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Article Film Thickness and Shape Evaluation in a Cam-Follower Line Contact with Digital Image Processing

Enrico Ciulli 1,* , Giovanni Pugliese 2 and Francesco Fazzolari 3

1 Dipartimento di Ingegneria Civile e Industriale, University of Pisa, Largo Lazzarino, 56122 Pisa, Italy 2 Direzione Edilizia e Telecomunicazione, University of Pisa, via Fermi 6/8, 56126 Pisa, Italy; [email protected] 3 Parker Hannifin–FCCE, Via Enrico Fermi 5, 20060 Gessate (MI), Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-050-2218-061



Received: 29 January 2019; Accepted: 25 March 2019; Published: 28 March 2019


Abstract: Film thickness is the most important parameter of a lubricated contact. Its evaluation in a cam-follower contact is not easy due to the continuous variations of speed, load and geometry during the camshaft rotation. In this work, experimental apparatus with a system for film thickness and shape estimation using optical interferometry, is described. The basic principles of the interferometric techniques and the color spaces used to describe the color components of the fringes of the interference images are reported. Programs for calibration and image analysis, previously developed for point contacts, have been improved and specifically modified for line contacts. The essential steps of the calibration procedure are illustrated. Some experimental interference images obtained with both Hertzian and elastohydrodynamic lubricated cam-follower line contacts are analyzed. The results show program is capable of being used in very different conditions. The methodology developed seems to be promising for a quasi-automatic analysis of large numbers of interference images recorded during camshaft rotation.

Keywords: digital image processing; optical interferometry; non-conformal contacts; cam-follower; Hertzian contacts; film thickness; elastohydrodynamic lubrication

1. Introduction It is well known that film thickness is one of the most important quantities to be determined for a lubricated contact. Conventionally, engineering methods used for the assessment of film thickness from which a lubrication regime can be determined are often based on numerical and empirical formulations obtained by experimental tests conducted in stationary conditions. However, many practical engineering and mechanical components are characterized by continuous variations of the operating parameters. For instance, non-conformal contacts such as those occurring in gears and cams, are characterized by rapid variations of speed, load and geometry. In these cases, experimental results are difficult to obtain and steady-state numerical solutions can lead to over or underestimation of the film thickness. Although very complex numerical models of the lubricated contacts are available—considering for instance also mixed lubrication conditions, thermal effects and transient conditions—real contacts remain difficult to simulate and experimental studies are therefore important. Only through experimental measurements, in fact, it is possible to obtain a better comprehension of what really happens in the lubricated contacts, providing the possibility of validating numerical models or setting up corrective coefficients for stationary case formulas. During the last decades, the number of experimental investigations on non-steady state lubricated contacts has increased, mainly due to

Lubricants 2019, 7, 29; doi:10.3390/lubricants7040029 www.mdpi.com/journal/lubricants Lubricants 2019, 7, 29 2 of 17 improvements in the experimental techniques and the more sophisticated instrumentation available. In Reference [1] a review of studies on transient conditions is presented. Sample recent studies are reported in References [2,3], in which start-up and sudden halting conditions and the transient behavior of transverse limited micro-grooves in EHL point contacts are investigated. Experimental tests on non-conformal lubricated contacts under transient working conditions are commonly performed using ball on disk test rigs. Often only one quantity is varied, usually the speed of the contacting bodies, while the geometry and the load are kept constant. Few experimental tests have been performed on test rigs for cam-follower contacts. The rapid variation of the operating conditions, typical of the cam-follower contacts, makes it difficult to record the different quantities, particularly those necessary for the evaluation of film thickness. Different methods were used for the measurement of film thickness in cam-follower contacts. A capacitance transducer [4], thin film micro transducers [5] and an electrical resistivity technique [6] were respectively used. Tests on real engines have been also performed, as for instance in Reference [7], where both friction and minimum oil film thickness were measured, the latter with a capacitance technique. However, optical interferometry has proven to be the most powerful and detailed method for measuring film thickness and it is currently a well-established experimental technique [8]. Two different kinds of light can normally be used: white and monochromatic light. Many research groups use these techniques. Some examples are briefly mentioned in the following. In Reference [9] white light interferometry was used with a digital image analysis. A spacer layer was introduced in Reference [10] to allow measurement of very thin film. White light cannot be used for thicknesses greater than about 1 µm; monochromatic light can be used in this case. Luo’s group reported a method based on the relative intensity of images obtained with monochromatic light [11]. This method was further developed by using a multi-beam interference analysis in Reference [12]. In Chen and Huang’s work [13], film thickness was evaluated using monochromatic light. The method is based on an actual intensity–thickness relation curve. Studies using dichromatic or trichromatic light were also performed that use both color and light intensity information. Dichromatic light was used, for instance in References [14,15]. An approach to achieve online measurement of film thickness in a slider-on-disc contact by using dichromatic optical interferometry was reported in the work [16]. Marklund et al. described the intensity base methods with a phase measurement approach using trichromatic light [17]. The combination of conventional chromatic interferometry with the computer image processing methods available nowadays offers good accuracy and the possibility of analyzing a great number of images in an automatic way [18,19] and can also be used to analyze images obtained in line contacts [20]. For the analysis of the large number of images recorded by a high-speed camera, a program for automatic digital image processing was developed for point contacts by the authors’ research group [21]. It was used for the analysis of interference images obtained in tests with constant load and geometry but variable speed using a ball-on-disc experimental apparatus. A test rig was successively designed and realized for a more realistic simulation of gear teeth and cam-follower contacts. The rig was tested using circular eccentric cams [22]. In this work, after a description of the experimental apparatus used, the main issues of the digital image processing of interference images obtained in the line contacts are presented and discussed. The former program, developed for point contact [21], has been improved and new versions for calibration and successive analysis of line contacts have been realized and used for a cylindrical cam in contact with a glass disc.

2. Materials and Methods

2.1. Experimental Test Rig The rig used for the experimental tests, also described in Reference [23], was entirely designed and developed at the University of Pisa in order to investigate non-conformal lubricated contacts between a specimen of suitable shape (usually a cam) and a counterface (usually the flat surface of Lubricants 2019, 7, x FOR PEER REVIEW 3 of 17

Lubricants 2019, 7, 29 3 of 17 a disc, simulating a follower). The rig allows simultaneous measurements of contact force and film thickness.Lubricants A2019 picture, 7, x FOR and PEER a schematic REVIEW drawing of the apparatus are shown in Figure1. 3 of 17

(a) (b)

Figure 1. (a) Picture of the experimental apparatus for testing cam-follower contacts; (b) Schematic drawing of the apparatus.

