47 EXPERIMENTAL DETERMINATION O CONTACT AREA BETWEEN A SPHERE AND A CIRCULAR PLATE USING A TECHNIQUE BASED ON LASER PROILOMETRY Marius TRANDAIR, Maria CIORNEI, Emanuel DIACONESCU Department of Mechanical Engineering, University of Suceava, ROMANIA trandafir_marius84@yahoo.com ABSTRACT This paper presents the experimental determination of contact area between a steel sphere and a sapphire circular plate, using a technique based on laser profilometry. The reflectivity value is smaller inside contact area than outside, modern laser profilometers can measure surface reflectivity and thus, it can offer information regarding the contact area. In order to investigate the thickness effect on the contact area, the contact is modelled in two situations, using two circular plates with different thicknesses. Keywords: circular plate, reflectivity, laser profilometer, steel sphere 1. INTRODUCTION Usually, the problems in Contact Mechanics are theoretically approached. The obtained theoretical results often need to be validated, validation that can be done by modelling the problem experimentally. The contact area is one of the unknown elements in contact problems. In time, many experimental techniques, used to determine contact area, were developed and improved. The most commonly used methods for the contact area experimental investigations are those based on ultrasonic techniques [1, 2], thin-film pressure sensors techniques [3], direct in situ techniques [4] and laser profilometry techniques [5, 6]. The best methods used to determine this contact element are those which can offer point-by-point information about it. At University of Suceava, a new method was purposed and advanced, concerning the experimental determination of the contact area, using laser profilometers, more exactly, a method based on laser profilometer capability to measure the reflectivity of the surfaces. This method not only fulfils the above request, but also it has other strong points like the lack of contact with the investigated surfaces, repeatability, information processing by computer, etc. igure 1 shows the principle scheme of the experimental device built by Glovnea [7] for investigating the contact area via laser profilometry technique. The modelled contact was an elastic contact between a punch, represented in the scheme by a sphere, and a sapphire flat that was clamped on its edge. After the two bodies are in contact, the steel sphere is pressed in vertical direction against the lower surface of the sapphire thick window with a force generated by two equal weights, then a laser beam, focused on the metallic surface of the sphere through the sapphire window, is sent by the laser head of a laser profilometer and the surface is scanned. As a result, the scanned and measured reflectivity had a smaller value inside the contact area than outside it, making it capable of recognition. The method was validated by investigating a circular Hertzian contact. The measured experimental contact area was in good agreement with the theoretical one. ig 1. The principle scheme of the experimental device [6]
48 This paper shows the obtained experimental results for two contact situations, one between a steel sphere and a 2mm thick sapphire circular plate and the other between the same sphere and a 3mm thick sapphire circular plate. In both cases, the plate was clamped on its edge. inally, the experimental results are compared to two theoretical results, one when the contact area is calculated using the classical theory of circular Hertzian contacts and one using a theory that takes into account the thickness parameter. a) b) ig. 3. The steel sphere, sapphire circular plate and support systems 2. EXPERIMENTAL SET-UP igure 2 presents: a) side view and b) top view of the experimental device used to investigate the contact area via the reflectivity method. This device was first built by Glovnea [7] and afterwards modified by Suciu [8]: 1- the loading screw, 2- the elastic lamella of normal loading, 3- the strain gauge marks applied on the elastic lamella, 4- the contact assembly between a steel sphere and a sapphire circular plate. ig. 4. The assembly image of the experimental set-up 3. EXPERIMENTAL PROCEDURE a) side view b) top view ig. 2. The experimental device igure 3 better highlights the components used for modelling the contact and their supports. The sphere is placed in a cone-shaped chuck and the circular plate is clamped on its edge in a special conceived socket. igure 4 shows an assembly image of the final experimental set-up, consisting of: 1- the experimental device, 2- laser profilometer Nanoocus µscan, 3- the strain gauge apparatus Vishay P3, 4- a computer. Before starting the actual experiments, a calibration of the strain gauge marks was needed to be performed. The calibration procedure consisted in applying known weights on the elastic lamella instead of the load screw. In this way, the applied force was known and a correlation between the applied force and the indications of the strain gauge apparatus Vishay P3 could be made. In igure 5, one may notice the resulted calibration graphic. