Abstract
Background: The non-conforming contact usually induce stress concentration as the interaction only occurs at a small interface. Theoretical and numerical investigations have shown that the contact stress distribution and maximum pressure are closely related to the length of the contact interface. Objective: Therefore, the characterization of the contact length is a key issue in studying the contact behavior and the corresponding structural safety. Methods: In this paper, we propose an indirect experimental identification approach that can reliably characterize the contact length between non-conforming frictionless surfaces. The relationship between the contact length and the local displacement is established based on the contact theory, and a modified digital image correlation method is implemented to acquire the displacement field near the contact area. The contact length is then identified with the established model and the measured displacement gradient through an identification algorithm, which can be easily calculated and does not require an optimization process. Results: Both simulations and experiments are performed to evaluate the precision and applicability of the proposed approach. The identification error maintains within a very low level during different load steps. Conclusions: The results indicate that the proposed method can accurately identify the contact length and has the ability to against the inevitable measurement inaccuracy of the displacement field.
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References
Wen Z, Wu L, Li W, Jin X, Zhu M (2011) Three-dimensional elastic-plastic stress analysis of wheel-rail rolling contact. Wear 271(1):426–436. https://doi.org/10.1016/j.wear.2010.10.001
Liu S, Wang Q (2000) A three-dimensional thermomechanical model of contact between non-conforming rough surfaces. J Tribol 123(1):17–26. https://doi.org/10.1115/1.1327585
Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge
Mao K (2007) Gear tooth contact analysis and its application in the reduction of fatigue wear. Wear 262 (11):1281–1288. https://doi.org/10.1016/j.wear.2006.06.019
Chunjiang Z, Xiaokai Y, Qingxue H, Shidong G, Xin G (2015) Analysis on the load characteristics and coefficient of friction of angular contact ball bearing at high speed. Tribol Int 87:50–56. https://doi.org/10.1016/j.triboint.2015.02.012
Xing W, Zhang J, Song C, Tin-Loi F (2019) A node-to-node scheme for three-dimensional contact problems using the scaled boundary finite element method. Comput Methods Appl Mech Eng 347:928–956. https://doi.org/10.1016/j.cma.2019.01.015
Güler M, Kucuksucu A, Yilmaz K, Yildirim B (2017) On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium. Int J Mech Sci 120:12–29. https://doi.org/10.1016/j.ijmecsci.2016.11.004
Roswell A, Xi FJ, Liu G (2006) Modelling and analysis of contact stress for automated polishing. Int J Mach Tools Manuf 46(3):424–435. https://doi.org/10.1016/j.ijmachtools.2005.05.006
Malits P (2011) Contact with stick zone between an indenter and a thin incompressible layer. Eur J Mech-A/Solid 30(6):884–892. https://doi.org/10.1016/j.euromechsol.2011.04.010
Johnson KL, Kendall K, Roberts AD, Tabor D (1971) Surface energy and the contact of elastic solids. Proc R Soc A Math Phys Sci 324(1558):301–313. https://doi.org/10.1098/rspa.1971.0141
Derjaguin B, Muller V, Toporov Y (1975) Effect of contact deformations on the adhesion of particles. J Colloid Interface Sci 53(2):314–326. https://doi.org/10.1016/0021-9797(75)90018-1
Greenwood JA, Williamson JBP, Bowden FP (1966) Contact of nominally flat surfaces. Proc R Soc A Math Phys Sci 295(1442):300–319. https://doi.org/10.1098/rspa.1966.0242
Hild P (2000) Numerical implementation of two nonconforming finite element methods for unilateral contact. Comput Methods Appl Mech Eng 184(1):99–123. https://doi.org/10.1016/S0045-7825(99)00096-1
Parsons B, Wilson EA (1970) A method for determining the surface contact stresses resulting from interference fits. J Manuf Sci Eng 92(1):208–218. https://doi.org/10.1115/1.3427710
Zhang H, Xie Z, Chen B, Xing H (2012) A finite element model for 2d elastic-plastic contact analysis of multiple cosserat materials. Eur J Mech-A/Solid 31(1):139–151. https://doi.org/10.1016/j.euromechsol.2011.07.005
Robert F (2019) Prediction of contact length, contact pressure and indentation depth of au/carbon nanotube composite micro electrical contact using finite element modeling. Appl Surf Sci 489:470–476. https://doi.org/10.1016/j.apsusc.2019.05.169
Rodríguez-Tembleque L, Buroni F, Abascal R, Sáez A (2011) 3D frictional contact of anisotropic solids using bem. Eur J Mech-A/Solid 30(2):95–104. https://doi.org/10.1016/j.euromechsol.2010.09.008