The camshaft is installed on a rocker arm and is driven by a planetary gearbox moved by a brushless electric motor. The rocker arm is connected to the motor by an elastic joint. An absolute encoder positioned after the(a) elastic joint allows the direct measurement of the(b )angular position and velocity of the cam. FigureFigure 1. (1.a) ( Picturea) Picture of theof the experimental experimental apparatus apparatus for for testing testing cam-follower cam-follower contacts; contacts; (b) ( Schematicb) Schematic The contact between the cam and the plane surface of the disc occurs in the measurement unit. drawingdrawing of theof the apparatus. apparatus. This includes a system of nine annular load cells mounted in three groups, each one composed of two tangential cells and one for normal load. In this way, all components of the contact force are measured. TheThe camshaft camshaft is installedis installed on on a rockera rocker arm arm and and is drivenis driven by by a planetarya planetary gearbox gearbox moved moved by by a a Different configurations are possible by changing the loading system or the measurement group. In the brushlessbrushless electric electric motor. motor. The The rocker rocker arm arm is connectedis connected to to the the motor motor by by an an elastic elastic joint. joint. An An absolute absolute basic version the glass disc, simulating the follower, is kept fixed while the cam axis is moving. The load encoderencoder positioned positioned after after the the elastic elasti jointc joint allows allows the the direct direct measurement measurement of of the the angular angular position position and and is applied through an adjustable spring system. Another approach is to apply the load with weights via velocityvelocity of of the the cam. cam. a lever mechanism mounted on the rocker arm on the opposite side of the spring; this configuration TheThe contact contact between between the the cam cam and and the the plane plane surface surface of of the the disc disc occurs occurs in in the the measurement measurement unit. unit. allows better regulation of the contact force, especially during the calibration procedure. ThisThis includes includes a system a system of nineof nine annular annular load load cells cells mounted mounted in threein three groups, groups, each each one one composed composed of twoof two The lubricant is directly supplied to the contact zone by an oil system. The temperature is regulated tangentialtangential cells cells and and one one for for normal normal load. load. In In this this way, way, all all components components of of the the contact contact force force are are measured. measured. using a thermostatic bath. Figure 2 shows the cam used for obtaining the results presented in this work DifferentDifferent configurations configurations are are possible possible byby changing th thee loading loading system system or orthe the measurement measurement group. group. In the mounted on the camshaft; the upper part of the measurement unit with the follower is removed in this Inbasic the basic version version the glass the glass disc, disc,simulati simulatingng the follower, the follower, is kept is fixed kept while fixed whilethe cam the axis cam is moving. axis is moving. The load picture to make the cam visible. Theis loadapplied is applied through through an adjustable an adjustable spring system. spring system.Another Anotherapproach approach is to apply is the to apply load with the load weights with via The test rig is instrumented and controlled using real-time National Instruments cRIO and weightsa lever via mechanism a lever mechanism mounted on mounted the rocker on thearm rocker on the arm opposite on the side opposite of the sidespring; of thethis spring;configuration this LabVIEW® software. A sampling frequency of 10 kHz is normally used during tests. configurationallows better allows regulation better of regulation the contact of force, the contact especially force, during especially the calibration during the procedure. calibration procedure. Film thickness and its shape are estimated using optical interferometry. In this case, the disc used TheThe lubricant lubricant is is directly directly supplied to to the the contact contact zone zone by an by oil an system. oil system. The temperature The temperature is regulated is for the experiments is made of glass coated with a thin semi-reflective layer of chromium, Cr, and a regulatedusing a usingthermostatic a thermostatic bath. Figure bath. 2 Figureshows 2the shows cam theused cam for usedobtaining for obtaining the results the presented results presented in this work layer of silicon dioxide, SiO2, to protect the surface from abrasion and to increase the range of inmounted this work on mounted the camshaft; on the the camshaft; upper part the of upper the meas parturement of the measurement unit with the unitfollower with is the removed follower in isthis thicknesses measurable. removedpicture into thismake picture the cam to makevisible. the cam visible. The test rig is instrumented and controlled using real-time National Instruments cRIO and LabVIEW® software. A sampling frequency of 10 kHz is normally used during tests. Film thickness and its shape are estimated using optical interferometry. In this case, the disc used for the experiments is made of glass coated with a thin semi-reflective layer of chromium, Cr, and a layer of silicon dioxide, SiO2, to protect the surface from abrasion and to increase the range of thicknesses measurable.

Figure 2. Picture of the top part of the measurement unit with the cover removed showing the cam Figure 2. Picture of the top part of the measurement unit with the cover removed showing the cam mounted on the camshaft and the final part of the oil supply system. mounted on the camshaft and the final part of the oil supply system.

Figure 2. Picture of the top part of the measurement unit with the cover removed showing the cam mounted on the camshaft and the final part of the oil supply system.

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The test rig is instrumented and controlled using real-time National Instruments cRIO and LabVIEW® software. A sampling frequency of 10 kHz is normally used during tests. Film thickness and its shape are estimated using optical interferometry. In this case, the disc used for the experiments is made of glass coated with a thin semi-reflective layer of chromium, Cr, Lubricantsand a layer 2019 of, 7, siliconx FOR PEER dioxide, REVIEW SiO 2, to protect the surface from abrasion and to increase the range4 of of17 thicknesses measurable. Interference images images are are recorded recorded by by means of a microscopemicroscope connected to, and moved via, a computer controlled XYZ positioner with an indepe independentndent step motor for moving each axis. Detail of the test rig rig with with the the optical optical system system is is shown shown in in Figure Figure 3.3.

Figure 3. Picture of the optical system.

A high-speed camera connected to the microscope allows the recording of interferenceinterference images with a frame rate of up to 1000 images per second fo forr film film thickness measurements also under transient conditions. The The images images are are recorded recorded in in the the 4 4 GB camera internal memory and transferred to the computer successively. successively. The methodology used used for for obtaining obtaining the the film film thic thicknesskness and and shape shape is is described described in in detail detail below. below. 2.2. Film Thickness Measurement Procedures 2.2. Film Thickness Measurement Procedures It is known that a peculiarity of a cam-follower system is the movement of the contact zone during It is known that a peculiarity of a cam-follower system is the movement of the contact zone during the rotation of the camshaft. Even using the computer controlled XYZ positioner, depending on the the rotation of the camshaft. Even using the computer controlled XYZ positioner, depending on the rotational speed and on the cam’s shape, it is not easy to synchronize the target area of the microscope rotational speed and on the cam’s shape, it is not easy to synchronize the target area of the microscope with the contact zone. This is due to the high velocities and accelerations that the contact area can with the contact zone. This is due to the high velocities and accelerations that the contact area can reach reach and also due to possible vibration problems. Thus, the recording of the interference images along and also due to possible vibration problems. Thus, the recording of the interference images along the the contact was often achieved by repeating tests in the same working conditions, adopting different contact was often achieved by repeating tests in the same working conditions, adopting different positions of the microscope. Images of the contact zone were also obtained by reducing the microscope positions of the microscope. Images of the contact zone were also obtained by reducing the microscope magnification but the limitation is that the used magnification must be sufficient to distinguish the magnification but the limitation is that the used magnification must be sufficient to distinguish the interference fringes. More details of these aspects are reported in Reference [24]. interference fringes. More details of these aspects are reported in Reference [24]. Once the interference images are recorded, film thickness and shape can be evaluated by a proper Once the interference images are recorded, film thickness and shape can be evaluated by a proper elaboration. The methodology developed and used for the elaboration of line contact images is elaboration. The methodology developed and used for the elaboration of line contact images is described below. For the sake of completeness, the fundamental aspects of optical interferometry and described below. For the sake of completeness, the fundamental aspects of optical interferometry and the color spaces are reported before describing the procedure used. the color spaces are reported before describing the procedure used.

