Timothé Rossa

Pierre Pompidor

Nancy Rodriguez

Arnaud Sallaberry

Pascal Poncelet

Marika Urbanski

Clémence Bourlon

Antoine Seilles

Guillaume Tallon

Experimental web service and eye-tracking setup for unilateral spatial neglect assessment

Keywords: Unilateral Spatial Neglect, IT Diagnostic Aid, Visual Variables, Eye-Tracking, Web Visualization

Unilateral Spatial Neglect is a cognitive impairment commonly observed in patients after right hemispheric lesions. A patient with this condition will show a lack of attention or response to visual stimuli presented to the left space.

In order to assess visual neglect, several "paper and pencil" tests are traditionally used, like the Albert's Test or the Bells Test. Computer supported tests have been also proposed like Visual Spatial Search Task (VISSTA) or Starry Night Test (SNT). In this kind of tests, the patient is asked to detect all occurrences of a target among distractors ("cancellation task"). However, it has been noticed that these tests are not able to identify subtle but relevant NSU, especially in the chronic stage. In addition, compensatory attentional strategies can be developed by the patients in order to pass a test in which they have unlimited time. It is then important to measure reaction time and to adapt tests to increase diagnostic accuracy.

This abstract presents READAPT an application supporting the Bells Test, with the aim of overcoming the limits of existing static paper-and-pencil diagnostic tools and to facilitate recording and analysis of patient's visual scanning.

Introduction

Unilateral spatial neglect (USN) is a syndrome commonly observed after a right brain damage [START_REF] Azouvi | Sensitivity of clinical and behavioural tests of spatial neglect after right hemisphere stroke[END_REF]. Spatial neglect has been defined by Heilman [START_REF] Heilman | Neglect and Related Disorders[END_REF] as « a failure to report, respond, or orient to contralateral stimuli that is not caused by an elemental sen-sorimotor deficit ». Patients with USN do not orient or respond to visual stimuli on their left side [START_REF] Heilman | Mechanisms underlying hemispatial neglect[END_REF][START_REF] Heilman | Neglect and related disorders[END_REF]. Although USN often reported with elementary sensory or motor neurological disorders, most researchers emphasize the role of impaired mechanisms of spatial attention [START_REF] Urbanski | Unilateral spatial neglect: A dramatic but often neglected consequence of right brain damage (in French)[END_REF] and non-spatially lateralized deficits of attention [START_REF] Husain | Non-spatially lateralized mechanisms in hemispatial neglect[END_REF]. USN is a complex and heterogeneous syndrome, which could affect personal (e.g patients can omit to shave/make up the left side of their face) peripersonal (e.g patients cannot eat the left part of their dish) and/or extrapersonal spaces (e.g patients can bump their wheelchair into left obstacles). This syndrome is one of the leading causes of handicap and long-term disability [START_REF] Bartolomeo | Attention Disorders After Right Brain Damage -Living in Halved Worlds[END_REF].

In order to assess visual neglect, several "paper and pencil" tests have been proposed like the Albert's Test [START_REF] Albert | A simple test of visual neglect[END_REF] and the Bells Test [START_REF] Gauthier | The Bells Test: A Quantitative and Qualitative Test for Visual Neglect[END_REF]. Computer supported tests like VISSTA [START_REF] Erez | Assessment of spatial neglect using computerised feature and conjunction visual search tasks[END_REF] or SNT [START_REF] Deouell | Assessment of spatial attention after brain damage with a dynamic reaction time test[END_REF] are also available. In this kind of tests, the patient is asked to detect all occurrences of a target among distractors. In the Bells Test, which is included in the French battery of USN [START_REF] Azouvi | A battery of tests for the quantitative assessment of unilateral neglect[END_REF], a 21.5 x 28 cm sheet is presented to the patient, 3 columns are on the left side of the sheet, one is in the middle and 3 on the right. The image contains different objects and a total of 35 bells (the target) distributed equally in the seven columns. The examiner notes by successive numbering the order of circling of bells. At the end of the task, the examiner can appreciate the spatial distribution of the omitted targets and evaluate the severity of the visual neglect. Indeed, the realization time, the number of omissions, and the analysis of the scanning strategy allow a quantitative and qualitative assessment of the unilateral spatial neglect. In addition, the test has a relatively weak learning effect. However, it have been noticed that these tests are not able to identify subtle but relevant USN, especially in the chronic stage [START_REF] Rengachary | Is the posner reaction time test more accurate than clinical tests in detecting left neglect in acute and chronic stroke[END_REF]. In addition, Pedroli [START_REF] Pedroli | Assessment and rehabilitation of neglect using virtual reality: a systematic review[END_REF] states that compensatory attentional strategies can be developed by the patients in order to pass a test in which they have unlimited time to identify static targets. The possibility to change the stimulus, the background and the time of presentation is useful to increase complexity and sensitivity of the test, even when only mild USN signs, and allowed for a better assessment of the deficit in spatial attention. On the other hand, one of the difficulties of detecting USN is that the patient's eyes are unimpaired, they can orient towards signals and the pupil can also react to signals.

In this study, we have created a computerized adaptation of the Bells Test called READAPT, which permit to manipulate different factors that could affect USN signs, and to realize eye tracking measures. Therefore, READAPT might overcome the limits of existing diagnostic tools and facilitate recording and analysis of patient's visual scanning.

The remainder of this paper is organized as follows. Section 2 discusses related work. Section 3 details READAPT application and how it implements the Bells Test. Section 4 presents eye-tracking functionality. The experimental protocol and results are presented in section 5. Finally, section 6 provides conclusions and directions for future work.

2

Related work

On clinical trials, numerous paper and pencil tests are used to assess USN. Neglect signs can occur on bisection tasks (rightward deviation), copy tasks (omission of the left part of drawings) or visual search tasks (omission of targets on the left side). More than 60 standardized and non-standardized tools were identified to evaluate USN [START_REF] Menon | Evaluating unilateral spatial neglect post stroke: working your way through the maze of assessment choices[END_REF]. The variability of these assessments affected the reported rate of occurrence of USN. Visual cancellation tests are often used but such task can fail to detect mild [START_REF] Bowen | Reasons for variability in the reported rate of occurrence of unilateral spatial neglect after stroke[END_REF]. Sensitivity results are different according batteries or tests used to assess USN [START_REF] Mizuno | Spatial and temporal dynamics of visual search tasks distinguish subtypes of unilateral spatial neglect: Comparison of two cases with viewer-centered and stimulus-centered neglect[END_REF]. Moreover, patterns of visual exploration are often lacking in such tests.

This has led to implement cancellation tests with a touchscreen interface [START_REF] Rabuffetti | Spatio-temporal features of visual exploration in unilaterally brain-damaged subjects with or without neglect: results from a touchscreen test[END_REF], eyetracking device [START_REF] Behrmann | Impaired visual search in patients with unilateral neglect: an oculographic analysis[END_REF][START_REF] Müri | Visual exploration pattern in hemineglect[END_REF]. The importance of using dynamic task in the assessment of USN has been previously highlighted by Peskine et al. [START_REF] Peskine | Virtual reality assessment for visuospatial neglect: importance of a dynamic task[END_REF] and Deouell et al. [START_REF] Deouell | Assessment of spatial attention after brain damage with a dynamic reaction time test[END_REF] who showed that a computerized dynamic Starry Night Test (SNT) was more sensitive than paper and pencil tests. Computerized visual search task like Visual Spatial Search Task (VISSTA) has been also developed allowing to manipulate the number of distractors, the colour of the target, the exposure time of the stimuli presentation and the repetition of presentation over different periods of times [START_REF] Erez | Assessment of spatial neglect using computerised feature and conjunction visual search tasks[END_REF].

