | In Situ Raman Spectroscopy Study of Oxidation of Double-and Single-Wall Carbon Nanotubes[END_REF] Figure 1aÀc shows representative transmission electron microscopy (TEM) images of the DWNT samples at different magnifications. Statistics on ∼130 DWNTs reveal that they have ∼1.1 nm inner and ∼1.8 nm outer mean diameters (Figure 1d,e). TEM images of ∼145 tubes also indicate that the purified samples contain ∼90% DWNTs, ∼8% SWNTs, and ∼2% triple-wall carbon nanotubes (TWNTs).

Optical absorption and photoluminescence excitation (PLE) spectroscopy of this purified nanotube sample dispersed with sodium dodecylbenzenesulfonate (SDBS) surfactant in deuterium oxide (D 2 O) is then used to characterize the DWNT samples. Using D 2 O instead of water allows extension of the spectral study region of the dispersions in the NIR. Pure water begins to absorb at ∼700 nm, followed by a series of strong absorption peaks above ∼900 nm, with complete absorption just above 1100 nm. Using D 2 O instead of H 2 O means OÀH is substituted by OÀD, pushing all these water-related absorption peaks by ∼ √ 2 times toward the higher wavelength, that is, to beyond ∼1300 and ∼1800 nm for the case of the strong peaks and complete absorption, respectively.

Figure 2 plots the absorption spectrum of the purified nanotubes dispersed in D 2 O. The peak at ∼1.1 μm corresponds to eh 11 excitonic transitions of 0.75À1.15 nm inner tubes, overlapping with the eh 22 of 1.5À1.9 nm outer tubes. [START_REF] Iakoubovskii | Optical Characterization of Double-Wall Carbon Nanotubes: Evidence for Inner Tube Shielding[END_REF][START_REF] Liu | An Atlas of Carbon Nanotube Optical Transitions[END_REF] The reference spectrum of D 2 O is also presented, highlighting that the eh 22 absorption peaks of the outer wall of DWNTs cannot be resolved above 1800 nm due to strong optical absorption from D 2 O.

Figure 3 plots the PLE map of the purified nanotube sample (∼90% DWNTs, ∼8% SWNTs, and ∼2% TWNTs). The chiralities are assigned according to ref 69. The PLE map shows strong emissions from the diameter range of ∼0.7À1.15 nm. This corresponds to that of the inner tubes as derived by TEM (Figure 1e). Tan et al. [START_REF] Tan | Photoluminescence Spectroscopy of Carbon Nanotube Bundles: Evidence for Exciton Energy Transfer[END_REF][START_REF] Tan | Optical Properties of Nanotube Bundles by Photoluminescence Excitation and Absorption Spectroscopy[END_REF] reported ∼2À3 meV red-shift in eh 11 and eh 22 of small SWNT bundles, which formed aggregations over a 2-month period after they were dispersed in waterÀ SDBS solution. Here, we observe a ∼5À7 meV red-shift in eh 11 and eh 22 of all the nanotube species compared to the aforementioned aggregated SWNTs. We attribute such red spectral shifts, even larger than those of the aggregated nanotubes, [START_REF] Tan | Photoluminescence Spectroscopy of Carbon Nanotube Bundles: Evidence for Exciton Energy Transfer[END_REF][START_REF] Tan | Optical Properties of Nanotube Bundles by Photoluminescence Excitation and Absorption Spectroscopy[END_REF] to the dielectric screening [START_REF] Walsh | Screening of Excitons in Single, Suspended Carbon Nanotubes[END_REF] of the inner tubes by the outer tubes in DWNTs. [START_REF] Hirori | Exciton Energy Transfer between the Inner and Outer Tubes in Double-Walled Carbon Nanotubes[END_REF] Such large red-shift could also be due to bundle formation of the individual s-SWNTs (i.e., not the inner tubes in DWNTs, but a % of the 8% SWNTs) present in the sample. However, we do not observe significant evidence of bundle formation through strong optical signatures of EET between s-nanotubes of similar diameter. In line with our TEM observation, this indicates that the population of individual s-SWNTs present in the sample is very low. We argue that the (eh 22 ,eh 11 ) emission from small tubes comes from the inner s-nanotubes of DWNTs which, despite bundling of the DWNTs, have weak EET due to larger physical spacing between themselves (>0.7 nm as opposed to ∼0.34 nm in standard SWNT bundles discussed previously [START_REF] Tan | Photoluminescence Spectroscopy of Carbon Nanotube Bundles: Evidence for Exciton Energy Transfer[END_REF][START_REF] Tan | Optical Properties of Nanotube Bundles by Photoluminescence Excitation and Absorption Spectroscopy[END_REF][START_REF] Qian | Exciton Energy Transfer in Pairs of Single-Walled Carbon Nanotubes[END_REF] ). This is because the EET process between s-nanotubes in small bundles occurs via Förster resonance energy transfer, whose efficiency is dependent on the inverse sixth power of the physical distance between the donorÀacceptor couple. [START_REF] Förster | Transfer Mechanisms of Electronic Excitation[END_REF] Note that our observation and explanation support PL from inner tubes as observed in previous reports [START_REF] Hirori | Exciton Energy Transfer between the Inner and Outer Tubes in Double-Walled Carbon Nanotubes[END_REF][START_REF] Hayashi | Selective Optical Property Modification of Double-Walled Carbon Nanotubes by Fluorination[END_REF][START_REF] Kim | Raman and Fluorescence Spectroscopic Studies of a DNA-Dispersed Double-Walled Carbon Nanotube Solution[END_REF] but contrast reports that the PL emission from the inner tubes in DWNTs is strongly quenched [START_REF] Green | Processing and Properties of Highly Enriched Double-Wall Carbon Nanotubes[END_REF] by the outer tubes by up to 4 orders of magnitude. [START_REF] Tsyboulski | Do Inner Shells of Double-Walled Carbon Nanotubes Fluoresce?[END_REF] We only detect very weak or no emissions above the 1375 nm range, from tubes with d t ∼1.2À1.3 nm. Indeed, tubes at this d t range constitute only a very small % of the overall population, as evident from the TEM (Figure 1e,f) and absorption spectra of nanotubes in the dispersion (Figure 2). As discussed later, the nanotubeÀpolymer composite (Figure 6) also shows weak absorption (from eh 11 excitonic transitions) in the 1400À 1600 nm range, that is, for d t ∼1.2À1.3 nm. The outer tubes of the DWNTs with a mean d t ∼1.8 nm are expected to emit in the ∼1800À2000 nm range from their eh 11 excitonic transitions and cannot be measured from their dispersed state in D 2 O because of strong optical absorption of D 2 O in this range (Figure 2).