2.2.1. Fundamentals of Optical Interferometry As mentioned in the introduction, optical interferometry is a well-known powerful technique for the estimation of the shape and thickness of non-conformal lubricated contacts, developed in the 1960s [25]. This technique is particularly efficient under transient conditions, for which the use of other methods such as capacitance or electrical resistivity is not strictly suggested. Optical interferometry is typically used in ball-on-disc test rigs, but it can be applied to contacts between bodies of different

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2.2.1. Fundamentals of Optical Interferometry As mentioned in the introduction, optical interferometry is a well-known powerful technique for the estimation of the shape and thickness of non-conformal lubricated contacts, developed in the 1960s [25]. This technique is particularly efficient under transient conditions, for which the use of other Lubricantsmethods 2019 such, 7, asx FOR capacitance PEER REVIEW or electrical resistivity is not strictly suggested. Optical interferometry5 of 17 is typically used in ball-on-disc test rigs, but it can be applied to contacts between bodies of different shapes (as a cylindrical cam) and a transparenttransparent surfacesurface (usually the plane surface of aa disc).disc). It is generally based on the interference pattern created by the light beam reflected by a semi-reflectingsemi-reflecting chromium layer applied to the surface of the disc an andd the portion of the light beam passing through the fluid, if present, and reflected by the body. Sometimes the glass disc can be coated, on the side of the contact, with a further layer of silicon dioxide to pr protectotect the surface from abrasi abrasionon and also to increase the measurement range towards lower thicknesses. The The two two beams cover different distances and a phase shift between the two light waves occurs. The interference of the two beams produces greater visibility when the intensity of the two reflected beamsbeams is similar.similar. Since the investigation is usually limited to the contact region, the angle formed by the incoming and the reflected beams is very little and practically negligible. The The resulting resulting wave wave will will ha haveve an amplitude ranging from zero to twice the amplitude of the original wave, that is, destructive and constructive interference, in reference to the phase difference between the two waves. Thus, the inte interferencerference pattern, consisting of bright and dark fringes, willwill bebe visible visible when when monochromatic monochromatic light light is used.is used. The The interference interference pattern pattern results, results, in white in white light, light,in a graduation in a graduation of colors of colors due to due the delayto the of delay the beams, of the beams, which is which related is torelated the film to thickness.the film thickness. In Figure In4 Figurethe basic 4 the principle basic principle of the optical of the interferometryoptical interferom techniqueetry technique for fluid for film fluid measurement film measurement is shown. is shown.

Figure 4. Basic principle of optical interferometry technique.

The interference light intensity I given by the interference of two beams, with intensities I and The interference light intensity I given by the interference of two beams, with intensities I11 and I h I2 respectively,respectively, can be approximately relatedrelated to thethe opticaloptical filmfilm thicknessthickness hoptopt with the following n h Equation (1),(1), takingtaking intointo account account the the refractive refractive indices indicesi nofi of the the traversed traversed media media of thicknessof thicknessi and hi and the phasethe phase difference differenceφ caused ϕ caused by the by reflectionthe reflection [26]: [26]:   2 2 4ππh p −ca−hchopt 4 hoptopt I =III1=+++ I2 + I2 2cosI1 I IIe2e a optcos + +φφ (1) 12 12 λλ0 0 being ca the attenuating coefficient of light intensity with the increase of the film thickness due to the being ca the attenuating coefficient of light intensity with the increase of the film thickness due to the low-coherent nature of light, λ0 the wavelength of the spectral light and hopt given by: low-coherent nature of light, λ0 the wavelength of the spectral light and hopt given by: = hopt =∑ nihi (2) hnhopti i i (2) i Monochromatic or white light can be used. Monochromatic light is characterized by a very Monochromatic or white light can be used. Monochromatic light is characterized by a very narrow spectrum around the wavelength λ0 which, as seen, the measurement of the film thickness narrow spectrum around the wavelength λ0 which, as seen, the measurement of the film thickness is is dependent on. In this case, destructive and constructive interference of the beams produces only dependent on. In this case, destructive and constructive interference of the beams produces only dark dark and bright fringes. With white light the changes in phase are revealed by a color transition, for and bright fringes. With white light the changes in phase are revealed by a color transition, for example, from yellow to red or blue to green and so forth. The interferometric image obtained with white light is therefore characterized by a graduation of colored fringes, each one corresponding to a value of the film thickness. These fringes are generated by the interference of beams with different wavelengths λ and refractive index n, therefore the mathematical description of the phenomenon is more complicated if compared with that of monochromatic light. The relationship between film thickness and the colors of the fringes is typically non-linear, thus a calibration table must first be obtained. White light allows greater resolution, commonly a few nm, but it might be limited by the human capacity to distinguish each color, which depends on color vision accuracy. To this purpose,

Lubricants 2019, 7, 29 6 of 17 example, from yellow to red or blue to green and so forth. The interferometric image obtained with white light is therefore characterized by a graduation of colored fringes, each one corresponding to a value of the film thickness. These fringes are generated by the interference of beams with different wavelengths λ and refractive index n, therefore the mathematical description of the phenomenon is more complicated if compared with that of monochromatic light. The relationship between film thickness and the colors of the fringes is typically non-linear, thus a calibration table must first be obtained. White light allows greater resolution, commonly a few nm, but it might be limited by the human capacity to distinguish each color, which depends on color vision accuracy. To this purpose, automatic algorithms have been developed. Anyhow, optical interferometry with white light also presents some disadvantages concerned with the limits of the range of measurement when only the semi-reflecting chromium layer is used: a film thickness lower than 0.1 µm leads to a dark zone tending to black (which would mean a thickness equal to zero) and values bigger than 1 µm, due to the low consistency of the light, leads to a vanishing of the fringes. The spacer layer of SiO2 on the glass disc is in fact used to reduce the lower limit (and the upper), shifting downward the range of measurement to the typical values of film thickness of EHL contacts. For monochromatic light tests, interference filters are often used for filtering the white light to select just the desired wavelength. This leads to a reduction of intensity and so, compared to the images captured using not filtered white light, longer exposure times are needed. Although it does not represent a big issue for steady state experiments, the longer time needed to capture each image might counteract the frame rate of the camera used for transient conditions—for cams typically in the order of milliseconds. Therefore, digital processing of interferometric images obtained with white light has been performed in this work.

2.2.2. Color Spaces in Optical Interferometry Digital image processing was historically based on RGB (Red, Green, Blue) color space. Another way to represent any chromaticity is the HSV (Hue, Saturation, Value) color space. Some details of the two color spaces and their relationships are reported in AppendixA. Either RGB or HSV color spaces can be used to analyze interferograms for EHL film thickness measurements since they represent different ways to describe the same information. In the interferometric images obtained with white light, the changes in phase lead to a color transition between fringes of the same hue. Adopting Equation (1) for the resulting interference light along the contact region, each RGB component reveals theoretically sinusoidal behavior with different phases and frequencies. In this case, the calibration process requires particular attention since all three color components must be taken into account. In addition, it is worth remarking that, when RGB deconstruction is applied to interferograms for EHL film thickness measurements, a strong sensitivity to the method used to illuminate the contact area is revealed. In particular, if the light is not uniform, as frequently happens, the RGB components could show different values even if related to the extent that the contact region has the same nominal film thickness. In order to overcome these kinds of difficulties, HSV color space was adopted by the authors. The variation of the H component is similar to an almost periodical signal ranging from 0 to 1, which is able to describe the resulting interference light without any sensitivity in respect to saturation and brightness. It means that, in order to evaluate the film thickness, the digital process of the image can be carried out adopting only the H component of the fringes overcoming in this way all the problems related to the illumination conditions of the contact area. Besides the greater insensibility to the shade and brightness of the light and the illumination conditions, the adoption of the HSV color space also leads to a simplification of the image processing and calibration procedures since only the H component must be analyzed instead of three as is the case for RGB space. In Figure5a,b sample theoretical distributions of RGB intensities and their correspondent HSV values as a function of optical thickness are given. They have been obtained using Equations (1) and (2) in a simple purposely developed program for the three Lubricants 2019, 7, x FOR PEER REVIEW 7 of 17 Lubricants 2019, 7, 29 7 of 17 leading to a pixel length of 1.32 μm. Note that the image is just a portion of the cam contact zone; even usingwavelength the lower for optical R, G and magnification, B and using it valueswas not similar possible to to those make reported the entire in width Reference of the [26 cam]. H, visible S and in V avalues single image. have been evaluated according to the conversion methods mentioned in AppendixA.

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leading to a pixel length( aof) 1.32 µm. Note that the image is just a portion of the(b) cam contact zone; even usingFigureFigure the lower 5. 5. ((aa)) optical TheoreticalTheoretical magnification, distributionsdistributions it of wasof RGB RGB not intensities possiintensitiesble and to and (makeb) corresponding (b )the corresponding entire width HSV values HSVof the values as cam function visible as in a singlefunctionof the image. optical of the thickness.optical thickness.

