Nicolas Haderer
email: nicolas.haderer@inria.fr

Romain Rouvoy
email: romain.rouvoy@univ-lille1.fr

A preliminary investigation of user incentives to leverage crowdsensing activities

Keywords: Mobile sensing, Feature Model, SaaS, Multicloud, Component-based software engineering, Middleware

With the continuous emergence of smart portable devices, like TabletPC or smartphones, crowdsensing is becoming an active research topic. While exploiting the wisdom of the crowd provides huge benefits to pervasive applications, one of the key challenges remains to motivate people to contribute to flow of data by sharing some of the capabilities of their device. In this paper, we therefore report on the APISENSE platform, a participative platform that help scientists to collect realistic datasets from a population of voluntary participants. More specifically, we provide a preliminary investigation of how user incentives can be integrated in such a platform to encourage people to contribute while leaving enough flexibility to the scientist for choosing the model that fits their requirements.

I. INTRODUCTION

For years, the analysis of activity traces has contributed to better understand crowd behaviors and habits [START_REF] Liu | Uncovering Taxi Driver's Mobility Intelligence through His Trace[END_REF]. As an example, the Reality Mining activity traces collected by the MIT Media Lab 1 or the Stanford University Mobile Activity TRAces (SUMATRA) 2 have become a reference testbed to validate mobile algorithms in ad hoc settings [START_REF] Ben Mokhtar | From Pervasive to Social Computing: Algorithms and Deployments[END_REF]. Nonetheless, the diversity of the activity traces available in these repositories remains limited and therefore often constrains scientists to tune inadequate traces by mapping some of the parameters to their requirements. More recent approaches mine the data exposed by location-based social network like Gowalla or Foursquare, but the content of these activity traces remains limited to coarse-grained locations collected from users check-ins.

In this context, it has been demonstrated that the new generation of mobile phones can revolutionize collection of crowd activities traces. The survey in [START_REF] Lane | A Survey of Mobile Phone Sensing[END_REF] identifies key points of its potential. Largely adopted by populations, with more than 472 millions sold in 2011 (against 297 millions in 2010) according to Gartner institute 3 , smartphones have become a central piece in people's life. Not only focusing on computing or communication capabilities, modern mobile devices are now equipped with a rich suite of sensors 1 http://reality.media.mit.edu 2 http://infolab.stanford.edu/pleiades/SUMATRA.html 3 http://www.gartner.com/it/page.jsp?id=1924314

enabling a new class of sensing applications that recognize user activities, their context, and environments. In addition, the generalization of app stores or markets provided by phone vendors allow scientists to deliver new sensing applications to large populations of users and thus leverages the enrollment of participants to a larger scale than it was possible previously.

Building a mobile sensing system involving a large communities of mobile users is not trivial, as it generally requires to implement the following phases. The recruitment phase consists in selecting a group in a population to execute a specific sensing task. The deployment phase is the ability to propagate the sensing task over selected participants and is followed by the execution phase where participants collect and report data from their mobile devices. And finally, the incentive phase where participants are rewarded, financially or not, for the performed task. In addition to that, due to the sensitive nature of data collected and the power limitations of mobile devices, a mobile sensing system must also support mechanisms to protect participants privacy and minimize the energy consumption of their devices.

For all these phases that constitute key challenges for the mobile sensing paradigm, we can find a plethora of models studied in the literature. Often, each model has only been elaborated for a specific case study. To the best of our knowledge, the state-of-the-art platforms implement one or part of these models, without providing any flexibility in the application design, but rather imposing a specific model which cannot be adapted in another context. For example, a mobile sensing experience allowing to build a network coverage map of a particular city does not need to store a participant identifier, while a sensing experiment aiming at observing the participants behavior in a city needs to store this information and therefore must provide different mechanisms to preserve participants privacy. We believe that this lack of flexibility prevents the wide adoption of crowdsensing by others research communities, which have specific requirements for their studies, without any expertise in mobile sensing technologies to develop their own systems and attract a large community of participants.

In this paper, we argue that current mobile sensing systems must evolve towards new research communities, which are not expert in mobile sensing systems. We are therefore particularly interested in discussing about user incentive that such a platform should implement in order i) to seduce scientists, and ii) encourage partipants to contribute to the sensing experiments. Scientist incentives include the modular integration of a wide variety of features that they can compose upon their need, while participant incentives deal with privacy and rewarding mechanisms that can be offered in order to catalyze the collection of datasets. This discussion is illustrated on the APISENSE platform, a crowd sensing platform we developed. Interestingly, we show how the cloud computing model and a component-based software architecture can be used to leverage such user incentives.

The remainder of this paper is organized as follows. In Section II, we briefly discuss of current mobile sensing model studied in the literature and limitations of current mobile sensing system architectures. In Section III, we report on the design choices of the APISENSE platform that illustrates our proposition before concluding (cf. Section IV).

II. STATE OF THE ART & LIMITATIONS

Mobile sensing has recently become an active research topic that aims at proposing new models and platforms to leverage the process of collecting data on the field. In this section, we report on the state-of-the-art models recently published and we discuss their key limitations. This discussion is organized along five criterias: the execution of sensing tasks, the description of sensing tasks, the recruitement of participants, the privacy issues, and the user incentives.

Sensing Task Execution In mobile sensing, the execution of a sensing task can follow two different models identified as participatory sensing or opportunistic sensing. Participatory sensing models used in systems like [START_REF] Ra | Medusa: A programming framework for crowd-sensing applications[END_REF], [START_REF] Froehlich | Myexperience: a system for in situ tracing and capturing of user feedback on mobile phones[END_REF] require explicit user actions to share sensor data (e.g. taking a picture, answering to a survey). In opportunistic sensing approaches, the sensing task is executed in background of the mobile devices without any explicit user involvement [START_REF] Brouwers | Pogo, a Middleware for Mobile Phone Sensing[END_REF], [START_REF] Das | Prism: Platform for Remote Sensing Using Smartphones[END_REF].

Sensing Task Description In the literature, several domainspecific language has been proposed to describe sensing tasks. MYEXPERIENCE [START_REF] Froehlich | Myexperience: a system for in situ tracing and capturing of user feedback on mobile phones[END_REF], proposed for Windows mobile smartphones, provides a configuration language based on XML in order to control the features of the application. MY-EXPERIENCE collects data using a participatory approachi.e., by interacting with users when a specific event occurs (e.g., asking to report on the quality of the conversation after a phone call ends). The definition of XML-based languages has also been explored by [START_REF] Ra | Medusa: A programming framework for crowd-sensing applications[END_REF].