Raman spectra of the purified nanotube powder are measured at 457 nm (2.71 eV), 488 nm (2.54 eV), 514.5 nm (2.41 eV), 632.8 nm (1.96 eV), and 785 nm (1.58 eV) to further characterize the nanotubes. In the low frequency region, the radial breathing modes (RBMs) are observed. Their position, Pos(RBM), is inversely related to SWNT diameter, d t , 82À84 as given by Pos

(RBM) = C 1 /d t þ C 2 .
Combining Pos(RBM) with excitation wavelength and a Kataura plot, [START_REF] Liu | An Atlas of Carbon Nanotube Optical Transitions[END_REF][START_REF] Kataura | Optical Properties of Single-Wall Carbon Nanotubes[END_REF] it is, in principle, possible to derive the SWNT chirality. [START_REF] Paillet | Raman Active Phonons of Identified Semiconducting Single-Walled Carbon Nanotubes[END_REF][START_REF] Jorio | Structural (n,m) Determination of Isolated Single-Wall Carbon Nanotubes by Resonant Raman Scattering[END_REF] A variety of C 1 and C 2 values were proposed for this relation. [START_REF] Telg | Chirality Distribution and Transition Energies of Carbon Nanotubes[END_REF][START_REF] Meyer | Raman Modes of Index-Identified Freestanding Single-Walled Carbon Nanotubes[END_REF][START_REF] Jorio | Structural (n,m) Determination of Isolated Single-Wall Carbon Nanotubes by Resonant Raman Scattering[END_REF][START_REF] Araujo | Third and Fourth Optical Transitions in Semiconducting Carbon Nanotubes[END_REF] Here, we use C 1 = 228.8 cm À1 and C 2 = 2.4 cm À1 from ref 89, derived by plotting the experimental Pos(RBM) to d t relationship for CVDgrown DWNTs. However, if one is interested in estimation of the band gap, the precise choice of constants is less critical, as the difference in the calculated diameter from the actual value is small. The typical Raman spectrum of nanotubes in the 1500À1600 cm À1 region consists of the G þ and G À bands. In s-SWNTs, they originate from the longitudinal (LO) and tangential (TO) modes, respectively, derived from the splitting of the E 2g phonon of graphene. 90À92 The positions of the G þ and G À peaks, Pos(G þ ), Pos(G À ), are diameter-dependent, and the separation between them increases with decreasing diameter. [START_REF] Piscanec | Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions, and Dynamic Effects[END_REF] In m-SWNTs, a wide, low frequency G À is a fingerprint of m-SWNTs. On the other hand, the absence of such features does not necessarily imply that only s-SWNTs are present but could just signify that m-SWNTs are off-resonance.

Thus, a large number of excitation wavelengths are necessary for a complete characterization of nanotubes. [START_REF] Fantini | Optical Transition Energies for Carbon Nanotubes from Resonant Raman Spectroscopy: Environment and Temperature Effects[END_REF][START_REF] Araujo | Third and Fourth Optical Transitions in Semiconducting Carbon Nanotubes[END_REF] In particular, we note that ref 93 reported that tubes with up to 100 meV off-resonance from the excitation wavelength can be detected. It is important to note that tubes in resonance with the same laser energy can also have a different diameter.

Figure 4a plots the RBM region for the nanotube samples. Note that the RBM detection range is limited by the cutoff of the notch and edge filters at 140, 160, 150, 130, and 150 cm À1 for 457, 488, 514.5, 632.8, and 785 nm, respectively. Thus, we can detect tubes with diameter up to 1.8 nm at 632.8 nm, while we cannot detect tubes with diameter >1.45 nm at 488 nm. For each excitation wavelength, we use Lorentzians to fit the RBMs from 20 different measurements to derive the statistics presented in Figure 5aÀe. The RBM spectra do not reveal a cluster distribution of inner and outer peaks around two well-defined diameters. Rather, they show a broad distribution, spanning the entire range from 140 to 400 cm À1 . This heterogeneous distribution was also observed in other Raman characterization of CVD-grown DWNTs. [START_REF] Villalpando-Paez | Tunable Raman Spectroscopy Study of CVD and Peapod-Derived Bundled and Individual Double-Wall Carbon Nanotubes[END_REF][START_REF] Barros | Raman Spectroscopy of Double-Walled Carbon Nanotubes Treated with H 2 SO 4[END_REF] The counts in Figure 5aÀe represent how many times the nanotubes of a particular diameter were observed due to resonance with the excitation wavelength. Keeping this in mind, the RBM results are in agreement with optical absorption and PLE measurements.

Figure 4b,c plots the Raman spectra in the G and 2D region obtained from the nanotube powders, respectively. Very weak D band contributions are also observed in the G region, indicating a small number of defects. [START_REF] Canc -Ado | Quantifying Defects in Graphene via Raman Spectroscopy at Different Excitation Energies[END_REF][START_REF] Tuinstra | Spectrum of Graphite[END_REF] The G þ and G À peaks are fitted with Lorentzians. The diameter dependence of G þ and G À peaks can be used to determine the diameter distribution of the nanotubes. [START_REF] Piscanec | Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions, and Dynamic Effects[END_REF] This gives an outer tube diameter range of 1.4À1.8 nm. On the other hand, inner tubes have a diameter distribution in the 0.6À1.0 nm range. The estimation for the inner tubes agrees well with the results of RBMs and the G region. For the case of the outer tubes, we cannot compare with the RBM data due to the cutoff of the notch/edge filter. However, the data agree with the Raman analysis of the G band and TEM, where a distribution of ∼1.7 nm is estimated for the outer tubes. The 2D bands in Figure 4c, under different excitations, show a spec-tral profile with multiple Lorentzian peaks, similar to other reports on DWNTs. [START_REF] Ren | Evidence for Atomic Correlation between the Two Constituent Tubes in Double-Walled Carbon Nanotubes[END_REF] Therefore, we expect strong absorption bands at ∼1.1 and ∼2 μm from this nanotube sample. This enables us to maximize the change in absorption under strong optical irradiation, [START_REF] Hasan | NanotubeÀPolymer Composites for Ultrafast Photonics[END_REF] making DWNTs ideal SA materials at these wavelengths.

We use the purified nanotubes to prepare nanotubeÀ polymer composites to take the fabrication and integration advantage of polymer photonics into various lightwave systems [START_REF] Hasan | NanotubeÀPolymer Composites for Ultrafast Photonics[END_REF] as well as the optical properties of the constituent ∼90% DWNTs. First, the nanotube sample is ultrasonically dispersed in water using SDBS surfactant, centrifuged to remove the large insoluble particles, mixed with aqueous poly(vinyl alcohol) (PVA) solution, and sonicated again to obtain a homogeneous and stable dispersion free of aggregations. We use water as the solvent and SDBS as the surfactant to obtain higher concentration of isolated nanotubes or small bundles [START_REF] Bonaccorso | Density Gradient Ultracentrifugation of Nanotubes: Interplay of Bundling and Surfactants Encapsulation[END_REF] than possible with nonaqueous solvents. 99À101 PVA is used for its solvent compatibility. Slow evaporation of water at room temperature produces a freestanding, ∼50 μm thick nanotubeÀPVA composite (∼90% DWNTs, 8% SWNTs, and 2% TWNTs).