The interference images obtained experimentally do not actually produce regular trends due to some shape irregularities such as surface roughness. In Figure6b,c an example of RGB and HSV components obtained along the x-axis indicated in the interference image of Figure6a are shown. The interferogram refers to the line contact occurring between a glass disc and the basic circle of a steel cam having a curvature radius of 14 mm, an axial width of 8 mm and an average value of the root mean square roughness Rq of 0.02 µm. A glass disc without the SiO2 spacer layer was used, as evident from the dark zone corresponding to the Hertzian contact zone. The cam was loaded against the disc using a load of 30 N, producing a Hertzian contact width and pressure equal to 66 µm and 73 MPa respectively. The image, having a size of 350 × 350 pixels, was captured adopting a magnification (a) (b) leading to a pixel length of 1.32 µm. Note that the image is just a portion of the cam contact zone; even usingFigure the lower 5. (a) optical Theoretical magnification, distributions it wasof RGB not possibleintensities to and make (b) the corresponding entire width HSV of the values cam as visible in a singlefunction image. of the optical thickness.

(a) (b) (c)

Figure 6. (a) Interferogram; (b) corresponding RGB and (c) HSV components on x-axis.

As expected, the variation of the H component, at least in the region close to the contact area, assumes an almost periodical behavior. The values of S and V components have an irregular behavior. They do not provide useful information about the changes in film thickness and are not used for the evaluation of the distance between the two bodies in contact.

2.2.3. Elaboration of the Hue Signal The trend of H is similar to a periodical signal often referred to as “wrapped” hue [21]. By using an algorithm that adds or subtracts an integer to all values subsequent to a discontinuity, a continuous signal—usually called “unwrapped” hue—is reconstructed. The methodology is described in detail in Reference [21]( afor) circular point contacts. The (mathematicalb) processing of the wrapped(c) hue values may lead to an amount of noise and uncertainty in the measurement, as shown in Figure 7 where an Figure 6. ((a)) Interferogram; Interferogram; ( b) corresponding RGB and (c) HSV components onon x-axis.-axis. example of conversion from H to the unwrapped signal, uwH, referred to the processing of the interferenceAs expected, image shownthe variation in Figure of the 6a, isH shown. component, at at least in the region close to the contact area, assumes an almost periodical beha behavior.vior. The values of of S S and and V V components components have have an an irregular irregular behavior. behavior. They do not provideprovide useful information about the ch changesanges in film film thickness and are not used for the evaluation of the distance distance between between the the two two bodies bodies in in contact. contact.

2.2.3. Elaboration of the Hue Signal The trend of H is similar to a periodical signal often referred to as “wrapped” hue [21]. By using an algorithm that adds or subtracts an integer to all values subsequent to a discontinuity, a continuous

signal—usually called “unwrapped” hue—is reconstructed. The methodology is described in detail in Reference [21] for circular point contacts. The mathematical processing of the wrapped hue values may lead to an amount of noise and uncertainty in the measurement, as shown in Figure 7 where an example of conversion from H to the unwrapped signal, uwH, referred to the processing of the interference image shown in Figure 6a, is shown.

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2.2.3. Elaboration of the Hue Signal The trend of H is similar to a periodical signal often referred to as “wrapped” hue [21]. By using an algorithm that adds or subtracts an integer to all values subsequent to a discontinuity, a continuous signal—usually called “unwrapped” hue—is reconstructed. The methodology is described in detail in Reference [21] for circular point contacts. The mathematical processing of the wrapped hue values may lead to an amount of noise and uncertainty in the measurement, as shown in Figure7 where anLubricants example 2019 of, 7, conversionx FOR PEER REVIEW from H to the unwrapped signal, uwH, referred to the processing of8 theof 17 interference image shown in Figure6a, is shown.

Figure 7. H and unwrapped signals uwH along a pixel row starting from the center of Figure6a. Figure 7. H and unwrapped signals uwH along a pixel row starting from the center of Figure 6a. 2.2.4. The Image Processing Program 2.2.4.The The image Image processing Processing program Program developed in Matlab® had already demonstrated its consistency for circular point contacts [21]. In this case, the algorithm did not operate directly on the original ® wrappedThe phaseimage map processing but along program a sequence developed of radial in linesMatlab at intervals had already of a predefined demonstrated angular its consistency increment startingfor circular from point the centercontacts of the[21]. contact. In this case, In this the way, algorithm the unwrapping did not operate procedure directly is performed on the original by a simplewrapped mono-dimensional phase map but algorithm along a thatsequ unwrapsence of radial the signal lines on at each intervals line, deciding of a predefined to add or subtractangular integerincrement values starting by comparing from the center the differences of the contact. between In this consecutive way, the unwrappi elementsng to aprocedure threshold is value performedT < 1. Thisby a pseudo-two-dimensionalsimple mono-dimensional algorithm algorithm works that unwraps properly the if the signal threshold on each value line, isdeciding set to be to no add less or thansubtract twice integer the maximum values by noise. comparing Finally, the the differen resultingces unwrapped between consecutive matrix is transformed elements to back a threshold into the originalvalue T coordinates.< 1. This pseudo-two-dimensional algorithm works properly if the threshold value is set to be noIn less order than to achievetwice the the maximum correlation noise. between Finally, the the fringes resulting and the unwrapped film thickness, matrix the is interferencetransformed imagesback into are the then original used coordinates. as input for the image process algorithm in addition to the gap values and pixel length.In order The to achieve program the is ablecorrelation to convert between the interference the fringes pattern and the in film the HSVthickness, color the space interference allowing operationimages are on then the singleused as H input component. for the Theimage conversion process algorithm from the wrappedin addition to theto the unwrapped gap values H and signal pixel is dependentlength. The on program the threshold is able value to convertT, which the can interference be modified pattern by the in user the in HSV order color to obtain, space asallowing much asoperation possible, on a monotonicthe single H progression component. of The the conversion unwrapped from signal the alongwrapped the contactto the unwrapped region. At H the signal end ofis thedependent unwrapping on the procedure, threshold value the user T, which can finally can be choose, modified among by the the user matrix in order of the to results obtain, obtained as much foras possible, each patterns, a monotonic which progression rows must beof the considered unwrapped for thesignal calibration along the and contact which region. rows At have the end to be of neglectedthe unwrapping in order procedure, to consider the only user the can progressions finally choos withe, among a monotonic the matrix behavior of the of results the signal; obtained in this for way,each itpatterns, is possible which to avoid rows the must calibration be considered being affected for the by calibration scratches onand the which glass rows disc orhave spots to onbe theneglected optical in instrumentation. order to consider The only mean the values progressions of the chosen with a unwrappedmonotonic behavior signals are of putthe insignal; relation in this to theway, theoretical it is possible gap to between avoid the the calibration specimen andbeing the affected disc in by order scratches to obtain on thethe calibrationglass disc or curve, spots whichon the allowsoptical the instrumentation. relation of the HThe components mean values to of the the film ch thickness.osen unwrapped signals are put in relation to the theoreticalAn improvement gap between of thethe mathematicalspecimen and processing the disc in of order the wrapped to obtain hue the has calibration been implemented curve, which in orderallows to the extend relation the automaticof the H components calibration procedureto the film tothickness. the line contact. The same algorithm is used to operateAn the improvement analysis of of line the contact mathematical images alongprocessing a sequence of the wrapped of parallel hue lines has instead been implemented of radial ones. in order to extend the automatic calibration procedure to the line contact. The same algorithm is used to operate the analysis of line contact images along a sequence of parallel lines instead of radial ones. The distance between two consecutive lines is given by the operator as a number of pixels (one single pixel can also be chosen). The operator also chooses a central zone of the contact from which the lines are swept alternatively to the right and to the left. The program has also been particularly optimized by making some procedures automatic: input data, such as working conditions, pixel length, optical magnification and refractive index can be automatically loaded allowing faster analyses of a large number of images commonly recorded during tests. A block diagram of the program is reported in Figure 8. More details on the basic algorithms used are reported in Reference [21].