FUNF [START_REF] Aharony | Social fmri: Investigating and shaping social mechanisms in the real world[END_REF] is an Android toolkit focusing on the development of sensing applications. FUNF in a box is a service provided by FUNF to easily build a dedicated sensing application by filling in a web form to configure the data collect as well as the periodicity of the sensing task. While this system proposes a lightweight way to describe a mobile sensing task, potentially accessible to scientists with no background in computer science, the expressiveness to describe a sensing task is still limited to collected raw data. On the contrary, Pogo [START_REF] Brouwers | Pogo, a Middleware for Mobile Phone Sensing[END_REF] proposes an API, based on JavaScript, to perform complex processing before reporting the collected datasets, but it requires a stronger background in programming languages to use the platform.

Participant Recruitment To recruit and deploy a sensing task over a population of participants, two strategies have mainly been studied by the community. The former, called pull-based approach, used in [START_REF] Shin | AnonySense: A System for Anonymous Opportunistic Sensing[END_REF] is a proactive deployment strategy where mobile phones, with or without an implication of the participant, download directly a sensing task from a remote server. The latter, push-based approach, automatically propagates the sensing tasks to the mobiles devices of participants. PRISM [START_REF] Das | Prism: Platform for Remote Sensing Using Smartphones[END_REF], for example, is a system implementing this approach, and using a dedicated recruitment model to select the candidate participants depending of their location and their battery resources available to push a sensing task. In [START_REF] Reddy | Recruitment framework for participatory sensing data collections[END_REF], a more complex model has been proposed to recruit participants based on reputation metrics.

Participant Privacy ANONYSENSE is an opportunistic collection platform with a strong emphasis on privacy [START_REF] Shin | AnonySense: A System for Anonymous Opportunistic Sensing[END_REF]. By combining novel techniques, such as k-Anonymity and tessellation, reported data collection time and location are blurred in order to preserve the privacy of participants and thus prevent attacks on geo-spacial data. Despite these techniques have been largely adopted in multiple studies [START_REF] Bettini | Anonymity in Location-based Services: Towards a General Framework[END_REF], [START_REF] Gruteser | Anonymous Usage of Location-based Services Through Spatial and Temporal Cloaking[END_REF], the cost of privacy enforcement implies the degradation of the quality of data, thus also potentially decreasing its utility. Even if these kinds of protection mechanisms can be considered as sufficient in some cases, they quickly become irrelevant for studies requiring a fine-grained location of participants. SENSORSAFE [START_REF] Choi | Sensorsafe: Managing health-related sensory information with fine-grained privacy controls[END_REF] is another participatory platform providing fine-grained temporal and location access control mechanisms to keep the control of data collected by sensors on mobile phone.

Participant Rewarding

In order to attract participants, a sensing platform has to provide appropriate levers to catalyze the collection of datasets. As cited by [START_REF] Dutta | Common Sense: Participatory Urban Sensing Using a Network of Handheld Air Quality Monitors[END_REF], one key challenge when cellphones are used as a research platform is to incite users to participate to a given experiment. Even if sensing applications represent a great interest for scientists, it does not offer any particular service to the participants, while consuming their resources (e.g., battery, bandwidth). Recently, [START_REF] Yang | Crowdsourcing to smartphones: incentive mechanism design for mobile phone sensing[END_REF] proposed two models to characterize incentive mechanisms. A platform-centric model, where initiators of the sensing task set the price they want assigned to some data and a user-centric model where the price is defined by the participants. However, current models focus essentially on financial aspect to reward participants, which cannot be accessible for small scientist laboratories. We believe that other incentive models can be incorporated in mobile sensing system, inspired by models like Foursquare4 , by incorporating serious games in their systems in order to attract and motivate participants.

Current solutions focus on one or part of the mobile sensing challenges. The state-of-the-art platforms impose a static choice to setup sensing experiments, thus limiting their reuse in other scientific context with different requirements. Indeed, none of the studied models represents an ideal solution, but rather strongly depends on the context (e.g. targeted population, type of collected data). Another important limitation resides in the server infrastructure of proposed platforms. Typical mobile sensing platforms adopt a Systemas-a-Service deployment model hosted by an infrastructure that uses multi-tenant architecture style. This architecture style imposes all the users of the platform to share the platform resources, storage mechanisms, and financial model implemented by the provider.

We believe that adopting a multi-tenant approach highlights several leaks for building a flexible mobile sensing platform. By hosting all the collected data in the same infrastructure, a malicious attack or a bad implementation of security mechanisms in the application design can taint scientists data integrity, thus causing a potential security leak. Processing data over a large population of mobile users requires considerable computing resources, which can impact the availability of the platform for the other tenants. And finally, multi-tenancy restraints platform customization, by imposing infrastructure defined in the Platform-as-a-Service level.

III. APISENSE SOFTWARE ARCHITECTURE

To illustrate our proposition to cope with the current limitations described in the previous section, we introduce APISENSE, a mobile sensing platform, targeting various scientist communities to help them to build and deploy sensing experiments over large population of mobile users. The APISENSE architecture principles focus mainly on three aspects: i) flexibility of the platform to be easily extensible to address unforeseen requirements, ii) customization including fine-grained configuration level to define a sensing experiment, and iii) scalability & security of the server infrastructure.

A. Multi-cloud architecture

Figure 1 illustrates an architecture overview of our APISENSE platform. Unlike current mobile sensing platforms, APISENSE adopts a multi-cloud orientation using a star topology where the central node is assumed as the trusted part of the system.

In this topology, the entry point for scientists that want to define and deploy a sensing experiment over mobile users is the central node. New scientists can login in from the web interface, and create their own SaaS instance (i.e., a sensing node). The newly created SaaS is a dedicaded environment, providing typical services of mobile sensing system to i) describe experiment requirements in a domain-specific language, ii) deploy sensing experiments in the central node, and iii) connect other services to the platform to extract and reuse collected datasets (e.g., visualize, analyze). From the central node, scientists can trigger the deployment (or the download) of the configured SaaS as a web archive (war) or as a virtual appliance [START_REF] Quinton | Leveraging Feature Models to Configure Virtual Appliances[END_REF].