Developing a digital diagnostic tool allows to:

• Ensure reproducibility under controlled experimental conditions (one of the limitations of current diagnostic tools is that conditions vary depending on the therapist and facility equipment). • Simplify data entry and saving, and therefore monitor patient outcomes and compare these results with those of other clinical cases • Take additional information, impossible to follow without a numerical tool, during the execution of the task, such as the movements of patients eyes • Couple this diagnosis with rehabilitation exercises adapted to the results

READAPT web application

Our application, READAPT, is a web application for USN assessment in the peripersonal space. It extends the traditional Bells tests by providing customizable scenes. The Bells test consists in finding specific graphical objects called targets, for instance bells, among many objects called distractors (apples, fishes…). Graphical objects differ from each other on shape and position, but are similar on other aspects, such as size, color… (Fig. 1). READAPT has been designed to provide a wider range of graphical aspects.

Design study

In the following, "marks" denote graphical objects and "visual channels" are the variables controlling the aspects of these marks [START_REF] Munzner | Visualization Analysis & Design. AK Peters Visualization Series[END_REF]. Since the raise of graphical semiology [START_REF] Bertin | Semiology of Graphics: Diagrams, Networks, Maps[END_REF], and more recently data visualization [START_REF] Ware | Information Visualization: Perception for design[END_REF][START_REF] Ward | Interactive Data Visualization: Foundations, Techniques, and Applications[END_REF], we consider that a scene is composed by three kinds of marks: points, lines and areas. Visual channels controlling the appearance of these marks are position, shape, size, tilt, color (hue, luminance, saturation), and motion. In the early development of semiology, in particular when cartographic maps were made manually, texture was also considered as a visual channel, but it is not employed anymore since the raise of computers. Another channel, curvature, is also often mentioned in the literature. We do not include it in our list because it highly interferes with shape and thus is not relevant in our context. In semiology and visualization, marks and channels are used to represent data. For instance, marks denote data elements and channels represent quantitative or qualitative attributes associated with these elements. This approach is not related for our work here. However, development in these fields pointed out interesting characteristics of visual channels (see [START_REF] Munzner | Visualization Analysis & Design. AK Peters Visualization Series[END_REF][START_REF] Ware | Information Visualization: Perception for design[END_REF]). In particular, perception of visual channels differs in terms of effectiveness and expressiveness. Our assumption here is that, while variation on the different channels are not perceived equally, it is worth to explore further channels instead of just varying position and shape. That is why the application we propose here includes many parameters enabling to customize the different aspects of the marks as described in the next section. The purpose is to provide a more flexible tool, where the practitioner can adapt the level of difficulty according to her patient by using various visual channels. For instance, instead of using shape, or in addition to shape, targets can be rendered with specific color to make them more salient in a rehabilitation process context.

Tool description

Performing a test. READAPT is a Web application to test USN. The patient performing a test is asked to find a particular object, called target, on successive scenes. Each attempt is called a trial. Fig. 1 shows such a scene, composed of 49 items: a target and 48 distractors. In the catch-trials (trials where the target is not present), the scene is composed of 49 distractors. In this example, the patient has to click on the red bell to success the trial. When she clicks on the screen, even if she does not succeed, a new trial is proposed. To launch the new trial, the patient is asked to click on a cross positioned at the center of the screen. Since the scene is divided as the original seven-column test, the order of appearance of the target in each column as well as the order of the trials, with and without a target, are randomized, in order to limit the learning effect. The result of each trial is recorded in a database. Customizing a test. In regard of the purpose defined above, before launching a test session, the practitioner has to set up the parameters listed in Table 1. Fig. 2 shows the interface given to the practitioner. When several values are available for a visual channel, a random value is computed for each mark when the trials are rendered. For instance, if "Tilt" is checked, a random angle is computed and then applied to the mark. In the same way, when the practitioner selects a range for the hue, a random hue within this range is computed.

Additional functionalities. When a practitioner access READAPT, she can select a patient or create a new one in the database. Each test session will be associated to this patient and the practitioner will have access to an interface showing his evolution over time. First a table shows the parameters of each session. Furthermore, the patient's response time, the distance from the click to the target (if present), and the relevance of his selection are recorded. A stacked bar chart is also provided. Each bar represents a session, and the portions of the bar represent the number of success (blue), nearby clicks, failures (red) and timeouts (orange).

Technical aspects

This application consists of a set of programs written in PHP and JavaScript. PHP programs allow to configure via forms the different elements of the scenes composing a test session. The context of the sessions (non-nominal identifiers of medical agents and patients, dates, etc.) is recorded in a PHP database. The test results (identification of the presence or absence of a target by a left or right mouse click) are saved in tabular format.

The JavaScript language, which permits to modify dynamically the structure of the web pages displayed by the browser, and to record the Internet user's activity, was used to:

• create dual sliders selecting the different color components (hue, saturation, brightness and opacity) when configuring the tests; • display in the browser, the different graphic elements of the scenes;

• record mouse usa and/or eye movements of patients.

Note that the d3.js JavaScript library is used to create sliders and display scene elements. This library allows to create graphical elements using the SVG (Scalable Vector Graphics) language, which produces vector graphics (all browsers host an SVG interpreter).

In addition, using the Node.js platform -a modular JavaScript interpreter running at the server level -we have also implemented JavaScript programs to record test settings and results, as well as the reconstruction of scenes as PNG images (again using SVG), on which the heat maps produced by the eye tracker are subsequently superimposed.

4

Eye-tracking

READAPT is coupled with an eye-tracking recorder. We use the Eye Tribe eye tracker [START_REF] Ooms | Evaluation of the accuracy and precision of a low-cost eye tracking device[END_REF] for our experimental set-up. The eye movements of the patient are collected and then processed to build heat maps and gaze trajectory animation (Fig. 3). This data is superposed to trial's image in order to analyse the patient's visual search strategy. It has been shown that subjects presenting an attentional deficit will demonstrate a disorganized and chaotic scanning [START_REF] Gauthier | The Bells Test: A Quantitative and Qualitative Test for Visual Neglect[END_REF]. Therefore, following the gaze trajectory step by step will help examiners to detect a disturbed visual search. The eye-tracker is calibrated for each user. During the calibration, the user is asked to focus at several points on the screen. The device will then make a mapping between the point on the screen that the user looked at (gaze point) and the eye-tracker output.

To use the eye-tracker within the web navigator, the EyeTribe-WebSocket [START_REF]The Eye Tribe Web Socket[END_REF] has been used, a javascript based websocket application to wrap the EyeTribe SDK and transmit data. The d3.js library is used to display graphic elements. An application has been developed to accessing the eye-tracker data and information from READAPT in order to superpose the image generated for a trial and the gaze measures [START_REF] Govin | Development of the READAPT application -Eye-tracking & Web[END_REF].

The heat map uses different shades of colour, here from yellow to red, to indicate the number of gaze positions of each zone (gaze positions are grouped into hexagons). Darker colours close to red indicate zones of high activity. An animation allows following the trajectory of the gaze. Once the animation is over, the positions are connected by lines representing the trajectory of the gaze [START_REF] Beuret | Analysis of visual characteristics using an eye-tracker[END_REF]. On the same basis, 8 control subjects (5 men / 4 women) aged between 30 and 71 (m = 49.37 ± 12.97) have been included. The two groups do not present any differences concerning age (t test ; t = -0.69, p = .500).