Figure 6 shows the optical absorption of the nanotubeÀpolymer composite. This has two absorption bands centered at ∼1.1 and ∼2 μm with a peak width of ∼250 and ∼350 nm, respectively. This corresponds to distinct diameter range d t ∼0.75À1.15 nm (eh 11 at ∼1.1 μm) and ∼1.5À1.9 nm (eh 11 at ∼2 μm and eh 22 at ∼1.1 μm), [START_REF] Liu | An Atlas of Carbon Nanotube Optical Transitions[END_REF] respectively. This matches the inner and outer diameter distributions of the DWNTs. The 8% SWNTs present in the sample have a diameter range similar to that of the inner wall of DWNTs. Thus, eh 11 absorption of these SWNTs also contributes to the strong ∼1.1 μm absorption peak from the eh 11 of inner and eh 22 of the outer walls of DWNTs. The inner walls of the 2% TWNTs have diameter ∼2 nm as observed by TEM. We do not observe any significant eh 11 or eh 22 absorption peaks from the inner walls of the TWNTs. Note that although the eh 22 excitonic transitions of s-SWNTs can extend the operation range of SWNTs to shorter wavelengths, 102 the eh 22 f eh 11 relaxation is over 1 order of magnitude smaller than eh 11 f ground state relaxation. 103 This increases the I sat at eh 22 transition by over 1 order of magnitude compared to that at the eh 11 transition, making the SA device difficult to saturate at the wavelengths corresponding to eh 22 . 102 We argue that the presence of inner walls in DWNTs and strong contribution from their eh 11 transition at 1.1 μm contribution ensures I sat comparable to that of the SWNTs. Similarly, MWNTs, as discussed before, also have high saturation intensity, [START_REF] Elim | Ultrafast Absorptive and Refractive Nonlinearities in Multiwalled Carbon Nanotube Films[END_REF][START_REF] Lim | Electronic and Optical Properties of Nitrogen-Doped Multiwalled Carbon Nanotubes[END_REF] which limits their SA applicability.

Small aggregation of CNTs (<1 μm), in general, is considered beneficial for saturable absorption. Indeed, such level of bundling improves carrier relaxation times by up to an order of magnitude 104 by providing multiple relaxation pathways for the excited carriers. 105 However, these bundles/aggregates are beyond the standard optical microscope resolution limit. Thus, typical optical microscopy is usually used to identify samples with large (>1 μm) aggregates, which are more likely to exhibit large scattering (i.e., nonsaturable) losses. [START_REF] Hasan | NanotubeÀPolymer Composites for Ultrafast Photonics[END_REF] Optical microscopy (Figure 6, inset) reveals no large nanotube aggregations or defects in the composite, thus avoiding such losses. 106 The polymeric film-based device is integrated by taking a ∼2 mm 2 nanotubeÀpolymer composite, sandwiching it between a fiber pigtailed fiber connector with physical contact (FC/PC) with index matching gel at both the fiber ends. The index matching gel is used to reduce the insertion losses. The SA device is used to demonstrate mode-locking at 1, 1.5, and ∼2.0 μm. The fundamental working principle for the nanotube-based SA devices is explained in refs 15 and 42.

Figure 7a shows the setup for 1 μm. A 2 m Yb-doped fiber-based optical amplifier is used to provide gain for lasing. This is a commercial IPG amplifier unit with 25 dB gain at the signal wavelength. A polarization controller is employed for mode-locking optimization. A fused 20/80 coupler is utilized as the output coupler. The 20% port is used for the measurements. All of the cavity fiber has positive group velocity dispersion (GVD) (β 2 ≈ 18 ps 2 km À1 ). A circulator and chirped fiber Bragg grating are inserted inside the ring cavity to set the overall GVD negative, to facilitate soliton-like pulse shaping through the interplay of group velocity dispersion and self-phase modulation. 109 The total cavity length is ∼12.5 m.

Stable mode-locking at 1 μm is achieved. No pulses are observed after removing the composite from the cavity, confirming that mode-locking is initiated by the DWNT composite. Figure 7b plots a typical second harmonic generation autocorrelation trace, which is well fitted by a sech 2 temporal profile. This gives a full width at half-maximum (FWHM) pulse duration of 4.85 ps. Such broad pulse is mainly caused by large overall negative GVD. 109 The output spectral data are shown in Figure 7c. The output spectrum peaks at 1066 nm with FWHM = 0.284 nm. The sidebands are typical of soliton operation; due to intracavity periodical perturbations, 108 the asymmetry can be attributed to the significant third-order dispersion introduced by the chirped fiber Bragg grating. 108,109 The timeÀ bandwidth product (TBP) of the output pulses is 0.36. The deviation from TBP = 0.31 expected for transformlimited sech 2 pulses 109 indicates the presence of minor chirping of the output pulses. 109 The output repetition rate is ∼16.37 MHz. Typical output power is 0.12 mW, with single pulse energy of 7.3 pJ. These results are comparable to those obtained with SWNTs at 1 μm. [START_REF] Kelleher | Generation and Direct Measurement of Giant Chirp in a Passively Mode-Locked Laser[END_REF][START_REF] Kelleher | Nanosecond-Pulse Fiber Lasers Mode-Locked with Nanotubes[END_REF] For 1.5 μm operation, we use an erbium-doped fiber (EDF) as the gain medium, pumped by a 980 nm diode laser via a wavelength division multiplexer (WDM). An isolator is employed after the gain fiber to ensure unidirectional operation. A polarization controller is used for mode-locking optimization. The 20% tap of the 20/80 coupler is used as output for measurement. The setup is presented in Figure 8a. The length of EDF is 0.8 m. The gain fiber has a ∼6/125 μm core/cladding geometry and has an absorption of ∼40 dB/m at a wavelength of 1531 nm. The total cavity length is 7.3 m. The output pulse duration is around 532 fs, assuming sech 2 pulse profile; see Figure 8b. The TBP of the output pulses at 1.5 μm is 0.42. The deviation from TBP = 0.31 is due to the minor chirping of the output pulses. In this case, the peak lasing wavelength is 1559 nm, with FWHM = 6.5 nm. Typical soliton sidebands are also observed. The sideband intensity difference is mainly because of higher EDF gain at ∼1545 nm compared to that at ∼1570 nm. 107,108 For ∼2.0 μm operation, we construct a ring laser cavity using a 3.5 m long Tm-doped silica fiber as the gain medium. The gain fiber is a single clad thulium-doped fiber from Nufern. It has a 9 μm/125 μm core/cladding geometry and has an absorption of ∼10 dB/m at 1560 nm. An amplified 1560 nm diode laser through a WDM pumps the gain fiber. A coupler is used to couple 50% light back into the cavity while guiding 50% of the incident power to the output port of the laser. The mode-locker device is on one end, connected to the wide-band coupler and on the other end, spliced to an isolator to ensure unidirectional light propagation (Figure 9a). A dichroic mirror is used to eliminate the residual pump power at 1560 nm. At ∼350 mW pump power, we achieve an output power of ∼1.2 mW. The autocorrelation trace is shown in Figure 9b, which closely follows a sech 2 shape. The mode-locked optical spectrum in Figure 9c Radio frequency (rf) spectrum measurements can be used to monitor the mode-locking stability. 110 The typical rf spectra at 1, 1.5, and 2 μm have a peak at an output repetition rate corresponding to the cavity round trip time (Figure 10). This confirms reliable continuous-wave mode-locking. 111 For the rf spectrum at 1066, 1559, and 1883 nm, the peak to pedestal extinction ratios are ∼60, 86, and 77 dB, respectively (>10 6 contrast). This confirms a stable output pulse. 111

CONCLUSIONS

Our demonstration of wide-band mode-locking optical pulses at 1, 1.5, and 2 μm using DWNTÀpolymer composites shows that they could potentially be useful for wide-band ultrafast photonic applications. In particular, building on our experiments, few-wall (e.g., <5) nanotubes (FWNTs) with broader absorption profile and I sat lower than large diameter FWNTs may become very attractive for wide-band mid-infrared applications.