APISENSE therefore reflects the features of the dedicated environment as a software product line (SPL), which is used by scientists to build their own sensing node SaaS product. This design breaks the vendor lock-in syndrome by offering the scientist the opportunity to select the IaaS or the PaaS she prefers, which can be a public or private infrastructure, depending on her preferences or on ethical and privacy issues related to the storage of collected traces. The other benefits of this design deal with customization, where scientists have the possibility to select an appropriate infrastructure at the IaaS level, such as supported language and specific database to store the datasets collected from mobile users. And finally, all scientists sensing node resources are completely isolated from others, improving security and availability as a scientist application can take down a server instance or perform a computation without affecting the other instances. Once deployed, the scientist can connect to her SaaS in order to create a new sensing experiment, which will be published in the central node with the experiment requirements (e.g. privacy and incentive mechanism, recruitment and deployment model) in order to make it available to mobile users.

Mobile phone users, identified as participants in the platform, can use the dedicated mobile phone application to register to the trusted central node indicating her incentive to participate to a sensing experiment. Once registered, the mobile application sends automatically sensing capabilities of her mobile device as well as the hardware configurations. Participants can complete this information by indicating a geographical zone and a period of the day they are willing to execute a sensing task. If they activate the push deployment model, the central node will propagate sensing tasks in their mobile devices without their involvements. All the user profiles will remain confidential, and cannot be directly accessed by others scientist sensing nodes in the system, thus improving the protection of their privacy. The participants can also proactively retrieve a list of the available sensing experiments, depending on the participant constraints and the requirements defined by scientists. For all the experiments, information about sensing experiments configuration is provided, including privacy mechanism (i.e., keep anonymous user identifier or not, privacy mechanism techniques), incentive mechanisms (i.e., financial rewarding, serious gaming, goal of the experiment) and data collected on their mobile devices. Once enrolled in a experiment in the central node, an anonymous user identifier is sent to the sensing node hosting the experiment to prevent a new recruitment in the sensing experiment. This anonymous user identifier is also returned to the participant, with the SaaS URL that will be used to upload the collected data. To enforce the privacy concerns, the mobile application allows participants to adjust their privacy preferences in order to constrain the sensing task to collect data. Three categories of privacy rules can be defined. Rules related to location and time specify geographical zone or time intervals conditions under which experiments are authorized to collect data, respectively. The last category of privacy rules refer to authorization rules, which prevent sensors activation or access to raw sensor data if the user does want to share this information.

B. Handling variability

As defined previously (cf. Section II), a plethora of models has been proposed to realize all phases of a sensing experiment.

To cope with this diversity and propose a fine-grained configuration level to define a sensing experiment, we decided to adopt Software Product Line (SPL) approach [START_REF] Pohl | Software Product Line Engineering: Foundations, Principles and Techniques[END_REF]. SPL engineering aims at generating specific products from the requirements expressed by customers by composing a set of complementary features. A Feature Model (FM) is used to compactly define all the features in an SPL and their valid combinations. A FM is composed of a hierarchy of features, where a feature can be mandatory or optional and and may form Xor or Or-groups. Constraints (e.g., implies or excludes) can also be specified using propositional logic to express inter-feature dependencies.

Figure 2 depicts the variability model used to customize a mobile sensing experiment. In APISENSE, FM contains mainly two configurations levels, infrastructure level and sensing experiment level. Once a scientist is connected to the web interface of the central node, she can visualize the FM and select all the features of the first level of configuration. Infrastructure variability includes essentially the configuration of the components to be deployed in the sensing node: programming languages, servlet container in charge to expose services, and database technology to store collected data. If the selected features represent a valid configuration, the central node generates a virtual appliance or a web archive (war) that the scientist can download and deploy on a cloud provider. Once deployed, the sensing node provides also a web interface where the scientist can manage all the services provided. To create a new experiment, the scientist must proceed to the second level of configuration by selecting a set features from the sensing node web interface. Once the features are selected, a new instance of sensing experiment is generated (cf. Section III-C), deploying all services for publish sensing task on the central server, store data reported by participants and process or export collected data. We describe below different configuration levels proposed by APISENSE FM: Sensing language. This variability point defines a domain specific language to describe a sensing task that will be executed by participants. We decided to adopt standard scripting languages in order to ease the description of sensing experiments by the scientists. We therefore propose the APISENSE scripting library as an extension of the JavaScript, CoffeeScript, and Python languages, which provides an efficient mean to describe an experiment without any specific knowledge of mobile device programming technologies (e.g., Android SDK). Listing 1 provides a simple description excerpt, written with the languages currently supported by the APISENSE mobile application runtime, which reports the level and battery state (charging, discharging) when a new battery event is tirggered in the mobile device. The scripting library supports a wide range of features to define data collected during a sensing experiments including traditional sensors proposed by smartphones technologies, such as GPS, Bluetooth, accelerometer, compas, phone call, sms, application status (installed, running), for opportunistic sensing activities and also a graphical user interaction framework to build user surveys in the case of participatory sensing activities. As a future work, we plan to provide also a graphical language, to allow a scientist with no background in programming languages to define her sensing tasks. Privacy. In addition to this script, the scientist can configure some privacy filters to limit the volume of collected data and enforce the privacy of the participants. In particular, APISENSE currently supports two types of filters. The area filter allows the scientist to specify a geographic area where the data requires to be collected. For example, this area can be the place where the scientist is interested in collecting a GSM signal (e.g., campus area). This filter guarantees to the participants that no data is collected and sent outside of this area. The period filter allows the scientific to define a time period during which the experiment should be active and collect data. For example, this period can be specified as the working hours in order to automatically discard data collected during the night, while the participant is expected to be at home.

Recruitment. This phase consists in selecting the recruitment mechanism to elect a subset of participants, and to deploy the candidate sensing tasks. Two deployment models can be used. A pull-based approach, which is a proactive deployment strategy where participants download a sensing task from the central node. Or a push-based approach, which automatically propagates the sensing tasks to the mobiles devices of participants whenever it matches the sensing requirements.

Incentive To help the scientists to encourage participants to contribute to their experiments, this variability point allows them to configure rewarding mechanisms in order to catalyze the sensing of relevant datasets. As the APISENSE mobile application provides several mechanisms to control the access to sensors, the rewarding mechanism is based on the quality and the volume of datasets produced by participants. Therefore, the more sensors are activated by participants and the more datasets are uploaded, the more credits the participant receives for its involvement in the experiment. For example, the scientist can allocate more credits to the GPS sensors in order to balance the energy consumption and the privacy sensitive of this sensor. The assigned credits are then used by the scientist to provide participant rankings, involvement badges, or even coupons to reward the participants. The participant is therefore free to disable some of the sensors for privacy or energy reasons, but in this case, she will receive less credits when uploading her datasets. Analysis This last configuration point consists in selecting features in charge of processing collected datasets. At this time, we propose analysis feature given database access, visualize geolocated data and export them in various format to be downloaded by scientists.

