Joachim Schöpfel

Eric Kergosien

Stéphane Chaudiron

Bernard Jacquemin

Éric Kergosien

Dissertation as Data

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Being originally handwritten by students and exclusively intended for teachers and professors, academic theses and dissertations have dramatically evolved in form, content and usages over the past century. By the beginning of the 20 th century, students began to have their writings typed using mechanic typewriter, conferring to the works a more professional status. Those documents became stored and catalogued in university libraries, and read or even used by academic communities for research purpose. A new step has been taken in the 90s when it became common for most of the students to type their works by themselves and directly on a personal computer. Even if those writings were (and very often still are) submitted in a paper format, they are initially produced in an electronic format, and can be stored and archived in that way. They represent the starting point of electronic theses and dissertations (ETDs). And despite the academic habits to deal with material writings, the mere existence of those numeric files, increasingly made available by the authors regularly driven by their academic institutions, has major consequences on both document processing and the way they may be taped by researchers. In particular, ETDs have obviously developed functional features specific to the three-fold nature of electronic documents studied by [START_REF] Pédauque | Le document à la lumière du numérique[END_REF]. The digital nature of ETDs, established by the distinction between materiality (form), content (sign) and social context (medium), offers inchoately new ways to take advantage of those them.

Dissertation as a document

According to [START_REF] Pédauque | Le document à la lumière du numérique[END_REF], a document has a triple reality, inseparable in paperwork, but that can be discriminated in electronic documents such as ETDs. In order to evaluate consequences of the digital transition, we first observe the pre-digital theses and dissertations in accordance to the same criteria as we will later for ETDs. Regarding the physicality of the dissertations (form), the material aspect of the works has to be taken into account. Traditional dissertations have format characteristics (e.g number of pages, paper size, font style and size), several media to be hold (e.g paper, microfilm, microfiche), internal structure rather formal but that may differ from an institution or a scientific field to another (e.g IRMED in experimental sciences, bibliography), they may include figures or charts, and sometimes annexes and other research materials such as corpora or recordings. The meaning of the textual contents on the physical support (sign) basically relies upon lexical semantics. Consequently, correct access to knowledge or even to information into the dissertations can be provided by considering two types of contexts: the scientific context (domain, bibliographic references) of the dissertation determines a semantic and terminological field where word meaning can be selected; and the lexical and syntactic context in which each term appears also applies semantic constraints. Finally, the dissertation is written and published in a purpose specific for a human society (medium): the author has to communicate his scientific approach and his achievements as a clue of abilities acquired along a doctoral program. The communication occurs in a social environment where it has to prove legitimacy, scientificity and authorship. For dissertations, the legitimacy is strongly attached to the institutional rules and processes of practicing science, writing and depositing a document, defending a scientific work before a jury, etc. The scientificity has to be measured by peers essentially in terms of publications and dissemination, or according to the way the contents are connected to previous research. As a creative work, a dissertation carries authorship for both text production and scientific development likely to have impact on technological and financial interests. Thus, dissertations have powerful links to the civil society.

Dissertations and data

All along a research work performed in view of writing and defending a doctoral these, research material and data are collected, processed and preserved. Besides their own data, researchers have always based their work on previous results and often on data collected by others in other circumstances. For decades, "outside" data would have been used more extensively for new research, had they been made easily accessible and operable. The electronic property that characterizes today's dissertations potentially offers technical ways to capture more directly research data. The current challenge is now to switch from the virtual to reality. Consequently, potentialities have to be identified. Several inquiries have been conducted these last years that make a significant overview of the situation, and two cases arise: research data may be included into the textual document, or the dissertation may provide links to research data, that are stored somewhere else.

Dissertations as a data vehicle

Including research material directly into the document is the most obvious way for dissertations to provide access to data. Several inquiries have been conducted among 780 print and electronic dissertations in sciences, social sciences and humanities from the Universities of Lille (France) and Ljubljana (Slovenia), submitted and defended between 1987 and 2015 [START_REF] Prost | Hidden Treasures: Opening Data in PhD Dissertations in Social Sciences and Humanities[END_REF],Schöpfel et al., 2016]. Those inquiries have been able to distinguish between different aspects of data, considering the primary (raw data from field practice, sources) or secondary (processed information, enriched results) nature, or taking into account if they appear into the dissertation text or attached to the text as an appendix. Results are also observed depending on the academic disciplines of the dissertations. When dissertations contain research data (526), the chance for an external user to reuse them for other purpose depends strongly on those parameters. Primary data consist mostly of interviews or surveys, experimental observations gathering or text samples (including scanned archives). As source of the research approach, those pieces are broad, and can be reused in many contexts, assuming that the information format allows it, which is not obvious for each format. Secondary data are obtained through the research operations, as a result of the source processing. Often more structured or more elaborated (tables and statistics, tagged text corpora, charts and drawings), the results are likely to be reused. Nonetheless the reusability is linked to documentation and to other factors: figures and tables into the dissertation text are given a caption, but remain difficult to be harvested properly by a computer tool; in appendices, results or even sources are less completely documented, not to mention the lack of metadata or simply of an unique identifier, and the large variety of formats and technical media makes them incompatible with content mining algorithms. According to the inquiries, habits of communicating research data directly in dissertations prove to depend strongly on the scientific domain. For example, many dissertations in historic science give access to large amount of data, in a wide variety of formats, including structured and reusable ones. If archaeology and history of arts dissertations providing data are fewer, the quantity of data supplied is significant, but more concentrated with iconography. In contrast, philosophy tends to communicate research data, but in small volumes, whereas political science deals with few data in few documents.