EXPERIMENTAL METHODS

Transmission Electron Microscopy. For TEM analysis, dispersions are drop-cast onto a lacey carbon support grid (400 mesh). Water is readily removed by an absorbent underneath, leaving DWNTs on the carbon grid. TEM images are taken using a JEM-3000F FEGTEM at 300 kV.

Raman and Optical Absorption Spectroscopy. Raman spectroscopy measurements are carried out using a Renishaw inVia spectrometer using a 50Â objective. A PerkinElmer Lambda 950 spectrophotometer is used for the visÀNIR absorption measurements with 1 nm step.

Preparation of DWNT Dispersions for Photoluminescence Excitation Spectroscopy. Purified DWNTs (0.01 wt %) are ultrasonicated with 0.2 wt % of SDBS in 10 mL of D 2 O inside a sealed glass test tube in a bath sonicator (Bioruptor; Diagenode) at 270 W, 20 kHz for 4 h. The homogeneous dispersion is then centrifuged in a TH-641 rotor using a sorvall WX 100 ultracentrifuge at ∼200 000g for 2 h and the top 30% decanted for PLE characterization.

Photoluminescence Excitation Spectroscopy. The PLE maps are taken from nanotube dispersions in a HORIBA Jobin Yvon excitationÀemission spectrofluorometer (Fluorolog-3) equipped with a xenon lamp excitation source and a liquid-nitrogen-cooled InGaAs detector (Symphony solo). The PLE maps are measured at right angle scattering by scanning the excitation wavelength from 300 to 900 nm with 5 nm steps and 60 s exposure for ∼850 to ∼1450 nm emission range. The entrance and exit slit widths are 14 and 30 nm, respectively.

Preparation of DWNTÀPVA Composites. Purified DWNTs (0.04 wt %) grown by CCVD method [START_REF] Sandler | Ultralow Electrical Percolation Threshold in Carbon-Nanotube-Epoxy Composites[END_REF] are ultrasonicated in 10 mL of DI water with 1 wt % of SDBS using a tip sonicator (Branson 450A, 20 kHz) at ∼100 W output power and 10 °C temperature for 4 h. The homogeneous dispersion is centrifuged at ∼100 000g for 30 min in a TH-641 rotor using a sorvall WX100 ultracentrifuge. The top 60% of the dispersion is then decanted. Then, 4 mL of this dispersion is mixed with a 1 wt % aqueous solution of 120 mg of PVA and is ultrasonicated again for 30 min. The homogeneous mixture has a viscosity of 1.6 mPa 3 s at 25 °C, measured using a TA Instruments Discovery HR-1 rheometer. This low viscosity mixture is then drop-cast and the solvent slowly evaporated at room temperature in a desiccator, resulting in a ∼50 μm freestanding DWNTÀPVA composite.

Characterization of Mode-Locked Pulses. The pump and average output power are monitored by a power meter. The pulse duration and spectrum are recorded using a second harmonic generation (SHG) intensity autocorrelator and an optical spectrum analyzer, respectively. To study the operation stability, we measure the rf spectrum using a photodetector connected to a spectrum analyzer.

Figure 1 .

 1 Figure 1. (aÀc) Representative TEM images of the purified DWNTs. Inner wall (d) and outer wall (e) diameter distributions as measured from the TEM images shows a mean inner and outer diameter of 1.1 and 1.8 nm, respectively.

Figure 2 .

 2 Figure 2. Absorption spectrum of DWNTs dispersed in D 2 O in the 300À1800 nm range. The contribution from D 2 O is subtracted. Spectrum of D 2 O is also presented.

Figure 3 .

 3 Figure 3. PLE map for DWNTs dispersed in D 2 O; (n,m) is assigned following refs 60 and 69.

Figure 4 .

 4 Figure 4. Raman spectra of DWNTs at different excitation wavelengths: (a) RBM region, (b) G region, and (c) 2D region.

Figure 5 .

 5 Figure 5. Diameter analysis from the RBMs of the nanotubes excited by (a) 457, (b) 488, (c) 515, (d) 633, and (e) 785 nm wavelengths, indicating d t ∼0.6À1.8 nm.

Figure 6 .

 6 Figure 6. Absorption spectrum of DWNTs embedded in ∼50 μm PVA polymer composite. The contribution from PVA is subtracted. Absorption spectrum of a pure PVA polymer of the same thickness is also presented. Inset: Optical microscopy of the DWNTÀpolymer composite reveals no large nanotube aggregation.

Figure 7 .

 7 Figure 7. (a) Laser setup at 1 μm. ISO, isolator; CBG, chirped Bragg grating; YDFA, Yb-doped fiber amplifier; PC, polarization controller. The DWNT polymer composite is sandwiched between the fiber connectors. (b) Second harmonic generation autocorrelation trace of the output pulses at 1 μm. (c) Output spectrum.

Figure 8 .

 8 Figure 8. (a) Laser setup at 1.5 μm. EDF, erbium-doped fiber; WDM, wavelength division multiplexer. (b) Second harmonic generation autocorrelation trace of mode-locked pulses at 1.5 μm. (c) Output spectrum.

  exhibits a center wavelength of 1883 nm with a FWHM spectral width of ∼3.2 nm. Typical sidebands are due to periodic perturbations from cavity components. The corresponding TBP is ∼0.44, which again indicates the presence of chirping. The repetition rate for the output pulse train is 17.82 MHz, as determined by the cavity length of ∼10.8 m.

Figure 9 .

 9 Figure 9. (a) Laser setup at ∼2 μm. TDF, thulium-doped fiber. (b) Second harmonic generation autocorrelation trace of modelocked pulses at ∼2 μm. (c) Output spectrum.

Figure 10 .

 10 Figure 10. RF spectrum measured around the fundamental repetition rate: (a) f 1 = 16.37 MHz, (b) f 1 = 27.4 MHz, (c) f 1 = 17.82 MHz showing peak to pedestal extinction ratios >60 dB in all three wavelengths.