C. SaaS Architecture

The main objective of APISENSE is to provide to scientists a platform, which is open, configurable in order to be reused in various contexts and easily extensible to deal with unforeseen requirements. To achieve this goal, we designed a SaaS architecture of APISENSE as an SCA distributed system running on the top of FraSCAti middleware [START_REF] Seinturier | A Component-Based Middleware Platform for Reconfigurable Service-Oriented Architectures[END_REF], a reference implementation of this open service model.

SCA promotes a vision of Service-Oriented Computing (SOC) where services are independent of implementation languages, remote communication technologies, interface definition languages and non-functional properties. SOC has proved to be an adequate solution for building flexible and agile software systems that are resilient to changes. SCA specifies a hierarchical component model, which means that components can be implemented either by primitive language entities or by subcomponents. In the latter case the components are called composites. To support serviceoriented interactions via different communication protocols, SCA provides the notion of binding. We therefore believe that SCA provides an flexible foundation for the APISENSE infrastructure by accommodating a wide diversity of programming languages and communication protocols in order to efficiently support the variety of scientists requirements.

In the APISENSE platform, all the features previously introduced are viewed as SCA components. Once deployed on a cloud provider, a sensing node mainly contains two components (cf. Figure 3), which exposes the services that can be remotely called. The former, the Experiment Manager component, allows the scientist to generate a sensing experiment instance from a valid Feature Model. This component exploits the reflective capabilities of the SCA platform to generate a new Sensing Experiment composite which includes all the selected components in the FM. The new instance thus automatically exposes new dedicated services to enable participants to report collected data (Data collector component), publish and describe a sensing task (Recruitment component), process (Query & Export components) and configure the rewarding mechanism (Serious game component).

The latter component, Reconfiguration engine, provides services for managing or adding new components in the architecture. This component represents the extension points which are used by the scientist to define custom component to process and visualise the datasets collected by participants. In this paper, we report on the design of the APISENSE crowdsensing platform. This platform distinguishes two roles: scientists requiring a sustainable environment to deploy sensing experiments and participants using their mobile devices to contribute to scientific experiments. This organization highlights two kinds of user incentives. From the scientist perspective, APISENSE is built on the principles of a multi-cloud infrastructure and offers a modular serviceoriented architecture, which can be customized upon their requirements. From the participant perspective, APISENSE supports a variety of privacy mechanisms and rewarding models to choose their level of involvement in a sensing task. We therefore believe that APISENSE can provide a sustainable foundation for building a new generation of context-aware services by leveraging the collection of realistic activity traces of mobile users.

Figure 1 .

 1 Figure 1. APISENSE Multi-Cloud Architecture

Figure 2 .

 2 Figure 2. APISENSE Feature Model

Figure 3 .

 3 Figure 3. Sensing Node Architecture

https://foursquare.com


Yann Quinsat

Christophe Tournier

In-situ non contact measurements of surface roughness

Keywords: In-situ measurements, non-contact sensor, 3D surface roughness, thermal compensation, polishing

Surface roughness measurements are often required to validate a machining process. However, when using a 3D surface roughness measuring instruments it is usually necessary to remove the part from the machine tool between two operations, potentially introducing systematic errors. Furthermore, surface roughness measuring instruments are not suited for measuring heavy and large parts such as stamping dies. This paper presents a method to measure the surface topography of a part in-situ, i.e. directly on the machine tool without removing the part. After introducing the sensor technology and the data acquisition chain, the effects of geometric imperfections of the machine tool and compensation for thermal effects on the measurement results are discussed.

An application of the method is then presented to assess a finishing process on a five-axis machining centre including milling and polishing operations.

Introduction

The manufacturing of molds, dies and medical implants requires the use of finishing operations such as machining and polishing so as to achieve the required surface quality. Surface roughness controls are mandatory to define the process and validate the quality of the machined part. The difficulty lies in the fact that the use of measuring instruments dedicated to 3D surface roughness measurement is limited to small parts with single orientation.

Furthermore, mounting and un-mounting the part leads to systematic errors and geometrical deviations. Thus our objective is to be able to control parts of any size without removing the part from the machine tool.

According to Vacharanukul et al. [START_REF] Vacharanukul | In process dimensionnal inspection sensors[END_REF], measurement of a part can be performed on the machine tool during the machining process (in-process measurement) or by interrupting the process and keeping the part in the part holder (in-situ measurement). Different techniques can be used for in-process and in-situ measurements [START_REF] Vacharanukul | In process dimensionnal inspection sensors[END_REF][START_REF] Yandayan | In-process dimensional measurement and control of workpiece accuracy[END_REF][START_REF] Shiraishi | Scope of in-process measurement, monitoring and control techniques in machining processes-part 2: Inprocess techniques for workpieces[END_REF]. These techniques can be categorized into six methods: mechanical, optical, pneumatic, ultrasonic, electrical and temperature detection methods. Optical techniques are often used as they provide a good compromise between acquisitions speed and axial measurement resolution.

However, in-process measurement techniques must take into account the difficulties linked to the machine tool environment such as tool deflection, coolant, vibrations, etc. Grosvenor et al. [START_REF] Grosvenor | In-process measurement problems in machine tool applications[END_REF] have investigated these difficulties within the context of in-process measurement of diameter in turning using proximity sensors. The in-process measurement method proposed by Persson [START_REF] Persson | In-process measurement of surface roughness using light scattering[END_REF] is based on an optical sensor using scattered light. The sensor is fixed on a grinding machine to evaluate surface roughness during grinding operations.

More recently [START_REF] Wang | Development of a laser-scattering-based probe for on-line measurement of surface roughness[END_REF] this kind of sensor has been used to conduct on-line measurement on a diamond turning lathe. The sensor is fixed on a grinding machine to evaluate surface roughness during grinding operations. This measurement method may also be enriched with hybrid vision system. Tian et al. [START_REF] Tian | Hybrid vision system for online measurement of surface roughness[END_REF] have proposed to associate two digital cameras to measure laser speckle pattern and scattering images simultaneously. Lin et al. [START_REF] Lin | High stability multiplexed fibre interferometer and its application on absolute displacement measurement and on-line surface metrology[END_REF] and Jiang et al. [START_REF] Jiang | Investigation of some critical aspects of on-line surface measurement by a wavelength-division-multiplexing technique[END_REF] have investigated the feasibility of spatial light-wave scanning to replace mechanical stylus scanning for in-situ surface roughness measurement. The developed sensor has been used for on-line nano scale surface measurement [START_REF] Wang | Actively stabilized optical fiber interferometry technique for online/in-process surface measurement[END_REF][START_REF] Yang | An integrated optical coupler used in a fibre interferometry system for on-line surface measurements[END_REF]. However, their work has focused on the development of the sensor regardless of the interactions between the sensor and the machine and the measurement range is not compatible with the considered application. Therefore, our approach consists in using a non contact optical sensor to achieve in-situ measurement of surface roughness on a 5-axis milling center.