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The distance between two consecutive lines is given by the operator as a number of pixels (one single pixel can also be chosen). The operator also chooses a central zone of the contact from which the lines are swept alternatively to the right and to the left. The program has also been particularly optimized by making some procedures automatic: input data, such as working conditions, pixel length, optical magnification and refractive index can be automatically loaded allowing faster analyses of a large number of images commonly recorded during tests. A block diagram of the program is reported in Figure8. More details on the basic algorithms used are reportedLubricants 2019 in Reference, 7, x FOR PEER [21 REVIEW]. 9 of 17

FigureFigure 8. Block8. Block diagram diagram of of thethe programprogram for for the the elaboration elaboration of interference of interference images. images. 3. Results 3. Results

3.1. Calibration3.1. Calibration In orderIn order to obtain to obtain an evaluation an evaluation of the of film the thickness film thickness starting starting from thefrom interferograms, the interferograms, a calibration a procedurecalibration must procedure first be carried must first out be to carried relate out the to H relate component the H component to the distance to the distance between between the two the bodies in contact.two bodies The in purpose contact. of The image purpose calibration of image is calibratio to find scalen is to and find offset scale factorsand offset that factors can bethat used can tobe relate the interferometricused to relate the fringes interferometric with the clearancefringes with gap the between clearance the gap two between bodies. the At two the bodies. end of At the the procedure, end a calibrationof the procedure, table containing a calibration for each table intensity containing color for theeach corresponding intensity color film the thicknesscorresponding is obtained. film thicknessThe calibration is obtained. of the interferometric images is usually performed by comparing the clearance The calibration of the interferometric images is usually performed by comparing the clearance gap and contact area given by the interferograms analysis with the analogous known values given by gap and contact area given by the interferograms analysis with the analogous known values given theoretical models of contact mechanics. Practically, the most common way to proceed is to capture the by theoretical models of contact mechanics. Practically, the most common way to proceed is to imagecapture of a Hertzian the image contact of a Hertzian and to thencontact correlate and to thethen H correlate value of the each H pointvalue ofof theeach interference point of the image withinterference the theoretical image gap with given the theoretical by a formula. gap given Different by a formula. formulas Different are available formulas for are point available and for for line point and for line contacts as reported for instance in Reference [27,28]. A transparent grid is normally used to evaluate the length of each image pixel so that the number of pixels can be converted into distance. In Figure 9 the color calibration curve obtained with the steel cam loaded against the glass disc is shown; the corresponding colors of the H values are given in the color bar.

Lubricants 2019, 7, 29 10 of 17 contacts as reported for instance in Reference [27,28]. A transparent grid is normally used to evaluate the length of each image pixel so that the number of pixels can be converted into distance. In Figure9 the color calibration curve obtained with the steel cam loaded against the glass disc is

Lubricantsshown;Lubricants 2019 the 2019, 7 corresponding, x, FOR7, x FORPEER PEER REVIEW REVIEW colors of the H values are given in the color bar. 10 of 17 10 of 17

FigureFigure 9. 9.Calibration table and color bar for cam on glass disc in test basic configuration. Figure 9.Calibration Calibration table table andand colorcolor barbar for cam on on glass glass disc disc in in test test basic basic configuration. configuration. 3.2.3.2. Sample Sample Result Result for for a Hertzian a Hertzian Contact Contact 3.2. Sample Result for a Hertzian Contact InIn order order to to highlight highlight the the efficiency efficiency of the of deve the developedloped algorithm, algorithm, interfer interferometricometric images imagesobtained obtained In order to highlight the efficiency of the developed algorithm, interferometric images obtained withwith static static contacts contacts between between the the cam cam base base circle circle and and the the disc disc were were first first analyzed. analyzed. The The calibration calibration curves with static contacts between the cam base circle and the disc were first analyzed. The calibration curves presented above have been used for the assessment of the distance between the two bodies. presentedcurves presented above have above been have used been for used the assessment for the assessment of the distance of the distance between between the two the bodies. two bodies. InIn Figure Figure 10, 10 ,an an example example of of the the application application of ofthe the procedure procedure described described above above in the in the case case of a of a static static contactIn Figure with 10,a load an ofexample 30 N in ofthe the presence application of lubricant of the isprocedure reported. described above in the case of a contact with a load of 30 N in the presence of lubricant is reported. staticThe interferogramcontact with a of load Figure of 30 10a, N inwith the a presence size of 213 of × lubricant 563 pixels, is wasreported. captured with a microscope The interferogram of Figure 10a, with a size of 213 × 563 pixels, was captured with a microscope magnificationThe interferogram leading to a pixel of Figure length 10a, of 1.55 with μ m.a size The of related 213 × 5633D unwrappedpixels, was capturedsignal (Figure with 10c) a microscope has magnification leading to a pixel length of 1.55 µm. The related 3D unwrapped signal (Figure 10c) beenmagnification obtained using leading 0.1 as to a athreshold pixel length value. of 1.55The μunwrappingm. The related procedure 3D unwrapped has been signal performed (Figure on 10c)a has sequencehasbeen been obtained of obtained lines crossing using using 0.1 the 0.1as interferometric a as threshold a threshold value. fringe value. Ths ine unwrapping Theorder unwrapping to obtain procedure the proceduregap distribution has been has performed beenthrough performed on a theon sequencecontact a sequence region. of lines of Figure lines crossing 10d,e crossing the show interferometric the the interferometric3D representation fringes fringesin and order the in cotontour orderobtain lines to the obtain ofgap the distribution body the gapdistance distribution through distributionthroughthe contact the obtained contact region. region.Figureby a successive 10d,e Figure show 10 d,eprocessi the show 3D ng,representation the while 3D representation a comparison and the co andntourbetween the lines contour theoretical of the linesbody and of distance the body evaluateddistancedistribution distributioncontact obtained profile obtained along by a the bysuccessive x a-axis successive in Figureprocessi processing, 10eng, is shownwhile while ina Figurecomparison a comparison 10f. between between theoretical theoretical and and evaluatedevaluated contact contact profile profile along along the thex x-axis-axis inin FigureFigure 1010ee is shown in in Figure Figure 10f. 10f.

(a) (b) (c)

(a) Figure(b) 10. Cont. (c)

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(d) (e) (f) (d) (e) (f) Figure 10. (a) Interferogram; (b) corresponding enhanced image and (c) related 3D unwrapped signals; (d) FigureFigure 10.10. ((a) Interferogram; (b (b) )corresponding corresponding enhanced enhanced image image and and (c) related (c) related 3D unwrapped 3D unwrapped signals; signals; (d) 3D representation of the gap; (e) contour lines; (f) comparison between theoretical and evaluated contact (d3D) 3D representation representation of the of gap; the gap;(e) contour (e) contour lines; lines;(f) comparison (f) comparison between between theoretical theoretical and evaluated and evaluated contact profile along the x-axis reported in subfigure (e)–static contact–load 30N. contactprofile profilealong the along x-axis the reportedx-axis reportedin subfigure in subfigure(e)–static contact–load (e)—static contact–load30N. 30N.