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Series1 Linear (Series1) 0 50 100 ig. 5. The strain gauge calibration graphic After the calibration was performed, the experiments could be carried out. irst, before arranging the two bodies in contact, the surfaces of both plate and sphere were cleaned with acetone. After the contact components were arranged, the contact assembly was closed and the strain gauge 150
49 marks placed on the elastic lamella were connected to the strain gauge apparatus Vishay P3, which was manually equilibrated to zero. Next, the experimental device was placed on the profilometer X-Y translation table and the contact was loaded with the desired force by screwing the loading screw until the correspondent value of the force was indicated by the Vishay P3 strain apparatus. Using the software provided with the laser profilometer, the scanning area was selected, not before placing the experimental device in the scanning position with the command joystick of the profilometer table. inally, the laser beam is focused on the metal surface so that the scanning operation could begin. The information data regarding the reflectivity of the scanned contact surface is automatically stored by a computer and analyzed afterwards. 4. EXPERIMENTAL RESULTS Experiments were carried out for two situations, one for the contact between a steel sphere of 18.3 mm diameter and a sapphire circular plate with 3 mm thickness, and one for the contact between the same sphere and a 2 mm thick sapphire circular plate. The contact was loaded in both cases with four levels of normal force with values of 83 N, 118 N, 152 N, 188 N, respectively. The software provided with the laser profilometer, has multiple functions, so that the scanned and measured reflectivity can be visualized in 3D or in plane images, images from which different profiles can be extracted. There are two possibilities to measure the radius or diameter of the contact area, namely, by examining a diametric profile of the scanned reflectivity drawn after X or Y direction or by direct selection with available software functions from plane representations of reflectivity. igure 6 shows a three dimensional representation of the scanned and measured reflectivity, when the contact was loaded with a force of 83 N, in the case when the 3mm thick sapphire plate was used. As it can be clearly seen, the area of reflectivity where the two bodies are in contact, has a smaller value than the reflectivity where the bodies are not in contact and can easily be distinguished having a circular form, this is because the reflectivity value in a steel-sapphire interface (where the bodies are in contact) is smaller than the reflectivity value in an airsapphire interface, as it was predicted and established by other authors in their previous work [5, 6]. Based on this, the contact area could easily be selected. ig. 6. The tree dimensional representation of the reflectivity for a 83N load and the 3mm thick plate Every contact area was determined using both selection methods mentioned above. igure 7 presents a plane representation of the scanned and measured reflectivity of the contact surface. The measured contact radius had a value of 164 µm. ig. 7. The plane representation of the reflectivity and selection of contact area for a load of 82 N, 3 mm thick plate In igure 8, the contact area is determined by measuring it from a reflectivity profile extracted after Y direction. The measured diameter of the contact area was of 326 µm, almost equal to that measured by the previous method, proving that both measuring possibilities are accurate. In igure 9, a three dimensional representation of the scanned and measured reflectivity is shown, for the same contact force used in the previous situation, namely 83 N, but when the contact was modelled using the 2mm thick plate. As it can be seen and as it was expected, the area where the value of reflectivity is smaller remained circular, but became larger, suggesting that the contact area increased once the plate got thinner.