Dissertations as a gateway to data

Another way for dissertations to give access to materials used for a research project is to provide link to primary or secondary datasets located elsewhere than into the document. Dissertation text and research data can be described and stored apart, in distinct repositories. Depending on situations, data can be located on either institutional or personal repositories, and if applicable, corresponding ETDs are uploaded to other specific facilities. Data formats can vary depending on the publication aim (data preservation, dissemination or even initial gathering to be shared between actors): institutional repositories have requirements for a rather structured information, and are often more demanding on this topic than social networks. The breakup of the dissertations into text and data creates a need: links have to be established between the documents and corresponding data; they may be provided by means of a (preferably permanent) URL or a unique data identifier determined in or outside the scientific domain (DOI). Several projects have studied actual cases of separation of text and data stored on different platforms in order to introduce workflow solutions or process recommendations. The Dataverse ETD program conducted at Emory University [START_REF] Doty | Making Student Research Data Discoverable: A Pilot Program Using Dataverse[END_REF] involves librarians to identify precisely dissertations submitted with supplemental files containing research data. They download and document research data in Dataverse repository, and establish an explicit link between the record in ETD system (for a given dissertation) and the record in the data archiving service (for the corresponding research data). ETDplus project carried out at Educopia Institute has leaded to guidelines that takes a similar position [START_REF] Schultz | Guidance Documents for Lifecycle Management of ETDs[END_REF]: research data should be stored in a repository separate from the dissertation text, and a permanent link between text and data should be provided into metadata by using persistent identifier such as handle, DOI, ARK or PURL. Furthermore, data files have to be processed to match archival format requirements. Bielefeld University has set up PUB, a functional workflow originally designed to provide a bridge between research data and working papers, and also able to cope with digital dissertations that may be accompanied with research material in additional files [START_REF] Vompras | Repository workflow for interlinking research data with grey literature[END_REF]. The working paper/dissertation and the data files are stored separately in respectively a disciplinary repository and an institutional repository. A DOI is assigned to each object according to the DataCite Metadata process, that ensure the linking between text and data by both DOI citations in the text and link explicitation in the DataCite Metadata Schema.

Dissertations as data

The approach we defend here differs from the previous ones by considering dissertations themselves as data. No distinction is made anymore between dissertation text and attached data, as the whole content is regarded the same way by content mining: structured data can be seized by the process, as contents can be collected, measured and analysed to provide useful information. Even metadata associated to dissertations and to research materials can supply a data mining system. The use of data mining techniques on dissertations entails that source dissertations are in digital format. The digital condition of documents is constitutive of considering ETDs as data, and to make it possible data to be processed by digital tools. Considering the document theory stated by [START_REF] Pédauque | Le document à la lumière du numérique[END_REF], a document is comprised of three dimensions: form, sign and medium. In the digital world, those dimensions have evolved: the paper document's form relies on an inscription performed on a medium, but digital documents dissociates inscription (stable) and supports (that can vary from writing to reading or storage). Thus electronic dissertation's form consists in a structure in which are organized data. Being expressed according to a specific language (XML, TEI), to an internal (DTD) and external (RDF) structure for a digital support (web), data fit information extraction and filtering systems. The paper sign has particular interest in the way that a content constructs the meaning. ETDs sign uses structured data to build knowledge, by using both lexical and semantic hints, and external information resources such as ontologies, DBpedia, geolocation or specialized vocabularies. Automated systems can identify (and virtually reuse) arguments and finality of ETDs. In physical documents, the medium dimension includes the notion of social communication and an accurate context specified by rules or even laws that legitimate the way the communication is performed. Transposition in ETDs implicates strong rules that prescript how dissertation or additional material has to be structured, which format is demanded, and what procedures are involved. Moreover, legal status is attached to ETDs, indicating precisely access permissions or restrictions to the document, licensing information and possible intellectual property specifications when applicable.

Using dissertations as data

While researchers and institutions are well aware of the interest and the need to organize storage and availability of ETDs and research data, very few projects have been undertaken to use those very files as research data.

SPECTRa-T

Yet the SPECTRa-T project [START_REF] Morgan | Extracting and re-using research data from chemistry e-theses: the SPECTRa-T project[END_REF] has designed a set of tools to perform text mining on chemistry ETDs and extract research data in order to build RDF triplestores and enable semantic queries. This proof-of-concept approach addresses issues attached to the three dimensions of the digital document. Although data mining tools are more efficient when applied on structured text, such as marked-up documents formatted in XML, MS Office Open XML (.docx) or OpenDocument XML (.odt), ETDs are often supplied in other, less suitable formats: PDF but also PostScript, LaTeX and MS Document Format (.doc). To struggle against this heterogeneity of form, in the absence of a marked-up document file, the process requires a modifiable Word version instead of PDF or a PostScript, in order to convert it to XML as a standard processing format (form). The access to meaning is granted by text and data mining tools, specialized vocabularies or ontologies (sign). These tools and resources can only be efficient if they are designed according to the advice of subject experts in the same discipline. Even more, the tools and resources implicated in the workflow have to be dedicated for an individual discipline. Repositories involved in data storage and especially in triplestores building offer services and processes that meet the needs of researchers of the field and that match the domain practices: those repositories are designed by working closely with researchers in different subjects. As scientific communication supports that legitimate both research skills and intellectual property (medium), ETDs have to be both preserved for the archival role of assessing students' research, and valued by the institutions responsible for the production (e.g universities) an the conservation (e.g repositories), because they are unique resources containing potentially valuable data that must be made extractable and re-usable. In order to overtake a simple archival process and foresee new research purposes, the whole approach of producing, depositing and processing ETDs has to be designed to ensure the chance to reuse. Discipline-specific policies have to be published to manage each step of the procedure and to match ETDs processed contents with data extraction tools and with new needs of research. SPECTRa-T has designed a workflow and guidelines to deal with heterogeneous ETDs formats and make it certain that the files are converted into standard XML, to take into account chemistry domain and subdomains while lexico-semantic resources and tools extract data, store them into repositories and build semantic links in triplestores. In this approach, technical issues and modelling seem to can be addressed: data can be seized by content mining algorithms, and information extraction leads to knowledge databases. [START_REF] Brook | The Social, Political and Legal Aspects of Text and Data Mining (TDM)[END_REF] note that the remaining gap lays in the choices to limit the access to ETDs and databases, either related to legal issues around copyright and database rights, or connected to publishers' restriction to physically access data. Those limitations have to be solved in a non-technical field.