Task

Readapt software is based on the Bells Test evaluating spatial neglect in a peripersonal reference frame. This computerized version displays a visual scene made of 49 items: 1 target and 48 distractors. During the catch-trials (trial without target to test the attention AL involvement of the subject), the display is made of 49 distractors. On each trial, the subject have to indicate the presence or not of the target using respectively the left or right button of the mouse (thumb or index of the right hand). The visual scene is divided in 7 columns and lines. To reduce the learning effect, the target is presented randomly in every column and the trials/catch-trials are in a random order. Time in each trial is limited to 8 seconds while the time between trials depends on the action of the subject (click with the left button on the gray cross). Before each trial, a gray fixation cross is presented with a random letter on the middle of it. The subject has to read it out loud to ensure the experimenter that the visual attention is stick to the letter. This letter has a angular size of 0,5° to be sure that the reading of it is in foveal vision [START_REF] Kristjánsson | Priming of color and position during visual search in unilateral spatial neglect[END_REF].

From this basic architecture, three versions were derived: 1. Standard: one block of 80 trials, including 10 catch-trials, during which the target appears 10 times in each column. No variation from the basic set-up is made here, to allow the strict comparison of the sensibility between the original test and ours. 2. Items: five blocks of 14 trials and 2 catch-trials corresponding to the 5 conditions of variation of the repartition of the distractors on the horizontal plan. This repartition evolves according to a gradient from the left to the right (in condition 1 and 2), from the right to the left (condition 4 and 5). The condition 5 is the control condition with no variation. 3. Interference: five blocks of 14 trials and 2 catch-trials corresponding to the 5 conditions of variation of the percentage of degradation of the scene on the horizontal plan. This degradation evolves according to a descending gradient from the left to the right (in condition 1 and 2), from the right to the left (condition 4 and 5). The condition 5 is the control condition with no degradation.

Procedure

All the participants have been tested in a quiet and isolated place, seating in front of the experimenter. Once the task has been explained, understood and that all the eventual interrogations have been cleared, the subject is tested with both the original Bells Test and the three versions of the task.

To evaluate the validity of our task, the subject is tested with the original Bells Test before the Readapt version, to allow the comparison between the results.

According to the set-up of [START_REF] Ooms | Evaluation of the accuracy and precision of a low-cost eye tracking device[END_REF], the subject is installed in front of the computer with the straightest position as possible at 60 centimeters of the screen with the eye in the axe of the center of the screen. The Eye-tracker is just under the screen at a distance between 30 to 45 centimeters of the participant.

The computerized version it-self is split in two stages. A first stage of training allows ensuring the comprehension of the task, to validate the posture and the comfort, and to calibrate the device. With the same instructions as for the experimental stage, the training is composed of one block of 16 trials including 2 catch-trials. Once the training completed, the subject can start the second stage.

This second stage is composed of 3 variations ("Standard", "Items", and "Interference") in a randomized order. Each trial is made of a fixation cross at the center of the screen in which a random letter appears that has to be named out loud. Then, the subject must click on the left button of the mouse controller to trigger the appearance of the scene. In this phase, the task is to indicate the presence or not of a target (a black bell) using respectively the left or right button of the mouse controller. This controller is placed under the right hand of the subject with a 90° rotation counter clockwise to avoid the stimulus-response compatibility effect, or "Simon Effect" [START_REF] Simon | Auditory S-R compatibility: the effect of an irrelevant cue on information processing[END_REF]. Depending of the subject's fatigability, breaks can be taken anytime during the appearance of the fixation cross whose time duration is determined by the action of the subject only.

Results

All the analysis realized for the study have been done with the RStudio software (open-source) and Microsoft Excel 2016. A control subject has been removed from the analysis because of abnormal performances in the computerized test. Possibly resulting of a slight vision anomaly due to a retinal surgery.

Original Bell test. The analysis of the performances is based on the following quantitative variables: total duration of the task (seconds), number of omissions (total, and per columns), and the position of the first target marked (starting column of visual search). The visual search strategy has been recorded as a qualitative variable. The average performances are presented below. • Total duration. The data follow a normal distribution (Shapiro-Wilk; Patient: W = 0.93, p = .63 ; Control : W = 0.95, p = .72) and the homoscedasticity is not refuted (Fisher ; F = 1.91, p = .43).The T-test confirm a significant difference between the 2 groups (Student ; t = -5.0115, p < .001). • Omissions. The comparison between omissions in the left half of the scene (col.

1,2,3) between groups reveals no significant difference (Mann-Whitney; U = 20, p = .216). However, the total number of omissions (in the 7 columns) is significantly different between patients and controls (U = 31, p = .005). Patients omit actually more target than the controls. • Starting point of the visual search. Investigate by the first bell crossed, this variable do not reveal an inter-group difference (U = 17, p = .911).

Readapt. The quantitative variables used for the performance analysis of the 3 versions of the computerized test are: the reaction time, number and position (column number) of the omissions, false alarms. The reaction time used corresponds to the trials with target during which it was correctly detected.

Standard version. Reaction time (RT) -The comparison of the RT in and between groups shows significant differences. The comparison has been done using nonparametric tests because of the distribution of the data (Shapiro-Wilk). In-group: A significant difference is observed in the patient group regarding of the position of the target in the visual scene (Kruskal-Wallis; H(6) = 37.594, p < .001). The Wilcoxon tests for paired samples show differences between the columns 1 and 5 (p = .001), 1 and 6 (p < .001), 1 and 7 (p < .001). In the control group (H(6) = 30.712, p < .001), the differences concern the columns 1-3, 1-4, 1-5, 2-4, 2-5, and 4-7.

Between-groups (see Fig. 4): The Mann-Whitney test shows evidence for significant differences for the columns 1 (p < .001), 2 (p < .001), 3 (p < .001), 4 (p < .001) et 5 (p = .001). Omissions (see Fig. 5) -Mann-Whitney tests show between-groups significant differences for the number of omissions in the columns 1 (U = 31.5, p = .008), 2 (U = 28.5, p = .028), 3 (U = 24, p = .049) et 4 (U = 24, p = .049).

Conclusion

Spatial neglect is the difficulty in detecting, responding to or pointing to significant stimuli located on the opposite side of a brain injury, which cannot be attributed to a sensory or motor deficit. Patients often have weak spatial neglect and only capture a portion of the signals from the left side of the image. The traditional technique for assessing USN is the Bells Test, which consist in finding specific graphical objects (bells) called targets, among many objects called distractors. However, this kind of tests fails to identify subtle impairments and compensatory attentional strategies. It is then important to accurately measure reaction time and to help examiners to easily adapt tests to increase diagnostic accuracy.

Our application, READAPT, is a web application for USN assessment. It extends the traditional Bells tests by providing customizable scenes. The purpose is to provide a more flexible tool, where the practitioner can adapt the level of difficulty according to her patient by using various visual channels. For instance, instead of shape, or in addition to shape, targets can be rendered with specific color to make them more salient in a process context. The application includes many parameters enabling to customize the different aspects of the marks: type (distractor or target), number, shape, size and colour of objects as well as the background colour and distribution of distractors and targets. A scene can also be created without targets. A session can be defined, regrouping several trials and a timeout.

Performances of several patients and control subjects were used to demonstrate the feasibility and the ability of the system to distinguish between normal and neglect subjects, based on reaction times and target omissions.

These results represent a proof of concept for our application and encourage us to continue its development. We hope that the new data acquired and the follow-up of patients will make it possible to better understand USN. In particular, we believe that there are many degrees of impairment and we hope that appropriate responses are possible depending on the different cases.

In addition to being usable with patients in a clinical evaluation context, the application allows for the construction of several personalized tests and therefore could be used for experiments concerning the evaluation of the relevance of visual variables in the HCI domain.

Figure 1 .

 1 Figure 1. A scene from READAPT application

Figure 2 .

 2 Figure 2. READAPT user interface

Figure 3 .