Acknowledgment. We thank R.C.T. Howe for the viscosity measurements. We acknowledge funding from EPSRC GR/ S97613/01, EP/E500935/1, the ERC Grant NANOPOTS, a Royal Society Brian Mercer Award for Innovation. A.C.F. is a Royal Society Wolfson Research Merit Award holder. V.N. wishes to acknowledge support from the European Research Council (ERC Starting Grant 2DNanoCaps) and Science Foundation Ireland, P.T. from National Natural Science Foundation of China, Grants No. 11225421, F.B. from the Newton International Fellowship, Z.S. from Teknologiateollisuus TT-100, the European Union's Seventh Framework Programme (No. 631610), and Aalto University, T.H. from NSFC (Grant No. 61150110487), and the Royal Academy of Engineering (Graphlex).

Conflict of Interest:

The authors declare no competing financial interest.


Sébastien Mandrile
email: sebastien.mandrile@turbomeca.fr

Gilles Cazenave-Larroche
email: gilles.cazenave-larroche@turbomeca.fr

Cyril Vernault
email: cyril.vernault@turbomeca.fr

Gilles Dessein
email: gilles.dessein@enit.fr

Jean Denape
email: jean.denape@enit.fr

Jean-Yves Paris
email: jean-yves.paris@enit.fr

Development of an in-house cutting forces simulation for fir tree broaching process

Keywords: broaching, specific cutting forces, cutting forces simulation, fir tree broach, broach design, fir tree slot

This article proposes a simulation of cutting forces in broaching of fir tree slots. Every step needed to build an in-house fir tree broaching simulation is presented. This simulation is based on the discretisation of each tooth of the broach, computation of elementary cutting forces of each discretised section, and finally the summation of each elementary cutting force into a global axes system. This work also presents orthogonal cutting experiments to implement realistic specific cutting forces into the model. The simulation obtained is compared with the real force signals of a fir tree broach to evaluate the quality of the simulation. At the end, the application to industrial context is developed.

expertise is based on the modelisation of cutting forces and on the process monitoring in machining.

Gilles Cazenave-Larroche obtained his Master degree in Engineering from the 'Ecole nationale supérieure d'arts et métiers' -France. He has been gaining an experience in aerospace industry for 25 years. His current position is the Head of the Engineering Service in the Rotating Parts Department of Turbomeca Safran Group Company. His domain of expertise is based on machining of aeronautic parts.

Cyril Vernault obtained his PhD grade in Material Science from the University of Poitiers -France, in 1998. He has been gaining an experience in aerospace industry for 14 years. His current position is Machining and Heat Treatment Group Leader in the Engineering Department of Turbomeca Safran Group Company. His domain of expertise is based on heat treatment and machining of aeronautic parts.

Gilles Dessein is a Professor at Ecole Nationale d'Ingénieurs de Tarbes, University of Toulouse, France. He is a member of Laboratoire Génie de Production (EA1905) and manages machining research activities in the laboratory. He received his PhD degree from the University of Toulouse (1997) and an accreditation to supervise research (HDR) from the Institut National Polytechnique de Toulouse (2008). His expertise domain concerns high performance machining, and he has worked on dynamics in milling, hard materials machining, surface integrity, and behaviour of machine tools in the context of many European projects. His main expertise is in the analysis, monitoring, modelling, and control of machining processes.

Jean Denape is a Professor at the National Engineering School of Tarbes (ENIT), University of Toulouse, France. He is a member of the Production Engineering Laboratory (LGP, EA1905) and manages the Interfacial and Functional Materials research team in the laboratory. He received his PhD degree from the Mining School of Paris (1986) and an accreditation to supervise research (DSc) from the National Polytechnic Institute of Toulouse (1993). His domain of expertise concerns the durability of rubbing hard materials (structural ceramics and hard metallic alloys) under dry conditions or limit lubrication. He has been at the origin of the tribology activity at the LGP and developed it for 25 years. He developed more than ten tribometers for better understandings of wear mechanisms, dynamics of interfacial elements trapped in the contact (third body approach) and heat flow generated by friction through several national projects and international programmes.

Jean-Yves Paris is an Assistant-Professor at the National Engineering School of Tarbes (ENIT), University of Toulouse, France. He is a member of the Production Engineering Laboratory (LGP, EA1905) and belongs to the Interfacial and Functional Materials research team. He followed academic studies in material science and received his PhD degree from the University of Toulouse (1994). For 17 years, he has worked on tribology studies and performs topographic characterisations and physicochemical analyses on different materials (zirconia, alumina, titanium and nickel-base alloys, hard coatings, but also polymers and composites) to model matter transfers under different sliding conditions (pressure, speed, temperature, and atmosphere) for various dynamic configurations (rotating, reciprocating and fretting). His domain of expertise is based on local mechanical and physicochemical properties in relation to microstructure and also studies of surface damages after machining through several national projects and international programmes.

Introduction

A fir tree slot is a junction between the disk and a blade in an aero-engine turbine. This assembly between the blade and the disk is an area of high thermal and mechanical loading. Broaching is used to machine the fir tree slot in the turbine disk. Turbine disks are usually in nickel-base alloys, called super-alloys. Nowadays, due to cycle time and machining quality, broaching is known to be the best process to machine fir tree slots in aero turbine disk. Broaching process guarantees a high quality level of surface integrity and slot geometry. However, some drawbacks can be observed: some expensive parts may be damaged as a consequence of tool wear and cutting disturbances, because of very tight geometrical tolerances of the fir tree and the very intrinsic difficulty to machine the nickel-base alloys.

Moreover, for a given broach shape, there is only one machining parameter which can be changed: the cutting speed. The others are given by the tool shape.

Fir tree broach does not produce constant force signals. The interpretation of these non-constant force signals is not possible to get directly because several teeth machine at the same time. For a better understanding of the broaching process, cut sections and specific cutting forces on each tooth must be taken into account with regard to the force signals. This article proposes a methodology to simulate cutting forces in broaching on the basis of the discretization of each tooth and computation of several cutting parameters. This simulation was done with MATLAB® software. Afterwards, the simulation was compared to a real fir tree broaching to evaluate its quality.

Bibliography

Simulation of cutting forces has become very common in the field of machining and in its literature. Nowadays, it is known as a great help to understand the cutting process.

More than 25 years ago, [START_REF] Amarego | Computer based modeling of popular machining operations for force and power prediction[END_REF] proposed a unified theory to simulate cutting forces in milling, turning and drilling based on a simple series of oblique cutting tests. Cutting force models in the three directions were estimated by regression depending on the oblique cutting tests. Simulation was operated by the discretization of the tool cutting edge and by application of the cutting forces model on each discretized section. Ten years after, [START_REF] Budak | Prediction of milling force coefficients from orthogonal cutting data[END_REF] proposed a simplified methodology of this prior model. They still used the cutting edge discretization with a three component cutting force model. The innovation came from the cutting force model which was not estimated by oblique cutting tests but by orthogonal cutting tests. This solution is an improvement due to the simplification of the characterisation of the model. [START_REF] Stephenson | Process -independent force characterization for metal cutting simulation[END_REF] presented another possible solution to simulate cutting forces. Their methodology was based on the computation of an equivalent cut section, in opposition to the discretization of the cutting edge. This is another possible solution to simulate cutting forces.