TERRE-ISTEX

This ongoing project 1 proposes an approach to identify and extract information (particularly geographic data) from scientific texts in order to develop an information research tool. TERRE-ISTEX is part of a larger project, ISTEX 2 -one of the "Investment for the future" program of the French Ministry for Education and Research -, whose main objective is to provide free and easy online access to retrospective collections of sciences literature in all disciplines, including scientific journals, databases, text corpora, etc. Being a subpart of this project, TERRE-ISTEX ambition is to identify, in a large heterogeneous corpus, named entities, geographic and thematic information linked to climate change. Our corpus is basically constituted of more than 8 million scientific articles from ISTEX data with linked metadata in MODS format, of 25,000 multilingual documents (articles and other grey literature texts) from CIRAD, and of 70,000 digital or digitalized dissertations and metadata from ANRT. Among those documents, only a small part is relevant for the climate change subject, but they have to be identified by the process. The first step of the general process is thus to automatically identify in this large, heterogeneous and multilingual corpus thematic, location and temporal data. After a semi-automatic validation performed by subject experts, data are indexed in the Elasticsearch 3 tool in order to plan search operations among identified information in plain text, and to enable geographic content/results analysis. As a proof-of-concept, we first processed 1,200 articles from the EGC conferences 4 , and we built an index from the relevant information automatically identified in those texts, including thematic, spatial, temporal and structural information. The NLP tool gathered data such as conference place, author city names (that can be linked to place or city geocodes), titles, abstracts, domains, author names, year of the conference... The automatic data-markup validation is performed in both French and English by thematic experts using the SentiAnnotator viewer [Farvardin et al., 2015], and the results can be stored in the Elasticsearch index. The analysis of the markups in Elasticsearch provide first interesting results: the thematic layout along the period under review indicates the evolution of relative thematic significance of the domain, assuming that more publications are accepted in an important topic; the thematic evolution can also be linked to locations of interest, considering the research laboratories and the conference places; relations of co-authorship and evolution of the co-authorship along the period has also been under review, linked or not to the identified topics 5 . From this first experimentation, we prospect now to scale up to the "big data", taking into account the heterogeneity (languages, formats, text typology) of the corpora, and to test other scientific domains like history, culture... We also need to integrate other analysis resources such as knowledge database, web contents, Open Archives... to narrow the results.

Barriers

For an easy operation of dissertations in a research perspective, several bolts -technical, psychological, legal, commercial... -have still to be unlocked. Availability: The text mining tools can process only electronic text or data. One part of dissertations, especially the older, do not exist in a digital format. Moreover, digitization of printed dissertations is not yet a solution, producing often inoperable images or little more usable document format such as PDF.

Accessibility: An access to dissertation should be provided to allow their reusability. One part of -even digital -dissertations are not made online available. And offline dissertations are alas mostly difficult to identify, and thus to find. Even when a digital documents exist, few of them cannot be shared because of confidentiality; a little more are embargoed according to a publisher contract because they are to be published as a book; and the other have access restrictions settled by a repository platform. Sometimes, non-institutional sharing is performed on a personal website or on social networks, making the dissertation difficult to find or to download. Legality: Legal questions remain in several countries about access to ETDs, and more about text and data mining in dissertations: just because ETDs are online does not necessarily mean information processes can be applied, because no law or license has made a legal framework to scientific TDM. Another pending question involves remuneration for the authorship (sometimes difficult to identify) and for the storage of ETDs, not often take into account: open access is not equal to free access, and providing someone with the right to read a dissertation is different to grant him to apply TDM on that very dissertation. Feasibility: Notwithstanding a positive view on text and data mining tools that can process online ETDs, those approaches are not optimal: the format (especially PDF) does not fit with marked up data, needed by analysis tools; the inner structure of text and data is often incorrectly identified by automated algorithms; metadata associated to ETDs could be of help, if comprehensive and provided by a discipline or domain expert also qualified in documentation, which is very rare; and above all, TDM tools and resources included in the process or the workflow have to be scientifically adapted to the discipline under review, preferably to a totally generic platform.

Concluding remarks

Under the Netherlands UE presidency, major actors of research (researchers), of research communication (commercial and open publishers) and of research and technology users (industrial partners) met in Amsterdam on April 2016. They together published a Call for Actions on Open Science 6 that prompts political, commercial and educational institutions to take up data mining in scientific document issues, and to initiate rules and actions to foster success in opening access to scientific documents for TDM. The Call for Actions propose 12 general measures that initiated the rallying of more specific claims: in October 2015, the LERU (League of European Research Universities) already demanded "a mandatory exception that will enable users to text and data mine all content to which they have legal access: the right to read is the right to mine" 7 . In France, a Law for a Digital Republic 8 has been published on October 8th, 2016, that institute an exception to copyright for text and data mining when scientific documents are legally accessed. exception is valid only for scientific purpose, and not for commercial use. The European Union should legalize in 2017 a similar exception for research and educational purpose, enabling text and data mining to texts and contents to which legal access is granted. Furthermore, publisher are asked to adapt both licensing and technical format to make mining easier. The conditions of success of these initiatives can be summed up in four words: availability, accessibility, legality, feasibility (A2LF), that have to be reached to unlock current bolts. ETDs and additional materials have to be made available by both retro-digitization and deposit of text and additional data on online repositories. Access has to be granted by free and technical open access to clearly identified institutional repositories. The legality of mining ETDs has to be ensured by a legal TDM exception; moreover, the issuing of prescription rules should systematize a third party agreement to clear rights in a mining context. Prescription rules could also ease the feasibility by proposing application standards and by promoting rich metadata and text structures.

  /ekergosien.net/DefiEGC/index.html. 6 https://english.eu2016.nl/documents/reports/2016/04/04/amsterdamcall-for-action-on-open-science. 7 http://www.leru.org/index.php/public/news/the-right-to-read-is-theright-to-mine/. 8 https://www.legifrance.gouv.fr/eli/loi/2016/10/7/ECFI1524250L/jo/te xte.

