Sinan Müftü

A Scale-Dependent Model for Multi-Asperity Contact and Friction

As loading forces decrease in applications such as MEMS and NEMS devices, the size of the asperity contacts which comprise the real contact area tend to decrease into the nano scale regime. This reduction in size of the contacts is only partially offset by the nominally increased smoothness of these contacting surfaces. Because the friction force depends on the real area of contact, it is important to understand how the material and topographical properties of surfaces contribute to friction forces at this nano scale. In this investigation, the single asperity nano contact model of Hurtado and Kim is incorporated into a multi-asperity model for contact and friction which includes the effect of asperity adhesion forces using the Maugis-Dugdale model. The model spans the range from nano-scale to micro-scale to macro-scale contacts. Three key dimensionless parameters have been identified which represent combinations of surface roughness measures, Burgers vector length, surface energy, and elastic properties. Results are given for the friction coefficient versus normal force, the normal and friction forces versus separation. and the pull-off force for various values of these key parameters.

Efficiency Considerations for the Purely Tapered Interference Fit (TIF) Abutments Used in Dental Implants

A tapered interference fit provides a mechanically reliable retention mechanism for the implant-abutment interface in a dental implant. Understanding the mechanical properties of the tapered interface with or without a screw at the bottom has been the subject of a considerable amount of studies involving experiments and finite element (FE) analysis. In this paper, approximate closed-form formulas are developed to analyze the mechanics of a tapered interference fit. In particular, the insertion force, the efficiency, defined as the ratio of the pull-out force to insertion force, and the critical insertion depth, which causes the onset of plastic deformation, are analyzed. It is shown that the insertion force is a function of the taper angle, the contact length, the inner and outer radii of the implant, the static and the kinetic coefficients of friction, and the elastic modulii of the implant/abutment materials. The efficiency of the tapered interference fit, which is defined as the ratio of the pull-out force to insertion force, is found to be greater than one, for taper angles that are less than 6 deg when the friction coefficient is 0.3. A safe range of insertion forces has been shown to exist. The lower end of this range depends on the maximum pull-out force that may occur due to occlusion in the multiple tooth restorations and the efficiency of the system; and the upper end of this range depends on the plastic deformation of the abutment and the implant due to interference fit. It has been shown that using a small taper angle and a long contact length widens the safe range of insertion forces.

Traction Between a Web and a Smooth Roller

Web traction over rollers is known to deteriorate due to air entrainment at high web speeds. In this paper, a general model is presented to predict the traction capability of an impermeable web over a smooth roller. The model considers the effects of the web and roller speeds, roller radius, combined roughness of the two surfaces, web tension and thickness, friction coefficient, and compressible air bearing. The change of tension ΔN due to mechanical slip between the roller and the web is calculated by a simultaneous solution of the in-plane and out-of-plane equilibrium of the web and the compressible Reynolds lubrication equation. The problem is nondimensionalized and the effects of nine of the eleven nondimensional parameters on traction are investigated for a range of values. Formulas involving the nondimensional parameters for the traction capability are presented in two-variable polynomial forms.

A NANO-SCALE MULTI-ASPERITY CONTACT AND FRICTION MODEL

As surfaces become smoother and loading forces decrease in applications such as MEMS and NEMS devices, the asperity contacts which comprise the real contact area will continue to decrease into the nano scale regime. Thus it becomes important to understand how the material and topographical properties of surfaces contribute to measured friction forces at this nano scale. We have incorporated the single asperity nano contact model of Hurtado and Kim into a multi-asperity model for contact and friction which includes the effect of asperity adhesion forces using the Maugis-Dugdale model. Our model spans the range from nano-scale to micro-scale to macro-scale contacts. We have identified three key dimensionless parameters representing combinations of surface roughness measures, Burgers vector length, surface energy, and elastic modulus. Results are given for the normal and friction forces vs. separation, and for the friction coefficient vs. normal force for various values of these key parameters.Copyright

Friction Induced Transverse Vibrations of an Axially Accelerating String

The purpose of this study is to investigate the dynamic response of axially translating continua undergoing both the effect of friction and axial acceleration. The axially moving continuum is initially modeled as a string, neglecting its flexural stiffness; the response, with particular interest given to transverse vibrations and dynamic stability, is studied through numerical methods. A finite element method is employed to discretize the space domain and an implicit α–method is employed to integrate the resulting matrix equation in the time domain. Results are given through time history diagrams and stability considerations.Copyright

A Nano-Scale Multi-Asperity Model for Contact and Friction

As surfaces become smoother and loading forces decrease in applications such as MEMS and NEMS devices, the asperity contacts which comprise the real contact area will continue to decrease into the nano scale regime. Thus it becomes important to understand how the material and topographical properties of surfaces contribute to measured friction forces at this nano scale. We have incorporated the single asperity nano contact model of Hurtado and Kim into a multi-asperity model for contact and friction which includes the effect of asperity adhesion forces using the Maugis-Dugdale model. Our model spans the range from nano-scale to micro-scale to macro-scale contacts. We have identified three key dimensionless parameters representing combinations of surface roughness measures, Burgers vector length, surface energy, and elastic modulus. Results are given for the normal and friction forces vs. separation, and for the friction coefficient vs. normal force for various values of these key parameters.Copyright

ASYMMETRIC ASPERITY HEIGHT DISTRIBUTIONS IN A SCALE-DEPENDENT MODEL FOR CONTACT AND FRICTION

The effect of an asymmetric distribution of asperity heights is accounted for in a recently developed scale-dependent multi-asperity model of contact and friction. A Weibull distribution of asperity heights is used which allows the skew and kurtosis to be varied, but not independently of each other. The contact and friction model used includes the effects of adhesion and of scale-dependent friction. The results obtained demonstrate that positive/negative skew decreases/increases both the friction coefficient and its dependence on the magnitude of the normal load.Copyright

Transverse Vibration of Two Axially Moving Beams Connected by an Elastic Foundation

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The Euler-Bernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that the natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated.Copyright

On Cohesion of Micron Scale Metal Particles in High Velocity Impact With a Metal Substrate

Impact of a single copper particle in cold gas dynamic spray is simulated by finite element method by including the effects of high strain rates and temperature on material plasticity and failure. In order to predict stick behavior of the particle, cohesive forces that act between the particle and the substrate are included in the model by defining an interfacial cohesive strength parameter. Effect of this parameter on the deformation and stick/rebound behavior of the particle is studied. It is found that significant particle deformation, large area of contact between particle and substrate is needed to generate enough cohesive force to absorb the rebound energy of the particle and achieve sticking. As the impact velocity and assumed interfacial cohesive strength increases, particle is more likely to stick on to the substrate. Critical velocities in the same range with experimental results are predicted.Copyright

A CYLINDRICAL CONTACT MODEL FOR TWO DIMENSIONAL MULTIASPERITY PROFILES

In practice, multi-asperity contact problems are often solved as two dimensional (2D) plane problems rather than true three dimensional (3D) problems. This is accomplished by assuming that each peak on a 2D scanned profile is the pinnacle of a half sphere. Hertz contact equations are then used to solve for the radius of contact and pressure profile. In reality, the local maximum in the plane may not be the maximum in the unmeasured depth direction, creating inherent errors in the contact model. This error is shown to be significant in contact problems when estimating the area of contact and total contact force over a single asperity. The pressure corrected Sternberg-Turteltaub model is introduced, in which a cylinder is used to model a sphere in a plane. This model is shown to improve the contact area and total force estimates for a range contact parameters.Copyright