50 ig. 8. The profile representation of the reflectivity and the selection of the contact area diameter for a load of 83 N, 3mm thick plate ig. 9. The tree dimensional representation of the reflectivity for a 83N load, 2mm thick plate igures 10 and 11 present the selection and the measurement of the contact area from both representations of the surface reflectivity. The measured contact area was about 340 µm in diameter, 170 µm in radius, respectively. Comparing the obtained results for the contact areas in both situations, it was found that the radius of the contact area is smaller when the thicker plate is used than the radius obtained when the thinner plate is used, 163 µm, 170 µm, respectively. This observation was done for all the loading cases, highlighting the thickness effect on the contact area. igures 12 and 13 show the profile reflectivity representations and the selection of the contact areas, when the largest load is used, that of 188N (ig. 12), for the 3 mm plate and for the 2 mm plate (ig. 13). After this selection, the measured values for the contact area diameters were: 441 µm for the 2 mm plate and 428 µm for the 3mm plate. igure 14 presents the variation of the contact area as functions of load and thickness for all cases, the red (grey) continuous line for the 2mm plate, the blue (darker) continuous line for the 3 mm thick plate. inally, the obtained experimental results are compared to two theoretical results, one taking in consideration the thickness parameter and one classically deduced from Hertz theory of the circular contacts. ig. 10. The plane representation of the reflectivity and the selection of the contact area for a load of 82 N, 2 mm thick plate ig 11. The profile representation of the reflectivity and the selection of contact area diameter for a load of 83 N, 2 mm thick plate ig. 12. The profile representation of the reflectivity and the selection of the contact area diameter for a load of 188 N, 2mm thick plate ig. 13. The profile representation of the reflectivity and the selection of the contact area diameter for a load of 188 N, 2mm thick plate
51 represented with red line, when the contact is modelled with the 3mm plate. The same comparison was done for the case when the 2mm plate was used, comparison shown in igure 16. or both situations, the experimental results were closer to the theoretical ones calculated by involving the thickness parameter than to those calculated with Hertz relations for the circular contacts. a2 a3 100 120 140 160 1 200 ig. 14. The variation of the contact area with load and thickness a a3 a3t 100 120 140 160 1 200 ig. 15. A comparison between the experimental results and the theoretical results for the circular contact, 3 mm plate: a classical Hertzian theory, a3 experimental results, classical Hertzian results, a3t theoretical results taking into account the plate thickness 4. CONCLUSIONS The contact area is one of the unknown elements in contact mechanics problems. In time there were advanced many techniques capable of determining it. The best experimental methods are those that can offer information in each point of the contact area. One experimental method capable of fulfilling the above request, proposed and developed at the University of Suceava, is based on laser profilometry. Glovnea validated the method by applying it to a circular Hertzian contact. A contact between a steel sphere and a sapphire circular plate, modelled in two situations, one using a 2mm thick plate and the other using a 3 mm thick plate, was investigated via a reflectivity method. The obtained experimental results have shown that the contact area grows with load and is smaller when the thicker plate is used. The experimental results were compared with two theoretical results, one obtained involving the thickness parameter and the other calculated from the classical Hertzian theory. As a result of this comparison, the experimental results were in good agreement with those calculated involving the plate thickness. REERENCES a a2 a2t 100 120 140 160 1 200 ig 16. A comparison between the experimental results and the theoretical results for the circular contact, 2 mm plate: a classical Hertzian theory, a2 experimental results, classical Hertzian results, a2t theoretical results taking into account the plate thickness igure 15 shows a comparison between the experimental results, represented with blue line, the theoretical results involving the thickness parameter, represented with black line, and the theoretical results as obtained from the classical Hertzian theory, 1. Aymerich., Pau M., Ginesu., 2003, Evaluation of nominal contact area and contact pressure distribution in a steel steel interface by means of ultrasonic techniques, JSME International Journal, Series C, vol. 46, no. 1, pp. 297-305. 2. Pau M., Leban B., Baldi A., 2006, Experimental analysis of contact for the indentation of a flat rounded punch, International Journal of Solids and Structures, 43, pp. 7959-7965. 3. Drewniak E. I., Crisco J. J., Spenciner D. B., leming C. B., 2007, Accuracy of circular contact area measurements with thin film pressure sensors, Journal of Biomechanics, vol.40, pp. 25692572. 4. Ovcharenko A., Halperin G., Etsion I., Varenberg M., 2006, A novel test rig for in situ and real time optical measurement of the contact area evolution during pre-sliding of a spherical contact, Tribology Letters, vol. 23, no. 1, pp. 55-63. 5. McBride J. W., 2006, The loaded surface profile: a new technique for the investigation of contact surfaces, ICEC 2006, pp. 150-156. 6. Diaconescu E., Glovnea M., 2006, Visualization and measurement of contact area by reflectivity, Transactions of the ASME, Journal of Tribology, vol. 128, pp. 486-492. 7. Glovnea M., 1999, Efectul discontinuităţilor geometrice de suprafaţă asupra contactului elastic (in Romanian), PhD Thesis Suceava. 8. Suciu C., 2006, Cercetarea contactelor hertziene încărcate normal şi tangenţial prin profilometrie laser (in Romanian), final project, Stefan cel Mare University Suceava, Romania.