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	5	First	results,	graphs	and	drawings	are	available	at
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Emmanuel Mermoz

Julien Astoul

Marc Sartor

Jean Marc Linares

Alain Bernard

A new methodology to optimize spiral bevel gear topography

Keywords: Optimization, Finite element, method, Spiral bevel gear

Introduction regarding MGB specificities

Main Helicopter Gearboxes (MGB) are high-tech devices that must transmit very high mechanical power, with a significant reduction in speed, at lower weight while occupying the least space possible. So, it is necessary to undertake a heavy and long development process before reaching a gearbox design that satisfies all the economic, technical and security requirements and especially that allows thousands of flight hours [START_REF] Mermoz | Benefits and Limitations of Parametric Design Implementation in Helicopter Gearbox Design Phase[END_REF]. Customers attach particular importance to weight criterion, this one being a key factor in terms of profitability. So, housings are generally made of light alloys like Aluminium or Magnesium. A large part of the rotor loads being transferred to the airframe by the MGB, especially very high torques, housing undergoes high deflections that make the design of MGB a specific case regarding gear optimization. Under flight loads, gears can suffer from a displacement in the order of magnitude of 1 mm. The gear specialist has to ensure a proper behaviour in a set of positions that are the results of MGB external loads conditions in conjunction with the MGB internal stiffness. An optimized mechanical behaviour is ensured mostly by a correct geometrical position of contact areas and an acceptable Hertz pressure. For that purpose, the designer has to optimize geometrically the initial tooth flank of the gears by a set of corrections between 10 and 200 mm. Finding the right optimization is sometimes very long and several loops of topography adjustments of a few microns may be required. The order of magnitude of the local deflection induced by Hertz pressure phenomena is no more than a few microns, so the optimization window is quite small. This sensitivity of the topography has also an impact on the manufacturing tolerances of power gears that are very narrow. The aim of this paper is to present a new methodology to optimize the topography of spiral bevel gears.

A review of previous works on spiral bevel gear simulation and optimization

Loaded meshing simulation

¨

In 1987, Madrosky [START_REF] Madrosky | Conception des engrenages spiro-coniques: Geometrie et simulation du comportement[END_REF] proposes a loaded meshing model rather advanced for his time. Indeed, it already takes into account the flexibility of teeth. Those are calculated by the finite element method. The other part of the system is considered infinitely rigid. The relative displacements of the axes of the gears result from the deformation of the complete device. The contact stiffness is deduced from the Hertz theory. The latter gives contact dimensions and pressure. Gosselin [START_REF] Gosselin | A General Formulation for the Calculation of the Load Sharing and Transmission Error Under Load of Spiral Bevel and Hypoid Gears[END_REF] simulates the meshing of various tooth flank topographies, using the same techniques as Madrosky. He recommends maximizing contact ratio to improve load sharing. Lelkes [START_REF] Lelkes | Numerical Determination of Cutting Parameters for the Control of Klingelnberg Spiral Bevel Gear Geometry[END_REF] simulates the behaviour of gears manufactured according to the Palloıd method, also referring to the same technique. However, the Hertz theory is based on assumptions inconsistent with some contact properties of spiral bevel gears. Indeed, the opposite surfaces are conforming, the bodies are finished and they slide in the contact zone. De Vaujany [START_REF] Vaujany | Numerical and Experimental Study of the Loaded Transmission Error of a Spiral Bevel Gear[END_REF] opts for an approach that combines finite elements analyses to evaluate tooth bending effects and the Boussinesq and Cerruti theory to model the contact deformations. Alves [START_REF] Alves | Set of Functions for the Calculation of Bending Displacements for Spiral Bevel Gear Teeth[END_REF] accelerates the computation of the stiffness of teeth, wheels and sails by introducing a set of interpolation functions. Bibel [START_REF] Bibel | Meshing of Spiral Bevel Gearset with 3D Finite Element Analysis[END_REF] deals with the loaded meshing using directly PATRAN finite element models. The contact is treated by the computational code MARC. Litvin [START_REF] Litvin | Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-milled Formate Generated Spiral Bevel Gears[END_REF] and Argyris [START_REF] Argyris | Computerized Integrated Approach for Design and Stress Analysis of Spiral Bevel Gears[END_REF] adopt the same approach. However, they use the software Abaqus. The meshes are automatically built from the This paper aims to present the new method developed to generate optimized spiral bevel gear surfaces. Thanks to a complex non linear finite element model, the geometrical gear meshing positions under operational loads are first precisely computed. These meshing positions are then used as inputs of a calculation process that seeks to define the best tooth surface topography. So far, this activity was based on sensitivity studies conducted directly by the designer, which led to repeat calculations whose progress was difficult to control.

EUROCOPTER uses now optimization algorithms to compute automatically the surfaces of the tooth contact flanks. This approach leads to higher performances of the gear while reducing the development time. This paper describes the new process implemented to design the tooth shape, and illustrates its interest through an example.

points generated on the tooth flanks without using a CAD software. The finite element modelling of the teeth is more accurate and faster. The work presented in this paper is based on a similar technique. The model proposed by Litvin [START_REF] Litvin | Computerized Design, Generation, Simulation of Meshing and Contact, and Stress Analysis of Formate Cut Spiral Bevel Gear Drives[END_REF] features three teeth (Fig. 1). The flexibility of the tooth is taken into account, the gear itself being considered fixed. A torque is applied along the pinion axis. The simulation results highlight every potential contact on tooth edges. Vimercati [START_REF] Vimercati | Mathematical Model for Tooth Surfaces Representation of Face-hobbed Hypoid Gears and Its Application to Contact Analysis and Stress Calculation[END_REF] also uses a computational code based on the finite element method. His work shows that the contact ratio increases with the torque while the quasi-static transmission error decreases.

Gear topography optimization

Papers dealing with the optimization of the loaded spiral bevel gear behaviour are relatively recent. Simon [START_REF] Simon | Head-cutter for Optimal Tooth Modifications in Spiral Bevel Gears[END_REF] analyses the and the magnitude of the quasi-static transmission error. The considered tool profile is made of two tangent arcs. Their radius and the tool diameter are settings to be corrected. Simon calculates different cases of relative displacements of the teeth, as well as different intensities of the torque.

Artoni [START_REF] Artoni | Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification[END_REF] proposes a fully automated optimization process. It consists of two steps. Firstly, an ideal «ease-off» is identified. Its shape must minimize the area that is not occupied by the contact path in a given zone. The latter is defined according to the ANSI/ AGMA 2005-D03 standard. Artoni refers to the loaded meshing model developed by Bracci [START_REF] Bracci | Geometric Contact Pattern Estimation for Gear Drives[END_REF]. The optimization variables are the coefficients of the quartic function which define the «ease-off». Secondly, the appropriate settings of the machine tool are sought.