 3 Figure 3. Heat map (left) and trajectory for a trial

  1 man and 3 women) aged between 34 and 75 years old (m = 55,5 ± 17.02), suffering spatial neglect after right hemispherical stroke have been recruited for the study. Patients with neurological or degenerative disease prior the stroke, with major comprehension deficit, and/or refusing the consent form, have been excluded. Patients come from the medicine and rehabilitation department of the Saint-Maurice hospitals (Paris, France. Dr R. Péquignot) and the medicine and rehabilitation department of the Pitié-Salpetriere hospital (Paris, France. Dr P. Pradat-Diehl).

Figure 4 .

 4 Figure 4. Evolution of the average response time in milliseconds for each group against target position (column number between 1 and 7)

Figure 5 .

 5 Figure 5. Average number of omissions with related errors per group against target position in the Standard version

Table 1

 1

	. Parameters
	Number of objects	Number of marks in a scene
	Number of trials	Number of trials of the test
		a
		grid.
	Tilt	If checked, a random rotation is applied to each mark.
	Gradient	If checked, different number of marks on each line
		(according to several models)
	Blurring	If checked, application of a cloaking mask
	Size of distractors	Single choice among 5 values
	Size of the target	Single choice among 5 values
	Shape of the distractors	Multiple choices among predefined shapes
	Shape of the target	Multiple choices among predefined shapes
	Background color	Range for hue, saturation, luminance and opacity
	Distractor color	Range for hue, saturation, luminance and opacity
	Target colos	Range for hue, saturation, luminance and opacity

Timeout

Length of a trial in seconds (if the patient doesn't click on the scene before the end of the trial, the patient fails it and the following trial is proposed).

Disorder

If checked, the marks are randomly positioned without overlapping, else, the marks are positioned within the cells of

Table 1 .

 1 Average performance to Bells Test, paper and pencil version, for patient and control groups.

		Total duration (s)	Total omissions	Omissions col. 1,2,3	Starting point (n° col.)
	Patient	203.25	1.75	0.75	1.75
	Control	116.125	0.125	0	1.25

Table 2 .

 2 Mann-Whitney tests for in-group response time comparison for the Items version, for each column. Significant results are shown in bold.

Omissions -Significant differences about the number of omissions per column emerged from the between group comparison for the column 1 in conditions 1 (p = .049), 3 (p = .009) and 4 (p = .01) ; for the column 2 in conditions 4 (p = .049) and 5 (p = .049) ; for the column 3 in condition 5 (p = .049) (cf. Annexe 7).

False alarms -The false alarms rates for the patient and control groups are respectively 0% and 2.5% in condition 1, 0% and 5% in condition 2, 2.5% and 8.75% in condition 3, 2.5% and 0% in condition 4, 5% and 1.25% in condition 5.

Interference version. Reaction Time -We used non-parametric tests because of the distribution of the data. The Mann-Whitney tests revealed evidence for differences of reaction time per columns and conditions between the two groups. Omissions -Significant differences about the number of omissions per columns emerged from the between group comparison for the column 1 in conditions 1 (p = .01), 2 (p = .001), 4 (p = .041) and 5 (p = .009); for the column 2 in conditions 3 (p = .049) and 5 (p = .049) ; for the column 4 in condition 1 (p = .049) ; for the column 7 in condition 1 (p = .041) (cf. Annexe 8).

False alarms -The false alarms rates for the patient and control groups are respectively 0% and 2.5% in condition 1, 0% et 5% in condition 2, 2% et 1,25% in condition 3, 2.5% et 3,75% in condition 4, 2,5% et 5% in condition 5.


Claudiu F Bisu
email: cfbisu@gmail.com

Philippe Darnis
email: philippe.darnis@u-bordeaux1.fr

Alain Gérard
email: alain.gerard@u-bordeaux1.fr

Jean-Yves K'nevez

Jean- Yves K'nevez

The actual research deals with determining by a new protocol the necessary parameters considering a three-dimensional model to simulate in a realistic way the turning process on machine tool. This paper is dedicated to the experimental displacements analysis of the block tool / block workpiece with self-excited vibrations. In connexion with turning process, the self-excited vibrations domain is obtained starting from spectra of two accelerometers. One three axes accelerometer placed on the tool and one unidirectional accelerometer placed on the front of bearing of spindle. The existence of a displacements plane attached to the tool edge point is revealed. This plane proves to be inclined compared to the machines tool axes. This plane contains an ellipse that is the place of the points of the tool tip displacements. We establish that the tool tip point describes an ellipse. This ellipse is very small and can be considered as a small straight line segment for the stable cutting process (without vibrations). In unstable mode (with vibrations) the ellipse of displacements is really more visible. A difference in phase occurs between the tool tip displacements on the radial direction and on the cutting one. The feed motion direction and the cutting one are almost in phase. The values of the long and small ellipse axes (and their ratio) shows that these sizes are increasing with the feed rate value. A weak growth (6%) of the

long and small axes ratio is obtained when the feed rate value decreases. The axis that goes through the stiffness center and the tool tip represents the maximum stiffness direction. The maximum (resp. minimum) stiffness axis of the tool is perpendicular to the large (resp. small) ellipse displacements axis. The self-excited vibrations appearance is strongly influenced by the system stiffness values, their ration and their direction. FFT analysis of the accelerometers signals allows to reach several important parameters and establish coherent correlations between tool tip displacements and the static -elastic characteristics of the machine tool components tested (see [4]). Main displacements direction angle of the tool edge point in the plane (x,y) θ e(yz)

Keywords Experimental model

Main displacements direction angle of the tool edge point in the plane (y,z)

1 Introduction
The machine tools dynamic phenomena come from the elastic system machine / cutting process interaction [17], [START_REF] Deacu | Vibrations des Machines-Outils[END_REF], [21], [START_REF] Ispas | Vibrations des systèmes technologiques[END_REF]. This interaction is thus the dynamic aspects generating source classically met in the machine tools use [18], [25]. The cutting process actions applied to the elastic machining system cause relative tool / workpiece displacements that generate vibrations [START_REF] Deciu | Vibratii nelinear cu aplicatii in ingineria mecanica[END_REF]. These modify the chip section, the contact pressure, the speed of relative movement etc. Consequently, the cutting process instability can cause the dynamic system instability of the machine tool: vibrations appear [START_REF] Merrit | Theory of self-excited machine tool chatter. Contribution to machine tool chatter research[END_REF].

They have undesirable effect on the machined workpiece surface quality and on the tool wear [START_REF] Benardos | Prediction of workpiece elastic deflections under cutting forces in turning[END_REF], [START_REF] Peigne | Etude et simulation des effets dynamiques de la coupe sur la stabilité de la coupe et la qualité géométrique de la surface usinée[END_REF]. Maintenance problems may occur, even ruptures of the machine tools elements [START_REF] Tlusty | The stability of machine tools against self-excited vibrations in machining[END_REF]. Thus, it is necessary to develop numerical and experimental models ensuring to study the vibratory phenomena during machining, in order to obtain the stable process in cutting [START_REF] Chiou | Analysis of tool wear effect on chatter stability in turning[END_REF], [21], [START_REF] Li | Real-time prediction of workpiece errors for CNC for turning centre, Part 4. Cutting-force-induced errors[END_REF], [START_REF] Thevenot | Contribution à la maitrise des phénomènes vibratoires en usinage de parois minces: application à l'usinage de pâles aéronautiques[END_REF]. Considerable efforts were developed to model the cutting process correctly. However, at the present time the suggested solutions are still far from providing sufficiently relevant and general models to translate in an acceptable way all the available experimental results [START_REF] Cahuc | Experimental and analytical balance sheet in turning applications[END_REF], [START_REF] Cahuc | Mechanical and thermal experiments in cutting process for new behaviour law[END_REF]. Models become very complex for studying the threedimensional model and nonstationary cutting conditions, particularly in the case of the vibratory situations, [START_REF] Benmohammed | Identification des lois d'effort de coupe de tournage en régime dynamique[END_REF], [START_REF] Chen | A stability analysis of regenerative chatter in turning process without using tailstock[END_REF], [18], [31], [START_REF] Mei | Active regenerative chatter suppression during boring manufacturing process[END_REF], [START_REF] Segreti | Vibrations en coupe orthogonale. Modélisation, étude de stabilité et validation expérimentale[END_REF]. A model for the expression of cutting forces uncertainty in different cutting conditions was proposed [START_REF] Axinte | Evaluation of cutting force uncertainty components in turning[END_REF]. The model enables the uncertainty prediction of cutting force measurements, for a defined cutting parameters range, based on calibration data and measurements collected in a few experiments run using a factorial design. The results showed that the contributions in the uncertainty budget from single cutting force measurements are balanced between the calibration error on the channel where the force is measured, and the cumulative error due to the cutting parameters variation. Being responsible for approximately 50% of the uncertainty in single force experiments, the cutting parameters variation may be responsible for the scatter of cutting force measurements found in the literature.

