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

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