Artoni [START_REF] Artoni | An Ease-off Based Optimization of the Loaded Transmission Error of Hypoid Gears[END_REF] then works on the minimization of the quasi-static transmission error. The maximum contact pressure is minimized simultaneously. The contact path must not touch a flank edge. Therefore, a constraint function requires zero contact pressure outside the area defined by the ANSI/AGMA 2005-D03 standard. The objective is the sum of the transmission error, pressure and constraint function. The optimization variables are bounded. The research of the optimal «ease-off» is based on the Hooke and Jeeves method. Artoni uses the loaded meshing model developed by Kolivand and Kahraman [START_REF] Kolivand | A Load Distribution Model for Hypoid Gears Using Ease-off Topography and Shell Theory[END_REF]. The results shown in Fig. 2 seem promising. However, the author does not specify whether they are obtained after determining the machine tool settings.

Gabiccini [START_REF] Gabiccini | Robust Optimization of the Loaded Contact Pattern in Hypoid Gears with Uncertain Misalignments[END_REF] uses Artoni's work [START_REF] Artoni | Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification[END_REF]. His aim is the reduction of the sensitivity of the loaded contact path in order to bear the relative displacements of the gear axes. Tolerance ranges are assigned to the misalignment components. Every combination of their bounds is taken into account. The envelope of the displaced contact paths is plotted in Fig. 3.

Mastering the gearbox deflection

As explained in the introduction, the specificity of helicopter gearbox design is the need for gears optimization not in one position but in a set of positions. So, before computing tooth topography, the relative positions of all gear stages have to be computed precisely according to the various load configurations that can be found in flight. To estimate the gear displacements, EUROCOPTER has been working for years on the improvement of non linear mechanical finite element models that are now used as ''Virtual Tests'' [START_REF] Mermoz | Benefits of Virtual Testing for Drive System Development[END_REF]. Fig. 4 illustrates the kind of models that has influence of the tool geometry on the maximum contact pressure been developed. These models simulate very well bearing behaviours [START_REF] Zamponi | Study of Bearing Modelling in the Helicopter Gearbox[END_REF] and give accurate load distributions and deflection on housings. A full meshing of all contact areas has then been introduced. To keep the computation time under control, specific meshing shapes of gear and bearing have been developed to minimize the number of contact elements. Even with those precautions the number of degrees of freedom can supersede easily several millions. After a batch of simulations, the displacements of the tooth flanks can be synthesized into sets of four values: the axial displacements of the wheel and the pinion, the offset distance between the two gears and the variation angle between both axes. These parameters are found to be the most influential regarding spiral bevel gears optimization. Based on all these values coming from the FE analyses, the optimization phase of the tooth flank can be launched. The efficiency of a manual correction process depends on the operator experience. The latter cannot perceive clearly the links between the tooth flank shape and the transmission error. It is very difficult for him to establish the links between the changes that he implements on the shape and the implications that follow in terms of load sharing. Therefore, the search for a minimum contact Fig. 2. Maximum contact pressure optimization [START_REF] Artoni | An Ease-off Based Optimization of the Loaded Transmission Error of Hypoid Gears[END_REF].

pressure by setting himself the different designs to be evaluated is Fig. 3. Envelope of the displaced contact paths [START_REF] Gabiccini | Robust Optimization of the Loaded Contact Pattern in Hypoid Gears with Uncertain Misalignments[END_REF]. Fig. 4. Example of complex FEM models [START_REF] Mermoz | Benefits of Virtual Testing for Drive System Development[END_REF]. an uneasy task. Indeed, it depends on both the number of teeth meshed and the local spread of contact areas. So, generally, trying to obtain manually a minimum contact pressure is a cumbersome work, based on a very repetitive trial and error process.

An automated process is proposed in this paper. It is described in Fig. 5. The optimization variables are the six coefficients of the modified roll method commonly used in the spiral bevel gear machining. These settings enable to precisely handle the contact path. The objective function to be minimized is the maximum contact pressure along the loaded contact path.

The process is driven by the application manager developed by Samtech: BOSS QUATTRO. The initial values of the optimization variables are imported from a pre-design software or a previous study. The optimization module runs external procedures which have been developed using a standard programming language to create the loaded meshing model, taking also into account the displacement of the gear axes. Then it launches the MECANO script which simulates the mechanism behaviour using the finite element meshes of the teeth and their positions provided by the external procedures. It gets back the value of the objective function. The variables are successively perturbed in order to evaluate their influence on the result and to estimate a combination of their values that should lead to an improvement. Each change results in a recalculation of the objective. The loop is iterated until reaching the convergence threshold of the objective function.

The FE model that is the heart of the process is shown in Fig. 6. Only three teeth of each part are considered. It is assumed that the loaded contact ratio is less than three teeth. Each node of the conical interface is connected by rigid bodies to the axis of the respective part. The relative position of the teeth due to load is reproduced by displacing the axes in accordance with the results of the whole FEM model described in Section 3. The boundary conditions of the simplified model are shown in Fig. 6. A torque is applied along the driving gear axis. The driven part axis is successively fixed at given angular positions.

The loaded contact simulation is based on a non-linear static analysis. The computation is done by the software MECANO. The initial meshing position gives a slight interpenetration of the two teeth in contact. It is the starting point of the iterative research of the static equilibrium of the system. The contact area is updated during the computation. It moves and spreads until the equilibrium is reached. The result is the starting point of the iterations for the next angular position of the driven gear. The algorithm solves the contact problem for each given meshing positions.

Application case

Data defining the example considered here are presented in the first six lines of Table 1. The second part of this table gives the values of the six coefficients of the modified roll method obtained after a manual optimization process. These six values are the starting point of the automated contact path improvement process.

The components of the relative displacement of the gear axes are deduced from a loaded FE analysis of the complete gearbox. They are given in Table 2.

The optimization process runs on a PC with 2 CPU clocked at 1800 MHz. It is stopped after about 7 h. No error is generated during the execution of the various modules, although a wide variety of configurations is considered. This confirms the robustness of the algorithms that have been developed [START_REF] Astoul | A Simple and Robust Method for Spiral Bevel Gear Generation and Tooth Contact Analysis[END_REF].