Today, the machine tools have rather high dynamic behaviours with regard to rigidities and damping capacities. However, the causes of the vibrations appearance, or unstable modes, are given by the the cutting dynamics process under various working conditions. In other words, under certain conditions, the cutting interaction process with the machine tool elastic system causes the appearance of vibrations. Self-sustained vibrations are observed. These vibrations, due to the cutting process, have frequencies close to the natural system frequencies, and are generated by the cutting actions variation, variation which depends on the various parameters characteristic of the process [START_REF] Calderon-Najera | Caractérisation dynamique du système Pièce/Outil/Machine: usinage des pièces minces[END_REF], [13], [START_REF] Deciu | Vibratii nelinear cu aplicatii in ingineria mecanica[END_REF].

These parameter modifications lead to the variations of relative displacements of tool / workpiece and tool / chip. Variations of the chip section are generated, inducing variations of the cutting actions, and thus maintaining the vibrations. It is thus advisable to take into account these parameter variations in a three-dimensional model cutting process which requires a specific determination. These problems were already studied in the past. Different methods were used to estimate workpiece elastic deflections under cutting forces in turning by using analytical modelling of workpiece elastic deflections, by finite element (via Castigliano's second theorem) [START_REF] Benardos | Prediction of workpiece elastic deflections under cutting forces in turning[END_REF], and by finite-differences [38]. In [START_REF] Li | Real-time prediction of workpiece errors for CNC for turning centre, Part 4. Cutting-force-induced errors[END_REF], a real-time compensation scheme is developed based on a cutting force induced error model.

In this paper, an experimental study is developed to determine and characterize a series of parameters necessary for the dynamic model of cutting process in agreement with static aspects obtained previously [4]. After having exposed the tests protocol used (see Sect. 2), displacements are measured and a frequency analysis is carried out (see Sect. 3). A displacement plane attached of the tool point (see Sect. 4) is highlighted starting from the accelerometer data. The deep analysis included in Section 5 shows that these displacements describe an ellipse. The evolution of the ellipse axis ratio can be characterized by a slightly increasing function depending on the feed motion while their ratio follows an opposite law. This ellipse is located in a tilted precise plane compared to the machine tool axes. Before concluding, Section 6 gives a correlation between the tool tip stiffness and displacements on the one hand, and on the other hand between stiffness center [4] and the central axis of the dynamic cutting process.

2 Test protocol

Approach

In turning operation, the workpiece has a rotary motion whereas the tool has a linear translation. It is obvious that both the tool and workpiece vibrate in material removal. Although workpiece vibrations impact both cutting instability and product quality including surface finishing, most models developed for investigating surface roughness [START_REF] Grzeski | A revised model for predicting surface roughness in turning[END_REF], [40], [START_REF] Thomas | Effect of tool vibrations on surface roughness during lathe dry turning process[END_REF] do not consider workpiece vibrations at all.

A new tests protocol is here proposed to determine a series of led phenomenologic parameters during the cutting process in particular in the self-sustained vibrations case. According to [4], the machining system static behavior presents couplings in all the directions. It is thus advisable to expect that it is the same in dynamics.

The approach adopted for this study constitutes a part of a global vision of research presented in the Fig. 1. As in the static case, the dynamic characterization is carried out starting from the interaction of two elements: block tool (BT) and block workpiece (BW) forming the machining system and knowing that, a priori, each element taken separately have a different vibratory behaviour (cf. figure 3), [START_REF] Bisu | Nouvelle analyse des phénomènes vibratoires en tournage[END_REF].

Experimental device

Dynamic cutting tests are carried out on a conventional lathe (Ernault HN 400) for which the spindle speed does not exceed 3 500 rpm. The main components of the test machining system used are presented without its dataprocessing environment in the Fig. 2. The machining system behavior is analyzed through one three-direction accelerometer fixed on the tool and using two unidirectional accelerometers positioned on the lathe, on the front bearing of the spindle, to identify the influence of this one on the cutting process. Moreover, a six-components dynamometer [START_REF] Couétard | Capteurs de forces à deux voies et application à la mesure d'un torseur de forces[END_REF], being used as tool-holder [START_REF] Toulouse | Contribution à la modélisation et à la métrologie de la coupe dans le cas d'un usinage tridimensionnel[END_REF], is positioned on the lathe to measure all the cutting forces (forces and torques). This study is presented in the paper [START_REF] Bisu | Nouvelle analyse des phénomènes vibratoires en tournage[END_REF]. The dynamometer used is an evolution of [START_REF] Couétard | Capteurs de forces à deux voies et application à la mesure d'un torseur de forces[END_REF]. The active part made of the strain gauges is replaced by piezoelectric sensors adapted for faster acquisitions and being adequate and compatible with the vibratory phenomena necessary to measure.

The three-dimensional dynamic character is highlighted by seeking the various existing correlations between the various parts of the machining system and the various parameters evolutions, which ensure to characterize the process.

Data acquisition protocol

The self-excited vibrations characterization method, is based on various work [START_REF] Kudinov | Dinamica Masinilor Unelten[END_REF], [START_REF] Moraru | Vibratiile si Stabilitatea Masinilor Unelte[END_REF], [START_REF] Rusu | O metoda theoretico experimentala de investigare a proprietatilor de stabilitate la autovibratii ale sistemului dinamic al masinilor unelte[END_REF] and on the results of the preliminary dynamic study undertaken in [START_REF] Bisu | The regenerative vibration influence on the mechanical actions turning[END_REF], is summarized in Fig. 3.

Fig. 3 Natural frequencies domain of different components of the machining system

The static study undertaken here (cf. [4] and [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF]) allows to identify perfectly the machine tool frequency domain and each one of its components under various operating conditions. Moreover, a virgin frequency band at any natural frequency was not found. The machine tool was turned on without part to machine. Thus, the appearance of frequencies in this zone when the cutting process exists, highlights the vibratory phenomenon induced by this one. In what follows, the cutting parameters are selected constant, excluding the depth of cut (ap).

On the test machining system, the instantaneous speed of rotation is controlled by a rotary encoder directly related to the workpiece. The connection is carried out by a rigid steel wire, which allows a better transmission of the behavior (Fig. 2). During the cutting process, the number of revolutions is controlled constantly at nearly 690 rpm and a negligible variation cutting speed of about 1 % is detected.