According to [START_REF] Minoni | Surface quality control device for on-line applications[END_REF], a confocal chromatic sensor has been chosen. This technology is the most adapted given the five axis milling environment constraints.

The sensor is part of a MICROMESURE 3D measuring system from STIL. It is a modular measurement system including a table unit, comprising motorized x,y,z stages on which an optical pen (measuring head) is mounted and connected to a controller through an optical fiber. Within the context of in-situ measurement, the optical pen is mounted in the spindle of the machine tool with a dedicated set-up and a standard HSK 63A tool holder attachment.

As the optical pen takes the place of the tool, this technique does not allow us to conduct in-process measurements.

Thus, the geometrical imperfections of the machine tool must be taken into account and the thermal expansion of the spindle has to be compensated.

The paper is organized as follows: first the sensor and the acquisition system are presented in section 2. Then in section 3, the in-situ geometrical error model is described as well as the identification of model parameters. Section 4 is dedicated to the measurement comparison between in-situ and conventional measuring system techniques. Finally, a polishing process oriented application of in-situ measurement is proposed in section 5 before concluding remarks.

In-situ measurement system

Non-contact sensor

The considered sensor to evaluate the surface topography is based on the chromatic confocal sensing technology from STIL [START_REF] Leach | Fundamental Principles of Engineering Nanometrology[END_REF] (figure 1). A chromatic lens L generates the image of a point white-light source as a continuum of monochromatic images. The backscattered light arrives at a pinhole P which filters out all wavelengths except a single wavelength, λ j . The position of the focus point M is directly related to the detected wavelength λ j .

Two different sensors have been used for our investigations. A sensor with a measuring range of 400 µm (22 nm of axial resolution), used in in-situ or in the measuring instrument and a 100 µm measuring range (5 nm of axial resolution) sensor dedicated to the measuring instrument.

Measurement procedure

The optical sensor is mounted on the machine tool spindle using a dedicated mounting system (figure 2). Thus measurements are conducted along z axis, the theoretical spindle axis of the machine tool. The sensor is connected to its dedicated controller through an optical fiber. The signal provided by the controller is recorded with an in-house visual-basic based interface. The measurement is performed by a succession of 2D profile measurements along scanning paths which are parallel to a plane passing through z axis, like xz plane or yz plane for instance. The positions of the measured points in the xy plane are not monitored but computed according to the distance between scanning path and the programmed sensor displacement velocity.

Measurement geometrical modeling

As the machine tool and the system on which the sensor is mounted may present geometrical deviations, a geometrical model is proposed in order to investigate the potential source of errors. Characteristic points of the assembly are presented (figure 2) as well as the transformation matrices which model geometrical deviations.

• O m : Origin of the machine tool measure coordinate system • R: Characteristic point of the tool holder attachment, defined as the Reference point

• P : Origin of the optical pen measurement

• M i : Measured point • R Om : Machine tool measure coordinate system • R Rm : Spindle coordinate system M R Om R Rm =         X I 3 Y Z 0 0 0 1         (1)
• R Rmδ : Spindle coordinate system including machine tool geometrical deviations (straightness, squareness)

M R Rm R Rmδ =         dX R 1 (ψ 1 , θ 1 , φ 1 ) dY dZ 0 0 0 1         (2)
• R Rm∆ : Spindle coordinate system including machine tool geometrical deviations and thermal expansion

M R Rmδ R Rm∆ =         δX R 2 (ψ 2 , θ 2 , φ 2 ) δY δZ 0 0 0 1         (3)
• R P mes : Optical pen coordinate system

M R Rm∆ R P mes =         a R 3 (ψ 3 , θ 3 , φ 3 ) b c 0 0 0 1         (4)
The coordinates of the point M i in R P mes are:

M i =         0 0 h 1         R P mes (5)
(0, 0, h, 1), h being the distance measured by the sensor.

• First assumption: Considering the small range of displacement during measurements, it has been stated that:

R 1 (ψ 1 , θ 1 , φ 1 ) = I 3 and dX = dY = dZ = 0
This assumption amounts to considering that the axes straightness is perfect along the small displacement. It is also assumed that the axes squareness is a second order error compared to the thermal deviation.

• Second assumption: measurement duration is supposed to be short compared to the thermal inertia of the machine tool structure. The thermal expansion of the spindle due to its cooling system is considered to be more significant. Spindle expansions leading to small rotations and expansions in the x and y directions are neglected: R 2 (ψ 2 , θ 2 , φ 2 ) = I 3 and δX = δY = 0

• Third assumption: the pen sensor is supposed to be collinear to the spindle axis which leads to state that:

R 3 (ψ 3 , θ 3 φ 3 ) = I 3
This hypothesis consists in neglecting the altitude measurement error (cosine error) which is a second order error.

These assumptions also mean that the position of the measured point in the xy plane remains unknown. However, the distance between two measurement lines is constant. This should have small consequences on the 3D roughness parameter values. This point is validated in section 4.

Then, the coordinates of the point M i in R Om are the following:

M i =         X + a Y + b Z + δZ + c + h 1         R Om (6)

Model identification

The model outlined above is only a geometrical model. The term δZ corresponding to the spindle expansion and the z axis repeatability of the machine tool needs to be identified.

Thermal behavior

The machine tool spindle is cooled by an air conditioning system so as to maintain a limited operating temperature. Thus, expansions of the spindle are contained in a range proportional to the temperature variation of the coolant (20 C • ± 1). As these expansions have an impact on the in-situ measurement, they need to be known. In order to take into account the existence of measurement variations due to thermal expansion, the same point on a polished surface has been measured without moving the sensor during 100 min. The acquisition frequency of measurements was set to 1 kHz (figure 3).

In parallel, the cooling cycle of the spindle has been recorded in order to establish a compensation model for measuring defects. Temperature variations of the coolant, of the nose of the spindle as well as the ambient temperature have been recorded during the measurement (figure 4).

Variations obtained during the measurement period clearly show the cyclical nature of the thermal behavior. As every first order system, temperature is following cycles of exponential functions, but in order to simplify the data interpolation, a sinusoidal model has been chosen T (t):

T (t) = A.sin(B.t + C) + D (7)
Sinusoidal functions associated with the two evolution curves of the fluid temperature and of the spindle are defined in table 6.