The process progression is illustrated in Fig. 7. The convergence discontinuity observed results from the surface discretization. The pressure peaks are due to contacts on flank edges. Nevertheless, the overall trend shows a reduction of the maximum contact pressure. The gear specialist chooses the combination of values of variables which gives the best result. The optimal design is achieved here at the 21st iteration. Table 3 lists the related variables. Use of wide mesh to discretize the teeth, as shown in Fig. 8, increases the speed of calculation. In return, the pressures are calculated with less precision. However, it is possible to make a comparative analysis based on models constructed with meshes of the same size. Fig. 9 shows a significant improvement in load sharing compared to manual correction. The contact pressure is 1985 MPa after manual correction and 1582 MPa after maximum pressure minimization. Fig. 10 shows that the contact area is significantly extended, while avoiding the occurrence of a contact at the edges.

Conclusion

An optimization process able to design in an automated way the shape of spiral bevel gear flanks has been presented. It leads to a significant reduction of the development time, while allowing a strengthening of the quality of contact patterns by the reduction of the contact pressure. Its extension to the minimization of tooth contact errors seems possible, in order to contribute to the reduction of noise and vibration levels and therefore a higher durability of helicopter gearboxes.

4 .

 4 New optimization process 4.1. Contact pressure optimization process

Fig. 1 .

 1 Fig. 1. Model and boundary conditions [9].

Fig. 5 .

 5 Fig. 5. New spiral bevel gear topography optimization process.Table1Initial manufacturing data.

Fig. 6 .

 6 Fig.6. Simplified model and boundary conditions. Fig.7. Progression of the contact pressure minimization process.

Fig. 9 .

 9 Fig. 9. Load sharing before and after optimization.

Fig. 10 .

 10 Fig. 10. Contact path before and after optimization.

Table 1

 1 Initial manufacturing data.

	Workpiece	Pinion	Gear
	Tooth number	23	30
	Module	5	5	mm
	Whole depth	10.24	10.24	mm
	Addendum	5.6	3.65	mm
	Face angle	40.2	54.283	8
	Pitch angle	37.483	52.517	8
	MR coefficient 1	0.639404	0.794488
	MR coefficient 2	ÿ0.005814	0
	MR coefficient 3	0.000598	0.001704
	MR coefficient 4	ÿ0.000997	0
	MR coefficient 5	0.000023	ÿ0.000024
	MR coefficient 6	ÿ0.000168	0
	Table 2
	Displacement compounds of the gear axes.
	Pinion axial displacement		0.441742	mm
	Gear axial displacement		ÿ0.065310	mm
	Offset displacement		ÿ0.401187	mm
	Shaft angle displacement		0.005277	8

Table 3

 3 Values of the variables after pressure minimization.

	` Piece	Pinion
	Modified roll coefficient 1	0.640054
	Modified roll coefficient 2	ÿ0.005219
	Modified roll coefficient 3	ÿ0.001244
	Modified roll coefficient 4	ÿ0.000292
	Modified roll coefficient 5	ÿ0.001435
	Modified roll coefficient 6	0.000445
	Fig. 8. Model mesh and contact areas.


Fabien Leroy
email: fabien.leroy@univ-orleans.fr

Sébastien Gogo

Christophe Guimbaud

Léonard Bernard-Jannin

Zhen Hu

Fatima Laggoun-Défarge

Vegetation composition controls temperature sensitivity of CO2 and CH4 emissions and DOC concentration in peatlands

Keywords: Ecosystem respiration, dissolved organic matter, soil temperature, Q10, Molinia, Sphagnum mosses

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Peatlands act as a global major carbon (C) store. They contain between 15 to 30% of the world soil C in only 3% of the global land area [START_REF] Turunen | Estimating carbon accumulation rates of undrained mires in Finland-application to boreal and subarctic regions[END_REF][START_REF] Gorham | Northern peatlands: role in the carbon cycle and probable responses to climatic warming[END_REF]. The Csink function of boreal peatlands results from particular environmental conditions (waterlogging, acidic soil and low temperature) and specific vegetation, i.e. Sphagnum mosses.

However, global change is expected to modify plant species composition in northern Sphagnum peatlands, with an increase in vascular plants (e.g. graminoids) to the detriment of Sphagnum mosses [START_REF] Dieleman | Climate change drives a shift in peatland ecosystem plant community: Implications for ecosystem function and stability[END_REF][START_REF] Buttler | Experimental warming interacts with soil moisture to discriminate plant responses in an ombrotrophic peatland[END_REF]. Disturbed peatlands represent a large potential source of CO2 and CH4 to the atmosphere and of dissolved organic carbon (DOC) export to rivers [START_REF] Limpens | Peatlands and the carbon cycle: from local processes to global implications -a synthesis[END_REF]. Thus, understanding the feedback between vegetation change and C fluxes in peatlands is required to predict the future of the peatland C budget. The response of CO2 and CH4 emissions and DOC concentration ([DOC]) to abiotic control is well documented [START_REF] Clark | Increased temperature sensitivity of net DOC production from ombrotrophic peat due to water table draw-down[END_REF][START_REF] Pypker | Shifting environmental controls on CH4 fluxes in a sub-boreal peatland[END_REF]. Nevertheless, studies on the sensitivity of plants have an extensive root systems, in comparison to Sphagnum rhizoids, able to exudate newly produced labile organic compounds (e.g. glucose; [START_REF] Saarnio | Rhizospheric exudation of Eriophorum vaginatum L.-potential link to methanogenesis[END_REF][START_REF] Fenner | Elevated CO2 effects on peatland plant community carbon dynamics and DOC production[END_REF]. According to Arrhenius function, the degradation rate of these compounds has a lower sensitivity to temperature than recalcitrant organic matter [START_REF] Davidson | Temperature sensitivity of soil carbon decomposition and feedbacks to climate change[END_REF]. Thus, Sphagnum peat mesocosms invaded by Molinia caerulea was sampled to investigate the three following hypotheses: (i) the presence of Molinia caerulea will increase the [DOC] due to a higher root exudate production compared to Sphagnum spp., (ii) these labile exudates will be rapidly consumed by microbial communities and will enhance both CO2 and CH4 emissions, (iii) as the C source will be more labile, the sensitivity to temperature of the C fluxes will decrease compared to recalcitrant C (with higher activation energies).