Unlike the other cutting processes (turning or milling) in which it is possible to find either commercial solutions of cutting force simulation or articles about cutting force simulation, there is still a lack of study about broaching and its simulation. Currently broaches are designed with norms, and only a few number of studies deals about cutting forces simulation in broaching. [START_REF] Bellais | Brochage[END_REF] described the norm used to develop a broach. He indicates how to choose the parameters of a broach, but it does not establish neither a methodology to simulate the cutting forces nor an evaluation of the cutting parameters in each discretized section of the broach. To determine broach parameters, [START_REF] Terry | Concurent tool and production system design for a surface broach cutting tool: a knowledge-based systems approach[END_REF] did not proceed by simulation of cutting forces, but by a series of equations like Taylor's tool life equation and maximum stress admitted by the broach. This solution, computer-assisted, proposes broach parameters not far away from the norms because the equations implemented in this software come from the norms themselves. This computation does not allow a simulation of the cutting forces. [START_REF] Ozturk | Modeling of broaching process for improved tool design[END_REF] and [START_REF] Kokturk | Optimisation of broaching tool design[END_REF] proposed a simulation of the cutting forces in broaching with an in-house software. Those two articles are very interesting because they deal about the broaching of fir tree slots. This simulation is used to determine the part deflection and then they could determine the maximal admissible force to limit the part deflection. Other criteria, like maximum tooth stress, were also determined, and a multi-criteria optimisation algorithm chooses tools parameters. Most of these articles use cutting force simulation only as a step of calculation to solve a multi-criteria optimisation algorithm. As far as we know, [START_REF] Sutherland | A model for the cutting force system in the gear broaching process[END_REF] is the only article which only deals about cutting forces in broaching, without multi-criteria optimisation algorithm… This article presents the simulation of cutting forces in helicoidal gear broach. Very recently [START_REF] Zhang | Finite element modeling of broaching process of Inconel 718[END_REF] proposed a simulation of the cutting forces in nickel-base alloys. This simulation was done by a two-dimension finite element method in orthogonal cutting with only one tooth. As a consequence, this simulation is not directly transposable to our case, which deals with simulation of cutting forces in broaching in order to understand cutting mechanisms in each section of the broach.

In conclusion, examples of cutting force simulation in classical machining operation (milling, turning, and drilling), as in broaching, demonstrate the interest of cutting force simulations to improve the understanding of the cutting process occurring in very complex machining operation. For classical machining process, commercial application of cutting force simulation are available as well as articles describing the methodology to manage a simulation. For broaching, it remains necessary to develop realistic in-house cutting force simulation software, to be as close as possible to the process.

Cutting experiments and modelisation

Experimental set-up

Simulation of the cutting force previously requires a series of experiments for two reasons: the implementation of the cutting force models the verification of the simulated cutting forces.

Each test, performed to identify the cutting force models and to verify the simulation, was done using a CNC broaching device equipped with an electric ram [Figure 1(a)]. This machine allows a maximum pushing force of 10 kN for a range of cutting speed from 0 to 20 m/min. Figure 1(a) presents the experimental set-up with the broaching machine and the dynamometer. Figure 1(b) presents the three axes system on the fir tree slots to measure the cutting forces. This machine is also equipped with an integrated force sensor to measure the pushing force of the machine. Force in the z axis represents the pushing force of the broaching machine. Measurement of the cutting forces was done by a Kistler 9255A three axes dynamometer [Figure 1(a)]. This sensor was chosen for two reasons:

Its loading capacity (40 kN in the axis z and 20 kN in the x and y axes).

The possibility to fix a platform on the top to clamp the workpiece and other sensors like accelerometers. The use of a platform for broaching has already been done by [START_REF] Axinte | Tool condition monitoring in broaching[END_REF].

To limit noise on the measure, a low pass-filter was applied on the measured signals with a cut-off frequency of 50 Hz. 3.2 Cutting force model

Experimental plan

The goal of these experiments is to provide a cutting force model to implement the cutting force simulations. But, as explained before, every cutting test was performed on an industrial broaching machine used by the production. It means that the experimental design must be very short, to limit the non-production time of the broaching machine.

The choice of orthogonal cutting test was done to reduce the number of tests. The cutting speed was chosen as a constant because, in broaching, during one machining, cutting speed is constant in every part of the tool. Due to the very complex shape of the fir tree slot [Figure 1(b)], feed per tooth and rake angle change along the cutting edge of each tooth. That is why the experimental design must include the rake angle and the feed per tooth with multiple levels. Rake angles used by the turbine disk manufacturers for nickel-base alloys are generally ranged from 8 to 18 degrees, and feed per tooth ranged from 0.02 mm in finishing to 0.08 mm in roughing. High speed steels tools are used. New tools were used for each trial. The influence of the tool wear is not taken into account in this work, but integration of wear can be a future development of the simulator. The cutting edge is sharp from the grinding and not prepared by a special radius or chamfer: its measure gives a radius around 4 to 7°µm. According to the explanations given just above, the experimental design follows a full factorial experimental approach as shown in Table 1. Each condition was repeated three times.

Orthogonal cutting test

During this study, the machined material is a nickel-base alloy, Udimet® 720, used to produce rotating parts in aero engines. The orthogonal cutting tests were carried out with one tooth orthogonal tools [Figure 2(a)]. Recorded outputs are the cutting force (F t ), the thrust force (F r ) and the chip thickness (h). Results of the orthogonal cutting tests are presented with a normalised form in Figure 4. This normalisation is presented in equation ( 1), K t and K r values are in megapascals. Figure 4 shows that normalised cutting forces decrease with the increase of the feed per tooth (f) and the rake angle ( ). Another important thing is the large range of variation of the normalised cutting forces, K t fluctuate from 9,000 MPa for f = 0.02 mm and = 8 to 3,500 MPa for f = 0.08 mm and = 18. As expected, specific cutting forces calculated for this nickel-base alloy are very high (Figure 4). These values of K t and K r induce very high forces and high temperature during machining which involves very fast broach wear. During this study, broaches are made out of high speed steel tools. Both graphs, on Figure 4, justify the interest to understand and to control each cutting parameter of the broach, to improve productivity and quality of the machined parts.

( ) ( )

t r t r F F K K b f b f (1)

Cutting models

Cutting models results from an experimental work implemented in the cutting force simulation. Two types of cutting models were applied for this simulation (one for orthogonal cutting and the other for oblique cutting):

Model 1 orthogonal cutting [START_REF] Albrecht | New developments in the theory of the metal-cutting process, part 1[END_REF] Model 2 oblique cutting model [START_REF] Budak | Prediction of milling force coefficients from orthogonal cutting data[END_REF].

