Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts

Medina, Simon; Nowell, D.; Dini, Daniele

doi:10.1007/s11249-012-0049-y

Cited by 79 publications

(59 citation statements)

References 27 publications

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“…Knowing R K and K N Rough , K T Rough can be obtained using equation (4). The influence of the surface roughness on R K has been reported in recent tribology research; Campañá et al (2011) and Medina et al (2013) assumed the same R K for both smooth and rough contacts. In contrast, a lower R K for rough contacts was reported by Gonzalez-Valadez et al (2010), whose ultrasound tests showed that R K Rough , R K Smooth , and R K Rough increases as the normal contact force increases.…”

Section: Theoretical Derivation Of Shear Modulus For Rough Elastic Comentioning

confidence: 84%

Quantitative assessment of the influence of surface roughness on soil stiffness

et al. 2015

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The nature of soil stiffness at small strains remains poorly understood. The relationship between soil stiffness (e.g. shear stiffness, G 0 ) and isotropic confining pressure ( p′) can be described using a power function with exponent (b), that is,, where A is a constant and p r is an arbitrary reference pressure. Experimentally determined values of b are usually around 0·5 and these are higher than the value of 0·33 that can be analytically determined using Hertzian theory. Hertzian theory considers contact between two smooth, elastic spheres; however, in reality, inter-particle contacts in soil are complex with particle shape and surface roughness affecting the interaction. Thus Hertzian theory is not directly applicable to predict real soil stiffness. It has, however, provided a useful basis to develop an analytical framework to consider the influence of particle surface roughness on small-strain soil stiffness. Here, earlier contributions using this framework are extended and improved by paying particular attention to roughness and the tangential contact stiffness. Stiffness values calculated using the newly derived analytical expressions were compared with the results of bender element tests on samples of borosilicate glass beads (ballotini) whose surface roughness was quantified using an optical interferometer. The analytical expression captures the experimentally observed sensitivity of the smallstrain shear modulus to surface roughness.

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Section: Theoretical Derivation Of Shear Modulus For Rough Elastic Comentioning

confidence: 84%

Quantitative assessment of the influence of surface roughness on soil stiffness

et al. 2015

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“…The tangential stiffness was measured experimentally as described in [42], leading to an average value per unit area of about 60000 [N/mm 3 ]. The corresponding normal stiffness was chosen to be the same, as in a rough dry contact the same order of magnitude is expected [43], and no measured values were available. It should be noticed that this assumption constitutes a simplification since the real ratio between the two stiffnesses depends on the geometry of the contact patch [44], but previous experience [45] has shown that it does not affect significantly the results.…”

Section: Contact Stiffnessmentioning

confidence: 99%

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

Pesaresi

Salles

Jones

et al. 2017

Mechanical Systems and Signal Processing

145

108

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Underplatform dampers (UPD) are commonly used in aircraft engines to mitigate the risk of high-cycle fatigue failure of turbine blades. The energy dissipated at the friction contact interface of the damper reduces the vibration amplitude significantly, and the couplings of the blades can also lead to significant shifts of the resonance frequencies of the bladed disk. The highly nonlinear behaviour of bladed disks constrained by UPDs requires an advanced modelling approach to ensure that the correct damper geometry is selected during the design of the turbine, and that no unexpected resonance frequencies and amplitudes will occur in operation. Approaches based on an explicit model of the damper in combination with multi-harmonic balance solvers have emerged as a promising way to predict the nonlinear behaviour of UPDs correctly, however rigorous experimental validations are required before approaches of this type can be used with confidence.In this study, a nonlinear analysis based on an updated explicit damper model having different levels of detail is performed, and the results are evaluated against a newly-developed UPD test rig. Detailed linear finite element models are used as input for the nonlinear analysis, allowing the inclusion of damper flexibility and inertia effects. The nonlinear friction interface between the blades and the damper is described with a dense grid of 3D friction contact elements which allow accurate capturing of the underlying nonlinear mechanism that drives the global nonlinear behaviour. The introduced explicit damper model showed a great dependence on the correct contact pressure distribution. The use of an accurate, measurement based, distribution, better matched the nonlinear dynamic behaviour of the test rig. Good agreement with the measured frequency response data could only be reached when the zero harmonic term (constant term) was included in the multi-harmonic expansion of the nonlinear problem, highlighting its importance when the contact interface experiences large normal load variation. The resulting numerical damper kinematics with strong translational and rotational motion, and the global blades frequency response were fully validated experimentally, showing the accuracy of the suggested high detailed explicit UPD modelling approach.

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“…Barthoud and Baumberger (1998) and Medina et al (2013) described an approximate expression for the total tangential contact stiffness as indicated below, Nakano andMaegawa (2009), Fuadi et al (2010), and Maegawa et al (2013) (Mindlin, 1949), in accordance to K T bulk = 4aE/(1+ν)(2-ν), where a is the contact radius of the apparent contact region, E is the Young's modulus of PDMS, and ν is the Poisson's ratio of PDMS. Thus, K Figs.…”

Section: Measurement Of Tangential Contact Stiffnessmentioning

confidence: 99%

Optical measurements of real contact area and tangential contact stiffness in rough contact interface between an adhesive soft elastomer and a glass plate

Maegawa

Itoigawa

Nakamura

2015

JAMDSM

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). These results provided beneficial information for improvement of the theories of the contact and sliding mechanisms for elastic materials. For example, Schallamach (1971) first discovered a surface instability, such as the propagation of the detachment waves across the contact zone during sliding motion. In recent years, as presented in the references by Chareauminois and Fretigny (2008) and Prevost et al. (2013), the digital image correlation (DIC) method has been focused on visualizing the surface displacement and stress fields within the contact interface. These research studies will be helpful for the understanding AbstractThis study demonstrates optical measurements of a real contact area and tangential contact stiffness in a rough contact interface between a soft adhesive elastomer and a glass plate. A friction tester developed in this study employs a rough contact interface between a rough rubber plate that is made of cross-linked poly-dimethyl siloxane (PDMS) and a smooth optical glass (BK7) hemisphere. This friction tester also equips a transmission optical system that is composed of a white light-emitting diodes (LED) light source, an objective lens system, and a charge coupled device (CCD) camera, for the in situ observation of the space distribution of the real contact area in the apparent contact region. Based on a simplified analysis, in accordance to the measurements of the transmitted light intensity, the amount of the real contact area was determined without any complicated calibrations. As a result, it was found that the amount of the real contact area linearly increased with normal load. Furthermore, using the digital image correlation (DIC) method, the time changes in the surface displacement field within the apparent contact region were visualized from the onset of the sliding motion to the onset of the steady sliding. These results provided a direct estimation of the tangential contact stiffness that resulted from the tangential deformation at the contacting asperity layer.

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Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts

Cited by 79 publications

References 27 publications

Quantitative assessment of the influence of surface roughness on soil stiffness

Quantitative assessment of the influence of surface roughness on soil stiffness

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

Optical measurements of real contact area and tangential contact stiffness in rough contact interface between an adhesive soft elastomer and a glass plate

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