Twelve peat mesocosms (depth and diameter: 30 cm) were collected in March 2015 in La Guette peatland (France). The studied site is an acidic fen invaded by Molinia caerulea, a graminoid plant invading numerous peatlands [START_REF] Tomassen | Stimulated growth of Betula pubescens and Molinia caerulea on ombrotrophic bogs: role of high levels of atmospheric nitrogen deposition[END_REF][START_REF] Gogo | Invasion of a Sphagnumpeatland by Betula spp and Molinia caerulea impacts organic matter biochemistry. Implications for carbon and nutrient cycling[END_REF]. The mesocosms were buried outside and surrounded with a tarpaulin containing water from the peatland. Air and soil temperature at 5 and 20 cm depth were monitored in each mesocosm.

The mesocosms were separated into 2 treatments: 6 containing only Sphagnum rubellum ('Sphagnum' cores) and 6 containing Sphagnum rubellum and Molinia caerulea ('Molinia' cores). Molinia caerulea started to grow in May and increased up to 60% of mesocosms on average until its senescence in November (see supplementary material).

Measurements were performed between two to eight times per month, from May 2015

to April 2016. Ecosystem Respiration (ER) was measured during 5 min using a closed chamber equipped with a GMP343 Vaisala [START_REF] D'angelo | Soil temperature synchronization improves representation of diel variability of ecosystem respiration in Sphagnum peatlands[END_REF]. CH4 emissions were measured during 15 min using the SPIRIT, a portable infrared laser spectrometer [START_REF] Guimbaud | A portable infrared laser spectrometer for flux measurements of trace gases at the geosphere-atmosphere interface[END_REF].

Water table level (WTL) was manually measured in each mesocosm piezometer. Water was collected from the piezometer to measure [DOC] with a Shimadzu TOC-5000 analyzer. All measurements were performed in the same day and were related to WTL, air and soil temperature at 5 and 20 cm depth with exponential regression. R 2 from exponential regressions were calculated after a logarithmic transformation (linearization of the date). Temperature sensitivity was expressed through the temperature coefficient (Q10; eq. 1), and energy of activation (Ea, eq. 2):

Q10=(k2/k1) [10/(T 2 -T 1 )] eq. 1 k1 and k2 are rates at two observed temperatures T1 and T2.

k=A.e (-Ea/RT) eq. 2 k is the reaction rate coefficient, A is the pre-exponential factor, R is the ideal gas constant and T is the temperature in Kelvin.

One-way ANOVAs with repeated measures were used to compare Molinia to Sphagnum cores.

Throughout the measurements, environmental conditions did not differ significantly between Sphagnum and Molinia cores other than the WTL which was 2.4 cm higher in Sphagnum cores than in the Molinia ones (Table I). WTL ranged from 2.5 cm to 17 cm (Fig 1a). Air temperature ranged from 0°C in January to 30°C in July (Fig 1b). Soil temperature at 5 and 20 cm depth varied from 2.3°C and 5°C in January to 27.3°C and 25.7°C in July, respectively (Fig 1c and1d).

[DOC] were significantly lower in Molinia cores compared to Sphagnum ones (Table I, Fig 2c), which disproves our first hypothesis but supports the mechanisms proposed by [START_REF] Freeman | Export of dissolved organic carbon from peatlands under elevated carbon dioxide levels[END_REF] who suggested that labile DOC release, through root exudates, stimulates microbial activity and enhances the degradation of organic matter, in particular the DOC fraction. Mimics of roots exudates have been revealed to enhance microbial biomass in peat soil [START_REF] Basiliko | Do root exudates enhance peat decomposition?[END_REF], that might, with Molinia caerulea occurrence, trigger a real priming effect leading to an increase of DOC consumption.

Furthermore, in contradiction to our third hypothesis, the presence of Molinia increased the [DOC] sensitivity to soil temperature (Q10, Ea, Table II andFig 2c). The Q10 values obtained were higher than those found by [START_REF] Freeman | Export of organic carbon from peat soils[END_REF]Q10= 1.36) but lower than those found by [START_REF] Clark | Increased temperature sensitivity of net DOC production from ombrotrophic peat due to water table draw-down[END_REF]Q10= 1.84 and 3.53 under anaerobic and aerobic conditions, respectively).

As postulated by the latter authors, we showed that vegetation cover plays an important role in the [DOC] and its sensitivity to soil temperature. Further studies on the DOC and vegetation relationship are essential to determine how vegetation change may alter this C pool.

CO2 and CH4 emissions were higher in the presence of Molinia caerulea comparing to Sphagnum, showing an average increase of 2.4 and 3.1 fold, respectively (Table I, Figure 2a and b). Similar observations have already been reported in peatlands with graminoids (e.g. [START_REF] Armstrong | Biotic and abiotic factors interact to regulate northern peatland carbon cycling[END_REF]. The greatest CH4 emissions were observed with Molinia occurrence, at the same time with an increase of the thickness of aerobic zone, which opposes with the general association of CH4 emissions under anaerobic conditions. Such potential effect could be compensated with the fueling of methanogens in anaerobic peat by the root exudates, already related to the difference of CH4 production among plants species [START_REF] Koelbener | Plant species from mesotrophic wetlands cause relatively high methane emissions from peat soil[END_REF].

Furthermore, variations of CH4 emissions are also controlled by the plant community and its ability to transport CH4 [START_REF] Schimel | Plant transport and methane production as controls on methane flux from arctic wet meadow tundra[END_REF] and their potential for rhizospheric oxidation [START_REF] Ström | Species-specific effects of vascular plants on carbon turnover and methane emissions from wetlands[END_REF]. If root exudates fuel the microbial communities, the C flux sensitivity to temperature is expected to decrease [START_REF] Davidson | Temperature sensitivity of soil carbon decomposition and feedbacks to climate change[END_REF]. This hypothesis was confirmed by the ER results: the presence of Molinia decreased the ER sensitivity to temperature (Table II). However, this did not hold for CH4. The temperature sensitivity of CH4 emissions increased in the Molinia cores (Table II). In natural systems, acetoclastic methanogens are dominant over hydrogenotrophic methanogens [START_REF] Kao-Kniffin | Methane dynamics across wetland plant species[END_REF].