The first model (orthogonal cutting) neglects the inclination angle ( s ) of the real fir tree broach (which is around 1.4 degrees). This approximation allows the use of a two-dimension model [as shown by equation ( 2)]. The forces F tc and F rc represent the cutting and the thrust forces due to the rake face. The forces F ts and F re represent the forces due to the cutting edge. Forces F tc , F rc F te and F re are given by equation (3).

t tc te r rc re F F F F F F (2) tc tc te te rc rc re re F K f b F K b F K f b F K b (3)
The parameter b is the width of cut of each discretized teeth and f is the feed per tooth of each discretized tooth. For this very simple model, modelisation of the chip thickness is not necessary. Coefficients K tc , K te , K rc and K re are evaluated by a polynomial equation from orthogonal cutting tests. The equation ( 4) shows the form used to calculate coefficient K tc . The coefficients a tc , b tc , c tc , d tc , e tc and f tc come from the regression. The polynomial form for the three other coefficients are similar.

2 2 tc tc tc tc tc tc tc K a f b c f d e f f ( 4
)
The second model (oblique cutting model), as the previous model, does not require approximation about the inclination angle ( s ) anymore. It means that it becomes necessary to add a third force. Equation (5) shows this third force included in the model.

t tc te r rc te a ac ae F K f b K b F K f b K b F K f b K b (5)
This three-dimension forces model requires to compute the coefficients K tc , K rc , K ac the modelisation of the shear angle ( n ) by equation ( 6), the shear stress in the primary ( s ) by equation ( 7) and the friction coefficient on the rake face ( n ) by equation ( 8). Parameters n , s and n are determined by polynomial equations as a function of feed per tooth (f) and rake angle ( ), as equation ( 4). Then, it is possible to compute k tc , k rc and k ac by the system of equation ( 9).

n n k c k c k c c (9)
The coefficients K ts and K re are also determined by polynomial regression from orthogonal cutting tests, like for the first model. The coefficient K as is determined by equation ( 10) as already done by [START_REF] Amarego | Computer based modeling of popular machining operations for force and power prediction[END_REF]. Due to the very small value of K ae , given by equation ( 10), most of the publications which use this model simplify this parameter K ae by zero like in [START_REF] Budak | Prediction of milling force coefficients from orthogonal cutting data[END_REF]. With s = 1.4° the value of K ae is equal to: K ae = K rs × 0.023, which is a very low value. Example of the low value of F a due to K ac and K ae is given in Section 6 of this article.

Geometrical description of the broach

Prior to simulate cutting forces in broaching and to use the cutting force models, it is necessary to characterise the fir tree broach geometrically. Because the most difficult point is not to obtain the cutting coefficient, the real difficulty is the geometrical description of the broach, and then to know the cutting section taken by each tooth. The first step is the description of the roughing and the finishing of the fir tree slot. Figure 5 shows in red the shape of the fir tree slot and in blue the shape left by the roughing. These two shapes are mathematically characterised by three matrixes. Matrixes are n lines and 1 colon matrixes. n is equal to the high of the fir tree (H) divided by the discretization on the fir tree (d). Generally, the value of d is 0.01 mm. The second step is the automatic generation of the broach teeth (by an algorithm) depending on the position of the first tooth, the rise per tooth, the roughing and the finishing shape matrixes. Figure 6 shows all the teeth of the broach between the roughing and the finishing shapes. Each different line deals with a different tooth of the broach.

Y

To compute the cutting coefficients of both models, and after elementary cutting forces, some preliminary computations are needed. These preliminary computations are the computations of parameters which characterise the cutting coefficients. These parameters of each discretized sections are: the feed per tooth (f), the width of cut (b), the vectors ( , t , r a ) which give the directions of the elementary forces F t , F r , F a , the normal rake angle ( n ) and the inclination angle ( s ). After that, for model 1, cutting coefficients are computed by equation ( 4) and elementary forces obtained by equations ( 2) and (3). For model two, cutting coefficients on the rake face are computed by equation 9 and elementary cutting forces by equation ( 5).

The first step is the computation of the radial ( ) r and axial ( ) a vectors of each discretized section of each tooth. Figure 7(a) shows the roughing and the finishing shape of the fir tree slot (like Figure 6). Figure 7(a) shows also one tooth with a discretized section and its radial and axial vectors. The second step is the computation of the rake angle and the inclination angle. To use both cutting forces models, the normal rake angle ( n ) and the inclination angle ( s ) have to be calculated. Equation ( 12) shows the three steps of computations needed to compute n and s . The rake angle is the angle given during the grinding of the broach, the angle o is the orthogonal rake angle. The angle is shown in Figure 6 is equivalent to the orientation angle (K r ).

After computation of f, b, , t , r , a n and s it is now possible to calculate (using parameters of both cutting models) the elementary cutting forces F t , F r , F a of each section of each tooth. Computation of the forces along the , x , y z axes [Figure 7 .sin( ).

. .sin( ). .cos( ).

z t x r a y r a F z F t F x F r F a F y F r F a (13)

Summation of the elementary cutting forces in the global cutting forces

Elementary forces F x , F y , and F z along the , x , y z axes are now associated to each discretized section of each tooth. But, because broaching is a non-constant cutting process due to the teeth entering/exiting, direct summation of each elementary force is not possible. Figure 8 illustrates the summation technic used to obtain global forces versus the broach displacement. Other parameters must be added to this algorithm: the pitch of the broach (P), the workpiece thickness (ep), the discretization of the broach displacement (disp), the length of the broach (le) and the inclination angle of the workpiece ( workpiece ).

The summation technic is the following: the broach displacement along the z axis is simulated by a loop. If the tooth is located between the lower and the upper limit, the elementary forces are summed in to 'Global Force of each Tooth matrixes'. These matrixes are called * , The maximum value of axial force F a was checked and was found around 14 N, which is a very low value compared to more than 1,000 N for the radial force F r . After projection on x and y axes, F a becomes negligible. Both models along the three axis present similar results with a maximum difference of 4%, as presented in Figure 10. As it is possible to see, simulated forces in the z axis agree very well with the measured forces. Simulated forces in the x and y axes agree very well until the abscissa of 600 mm. After this abscissa, cutting forces present the same proportions but with a deviation. Because of the symmetrical shape of the fir tree (Figure 1), the force on the x axis has to be centred on zeros as for simulation [Figure 11(a)]. This deviation can be explained by the roughing of the fir tree (Figure 5). By opposition to the finishing shape done with one tool, the roughing shape is done with nine consecutive tools. Each tool of the roughing has a position tolerance in the shape. This tolerance can change the shape of the roughing and then change the cutting sections taken by the teeth of the finishing tool. This modification of shape can induce a more important wear of the teeth which cuts this area, as already pointed in [START_REF] Mandrile | Identification and modelization of cutting phenomena in broaching to understand tool wear[END_REF].

This hypothesis based on the deviation of F x has to be confirmed by metrology of the roughing and the finishing shapes. In the simulation, if the roughing or the finishing shapes are modified, to take into account the lack of alignment of certain tools of the broach, the simulation becomes a way to evaluate the broach manufacturing tolerance and then a possibility to improve the process in terms of conception and process monitoring. Except for the problem of force direction deviation, the maximum error of the simulation is 10%, mainly due to the manufacturing precision of the broach and the accuracy of the cutting models. The broach used for Figure 11(b) presents only a fir tree machining strategy and not a dovetail machining strategy at the end of the tool.