The frequency B of the two curves is identical and corresponds to a period of 20 min. A phase shift between the two curves due to heat transfer by conduction is also observed. With these curves, the thermal effects due to cooling cycle can be compensated. The thermal effects compensation allows us to conduct a study on the influence of the repeatability of the machine tool.

Z-axis repeatability study

The purpose of this section is to determine the influence of the z axis repeatability of positioning on measurement results. According to ISO 230-2

[13], a series of measurements of three points M i in three different locations of the z axis (spaced 100 mm) has been conducted. Each point has been measured 650 times. For each measurement m ij , the measurement frequency is fixed to 1 kHz for a period of 4 s. The measurement cycle is thus composed of a slow approach (20 mm/min) over a 1 mm downward displacement along z axis, the measurement, and a fast retract (200 mm/min).

After the compensation of the thermal effect, measured values z ij are normally distributed (figure 5) and the estimators of standard uncertainty in the downward direction s i ↓ are equal to 0.0704 µm, 0.1044 µm and 0.0714 µm.

This leads to a repeatability of positioning R ↓ equal to 0.328 µm (R ↓= max(4.s i ↓).

The conclusion of this study is that below 0.3 µm, measurement uncertainty becomes too important to evaluate geometrical deviations.

Model validation

The proposed measurement model (eq.6) consists in neglecting most of the geometrical defects (assumptions 1,2 and 3) of the machine tool. In order to validate the method and the measurement model, two parts have been measured with the same sensor on the machine tool and on the dedicated measuring system.

Single groove measurement

The first part to be measured presents a calibrated groove (1 µm depth, 100 µm width) on a polished plane (ISO 12179 type A artefact [START_REF]Geometrical product specification (GPS) -Surface texture: protocole method -Calibration of contact (stylus) instruments[END_REF]). This calibrated groove has been chosen to validate the assumptions regarding the misalignment of the sensor compared to the z axis and the geometrical errors of the machine tool (straightness and squareness). Both sensors have been employed on the measuring system or in-situ leading to three different measurement configurations. Groove measurement results are gathered in configuration fits to the calibrated depth. Furthermore, since the result for in-situ measurement is consistent with the calibrated depth of the groove, the orientation of the optical pen is aligned with the z axis, which validates the assumptions leading to neglect the rotation matrices R i (ψ i , θ i , φ i ). It also shows that the measurement noise generated during machine tool displacement is normally distributed as there is no significant slope. This is a first validation showing that the straightness deviations of the x and y axes are also insignificant.

Groove depth

In-situ 22 nm sensor x = 0.999 µm Instrument 22 nm sensor x = 0.919 µm Instrument 5 nm sensor x = 0.931 µm

Complex topography measurement

The surface belongs to a roughness sample presenting a certified 2D arithmetic roughness Ra equal to 2.97 µm. It has been used to validate straightness along

x and y axes (dX = dY = 0) and thermal distortion along x and y axes (δX = δY = 0). The in-situ measurement is compared to measuring instrument measurement through the evaluation of several roughness parameters, Ra, Sa and St [START_REF] Leach | Fundamental Principles of Engineering Nanometrology[END_REF] (table 6). The first two parameters are mean parameters whilst the last one is a maximum value parameter. The error in the evaluation of Ra and Sa is about 10 % and is probably due to the larger spot size of the 22 nm optical pen that produces a local averaging. Regarding the evaluation of St, results with the 22 nm sensor are twice as large as the result given by the 5 nm sensor. The higher resolution 5 nm sensor has a higher spatial resolution, seeing more details, leading to somewhat higher averaging parameters like Ra and Sa. The peak parameter St becomes on the contrary smaller for the higher resolution sensor, because it produces fewer edge effects on the rough surface, which are evident on the groove profiles in figure 6.

It shows that it is possible to measure correctly complex topography although the measured point in the xy plane is never known exactly. However, it seems that the machine tool does not introduce large straightness deviations compared to the measuring instrument. According to the results of the two sample measurements, the three assumptions stated in 2.3 seem to be validated for the application.

Ra µm Sa µm St µm

In

13

Application

The proposed application deals the finishing operation of a plane surface.

By using in-situ measurement, it is possible to know when the surface roughness of the part has been reduced to the desirable level. The plane is machined in a 50 mm × 50 mm section block made of X38CrMoV5 steel. The part is machined on a 5-axis Mikron UCP710 machine tool to reach a milling finishing state before polishing. Three different grades of abrasive have been used for rough polishing operations (grade 120, 240 and 600). Abrasives are 18 mm diameter disks of silicon carbide pasted on the flexible support [START_REF] Pessoles | Automatic polishing process of plastic injection molds on a 5-axis milling center[END_REF]. The polishing operations were carried out with a tilt angle of the tool in the feed direction equal to 10 • . Surface roughness has been measured in-situ after each of the five operations using the proposed method. Measurements have been carried out in a restricted area (4 mm × 1 mm) of the machined plane and with a scanning direction perpendicular to the tool path (figure 7, 8-12). generates smaller deviations (3 µm) as can be seen in the zoom area with some details of about 0.5 µm. Beyond this value, it may be difficult to distinguish the part roughness from the noise of the instrument.

6.

The purpose of this paper was to introduce a method for measuring surface roughness in-situ, i.e. on the machine without removing the part. A study of the thermal effects of the cooling cycle of the spindle on which the sensor is mounted enabled compensation of most of the effects due to thermal expansion. The results of different experiments show that the stability of the machine tool leads to the largest errors, especially regarding the repeatability.

However, it is quite possible to measure the evolution of surface roughness during milling and polishing operations in order to optimize the processes.