All measurements are collected on a PC and are thus treated in real time. For these tests, the used tool was a noncoated carbide tool (TNMA 16 04 12) without chip break geometry. The cutting material is a chrome molybdenum alloy type (AiSi 4140). The cylindrical test-tubes have a diameter of 120 mm and a length of 30 mm (Fig. 4). The dimensions retained for these test-tubes were selected using the finite elements method coupled to an optimization method using SAMCEF R software presented in [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF]. Moreover, the geometry of the tool (Fig. 5) [27] is characterized by the cutting angle γ, the clearance angle α, the edge angle of inclination λ s , the direct angle κ r , the nozzle radius r ǫ and the sharpness radius R. The tool insert is examined after each test and is changed if necessary of wear along the cutting face (Vb ≤ 0.2 mm ISO 3685), that may disturb the studied phenomenon. The tool characteristics used are presented in the Table 1.

Remember that the assembly of BW detailed in [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF] is considered as a block of interdependent elements, which is subjected to the vibrations due to the cutting process. 1 The tool geometrical characteristics Fig. 5 The tool geometrical details.

γ α λs κr rǫ R -6 • 6 • -6 • 91 • 1,2 mm 0,02 mm Table
The machining system is presented as an elastic system and the interface BW / BT is the closure of this system (Fig. 6). The vibrations appearance is strongly conditioned by the elastic structure behaviour of the studied system [7]. 3 Tests and analyses

Experimental conditions

Many tests are carried out under the conditions specified in the previous paragraph. They are considered for the depth of cut ap = 1 mm, 2 mm, 3 mm and 5 mm in order to compare signals and to dissociate the machine vibration influence of those generated by the cutting process itself.

Workpiece/Tool/Chip displacements

The signals treatment of the three-direction accelerometers gives, by integration, displacements according to the three directions. An example is presented in the Fig. 7 related to a cutting depth of 2 mm. For these tested conditions, the system is stable; the signal has very low amplitudes, on the order of micrometer; and the chip section remains constant (Fig. 7 and8). The part surface quality is correct, with a total roughness (R t ) of 4.3 µm. The analysis of measurements for the depth of 3 mm cut, give similar results; the displacements amplitudes are in the same region, lower than 10 micrometers, and the chip section does not vary (Fig. 8); this one has the same continuity characteristics as for ap = 2 mm (Fig. 7), but very light undulations appear on the workpiece surface.

Actually, the characteristics start to change distinctly from the depth of 4 mm cut. The tool point displacements amplitudes increase, and the signal sinusoidal character has high amplitude compared to the previous cases. The system starts to become unstable. The chip develops important periodic undulations and significant section variations appear (Fig. 9). All chips are type 1.3 (ISO 3685). The machined surface part has weak undulations.

The increase of cutting depth until 5 mm allows to reach a mode of totally unstable cutting and the selfexcited vibration appearance is clearly identified for ap = 5 mm (Fig. 11). Around this working point, many tests are carried out in order to determine the self-excited vibrations extent. These tests are carried out maintaining the same ap value and the same workpiece revolutions number N but for various feed motion f, illustrated in the Table 2. It is important to specify that, for the four feed values used (Table 2), the cutting process was in unstable mode, more or less marked, with chip section variations and very different surface undulations on the workpiece for each imposed feed value. In order to reach the best possible precision, we then study the extreme case obtained with the maximum values which involve the most important dynamic effects: cutting depth ap = 5 mm, and feed motion value f = 0,1 mm/rev, but maintaining a constant cutting speed.

In Fig. 10 are presented the three signals related to the tool tip displacements components according to the three directions of workspace. In this situation, the chip presents important tightened periodic undulations. The section variations seem to be in the case of a discontinuous cutting. The workpiece surface quality becomes poor and the undulations left on the workpiece after the tool passage are very important (Fig. 11). The chip characterizations and the workpiece are detailed in [4]; in particular, the undulations and the chip section variations are quantified there.

Displacements frequency analysis related to the tool tip

The tool tip displacements components frequency analysis considering the three directions related to the machine tool is carried out starting from a Fast time Fourier Transformation (FFT). An FFT spectrum example of the three acceleration components delivered by the threedirectional accelerometer placed on the tool is given in the Fig. 11. The frequencies above 1 000 Hz are eliminated knowing that, according to the literature, the selfexcited vibration frequency domain is situated between 120 Hz and 200 Hz [START_REF] Ispas | Vibrations des systèmes technologiques[END_REF], [START_REF] Kudinov | Dinamica Masinilor Unelten[END_REF], [31], [32], [START_REF] Moraru | Vibratiile si Stabilitatea Masinilor Unelte[END_REF], [42]. The FFT analysis of several tests shows that the acceleration frequencies of vibrations during the cutting process are about 150 Hz to 200 Hz. They are slightly lower than the machine natural frequencies (Fig. 3). However, we know that the self-excited vibrations appear near the natural and the machining system are not depending on the number of workpiece revolutions [24], [START_REF] Moraru | Vibratiile si Stabilitatea Masinilor Unelte[END_REF].

On the example of vibrations measurements during the machining, presented in the Fig. 12, it should be noted that the cutting vibrations fundamental frequencies are around 190 Hz for the three axes, with a dominating amplitude on the y axis (cutting axis, according to Fig. 2). These frequencies are lower than those obtained ( [START_REF] Bisu | Optimization and dynamic characterization system part in turning[END_REF]) during the machining system dynamic characterization with a no-cutting process, which are located at approximately 550 Hz (Fig. 3) [START_REF] Bisu | Nouvelle analyse des phénomènes vibratoires en tournage[END_REF]. The recorded frequencies, therefore, correspond well to the self-excited vibrations related to the cutting process. The frequency peak around 190 Hz is found for the other tests, and it is constant according to the feed motion in turning.

Another very important parameter for the self-excited vibrations is their amplitude. It depends on the energy quantity introduced into the system. Therefore, the amplitude is influenced on the one hand by the system elastic parameters, and, on the one other hand, by the cutting parameters: cutting speed, feed motion and depth of cut. The parameter that presents the most important influence is the depth of cut. The vibrations amplitude increases in a quasi linear way according to the increase Fig. 12 FFT spectrum corresponding of the accelerations acquires on the three directions; cutting parameters selected ap = 5 mm, f = 0.1 mm/rev. and N = 690 rpm depth of cut until it exceeds the elastic system stability limit in agreement with literature data published by Kudinov [START_REF] Kudinov | Dinamica Masinilor Unelten[END_REF].

Tool point displacements plane

Acceleration analysis of vibration data

After integration, the acceleration data analysis allows to establish the existence of an attached displacements plane of the tool tip, which, describes an ellipse (Fig. 13). Certain parameters are a slightly increasing depending of the feed motion, as we will demonstrate further. The determination of this plane is presented in appendix (Sect: 8.2). The existence of this plane is confirmed by the displacements signals observation (Fig. 11). It is henceforward a question of locating this plane in three dimension space.

The tool tip displacements plane localization

The tool tip displacements plane P u is characterized by its normal vector noted n u (Fig. 14).

Fig. 14 The tool tip displacements plane Pu: projection of the normal vector nu on the axis related to the machine tool

The characterization of this plane by its normal is carried out for each test depending on the feed motion in turning (Table 3). Table 3 The normal nu of the plane Pu attached of the tool tip displacements on three directions of cutting, depending on feed motion

We note that the normal component according to the feed motion direction almost does not evolve according to this one. On the other hand, a very light decrease (respectively growth) according to the radial direction (respectively, the axis of cutting) is observed in dependence with the feed motion values. These variations are, however, so weak that they do not affect the standard of the plane direct normal which thus can be considered constant according to the feed motion. The existence and the determination of this plane provide simplifying important informations about the configuration to be adopted in order to write a semianalytical model that is under development [4], [START_REF] Cahuc | Mechanical and thermal experiments in cutting process for new behaviour law[END_REF]. In particular, we will further see that this plane allows to bring back the cutting three-dimensional problem, with three directions displacements, using a simpler plane model that is inclined compared to axes (x, y, z) related to the machine tool.