However, as reported in the latter study, graminoid soils are colonized primarily by hydrogenotrophic metabolisms. These two methanogenesis pathways require different levels of energy: 195 kJ mol -1 for hydrogenotrophic methanogenesis and 50 kJ mol -1 for acetoclastic methanogenesis [START_REF] Beer | Transport and thermodynamics constrain belowground carbon turnover in a northern peatland[END_REF]. Thus the increased temperature sensitivity under Molinia caerulea could reflect the promotion of hydrogenotrophic communities.

ER, CH4 emissions and [DOC] were correlated to WTL and soil temperature (Table II).

Increased soil temperature enhanced exponentially these three C-fluxes under both plant communities (Fig 2). Soil temperature explained the higher amount of variability compared to the WTL, even for CH4 emissions. Such weak correlation with the WTL could also be due to the little WTL variation over the experiment. Our best fit between ER and temperature differed with the vegetation: ER in Sphagnum cores was more correlated to soil temperature at 5 cm, whereas with Molinia caerulea ER was more influenced by soil temperature at 20 cm (Table II; Figure 2a). Sphagnum photosynthesis occurs in the first centimeters of the peat profile, whereas root exudates excreted by Molinia could stimulate microbial activity deeper in the peat profile. These physiological differences between Sphagnum and Molinia may explain the best fit observed for ER and also for CH4 emission and [DOC] (Table II).

In conclusion, both biotic (vegetation cover) and abiotic (mainly temperature) factors

C

  fluxes and [DOC] to abiotic factors in a context of vegetation change are lacking. Our aim was to assess to what extent CO2 and CH4 emissions and [DOC] sensitivities to abiotic factors in Sphagnum peat mesocosms could be modulated by the occurrence of vascular plants. The presence of graminoids in Sphagnum mesocosms is expected to change C fluxes through a more efficient C uptake that allocates C to the above-and belowground parts of the plant. Vascular

  control CO2 and CH4 emissions and [DOC] in peat mesocosms. Molinia caerulea can deliver labile C stimulating microbial activity and promoting DOC consumption and CO2 and CH4 emissions. The increase in soil temperature enhanced [DOC] as well as CO2 and CH4 emissions. Moreover, our findings demonstrate that the two controlling factors interact and that vegetation modification changes the C-fluxes' sensitivities to temperature. Under global change, Cdynamics in peatlands are thus subjected to many alterations through plant community modification. This study advocates taking vegetation change into account in global models with a concomitant variation in the temperature sensitivity.

Figure 2 :

 2 Figure 2: Exponential relationship between Ecosystem Respiration (a), CH4 emission (b), Dissolved Organic Carbon (c) and soil temperature at 5 cm for Sphagnum cores and at 20 cm for Molinia cores

Table I :

 I Mean values of 12 months' measurements of Ecosystem Respiration (ER), CH4 emissions (CH4), Dissolved Organic Carbon (DOC), Water Table Level (WTL), photosynthetically active radiation (PAR) and air (Ta) and soil temperature (Ts) in Molinia and Sphagnum cores. Significance levels of one way ANOVAs with repeated measured are expressed as *p < 0.05, **p < 0.01, ***p < 0.001 (n = 6). DOC) with Water Table Level, Air and Soil Temperature at 5 and 20 cm. Bold numbers represent the highest determination coefficient for each variable in Sphagnum and Molinia cores. Significance correlation are expressed as -/ + p < 0.05, --/ ++ p < 0.01, ---/ +++ p < 0.001.

	Determination coefficient (r 2 ) Mean Molinia Sphagnum ER (μmol m -2 s -1 ) GHG fluxes 2.39 0.99 CH4 (μmol m -2 s -1 ) 0.094 0.030 Water compartment DOC (mg L -1 ) 31.9 55.7 WTL (cm) -7.04 -4.58 Environmental parameters PAR (μmol m -2 s -1 ) 711 741 Ta (°C) 12.0 12.1 Ts at 5 cm (°C) 13.1 13.1 Ts at 20 cm (°C) 13.7 13.9 Table II: Determination coefficient (r 2 ) of exponential regressions for mean values of 12 Q10 Ea Tables Molinia / Sphagnum P 2.39 *** 3.14 * 0.57 *** 1.54 *** 0.96 0.99 1 0.99 months' measurements of Ecosystem Respiration (ER), CH4 emissions (CH4), Dissolved Sphagnum Molinia Sphagnum Molinia Sphagnum Molinia Water Table Level ER 0.38 ---0.23 ---CH4 0.49 ---0.18 --DOC 0.12 -0.14 -Air Temperature ER 0.72 +++ 0.60 +++ 3.75 2.58 92.2 65.7 CH4 0.00 0.01 1.00 1.01 2.3 4.7 DOC 0.55 +++ 0.46 +++ 1.56 1.66 31.7 35.9 Soil Temperature at 5 cm ER 0.76 +++ 0.67 +++ 4.09 2.86 97.6 72.9 CH4 0.68 +++ 0.86 +++ 5.61 7.61 119.4 140.2 DOC 0.64 +++ 0.60 +++ 1.68 1.91 36.0 44.5 Soil Temperature at 20 cm ER 0.65 +++ 0.75 +++ 4.01 3.38 97.3 85.0 CH4 0.59 +++ 0.88 +++ 4.05 9.13 94.6 153.1 Organic Carbon (Variables DOC 0.37 +++ 0.70 +++ 1.47 2.38 25.3 60.0

-/ + represents a negative or positive relationship, respectively.

Figures

Figure 1: Time series of water table level (a), air (b) and soil temperature at 5 (c) and 20 cm (d) in Sphagnum and Molinia cores (±SE, n=6) from May 2015 to April 2016. Data were collected during greenhouse gas emission measurements.

Acknowledgements

This paper is a contribution to the research conducted in the Labex VOLTAIRE (ANR-10-LABX-100-01). The authors would like to thank X. Yin, G. Belot, A. Menneguerre for their contribution to gas measurements, P. Jacquet and C. Robert for their assistance in SPIRIT maintenance and N. Lothier for DOC analysis. We also thank E. Rowley-Jolivet for revision of the English version.

Supplementary materials