Geometrical deviations down to 0.5 µm can be measured, which is approximately the limit that abrasive paper can reach before diamond paste polishing is required. Table3: Topography measurement results

Figure 1 :

 1 Figure 1: Non contact sensor description

Figure 2 :

 2 Figure 2: Measurement devices and data acquisition

Figure 3 :Figure 4 :

 34 Figure 3: Measurement of a given point during 100 min

Figure 5 :

 5 Figure 5: Z-axis repeatability (point M 1 )

Figure 6 :

 6 Figure 6: Measured groove profiles

Figure 8 :Figure 9 :Figure 10 :Figure 11 :Figure 12 :

 89101112 Figure 7: In-situ measurement 2D profiles

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 : 1 )Figure 6 :Figure 7 :Figure 8 :Figure 9 : 1 Figure 10 : 2 Figure 11 :Figure 12 :

 123451678911021112 Figure 1: contact sensor description Figure 2: Measurement devices and data acquisitionFigure 3: Measurement of a given point during 100 min Figure 4: Temperatures monitoring Figure 5: Z-axis repeatability (point M 1 ) Figure 6: Measured groove profiles Figure 7: In-situ measurement 2D profiles Figure 8: In-situ measurement ; Milling Figure 9: In-situ measurement ; Grade 120-1 Figure 10: In-situ measurement ; Grade 120-2 Figure 11: In-situ measurement ; Grade 240 Figure 12: In-situ measurement ; Grade 600

Table 1 :

 1 Thermal behavior

	9

table 2

 2

	and in figure 6. Values reported in table 2 are computed in the central
	orange area of figure 6. It can be observed that the in-situ measurement is
	very noisy compared to the others. The same artifacts are visible on both
	sides of the groove for 22 nm sensor due to sensor saturation, which could not
	be corrected on the used sensor. However, the groove depth result for in-situ

Table 2 :

 2 Groove measurement results

Table 3 :

 3 Topography measurement results

	-situ 22 nm	2.61	2.69	22.6
	Instrument 22 nm 2.75	2.79	25.2
	Instrument 5 nm	3.00	3.01	12.5

Table 2 :

 2 Groove measurement results

		Ra µm	Sa µm	St µm
	In-situ 22 nm	2.61	2.69	22.6
	Instrument 22 nm 2.75	2.79	25.2
	Instrument 5 nm	3.00	3.01	12.5


Christophe Tournier

Christophe Iabassene

Anthony Guiot

Yann Quinsat

GRINDING OF MEDICAL IMPLANTS IN COBALT-CHROMIUM ALLOY

Keywords: Grinding, cobalt-chromium, surface roughness, medical implants

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

INTRODUCTION

As mentioned in [START_REF] Pessoles | Automatic polishing process of plastic injection molds on a 5-axis milling center[END_REF], automatic polishing and grinding of free form surfaces is a convenient solution to reduce cost and improve quality. Thus the aim of this paper is to study the performance of a grinding (or rough polishing) spherical flexible tool for the machining of prostheses on 5-axis machine tool. The particularity of this tool compared to a conventional grinding wheel is to be composed of an abrasive cap mounted on a rubber body, which gives it some flexibility. Recent research works have investigated the use of filleted or ball end tools for grinding and polishing operations. Denkena et al. [START_REF] Denkena | Prediction of contact conditions and theoretical roughness in manufacturing of complex implants by toric grinding tools[END_REF] have developed an analytical model to evaluate the material removal rate in 5-axis grinding of medical implants with a filleted end tool. This approach was conducted in the past in 5axis milling to evaluate machining strip width as well as scallop heights [START_REF] Lee | Surface interrogation and machining strip evaluation for 5-axis cnc die and mold machining[END_REF]. Tam et al [START_REF] Tam | An investigation of the effects of the tool path on the removal of material in polishing[END_REF] have proposed a study of the influence of the tool path on the surface roughness with a similar tool (alumina mixed in a binding material of synthetic rubber). The tool contact and removal profiles are computed thanks to the assumptions of Hertzian contact stress leading to elliptical contact. However, modelling is purely geometrical and does not include polishing parameters such as cutting speed and feedrate. Furthermore, the roughness parameter used to evaluate surface roughness in these works is the theoretical roughness Rth, computed in cross sections, which is well adapted when the scallop left on the part by the tool are predominant. Surface finish is better evaluated by considering surface roughness parameters like Sa [START_REF] Pessoles | Automatic polishing process of plastic injection molds on a 5-axis milling center[END_REF][START_REF] Charlton | Surface and form metrology of polished freeform biological surfaces[END_REF] or at least, profile measurements in two perpendicular directions. Wang et al [START_REF] Wang | Numerical characterisation of biomedical titanium surface texture using novel feature parameters[END_REF] have proposed an innovative use of surface texture parameters to illustrate biomedical functions. However, according to them, a large amount of biomedical experiments would be needed to fully validate this correlation. The work presented in this paper focus on knee prosthesis machining in cobalt-chromium alloy (KC 28). Surface quality on external surface of knee prosthesis is specified with the arithmetic roughness such as 0.025µm <Ra<0.05µm. Since mirror effect is also expected, polishing operations are mandatory to finish the part. The aim of this work is to perform experimentations to assess the use of the considered tool and find the grinding process parameters to minimize geometrical deviation and especially Ra and Sa.

EXPERIMENTATION

EXPERIMENTAL SET-UP

The description of the tool as well as the geometrical parameters are illustrated (Figure 1). The most influent factor on the surface roughness is the distance between path p during grinding which is a well-known result. For the experiments, e is set to 0.2 mm, α to 45 degree and p to 0.1mm. Thus, the study focuses on two parameters: the cutting speed Vc and the feedrate Vf. Two levels are considered for both factors (Vc 1 = 50m/min; Vc 2 =200 m/min; Vf 1 =250 mm/min; Vf 2 =10 3 mm/min). The study is also conducted on a general purpose steel (C10) in order to emphasize the behaviour of the cobalt-chromium alloy. At last, the grit of the abrasive tool is equal to 320 according to ISO standard. The design of experiment leads to the use of the L 8 Taguchi table (Table 1).

Experimentations are carried out on planar samples on a 5-axis Mikron UCP 710 machine tool. Before the grinding operation, the samples are machined with a Ø12 mm ball end mill along parallel planes separated by 0.1 mm. The tilt angle between the tool axis and zaxis is set to 15° to avoid null cutting speed at the tool extremity.

Figure 1: Grinding tool and parameters

EXPERIMENTAL RESULTS

The data analysis procedure consists in a non-contact measurement of surface roughness on a 6 mm by 6 mm patch. The eight surface measurements are illustrated on Figure 2. Surface parameter Sa is evaluated without filtering and thus includes form, waviness and roughness deviations. Figure 2 shows that geometrical deviations are much larger for (Vc = 200m/min; Vf = 250 mm/min). For a small ratio Vf/Vc, test # 3, the tool does not engage in the material the same way and appears to float on the part more than in other cases (Figure 2). There are no grinding mark generated by the abrasive particles as test # 1 and # 4.

Five profiles are extracted along and perpendicularly to the grinding tool paths on each sample to evaluate the profile parameters Ra ⊥ , Ra // Rt ⊥ and Rz ⊥ with a Gaussian filter and a cut-off set to 0.8mm according to ISO 11562. The factor effects are illustrated in Figure 3.

