A Three-Dimensional Thermomechanical Model of Contact Between Non-Conforming Rough Surfaces

2000 ◽  
Vol 123 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Rough Surfaces ◽  
Frictional Heating ◽  
Three Dimensional ◽  
Point Contact ◽  
Numerical Algorithms ◽  
Normal Surface ◽  
Thermomechanical Model ◽  
Influence Coefficients ◽  
Surface Displacements ◽  
Thermomechanical Contact

A necessary step in understanding failure problems of tribological elements is to investigate the contact performance of rough surfaces subjected to frictional heating. It is essential that the interfacial variables are obtained through solving the interactive thermomechanical contact problem. This paper studies the three dimensional thermomechanical contact of non-conforming rough surfaces, the model of which includes the normal surface displacements caused by the contact pressure, frictional shear, and frictional heating. Influence coefficients and frequency response functions for elastic and thermoelastic displacements, as well as those for temperature rises, are investigated for model construction. In order to develop an accurate and efficient solver, the numerical algorithms with the discrete convolution and fast Fourier transform techniques and the single-loop conjugated gradient method are used. The model modules are numerically verified and the thermomechanical performance of the rough surfaces in a point contact is studied.

scholarly journals Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter

2016 ◽  
Author(s):  
L. Salles ◽  
M. Vahdati
Keyword(s):  
Numerical Models ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Mode Shapes ◽  
Minimal Amount ◽  
Aeroelastic System ◽  
Cpu Time ◽  
Influence Coefficients ◽  
Non Linear ◽  
The Time Domain

The aim of this paper is to study the effects of mistuning on fan flutter and to compare the prediction of two numerical models of different fidelity. The high fidelity model used here is a three-dimensional, whole assembly, time-accurate, viscous, finite-volume compressible flow solver. The Code used for this purpose is AU3D, written in Imperial College and validated for flutter computations over many years. To the best knowledge of authors, this is the first time such computations have been attempted. This is due to the fact that, such non-linear aeroelastic computations with mistuning require large amount of CPU time and cannot be performed routinely and consequently, faster (low fidelity) models are required for this task. Therefore, the second model used here is the aeroelastic fundamental mistuning model (FMM) and it based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from the time domain non-linear Code by shaking one blade in the datum (tuned) frequency and mode. Once the influence coefficients have been obtained, the computations of aero damping require minimal amount of CPU time and many different mistuning patterns can be studied. The objectives of this work are to: 1. Compare the results between the two models and establish the capabilities/limitations of aeroelastic FMM, 2. Check if the introduction of mistuning would bring the experimental and computed flutter boundaries closer, 3. Establish a relationship between mistuning and damping. A rig wide-chord fan blade, typical of modern civil designs, was used as the benchmark geometry for this study. All the flutter analyses carried out in this paper are with frequency mistuning, but the possible consequences of mistuned mode shapes are briefly discussed at the end of this paper. Only the first family of modes (1F, first flap) is considered in this work. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. For the mode shape mistuning computations, an FE analysis of the whole assembly different mass blades is performed. The results of this work clearly show the importance of mistuning on flutter. It also demonstrates that when using rig test data for aeroelastic validation of CFD codes, the amount mistuning present must be known. Finally, it should be noted that the aim of this paper is the study of mistuning and not steady/unsteady validation of a CFD code and therefore minimal aerodynamic data are presented.

Thermomechanical Analysis of Elastoplastic Bodies in a Sliding Spherical Contact and the Effects of Sliding Speed, Heat Partition, and Thermal Softening

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
W. Wayne Chen ◽  
Q. Jane Wang
Keyword(s):  
Half Space ◽  
Frictional Heating ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Thermomechanical Analysis ◽  
Thermal Softening ◽  
Sliding Speed ◽  
Dependent Strain ◽  
Steady State Heat ◽  
Strain Hardening Behavior