3.3. Sample 3.3. Sample Results Results for for EHL EHL for EHL Contacts Contacts Contacts InIn orderorderIn order toto givegive to give anan ideaidea an idea ofof the theof the differentdifferent different imagesimages images thatthat that cancan can be bebe elaborated elaboratedelaborated by by the thethe program, program,program, some somesome imagesimagesimages recordedrecorded recorded at at some some at particularsome particular particular points points duringpoints duri duri thengng rotation the the rotationrotation of the same ofof the cam samesame used camcam for theusedused calibration, for for the the showncalibration,calibration, in Figure shown shown11 ina, haveFigure in Figure been 11a, 11a, selected. have have been been A selected. synthetic selected. A motorA synthetic synthetic oil SAE motor motor 5W-40 oil SAESAE was 5W-40 5W-40 used was aswas aused lubricantused as asa a lubricant (viscosity and pressure-viscosity coefficient 0.145 Pas and 2.2 × 10−8 Pa−1 respectively at the test (viscositylubricant (viscosity and pressure-viscosity and pressure-visco coefficientsity coefficient 0.145 Pas 0.145 and Pas 2.2 and× 2.210− ×8 10Pa−8− Pa1 −respectively1 respectively at at the the testtest temperature of 26.7 °C). The images reported in the following refer to a test with the cam rotating at temperaturetemperature of 26.7 °C).◦C). The The images images reported reported in in the following refer to a test with the cam rotating at 60 rpm contacting the follower with a preload of 30 N (produced by a spring when the contact occurs 60 rpm contacting the follower with a preload of 30 N (produced by a spring when the contact occurs 60 rpmon contacting the base circle). the follower Due to the with not a preloadhigh rotational of 30 N speed, (produced the trend by aof spring the normal when force the contact is similar occurs to on thethat basebase of circle).thecircle). lift (vertical Due to displacement) the not high rotationalshown in Figure speed, 11b, the with trend a maximum of the normal value of force about is 250 similar N in to thatthat ofofcorrespondence thethe lift (vertical with displacement)displacement) the cam’s nose shownshown (position in Figure correspo 1111b,ndingb, with to a0° maximum in the diagram; value the of abscissa about 250 starts N in ◦ correspondencefrom the point withwith on thethe the cam’scam’s base circle nosenose opposite (position(position to correspondingcorrespo the cam ndingnose). Note toto 00° that,in the as diagram;reported in the Reference abscissa [24], starts fromfrom thethethe pointhorizontalpoint onon thethe displacement basebase circlecircle of oppositeopposite the contact to point thethe camcam corre nose).nose).sponds Note with that, the vertical as reported velocity in divided Reference by the [24], [24 ], thethe horizontalrotational displacementdisplacement speed. ofof thethe contactcontact pointpoint correspondscorresponds withwith thethe vertical velocity divided by the rotational speed.speed.

(a) (b)

Figure 11. (a) Cam; (b) vertical and horizontal displacement of the contact zone. (a) (b) The contact positions at −49°, 0° and 125° of rotation angle, indicated by the black circles in Figure Figure 11. (a) Cam; (b) vertical and horizontal displacement of the contact zone. 11b, haveFigure been selected 11. (a) Cam; in order (b) vertical to test andthe horizontalcapabilities displacement of the program of the in contactvery different zone. conditions. Also, different dimensions of the interference images have been chosen. The images were recorded The contact positions at −49◦, 0◦ and 125◦ of rotation angle, indicated by the black circles Thewith contact a frame positions rate of 500 at frames/s.−49°, 0° and 125° of rotation angle, indicated by the black circles in Figure in11b, Figure have 11beenb, haveselected been in selected order to in test order the tocapabilities test the capabilities of the program of the in programvery different in very conditions. different conditions.Also, different Also, dimensions different dimensions of the interference of the interference images have images been havechosen. been The chosen. images The were images recorded were recordedwith a frame with rate a frame of 500 rate frames/s. of 500 frames/s.

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The interference image shown in Figure 12a (683 × 1147 μm) was recorded at the inversion of the contact motion on rising flank (rotation angle = −49°). The oil inlet is on the left of the image. The Lubricants 2019, 7, 29 12 of 17 normal load was 165 N, the entraining velocity 47 mm/s and the curvature radius 17.6 mm. The enhanced image and the related 3D unwrapped signals are also shown. The 3D representation of the Thefilm interferencethickness andimage the contour shown lines in are Figure shown 12 ina (683Figure× 12d,e1147 whileµm) wasthe film recorded thickness at thealong inversion the x- of the contactaxis reported motion in onFigure rising 12e flankis shown (rotation in Figure angle 12f. = −49◦). The oil inlet is on the left of the image. Note that the image refers to the zone close to the extremity of the cam where some contacts The normal load was 165 N, the entraining velocity 47 mm/s and the curvature radius 17.6 mm. between the two bodies seem to be present. In addition, the central part of the lubricated contact is The enhancednot perfectly image rectangular, and the showing related 3Da certain unwrapped tapering signals that can are bealso related shown. to an Theimperfect 3D representation parallelism of the filmof the thickness two surfaces. and theHowever, contour the lines typical are EHL shown restrict inion Figure at the 12 exitd,e appears while thein the film diagrams thickness of Figure along the x-axis12f. reported in Figure 12e is shown in Figure 12f.

(a) (b) (c)

(d) (e) (f)

FigureFigure 12. (a 12.) Interferogram (a) Interferogram at theat the inversion inversion point point− −49°;49◦ ;((bb) corresponding) corresponding enhanced enhanced image; image; (c) related (c) related 3D unwrapped3D unwrapped signals; signals; (d) ( 3Dd) 3D representation representation of of thethe gap; ( (ee) )contour contour lines; lines; (f) (filmf) film thickness thickness along along the the x-axisx reported-axis reported in subfigure in subfigure (e). (e). In Figure 13 the cam nose being in contact with the follower (rotation angle = 0°) is shown. The Note that the image refers to the zone close to the extremity of the cam where some contacts normal load was 250 N, the entraining velocity 38 mm/s and the curvature radius was 6.3 mm. The between the two bodies seem to be present. In addition, the central part of the lubricated contact is not interference image of Figure 13a refers again to the zone close to the cam’s extremity. The bigger load perfectlyand rectangular,lower velocity showing together awith certain the slope tapering of the that cam can produce be related very low to anvalues imperfect of the film parallelism thickness of the two surfaces.captured However,by the elaboration, the typical as shown EHL restrictionin the 3D di atagram the exitof Figure appears 13b in(note the the diagrams different of full Figure scale 12f. ◦ Inof Figurethe vertical 13 theaxis camcompared nose to being that of in Figure contact 12d). with the follower (rotation angle = 0 ) is shown. The normal load was 250 N, the entraining velocity 38 mm/s and the curvature radius was 6.3 mm. The interference image of Figure 13a refers again to the zone close to the cam’s extremity. The bigger load and lower velocity together with the slope of the cam produce very low values of the film thickness captured by the elaboration, as shown in the 3D diagram of Figure 13b (note the different full scale of the vertical axis compared to that of Figure 12d). Lubricants 2019,, 7,, 29x FOR PEER REVIEW 13 of 17 Lubricants 2019, 7, x FOR PEER REVIEW 13 of 17

(a(a) ) (b) ◦ FigureFigure 13. 13. ( a()a )Interferogram Interferogram at at 00°0° (cam(cam nose); nose); ( (b) fluid fluid film film 3D 3D representation. representation. × AnAn interferenceinterference interference image image image (294 (294 (294 318 ×× 318318 pixels) pixels)pixels) recorded recordrecord wheneded when the contact the contact was on waswas the on basicon thethe circle basicbasic (rotation circle circle ◦ angle(rotation(rotation = 125 angle angle) is = shown =125°) 125°) inis is shown Figure shown 14in in a.Figure Figure The normal 14a.14a. TheThe load normalnormal was30 load N, thewas entraining 3030 N,N, thethe entraining velocityentraining 44 velocity velocity mm/s and44 44 themm/smm/s curvature and and the the radiuscurvature curvature 14 mm. radius radius The 14 14 interferogram mm. mm. The The interferogra interferogra refers to them refers central to partthe centralcentral of the contact partpart of of the withthe contact contact dimensions with with 294dimensionsdimensions× 318 µm. 294 294 × ×318 318 μ μm.m.