5 Displacements analysis of the tool point

Stable and unstable process comparison

In the tool tip displacements plane P u , it is possible to establish that the tool tip point describes a very small ellipse in the stable case cutting process (without vibrations); this ellipse could be assimilate with a small segment of straight lines (ap = 2 mm), according to the Fig. 15-a. On the other hand, in unstable mode (with vibrations), the ellipse (according 8.3) of tool tip displacements (ap = 5 mm) is really more visible (Fig. 15-b).

Phase control between the tool tip displacements components

A phase difference is occurring between the tool tip displacements following the x radial direction and the y cutting direction or the z feed motion direction (these last two being almost in phase). This phase difference is evaluated starting from the comparison of two signals that have different phases. More precisely, phase difference ϕ u is evaluated starting directly to the temporal signals and using the relation:

ϕ u = ±2π ∆t T , ( 1
)
where T is the time corresponding to a phase difference of 360 • and ∆t to temporal phase difference between the two compared components signals. Fig. 16 presents an example of phase difference ϕ u between radial displacement x and the two displacements components following y and z; they are almost in phase. A phase difference of 28 • is thus obtained for the studied case, ap = 5 mm and f = 0.1 mm/rev. During the experimental tests according to different feed motion values, the variation of this phase difference is very weak. For the value f= 0,05 mm/rev, the phase difference remains equal to the phase difference obtained for the feed value f = 0,1 mm/rev.

Tool tip displacements ellipse approximation

The ellipse is characterized in detail in the appendix (cf. Sect: 8.3) on the plane P u , with the normal direction n u , by its large axis a u and its small axis b u determined using the method of least squares, in the reference system (n ua , n ub ) unit vector related to the ellipse axes (Fig. 17).

The values of a u , b u and their ratio a u /b u are presented in the Table 4. The value analysis of the large and small ellipse axis shows that these two sizes are increasing with the feed value. On the other hand, a weak growth (6%) of the ratio a u /b u is obtained when the feed value decreases. The ellipse geometrical proportions are thus quasiconstant according to the feed weak evolution chosen here.

6 Discussion on static and dynamic aspects

Stiffness / displacements correlation

Taking into account the machining system static study realized in [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF], it is possible to check that the stiffness Table 4 Values depending on the feed for large and small ellipse axes that correspond to tool tip displacements for ap = 5 mm, f = 0.1 mm/rev principal directions angles are comparable with the ellipses angles attached to the tool tip displacements (Table 5).

static case dynamic case α K(yz) α K(xy) θ e(yz) θ e(xy) f (mm/rev) 77 • 69 • 0.1 76 • 65 • 77 • 69 • 0.075 79 • 67 • 0.0625 79 • 65 • 0.05
Table 5 Comparison values between the principal directions angles of the tool tip displacements and the stiffness principal directions of the machining system

Between the vector n f (characterizing the stiffness principal directions) and the normal vector n u situated in the attached tool tip displacements plane, another correlation exists. Indeed, calculation shows that the angle between these two vectors does not exceed 2.5 • , in our case (Table 6). It is advisable, moreover, to note that the difference between the two vectors is slightly increasing depending on the feed value.

f(mm/rev) arccos

n f .nu n f . nu| 0.1 2.5 • 0.075 1.9 • 0.0625 1 • 0.05 0.8 •
Table 6 Correlation between nf -stiffness principal directions and nu -normal direction of the plane Pu attached of the tool tip displacements

Correlation between tool displacements / stiffness center

By comparison with the static analysis results developed in [4], it is highlighted a coupling between the system elastic characteristics BW and the vibrations generated by cutting process. As we could expect it, the self-excited vibrations appearance is strongly influenced by the system stiffness values, their ratio and their direction. The stiffness center (CR) is given in [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF] (and a summary of the stiffness center determination is given in appendix 8.1). The axis, which passes by the stiffness center and the tool tip, represents the maximum stiffness direction. This maximum stiffness axis is drawn in Fig. 18. It is orthogonal with the normal of the plane P u , and it is also perpendicular to the large ellipse axis. This explains well why the greatest displacement takes place, logically, on the axis where the stiffness is minimal. This correlation validates the experimental protocol established [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF] for this case of turning.

To continue, the P u displacements plane determination and the elliptic characterization of this plane motion provide significant information on the configuration to be adopted writing a simplified three dimensional model. It is clear at the end of this research that the system must be considered according to this plane axes and not according to those of the machine tool. Compared to other authors who use only the tool stiffness [START_REF] Calderon-Najera | Caractérisation dynamique du système Pièce/Outil/Machine: usinage des pièces minces[END_REF], [START_REF] Liu | The mechanism of ductile chip formation in cutting of brittle materials[END_REF], [36], this study takes into account, moreover, stiffness resulting from the system fixture/tool-holder (BT). The important information on the static stiffness, obtained in [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF], certainly makes it possible to determine the privileged displacements directions.

The stiffness center and the rotation center were obtained experimentally [START_REF] Bisu | Un mouveau modèle expérimental d'analyse des phénomènes vibratoires lors d'une opération de tournage, 4 e Assises Machines et Usinage à Grande Vitesse -ENSAM, Aix en Provence[END_REF]. The direction of minimum displacement was also defined starting from the experimental model. The confrontation of these results: stiffness center, principal stiffness directions, central axis and the tool tip displacements place show the coherence of the presented new approach and consolidates the experimental procedures implemented.

From the present work, the following conclusion can be drawn:

-The acceleration data analysis allows to establish the existence of an attached plane of the tool tip displacements tilted compared to axes related to the machine tool. -In this plane, the tool tip displacements describes an ellipse. -We have established that the tool tip point describes a very small ellipse (assimilated with a straight-line small segment) in the case of the stable cutting process (without vibrations); in unstable mode (with vibrations) the ellipse of displacements is really more visible. -A phase difference is occurring between the tool tip displacements following the radial and cutting direction or the feed motion direction (these two last being almost the same phase). -The long and small ellipse axis values show that these two sizes are increasing with the feed value. -A weak growth (6%) of the ratio long on small axes is obtained when the feed value decreases. The ellipse geometrical proportions are, thus, quasiconstant according to the feed weak evolution chosen here. -The axis which passes by the stiffness center and the tool tip represents the maximum stiffness direction. -The maximum (resp. minimum) stiffness tool axis is perpendicular to the large (resp. small) ellipse displacements axis. -The self-excited vibrations appearance is strongly influenced by the system stiffness values, their ratio and their direction.

It is also important to note for this research the plane determination attached to the tool tip displacements which is carried out according to an ellipse the surface of which is an increasing function depending on the feed motion value; this aspect is in perfect coherence with the power level injected in the system during machining.

Appendix

Reminder of stiffness center determination

It is well known that any machine tool is characterized by principal directions of deformation. These principal directions of displacement are a function of the machine structure, its geometrical configurations, and cutting parameters used. We can observe either a very stiff behavior, or very rubber band according to the direction. Here, the tool is regarded as forming integral part of block tool BT. The aim is to determine the stiffness center CR BT of elastic system BT [START_REF] Marinescu | Handbook of Machine Tool Analysis[END_REF]. This stiffness center corresponds to the block BT rotation center compared to the lathe bed. Obtaining CR BT consists in finding the intersection points of different perpendicular to displacements.

The stiffness center is obtaining based on the tool point O that is origin of the coordinate system (x, y, z). The procedure to obtain the stiffness center is based on the virtual work principles and detailed in the figure 20; the imposed charge follows all three directions, Fi being known; (i = x, y, z). Measurement of the displacement vector (linear and rotation displacement) under the charge di,j is obtained in two points Pi,j in each direction (i = x, y, and z) and (j = 1 and 2). The direction (Dij) is released being straight line containing di,j vector that includes the point Pi,j . In the next step, three mean plans P i are defined by approximation of the points M i and containing the lines D ij . We can draw the normal n i of each plan P i that include the point M i .