Li Q, Popov VL (2018) Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials. Comput Mech 61(3):319–329. https://doi.org/10.1007/s00466-017-1461-9
Wu JJ, Lin YJ (2017) Boundary element analyses on the adhesive contact between an elastic sphere and a rigid half-space. Eng Anal Bound Elem 74:61–69. https://doi.org/10.1016/j.enganabound.2016.10.011
Li S (2007) Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications. Mech Mach Theory 42(1):88–114. https://doi.org/10.1016/j.mechmachtheory.2006.01.009
Patil SS, Karuppanan S, Atanasovska I, Wahab AA (2014) Contact stress analysis of helical gear pairs, including frictional coefficients. Int J Mech Sci 85:205–211. https://doi.org/10.1016/j.ijmecsci.2014.05.013
Petrov EP, Ewins DJ (2005) Effects of damping and varying contact area at Blade-Disk joints in forced response analysis of bladed disk assemblies. J Turbomach 128(2):403–410. https://doi.org/10.1115/1.2181998
Scheibert J, Prevost A, Debrégeas G, Katzav E, Adda-Bedia M (2009) Stress field at a sliding frictional contact: Experiments and calculations. J Mech Phys Solid 57(12):1921–1933. https://doi.org/10.1016/j.jmps.2009.08.008
Kane BJ, Cutkosky MR, Kovacs GTA (2000) A traction stress sensor array for use in high-resolution robotic tactile imaging. J Microelectromech Syst 9(4):425–434. https://doi.org/10.1109/84.896763
Jones IA, Truman CE, Booker JD (2008) Photoelastic investigation of slippage in shrink-fit assemblies. Exp Mech 48(5):621–633. https://doi.org/10.1007/s11340-008-9140-6
Khaleghian S, Emami A, Tehrani M, Soltani N (2013) Analysis of effective parameters for stress intensity factors in the contact problem between an asymmetric wedge and a half-plane using an experimental method of photoelasticity. Mater Des 43:447–453. https://doi.org/10.1016/j.matdes.2012.07.038
Papadopoulos GA (2004) Experimental estimation of the load distribution in bearings by the method of caustics. Exp Mech 44(4):440–443. https://doi.org/10.1007/BF02428098
Spitas V, Papadopoulos GA, Spitas C, Costopoulos T (2011) Experimental investigation of load sharing in multiple gear tooth contact using the stress-optical method of caustics. Strain 47(s1):e227–e233. https://doi.org/10.1111/j.1475-1305.2008.00558.x
Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20(6):062001. https://doi.org/10.1088/0957-0233/20/6/062001
Cai Y, Zhang Q, Yang S, Fu S, Wang Y (2016) Experimental study on three-dimensional deformation field of portevin–le chatelier effect using digital image correlation. Exp Mech 56(7):1243–1255. https://doi.org/10.1007/s11340-016-0138-1
Yang L, Xie X, Zhu L, Wu S, Wang Y (2014) Review of electronic speckle pattern interferometry (espi) for three dimensional displacement measurement. Chin J Mech Eng 27(1):1–13. https://doi.org/10.3901/CJME.2014.01.001
Badulescu C, Grédiac M, Mathias JD (2009) Investigation of the grid method for accurate in-plane strain measurement. Meas Sci Technol 20(9):095102. https://doi.org/10.1088/0957-0233/20/9/095102
Passieux JC, Bugarin F, David C, Périé JN, Robert L (2015) Multiscale displacement field measurement using digital image correlation: Application to the identification of elastic properties. Exp Mecha 55 (1):121–137. https://doi.org/10.1007/s11340-014-9872-4
Chalal H, Avril S, Pierron F, Meraghni F (2006) Experimental identification of a nonlinear model for composites using the grid technique coupled to the virtual fields method. Compos Part A Appl Sci Manuf 37 (2):315–325. https://doi.org/10.1016/j.compositesa.2005.04.020
Mathieu F, Hild F, Roux S (2012) Identification of a crack propagation law by digital image correlation. Int J Fatigue 36(1):146–154. https://doi.org/10.1016/j.ijfatigue.2011.08.004
Sun C, Zhou Y, Chen J, Miao H (2015) Measurement of deformation close to contact interface using digital image correlation and image segmentation. Exp Mech 55(8):1525–1536. https://doi.org/10.1007/s11340-015-0055-8
Pan B, Asundi A, Xie H, Gao J (2009) Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements. Opt Lasers Eng 47(7):865–874. https://doi.org/10.1016/j.optlaseng.2008.10.014
Zhu H, He Z, Zhao Y, Ma S (2017) Experimental verification of yield strength of polymeric line contact structures. Polym Test 63:118–125
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This research work was supported by the National Natural Science Foundation of China, Grant Nos. 11902196 and 11732009, the supports are gratefully acknowledged.
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Lin, Q., Gong, Y., Sun, C. et al. An Indirect Experimental Measurement Method for Contact Length Identification in Non-conforming Frictionless Contact. Exp Mech 60, 801–813 (2020). https://doi.org/10.1007/s11340-020-00600-w
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DOI: https://doi.org/10.1007/s11340-020-00600-w