Material factor effect analysis: regardless of the roughness parameter, values are lower for the KC28 alloy than for C10 steel. In addition, the effect of this parameter is much more important than the other two.

Cutting speed factor effect analysis: increasing the cutting speed Vc increases the arithmetic mean deviation of the surface Sa but decreases profile parameters Ra ⊥ et Ra // .

Feedrate factor effect analysis: increasing the feedrate Vf decreases the arithmetic mean deviation of the surface Sa but increases creases profile parameters Ra ⊥ et Ra // . The effect of this parameter is in complete opposition to the cutting speed Vc. The evolution of the parameters based on the four experimentations for each material is illustrated on Figure 4. Besides the fact that the roughness is always higher for the C10, it can be clearly observed that the evolutions of the parameters Ra ⊥ and Ra // are similar, showing that Vc and Vf are key parameters.

Regarding the machining parameters Vc and Vf, the influence of these parameters on the value of Ra // is very close to the one found in conventional milling. The relationship between these two parameters depends on the value of the feed per revolution, which amounts to saying that there exists a pseudo feed per tooth in abrasion. The parameter Ra // decreases as the cutting speed Vc increases and the feedrate Vf decreases, that is to say when Vf/Vc decreases.

PSEUDO FEED

PSEUDO FEED MODEL

The aim is to show the existence of a pseudo feed per revolution and its effects on surface quality. The pseudo feed f is defined by equation ( 3) and refers to Figure 1 with α equal to 45. R i is the effective radius of the tool T i used for each experiment. Figure 5 shows grinding profiles parallel to the trajectories for f * = 1.25, f * = 5 and f * = 20. So there is a ratio of 4 for the factor f * between each experiment. We therefore measured the value of the pseudo feed f for f * = 1.25 and f * = 5 or a mean value for f * = 20 (Figure 5). Measuring the number of peaks or valleys per mm shows a pseudo feed per revolution f of about 0.03mm for f * = 1.25, 0.12mm for f * = 5 and 0.48mm for f * = 20. So there is consistency between the picks observed on the profiles and the ratio f * which tends to prove the existence of a pseudo feed per revolution. It is possible to calculate the theoretical value of the pseudo feed f taking into account the effective radius R i of the tools and the tilt angle of inclination equal to 45 degrees (equation ( 3)).

Vf = f ⋅ N (1) N = 10 3 ⋅Vc π ⋅ 2 ⋅ R i (2) f = Vf Vc ⋅ π ⋅ 2 ⋅ R i 10 3 = f * ⋅ π ⋅ 2 ⋅ R i 10 3
(3) The results are very convincing because there is perfect correspondence between experiments and model, regardless of the material (Table 2). What is also remarkable is that the pseudo advance is the same as we used different caps, so different geometry for each experiment.

EFFECTS OF THE PSEUDO FEED FACTOR

Therefore variations of roughness parameters have been studied according to the ratio f * =Vf/Vc which is proportional to the pseudo feed per revolution.

Additional tests with ratios of 1 and 4/3 have been conducted.

As for Ra // , evolution is increasing according to the ratio f * =Vf/Vc (Figure 6) which is consistent with the existence of a pseudo feed per revolution. However, if the decrease in the value of f * decreases the values of Ra // , experiments show that other parameters evolve differently.

It is observed that the evolution of the parameter Ra ⊥ has a minimum when f * is in the interval [3; 5]. In this interval, the value of Ra ⊥ is less than 0.06 µm (Figure 6). The evolution of the parameters Rz ⊥ and Rt ⊥ also presents a minimum when f * is in the interval [3; 5] (Figure 10). The difference between the two parameters is almost always the same, i.e. Rz ⊥ < Rt ⊥ that is consistent with their definitions. Indeed, Rz ⊥ is calculated on lengths corresponding to the wavelength of the cut-off while Rt ⊥ is calculated on the total length of evaluation. Part of the waviness deviation is not filtered and remains in the value of Rt ⊥ , which explains the difference between the values of these two parameters. The best parameter to evaluate geometrical deviations of the first and second order is the parameter Sa that was evaluated without filter (Figure 7). The evolution of the parameters Sa also presents a minimum lower than 0.15 µm when f * is in the interval [3; 5]. The evolution of the difference between Rz ⊥ and Rt ⊥ does vary in the same way that the value of Sa (Figure 7), which is consistent.

CONCLUSIONS

The results show that there is an operating point to minimize the geometrical deviation of surfaces when using the considered abrasive tool in Cobalt-Chromium alloy. To minimize Ra // , the ratio Vf/Vc must tend to 0 whereas to minimize Sa and Ra ⊥ , the ratio Vf/Vc must be within the range [3; 5]. Outside this range, the tool should not engage properly in the material and seems to float upon the part while degrading form deviation, waviness and roughness. Moreover, this behaviour occurs in both materials.

To ensure a polishing time as short as possible, it would be better to have high feedrates and therefore high cutting speeds, to maintain the operating point. It would then be necessary to evaluate the wear of the abrasive caps.

Finally given the quality requirements on medical implants, this grinding operation should be followed by fine polishing with diamond paste.

Figure 2 :

 2 Figure 2: measured surface topology

Figure 3 :Figure 4 :

 34 Figure 3: Effects of the three factors

Figure 5 :

 5 Figure 5: Grinding profiles (Top: f * =1.25; Middle: f * =5; Bottom: f * =20)

Figure 6 :Figure 7 :Figure 8 :

 678 Figure 6: Evolution of Ra⊥ and Ra // for KC28

Table 1 :

 1 experimental results

	Mat.	Vc m/min	Vf mm/min	Ra ⊥ µm	Ra // µm	Rt ⊥ µm	Rz ⊥ µm	Sa µm
	KC28	50	250	0.06 0.08 0.59 0.44 0.12
		50	1000	0.12 0.09 0.81 0.62 0.27
		200	250	0.08 0.05 0.74 0.48 0.35
		200	1000	0.06 0.06 0.50 0.38 0.14
	C10	50	250	0.13 0.13 1.28 0.76 0.28
		50	1000	0.19 0.15 1.32 0.93 0.32
		200	250	0.12 0.08 1.00 0.69	0.3
		200	1000	0.12 0.16 1.38	0.7	0.3

Table 2 :

 2 pseudo feed analysis for f * = 5 in both material

	Material	Vc	Vf	f	*	R i	f comp.	f meas.
		m/min	mm/min			mm	mm	mm
	KC28	50	250	5	5.53	0.123	0.124
		200	1000	5	5.53	0.123	0.125
	C10	50	250	5	5.45	0.123	0.122
		200	1000	5	5.51	0.123	0.126