(a()a ) ((bb)) ((cc)) ◦ FigureFigure 14. 14. ((a ()a Interferogram Interferogram) Interferogram at at 125°; 125 125°;;( ( b(b)) )fluid fluidfluid film filmfilm 3D 3D3D representation; representation; ( c)) filmfilm film thickness thickness along along the the x x and and y axes shown in subfigure (a). y axes shown in subfiguresubfigure ((aa).).

TheThe 3D 3D diagram diagram of of the the film film thickness thickness isis shownshown inin FigureFigure 1414bb and the trend trend of of the the film film thickness thickness The 3D diagram of the film thickness is shown in Figure 14b and the trend of the film thickness alongalong the thex xand andy yaxes axes shown shown in in Figure Figure 14 14aa is is reported reported inin FigureFigure 1414c.c. along the x and y axes shown in Figure 14a is reported in Figure 14c. 4.4. Discussion Discussion 4. Discussion TheThe results results presented presented above show show that that the the program program developed developed for forthe line the linecontacts contacts between between cam The results presented above show that the program developed for the line contacts between cam camand and follower follower is able is able to toanalyze analyze very very different different images images recorded recorded during during the the revolution revolution of of the the cam. cam. and follower is able to analyze very different images recorded during the revolution of the cam. However,However, there there are are some some aspects aspects related related to to the the peculiarities peculiarities of of the the cam-follower cam-follower contacts contacts that that make make the analysesHowever,the analyses difficult there difficult are and some canand explainaspects can explain somerelated some irregularities to irregularithe peculiarities inties the in diagramsthe of diagrams the cam-follower shown shown in thein contacts the above above figures. that figures. make the analysesTheThe presence presence difficult of of and machiningmachining can explain marks some (see (see irregulari for for instance instanceties Figure in Figure the 12a)diagrams 12 a)and and surface shown surface defects in defectsthe aboveas well as figures. wellas the as thepresence presenceThe presence of ofcavitation cavitation of machining zones zones can marks can create create (see some somefor instancediff difficultiesiculties Figure for for the12a) the image imageand surface analysis. analysis. defects Shape Shape as errors well errors as and and the roughnesspresenceroughness of can cavitationcan significantly significantly zones influence influencecan create thethe some locallocal diff valuesvaluesiculties ofof thethefor filmfilmthe image thickness.thickness. analysis. These These Shape defects defects errors can can also alsoand explainroughnessexplain the the can differences differences significantly between between influence the the theoretical theoretical the local and andvalues experimental experimental of the film Hertzian Hertzian thickness. profiles profiles These shown shown defects in Figurein can Figure also 10 f. explain10f.The the not differences perfect parallelism between betweenthe theoretical the cam and and experimental the follower Hertzian can create profiles a zone inshown which in the Figure film thickness10f. The is not not perfect sufficient parallelism to separate between the bodiesthe cam (local and th contacts,e follower mixed can create or even a zone boundary in which lubrication the film conditions),thicknessThe not is asperfect not shown sufficient parallelism in Figure to separate 13between. Under the the bodies these cam conditions (localand th contacts,e follower some mixed wear can createor can even occur a zoneboundary (some in which scratches lubrication the film are visiblethicknessconditions), in Figureis not as sufficient shown13a). On in toFigure the separate other 13. hand,Under the bodies zonesthese (localco withnditions acontacts, film some thickness mixed wear canor greater even occur thanboundary (some expected scratches lubrication can are be presentconditions),visible on in theFigure as oppositeshown 13a). in partOn Figure the of theother 13. contact.Under hand, these zones co winditionsth a film some thickness wear cangreate occurr than (some expected scratches can beare visiblepresentContact in onFigure the conditions opposite 13a). On vary part the very ofother the quickly contact.hand, atzones certain with angular a film positionsthickness ofgreate the cam,r than for expected instance can when be closepresent toContact on the the inversion conditionsopposite point part vary (of− very49 the◦). contact.quickly The contact at certain point angular moves positions very quickly of the after cam, the for inversion instance when while theclose entrainingContact to the inversionconditions velocity point is vary close ( −very49°). to zero quickly The at contact− 45at◦ certain. Thepoint situation movesangular very atpositions this quickly point of after isthe shown thecam, inversion infor Figure instance while 15. when Note the close to the inversion point (−49°). The contact point moves very quickly after the inversion while the

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entraining velocity is close to zero at −45°. The situation at this point is shown in Figure 15. Note that thatthe thefilm film thickness thickness is low is but low not but zero, not zero,apart apart from fromat the at border the border of the ofcam the (image cam (image top), due top), to duesome to someinclination inclination and squeeze and squeeze effect. effect.The contact The contact point is point also moving is also moving quickly quicklyclose to the close cam to nose the cam (Figure nose (Figure13). In these13). In conditions these conditions a sufficiently a sufficiently high frame high rate frame is important, rate is important, as it is related as it to is the related pixel todefinition the pixel definitionand also andto avoid also toblurry avoid effects. blurry For effects. the Forpresent the presenttests, the tests, recording the recording frame framerate was rate limited was limited to 500 to 500frames/s frames/s in order in order to have to have enough enough time time to store to store the images the images corresponding corresponding to some to some cam cam revolutions revolutions in inthe the internal internal memory memory of of the the camera. camera. However However higher higher frame frame rates rates could could be be used used with with the the drawback drawback thatthat a a reduced reduced number number ofof camcam revolutionsrevolutions wouldwould bebe recorded.recorded.

(a) (b) (c)

FigureFigure 15. 15.( (aa)) InterferogramInterferogram atat −−45°;45◦ ;((bb)) fluid fluid film film 3D 3D representation; representation; (c (c) )film film thickness thickness along along the the xx andand yyaxes axes shown shownin in subfiguresubfigure ((aa).).

TheThe definition definition ofof aa singlesingle value for the minimu minimumm or or for for the the central central film film thickness—the thickness—the commonly commonly investigatedinvestigated quantitiesquantities ofof aa lubricatedlubricated contact—iscontact—is not not a a simple simple matter matter for for contacts contacts like like those those investigated.investigated. TheseThese quantitiesquantities cancan varyvary sometimes in in a a significant significant way way along along the the contact contact (the (the vertical vertical directiondirection inin thethe imagesimages reportedreported inin thisthis work).work). SomeSome investigations could could be be carried carried out, out, averaging averaging methodsmethods of of thethe filmfilm thicknessthickness valuesvalues obtainedobtained alongalong the y direction for each xx position.position. TheseThese aspectsaspects deservedeserve specificspecific furtherfurther investigation.investigation.