Choice of the cutting model for industrial application

This study presents two cutting models: one for orthogonal cutting, the other for oblique cutting. Difference between both models for the fir tree broach tested here is very low: less than 4% (Figure 10) because of the very low inclination angle of this broach.

For similar case to this study (low s ), orthogonal cutting model is sufficient enough to simulate the cutting forces. This model provides two main advantages: it only requires measurement of F t and F r and modelisation is very easy (no mechanical knowledge of cutting is needed), so this model can be used very easily in the industrial field.

In the case of an important inclination angle, the oblique cutting model is compulsory. This model allows, by means of orthogonal cutting test, the modelisation of oblique cutting process, but requires measurement of the chip thickness in addition to F t and F r . This model also implies a better knowledge of metal cutting to model and understand shear stress, shear angle and friction coefficients. This model seems to be less usable in the field of industry but it is very interesting in the field of research.

The border between the need of orthogonal cutting model and oblique cutting model has not been verified by experimental investigations because of the cost of a new broach to verify this point only. Both models are mechanistic models. They are sufficient to modelise cutting forces but they are not sufficient to understand the cutting process. Analytical models, as already done by [START_REF] Germain | Development of a Cutting Force Model Which Integrates Tool Flank Contact: Application on Cupper Turning in Super-Finition[END_REF] for turning, can be a great help to go further. But, because of even more difficult realisation of analytical models, they are not directly suitable for the industrial field.

With both cutting force models of the simulation the industrial can simulate cutting force for new tools design, develop process monitoring strategies based on a better understanding of the cutting process, and also modify the roughing or the finishing shapes to evaluate the influence of miss aligned tools on the cutting forces.

Conclusions

A methodology to simulate cutting forces in fir-tree broaching is proposed in this article. By means of orthogonal cutting tests, two cutting force models are provided: one for orthogonal cutting and the other for oblique cutting. By computation of cutting parameter (f, n , s …) of each discretized section of each tooth, cutting models are implemented in a MATLAB® code to simulate the cutting forces. Elementary forces are associated to each discretized section according to the cutting parameters also computed in the MATLAB® code. Cutting forces variations are associated to the cutting section variation and explain force peaks. The orthogonal cutting model is accurate enough to simulate the cutting forces with a low inclination angle. To go further, analytical models will be a great help to understand the cutting process in broaching.

This simulation allows to collect a lot of important data and measured cutting forces of fir tree broach become understandable. Simulation was compared with measured cutting forces and some lack of fit was explained by the miss of alignment of roughing and finishing tools. Future work will be concentrated to develop an interval of tolerance of cutting forces, and simulations of miss-aligned tools. This simulated cutting forces with tolerance will be used for the development of process monitoring strategies and develop new broach designs. For example, to prevent tool breakage, the maximum force loading on each tooth could be determined; the rake angle variation along the cutting edges could be evaluated; finally, the period of new broach development could be decreased by simulation of cutting forces and then limitation of cutting trials.

Nomenclature

Figure 1

 1 Figure 1 Broaching machine and dynamometers experimental set-up (see online version for colours)

  Figure 2(b) shows the workpiece and the broaching tool with the chip formation, recorded with a high speed camera. Those videos were used to explain the shape of the force signals illustrated in Figure 3.

Figure 2

 2 Figure 2 Orthogonal cutting test configuration and a picture extracted from the high speed camera film (see online version for colours)

Figure 3

 3 Figure 3 Shape of the forces signals (see online version for colours)

Figure 4

 4 Figure 4 Evolution of normalised forces versus the rake angle and the feed per tooth (see online version for colours)

Figure 5

 5 Figure 5 Roughing and finishing shape of the fir-tree slot (see online version for colours)

Figure 6

 6 Figure 6The broach teeth between the roughing and the finishing shapes (see online version for colours)

Figure 7

 7 Figure 7 Axial and radial vector of each discretized section of a tooth (see online version for colours)

  (b)] is carried out by equation (13). The outputs of this paragraph are three matrixes, * ,

  and m colons. m is still the number of teeth in the broach and r is equal to the equation (14). These matrixes give the forces during the broach displacement for each tooth, which means that most of the lines (broach position r) of each colon (tooth m) are filled with zeros. The 'Global Forces' along the broach displacement are obtained by summation of every colon of each line of * , the final outputs of this computation. The next paragraphs will present the results of global forces matrices.

Figure 8 Figure 9

 89 Figure 8 Broach displacement for the summation of the elementary forces

  Figure9shows the global cutting forces along the , x , y z axes for both models. Figure9(a) shows the results of the first model and Figure9(b) the results of the second model. Both models give very similar results. This observation can be explained by the very low inclination angle. For most of the discretized sections of each tooth s = 1.4°, it means a very low value of k ac . The maximum value of axial force F a was checked and was found around 14 N, which is a very low value compared to more than 1,000 N for the radial force F r . After projection on x and y axes, F a becomes negligible. Both models

Figure 9 Figure 10

 910 Figure 9 Global forces versus the broach displacement in the , x , y z axes, (a) model 1 (b) model 2 (see online version for colours)

Figure 11

 11 Figure 11 Simulated and measured forces (see online version for colours)

s

  Shear stress in the shear plane[MPa].HHigh of the fir tree [mm]. d Discretization of the fir tree along the y axis [mm]. m Number of teeth of the broach [mm]. the fir tree. Matrix n lines and 1 colon [mm]. each tooth of the broach. Matrix n lines and m colons [mm]. Feed of each discretized section of each tooth. Matrix n lines and m colons [mm]. disp Discretization along the z axis of the broach displacement [system. Matrixes r lines and 1 colon [N].

  Tangential, radial and axial cutting forces [N]. Ftc, F rc , F ac Tangential, radial and axial forces due to the rake face [N]. Normalised cutting forces in orthogonal cutting [MPa]. K tc , k rc , K ac Tangential, radial and axial cutting coefficients due to the rake face [MPa]. K te , k re , K ae Tangential, radial and axial cutting coefficient due to the cutting edge [M/mm].

	b	Width of cut [mm].
	f	Feed per tooth [mm].
	h	Chip thickness [mm].
	P	Pitch of the broach [mm].
	ep	Thickness of the machined workpiece [mm].
	F x , F y , F z	Cutting forces in the , x	, y z axes system [N].
	F t , F r , F a
	Fte, F re , F ae	Tangential, radial and axial forces due to the cutting edge
		[N].
	K t , K r

n , o

Normal and orthogonal rake angles [degrees].

This paper is a revised and expanded version of a paper entitled 'Identification and modelisation of cutting phenomena in broaching to understand tool wear' presented at 7th Conference on High Speed Machining (MUGV 2012), Saint-Etienne, France, October 2012.

Acknowledgements

This study has been done by the financial and technical support of Turbomeca. All the experimental tests have been performed in Turbomeca workshop.