We obtain a linear system with three vectors' equations and three unknown factors, after that is seeking to obtain the intersection point CR BT using least squares minimization method. In reality, the directions of these three normal lines cross (nearly at r = 1.2 mm) in only one point noted CR BT which corresponds with stiffness center.

Determination of the attached plane of the tool tip displacements

The modeling of the attached plane of the tool tip displacements starting from the experimental results is carried out using the software Mathcad c . We seek to de-termine the plane that passes by the points cloud representing tool point displacements (Fig. 13 The vector V is computed now by minimization:

V = min(E rr , x p , y p , z p , x n , y n , z n ),

where:

V =              V 1 = x p , V 2 = y p , V 3 = z p , V 4 = x n , V 5 = y n , V 6 = z n .
It results from it that the n u normal components in the plane of the tool tip displacements are given by:

n u =    V 4 , V 5 , V 6 .
For the present case study in the section 5.3 (Table 3), with ap = 5 mm and f = 0.1 mm, it comes:

n u =
   -0.056, -0.216, 0.975, the equation of the searched plane is then :

P u (s, t) = V p + s.u 1 + t.u 2 ,
where s and t are constants, and V p is equal with:

V p =    V 1 , V 2 , V 3 ,
and u 1 , u 2 are given by:

u 1 = u 0 ∧ n u n 0 ∧ u u , u 2 = n ∧ u 1 ,
u 0 being the plane orientation vector:

u 0 =    1, 1, 1.

Ellipse approximation

Using the ellipse plane determination, it is possible to build the matrix M rep expressed by: .

Another matrix is defined by :

[M u ] = [U ] -[P ],
with [P ] defined by the equation ( 2) and [U ], being the vector of the tool tip point displacement given by:

[U ] =    u x u y u z    .
Now, we determine the new ellipse configuration centered on the origin of the basic reference system (x, y, z):

[M u2 ] = [M rep ] t .[M u ].
The new displacements of the tool tip are :

[U 1 ] = [M u2 ].
By changing the coordinate system, we project the ellipse in the new two-dimensional reference system (Fig. 21), (α 1 , α 2 ) using the rotation matrix [M rot ] The angle θ α is obtained using minimization method and Mathcad c software. We obtain:

[M u3 ] = [M rot ] t .[M u2 ],
and after that is obtained the tool tip displacement related to the base system (α 1 , α 2 ):

[U 2 ] = [M u3 ].
Consequently, the ellipse equation is:

(u α1 ) 2 a 2 + (u α2 ) 2 b 2 = 1,
using parameters f = 0.1 mm/rev and ap = 5 mm.

Fig. 1

 1 Fig. 1 General approach considered

Fig. 2

 2 Fig. 2 Experimental machining system and metrology environment in turning process

Fig. 4

 4 Fig. 4 Tested workpiece

Fig. 6

 6 Fig. 6 Model of machining system and BW -BT interaction

Fig. 7

 7 Fig. 7 Displacements components signals of the tool tip for a turning operation: ap = 2 mm, f = 0.1 mm/rev, and the spindle speed N = 690 rpm

Fig. 8

 8 Fig. 8 Chip related to ap = 3 mm, f = 0.1 mm/rev and the spindle speed N = 690 rpm

Fig. 9

 9 Fig. 9 Chip related to ap = 4 mm, f = 0.1 mm/rev , and the spindle speed N = 690 rpm.

Fig. 10

 10 Fig.10The tool tip displacements on the three directions x, y, and z related to the machine tool and considering ap = 5 mm, f = 0,1 mm/rev, N = 690 rpm

Fig. 11

 11 Fig. 11 Signals zoom related to the tool tip displacements components according with cutting parameters: ap = 5 mm, f = 0,1 mm/rev., N = 690 rpm

Fig. 13

 13 Fig.13The tool tip displacements plane Pu

Fig. 15

 15 Fig. 15 Comparison between the stable (a) and unstable cutting process (b)

Fig. 16

 16 Fig. 16 Example of phase difference between x radial tool tip displacements and other displacement components (following cutting direction and feed motion direction).

Fig. 17

 17 Fig.17Coordinate system changing to obtain the ellipse attached to the tool point displacements

Fig. 18

 18 Fig. 18 Correlation between stiffness center and the ellipse attached of the tool tip displacements

6. 3

 3 Correlation between stiffness center and central axis of the dynamic process in turningAs example, for a bearing test on 68 revolutions (ap = 5 mm, f = 0.1 mm/rev. and N= 690 rpm) we calculated the beam of the central axis of the tip tool point small displacements torsor, their intersection point and the stiffness center corresponding to this configuration. All these results are presented on Fig.19. The line that binds the stiffness center (CR) and the point of central axes intersection passes by the tool tip point.

Fig. 19

 19 Fig. 19 Central axis / stiffness center

Fig. 20

 20 Fig. 20 Experimental procedure to obtain stiffness center CRBT

  ) : ax + by + cz + d = 0.Using the parameter e rr for the errors, the following is obtained :e rr (x, y, z, x p , y p , z p , x n , y n , z n ) = [M (x, y, z) -P (x p , y p , z p ).n u (x n , y n , z n )] ,where:M = {x, y, z} t , P {x p , y p , z p } t , n u = {x n , y n , z n } t , (2)in this equation, superior index t indicates the transposition operation. Let us express the E rr function using e rr and introduce the components of displacements (u xi , u yi , u zi ) on the three space directions, it comes:E rr (x, y, z, x p , y p , z p , x n , y n , z n ) = N i=0e rr (u xi , u yi , u zi , x p , y p , z p , x n , y n , z n ),

[M rep ] = u 11 u 21 n u1 u 12 u 22 n u1 u 12 u

 12 [START_REF] Ispas | Vibrations des systèmes technologiques[END_REF] n u1

Fig. 21 1 .

 211 Fig. 21 2D projected ellipse attached of the tool tip point displacements

•

  Displacement plane • Self-excited vibrations • Turning

	Nomenclature
	T	Time that corresponding to one workpiece
		revolution
	u	Tool edge point displacement (m)
	x (z)	Radial (axial) direction
	y	Cutting feed axis
	α	Clearance angle (degree)
	α κ(xy) Angle of the main stiffness direction in the
		plane (x,y) (degree)
	α κ(yz) Angle of the main stiffness direction in the
		plane (y,z) (degree)
	∆t	Temporal dephasing between two signals
	ϕ u	Dephasing between the displacements com-
		ponents attached to the tool edge point (de-
		gree)
	γ	Cutting angle (degree)
	λ s	Inclination angle of edge (degree)
	κ r	Direct angle (degree)
	θ e(xy)
		Nomenclature
		ap	Depth of cut (mm)
		a u (b u ) Large (small) axis of ellipse attached with
			the cutting tool tip displacements (m)
		a f (b f )	Large (small) axis of ellipse attached with
			the forces charge points (m)
		BT	Block Tool
		BW	Block Workpiece
		f	Feed rate (mm/rev)
		N	Number of revolutions (rpm)
		n f	Vector attached to the components system
			stiffness
		n u	Normal direction of the plane P u
		n ui	Unitary vector, support of the ellipse axis i
			(i = a, b) situated in the plane P u
		P u	Plane attached with the cutting tool edge
			displacements
		r ǫ	Cutting edge radius (mm)
		R	Cutting tool edge radius (mm)
		R t	Total roughness (µm)

Table 2

 2 The cutting process parameters

Claudiu F.Bisu et al.

Acknowledgements The authors would like to thank the Centre National de la Recherche Scientifique (UMR 5469) for the financial support to accomplish the project.