5.5. ConclusionsConclusions andand FutureFuture DevelopmentsDevelopments TheThe opticaloptical systemsystem ofof aa testtest rigrig forfor investigationsinvestigations of cam-follower contacts contacts allows allows the the recording recording ofof interferenceinterference imagesimages that are used used for for the the evalua evaluationtion of of film film thickness thickness an andd shape. shape. A description A description of ofthe the interferometric interferometric technique technique and and the thedigital digital image image proc processess usedused to obtain to obtain the 3D the profile 3D profile starting starting from fromthe recorded the recorded images images is presented. is presented. The The color color space space used used to todescribe describe the the color color components components of of the the fringes,fringes, and and the the methodology methodology and and procedures procedures and theand essential the essential steps necessarysteps necessary to set up to the set numerical up the algorithm,numerical arealgorithm, discussed. are Numerical discussed. programs Numerical developed programs in developed Matlab® for in the Matlab analysis® for of the interferometric analysis of imagesinterferometric that are ableimages to reproduce that are able the three-dimensionalto reproduce the three-dimensional profile of line contacts profil aree of developed line contacts starting are withdeveloped previous starting versions with developed previous forversions point developed contacts. The for programspoint contac arets. first The used programs for the are digital first imageused processfor the ofdigital thewrapped image process color componentsof the wrapped for colo the calibrationr components procedure. for the calibration The fluid filmprocedure. thickness The is assessedfluid film by thickness means of is the assessed calibration by means table given of the adopting calibration the table unwrapping given adopting procedure. the unwrapping procedure.Some presented results evidence the capabilities of the programs developed and, at the same time, someSome practicalpresented problems results evidence intrinsically the relatedcapabilities to the of cam-follower the programs contacts developed as the and, quick at the motion same of thetime, contact some point, practical the problems geometrical intrinsically errors and related the surface to the defects cam-follower and the contacts not perfect as the parallelism quick motion of the contactingof the contact bodies. point, However, the geometrical the methodology errors and developedthe surface seems defects able and to the perform not perfect the analysis parallelism of very of differentthe contacting images bodies. by catching However, the values the methodology of the film thicknessdeveloped during seems the able camshaft to perform rotation. the analysis of verySeveral different aspects images need by catching to be specifically the values addressed of the film in thickness future investigations. during the camshaft Tests with rotation. cams with differentSeveral geometrical aspects need precision to be specifically will provide addressed more indications in future ofinvestigations. the influence Tests of this with factor cams on with the measurements.different geometrical The possible precision influence will provide of the more frame indications rate on the of images the influence and the of corresponding this factor on the film thicknessmeasurements. can be The investigated, possible influe recordingnce of the the images frame withrate differenton the im frameages and rates. the Finally, corresponding investigations film thickness can be investigated, recording the images with different frame rates. Finally, investigations

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at different loads, rotational speeds and with different lubricants will be planned to investigate their ateffects different on the loads, evolution rotational of the speeds film shape and with during different rotation. lubricants will be planned to investigate their effects on the evolution of the film shape during rotation. Author Contributions: conceptualization, all authors; methodology, all authors; software, G.P. and F.F.; validation, G.P.; formal analysis, all authors; investigation, G.P. and F.F.; resources, E.C.; data curation, G.P. and Author Contributions: Conceptualization, all authors; methodology, all authors; software, G.P. and F.F.; validation, G.P.;F.F.; writing—original formal analysis, alldraft authors; preparation, investigation, E.C. and G.P.G.P.; andwriting—review F.F.; resources, and E.C.; editing, data all curation, authors. G.P. and F.F.; writing—original draft preparation, E.C. and G.P.; writing—review and editing, all authors. Funding: This research received no external funding. Funding: This research received no external funding. Acknowledgments: The authors would to thank to Eng. Alessio Lazzaretti and Eng. Giacomo Bassi for their Acknowledgments:contribution to the experimentalThe authors wouldwork. to thank to Eng. Alessio Lazzaretti and Eng. Giacomo Bassi for their contribution to the experimental work. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

AppendixAppendix AA RGBRGB colorcolor space represents represents any any chromaticity chromaticity as as th thee results results of ofthe the components components of Red, of Red, Green Green and andBlue. Blue. In a In 3D a 3DCartesian Cartesian coordinate coordinate system, system, it itca cann be be represented represented by by a a cube cube with the threethree colorcolor componentscomponents asas axesaxes (see(see FigureFigure A1 A1).). InIn thisthis systemsystem anyany pointpoint isis identifiedidentified byby aa combinationcombination ofof threethree integerinteger values values from from 0 to0 255.to 255. Thus, Thus, each each chromaticity chromaticity will bewill expressed be expressed as a tern as of a valuestern of (e.g., values [255,0,0] (e.g., for[255,0,0] red, etc.) for spacing red, etc.) from spacing [0,0,0] tofrom [255,255,255] [0,0,0] to corresponding [255,255,255] tocorresponding black and white to respectively.black and Forwhite a digitalrespectively. image process,For a digital 8 bits image for each process, component 8 bits for are each needed. component are needed.

Figure A1. Conversion RGB cube to HSV hexcone color space. Figure A1. Conversion RGB cube to HSV hexcone color space. Another way to represent any chromaticity is the HSV space which describes each color (Hue) in termsAnother of shade way (Saturation) to represent and any brightness chromaticity (Value). is the TheHSV hue space of awhich color refersdescribes to which each color pure (Hue) color itin resembles terms of shade (e.g., all(Saturation) tints, tones and and brightness shades of (Value). red have The the hue same of a hue); color it refers is expressed to which by pure a fraction color it fromresembles 0 to 2 π(e.g.,representing all tints, tones the position and shades of the of correspondingred have the same pure hue); color it onis expressed the color wheelby a fraction (e.g., value from 00 correspondsto 2π representing to red; πthe/3 position to yellow; of 2theπ/3 corresponding to green; etc.). pure The saturationcolor on the of color a chromaticity wheel (e.g., describes value 0 howcorresponds white the to colorred; π is/3 (e.g.,to yellow; a pure 2π red/3 to is green; fully saturated,etc.). The saturation with a saturation of a chromaticity of 1, tints describes of red have how saturationswhite the color less is than (e.g., 1 anda pure white red hasis fully a saturation saturated, of with 0). Finally, a saturation the value of 1, tints is related of red to have the brightness,saturations whichless than describes 1 and howwhite dark has the a saturation chromaticity of is;0). VFina is expressedlly, the value by a is fraction related from to the 0 to brightness, 1 corresponding which todescribes black and how white, dark respectively. the chromaticity In a 3Dis; V Cartesian is expres coordinatesed by a fraction system, from the HSV0 to 1 color corresponding space can be to representedblack and white, by a hexcone respectively. having In thea 3D vertical Cartesia axisn correspondingcoordinate system, to the the brightness HSV color (see space Figure can A1 be). Therepresented angle around by a thehexcone vertical having axis givesthe vertical the hue axis with corresponding red at θ equal to to the 0. The brightness saturation (see is Figure given byA1). a ratio,The angle ranging around from the zero, vertical on the axis vertical gives axis, the hue to one with on red the at sides θ equal of the to hexcone. 0. The saturation is given by a ratio,The ranging conversion from zero, between on the RGB vertical and axis, HSV to color one on space the componentssides of the hexcone. can be obtained through a non-linear,The conversion bijective relation between which RGB isand illustrated HSV color in spac Figuree components A1 and given can by be the obtained formulas through reported a non- in Referencelinear, bijective [29]. Particularly relation which for hue is illustrated the following in equationFigure A1 can and be given used: by the formulas reported in Reference [29]. Particularly for hue the following equation can be used:  2G − R − B  H = arctan2 2GRB−−, (A1) H = arctan 2R − B , (A1) RB−

Lubricants 2019, 7, 29 16 of 17 where arctan2 is the four-quadrant inverse tangent. Unfortunately, this relation, which requires a case differentiation depending on the quadrant of the argument, might lead to some difficulties in the mathematical modeling performed by numerical programs, such as the computing language Matlab®. Thus, for the conversion from RGB to HSV the following formulation suggested in Reference [30] was chosen and efficiently tested by the authors: ( ) θ with B ≤ G H = , (A2) 2π − θ with B > G being 0.5(2R − G − B) θ = arccos (A3) [(R − G) + (R − B)(G − B)]0.5 The maximum and minimum values of H are then chosen in order to obtain the red for θ equal to 0 and 2π. For the aim of this work, the HSV components were normalized and ranged between zero and one [31].

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