Melih Eriten

Application of Elastic-Plastic Static Friction Models to Rough Surfaces With Asymmetric Asperity Distribution

The asymmetric height distribution in surface roughness is usually indispensable in engineering surfaces prepared by specific manufacturing process. Moreover, the running-in process develops severe asymmetric roughness distribution in the surface interfaces. In this paper, the effect of asymmetric asperity distribution on static friction coefficient is investigated theoretically and by comparing it with experimental results. In order to generate a probability density function of non-Gaussian surface roughness, the Pearson system of frequency curves was used. Subsequently, the Kogut and Etsion (KE) model of elastic-plastic static friction was modified to calculate the contacting interfacial forces. For the experiments, actual roller and housing surfaces from a CV (Constant Velocity) joint were prepared to measure the static friction coefficient as it clearly shows the asymmetry of roughness distribution due to the manufacturing and also running-in process. The experimental measurements were subsequently compared with the modified KE static friction model with Gaussian as well as Pearson distributions of asperity heights. It was found that the model with Pearson distribution captures the experimental measurements well in terms of the surface conditions.Copyright

A Physics-Based Friction Model and Integration to a Simple Dynamical System

Dynamical modeling and simulation of mechanical structures containing jointed interfaces require reduced-order fretting models for efficiency. The reduced-order models in the literature compromise both accuracy and the physical basis of the modeling procedure, especially with regard to interface contact and friction modeling. Recently, physics-based fretting models for nominally flat-on-flat contacts, including roughness effects, have been developed and validated on individual (isolated) mechanical lap joints (Eriten , 2011, “Physics-Based Modeling for Fretting Behavior of Nominally Flat Rough Surfaces,” Int. J. Solids Struct., 48 (10), pp. 1436-1450). These models follow a “bottom up” modeling approach; utilizing the micromechanics of sphere-on-flat fretting contact (asperity scale), and statistical summation to model flat-on-flat contacts at the macroscale. Since these models are physical, the effects of surface roughness, contact conditions, and material properties on fretting and dynamical response of the jointed interfaces can be studied. The present work illustrates an example of how the physics-based models can be incorporated into studies of the dynamics of jointed structures. A comparison with friction models existing in the literature is also provided.

A rigorous dynamical-systems-based analysis of the self-stabilizing influence of muscles.

In this paper, dynamical systems analysis and optimization tools are used to investigate the local dynamic stability of periodic task-related motions of simple models of the lower-body musculoskeletal apparatus and to seek parameter values guaranteeing their stability. Several muscle models incorporating various active and passive elements are included and the notion of self-stabilization of the rigid-body dynamics through the imposition of musclelike actuation is investigated. It is found that self-stabilization depends both on muscle architecture and configuration as well as the properties of the reference motion. Additionally, antagonistic muscles (flexor-extensor muscle couples) are shown to enable stable motions over larger ranges in parameter space and that even the simplest neuronal feedback mechanism can stabilize the repetitive motions. The work provides a review of the necessary concepts of stability and a commentary on existing incorrect results that have appeared in literature on muscle self-stabilization.

Experimental Assessment of Joint-Like Modal Models for Structures

Several of the authors, and others, have explored the use of modal-like models for structures having nonlinearities associated with compressive joints (such as bolted connections.) In these models, the deformations are treated as consisting of modal expansions, but with the modal coordinates that evolving nonlinearly over time. There have been several theoretical treatments of this strategy and the authors report here on an early effort to confirm the approach through experiment.For this purpose simple structures consisting of pairs of plates were assembled using four bolted connections. The structures were excited by modal hammer at various locations and the modes identified by scanning laser vibrometer. In each case, multiple modes were excited and the evolution of modal coordinates was achieved by band-pass filtering at the relevant frequencies.Making some simple kinematic assumptions about relative deformations of the component plates and exploiting symmetries permits the mapping from ring-down of each mode to constitutive behavior of each joint. If the strategy of using joint-like modal models for bolted structures is valid, the joint constitutive models deduced from any mode should be adequate to predict the apparent, but nonlinear modal behavior at other resonances. Multiple test specimens were manufactured to assess this predictive capability in the context of part-to-part variability intrinsic to the dynamics of such structures.Copyright

Effects of Interfacial Strength and Roughness on the Static Friction Coefficient

A finite element model is used to simulate sliding inception of a rigid flat on a deformable sphere under combined normal and tangential loading. Sliding inception is treated as the loss of tangential contact stiffness under combined effects of plasticity, crack propagation and interfacial slip. Energy dissipation distribution is used to quantify the relative contribution of these mechanisms on the increased compliance during tangential loading. Materials with different strength and toughness properties, and varying local interface conditions ranging from fully adhered to finite friction, are studied to relate variations in plastic deformations, crack and slip to the sliding inception. For fully adhered contact condition, crack and fracture toughness have no effect on sliding inception, with plasticity, the dominant failure mechanism. A measure of recoverable strain (yield strength to Young’s modulus ratio) is found to be the most influential parameter in sliding inception. Interfacial slip is expectedly the dominant mechanism for sliding inception for lower coefficient of friction, modeling lubricated contacts. Interplay of plasticity and interfacial slip is found to govern the onset of sliding for higher local friction coefficients. Furthermore, the single asperity results are incorporated in a statistical model for nominally flat contacting rough surfaces under combined normal and tangential loading to investigate the stochastic effects due to surface roughness and material property uncertainties. The results show that the static coefficient of friction strongly depends on the normal load, material properties, local interfacial strength and roughness parameters.

A Physics-Based Fretting Model With Friction and Integration to a Simple Dynamical System

Dynamical modeling and simulations of structures containing joint interfaces require reduced-order fretting models for efficiency. The reduced-order models in the literature compromise accuracy and physical basis of the modeling procedure, especially in regards to interface contact and friction modeling. Recently, physics-based fretting models for flat-on-flat contacts, including roughness effects have been developed and tested on individual (isolated) mechanical lap joints [1]. These models follow a “bottom up” modeling approach; utilizing the micromechanics of sphere-on-flat fretting contact (asperity scale), and statistical summation to model flat-on-flat contact (macroscale). Since these models are derived from first principles, the effects of surface roughness, contact conditions, and material properties on fretting and dynamical response of the jointed interfaces can be studied. The present work illustrates an example of how the physics-based models can be incorporated in dynamics of jointed structures. A comparison with the friction models existing in the literature is also provided.Copyright

A rigorous dynamical-systems-based analysis of the self-stabilizing influence of muscles

In this paper, dynamical systems analysis and optimization tools are used to investigate the local dynamic stability of periodic task-related motions of simple models of the lower-body musculoskeletal apparatus and to seek parameter values guaranteeing their stability. In particular, the dynamics of a two-link model of a leg undergoing periodic excitation through one or several contractile muscle elements corresponding to a simple knee-bending motion is studied. Several muscle models incorporating various active and passive elements are included and the notion of self-stabilization of the rigid-body dynamics through the imposition of muscle-like actuation is investigated. It is found that self-stabilization depends both on muscle architecture and configuration as well as the properties of the reference motion. Additionally, antagonistic muscles (flexor-extensor muscle couples) are shown to enable stable motions over larger ranges in parameter space and that even the simplest neuronal feedback mechanism can stabilize the repetitive motions. The work provides a review of the necessary concepts of stability and a commentary on existing incorrect results that have appeared in the literature on muscle self-stabilization.Copyright

Direct Detection of Nonlinear Modal Interactions and Model Updating Using Measured Time Series

We describe a new method for identifying mechanical systems with strongly nonlinear attachments using measured transient response data. The procedure is motivated by the desire to quantify the degree of nonlinearity of a system, with the ultimate goal of updating a finite-element or other mathematical model to capture the nonlinear effects accurately. Our method relies on the proper orthogonal decomposition to extract proper orthogonal mode shapes (POMs), which are inherently energy dependent, directly from the measured transient response. Using known linear properties, the system’s frequencies are estimated using the Rayleigh quotient and an estimated frequency-energy plot (FEP) is created by them as functions of the system’s mechanical energy. The estimated FEP reveals distinct linear and nonlinear regimes which h are characterized by constant frequency (horizontal lines) and large frequency changes, respectively. The nonlinear regimes also contain spikes that connect different modes and indicate strongly nonlinear modal interactions. The nonlinearity is identified by plotting the estimated frequencies as functions of characteristic displacement and fitting a frequency equation based on the model of the nonlinearity. We demonstrate the method on the response of a cantilevered, model airplane wing with a nonlinear energy sink attached at its free end.

Advanced Nonlinear System Identification for Modal Interactions in Nonlinear Structures: A Review

In this work, we review a recently developed method for the characterization and identification of strongly nonlinear dynamical systems, including the detection of strongly nonlinear modal interactions, directly from transient response data. The method synergistically combines the proper orthogonal decomposition and the Rayleigh quotient to create estimated frequency-energy plots (FEPs) that capture the rich and interesting nonlinear dynamical interactions. The method is first applied to the experimentally measured response of a cantilever beam with a local, smooth nonlinearity. In this application, the estimated FEP reveals the presence of nonsmooth perturbations that connect different nonlinear normal modes (NNMs) of the system. The wavelet-bounded empirical mode decomposition and slow-flow analysis are used to demonstrate that the nonsmooth perturbations correspond to strongly nonlinear internal resonances between two NNMs. In the second example, the method is applied to the experimentally measured response of a cantilever beam with a local, nonlinear attachment in the form of a nonlinear energy sink (NES). An estimated frequency-displacement plot for the NES is created, and an optimization routine is then used to identify the unknown parameters for a given model of the nonlinearity. Ultimately, the method is conceptually and computationally simple compared to traditional methods while providing significant insight into the nonlinear physics governing dynamical systems with strong, local nonlinearity directly from measured time series data.

Effect of relaxation-dependent adhesion on pre-sliding response of cartilage

Possible links between adhesive properties and the pre-sliding (static) friction response of cartilage are not fully understood in the literature. The aims of this study are to investigate the relation between adhesion and relaxation time in articular cartilage, and the effect of relaxation-dependent adhesion on the pre-sliding response of cartilage. Adhesion tests were performed to evaluate the work of adhesion of cartilage at different relaxation times. Friction tests were conducted to identify the pre-sliding friction response of cartilage at relaxation times corresponding to adhesion tests. The pre-sliding friction response of cartilage was systematically linked to the work of adhesion and contact conditions by a slip-based failure model. It was found that the work of adhesion increases with relaxation time. Also, the work of adhesion is linearly correlated to the resistance to slip-based failure. In addition, as the work of adhesion increases, the adhered (stick) area at the moment of failure increases, and the propagation rate of the annular slip (crack) area towards its centre increases. These findings offer a mechanistic explanation of the pre-sliding friction behaviour and stick–slip response of soft hydrated interfaces such as articular cartilage and hydrogels. In addition, the linear correlation between adhesion and threshold to slip-based failure enables estimation of the adhesive strength of such interfaces directly from the pre-sliding friction response (e.g. shear wave elastography).