A thermomechanical analysis of elasto-plastic bodies is a necessary step toward the understanding of tribological behaviors of machine components subjected to both mechanical loading and frictional heating. A three-dimensional thermoelastoplastic contact model for counterformal bodies has been developed, which takes into account steady state heat flux, temperature-dependent strain hardening behavior, and interaction of mechanical and thermal loads. The fast Fourier transform and conjugate gradient method are the underlying numerical algorithms used in this model. Sliding of a half-space over a stationary sphere is simulated with this model. The friction-induced heat is partitioned into two bodies based on surface temperature distributions. In the simulation, the sphere is considered to be fully thermoelastoplastic, while the half-space is treated to be thermoelastic. Simulation results include surface pressure, temperature rise, and subsurface stress and plastic strain fields. The paper also studies the influences of sliding speed and thermal softening on contact behaviors for sliding speed ranging three orders of magnitude.

Point Contact EHL Based on Optically Measured Three-Dimensional Rough Surfaces

1997 ◽  
Vol 119 (3) ◽  
pp. 375-384 ◽  
Author(s):  
Dong Zhu ◽  
Xiaolan Ai
Keyword(s):  
Rough Surface ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Peak Height ◽  
Machining Process ◽  
Maximum Pressure ◽  
Pressure Peak ◽  
Surface Profiles

This paper presents a numerical solution for the elastohydrodynamic lubrication in point contacts, using optically measured three-dimensional rough surface profiles as input data. The multi-grid computer program originally developed by Ai and Cheng (1993, 1994) is modified, so that both contacting surfaces can be three-dimensional measured rough surfaces moving at different velocities. Many different engineering surfaces are measured and analyzed in the present study, demonstrating that the numerical analysis is practical for real surfaces of bearings, cams, gears and other components, as long as a significant EHL film still exists. In addition, discussions are given in this paper for the effects of three-dimensional rough surface topography, which is related to machining process. It appears that, for the circular contact cases analyzed, surface roughness texture and orientation do not have a significant effect on the average film thickness, but they do affect the maximum pressure peak height and asperity deformation in the contact zone considerably.

A Numerical Three-Dimensional Model for the Contact of Layered Elastic/Plastic Solids With Rough Surfaces by a Variational Principle

2000 ◽  
Vol 123 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Wei Peng ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Fast Fourier Transformation ◽  
Three Dimensional Model ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Influence Coefficients ◽  
Elastic Perfectly Plastic

A new numerical model for the three-dimensional contact analysis of a layered elastic–perfectly plastic half space with another rough surface is presented. The model is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. A quasi-Newton method is used to find the minimum. The influence coefficients matrix is determined using the Papkovich–Neuber potentials with fast Fourier transformation. The model is extended to elastic–perfectly plastic contacts in dry and wet conditions. Contact analyses have been performed to predict contact statistics of layered elastic/plastic solids with rough surfaces using this model. The effects of the stiffness of the layer and the substrate, layer thickness, as well as normal load are studied. Optimum layer parameters are identified to provide low friction/stiction and wear.

Transient Three-Dimensional Solution for Thermoelastic Displacement Due to Surface Heating and Convective Cooling

2005 ◽  
Vol 127 (4) ◽  
pp. 750-755 ◽  
Author(s):  
Ashlie Martini ◽  
Shuangbiao Liu ◽  
Q. Jane Wang
Keyword(s):  
Frictional Heating ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Dimensional Solution ◽  
Convective Cooling ◽  
Surface Convection ◽  
Tribological Contact ◽  
Thermoelastic Displacement

In tribological contact, frictional heating may lead to temperature rise, which in turn may result in thermal displacement of the contacting bodies. The quantification of these effects is desirable in order to more accurately predict wear and failure of contacting surfaces. The change in temperature at a contact area may be attributed to the combined effects of frictional heating and convective cooling. This paper presents a transient, three-dimensional solution for the normal surface displacement of an elastic half-space due to an arbitrarily distributed, moving heat source and surface convection.

A Fast Approximate Method for Heat Conduction in an Inhomogeneous Half-Space Subjected to Frictional Heating

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Xiujiang Shi ◽  
Liqin Wang ◽  
Qinghua Zhou ◽  
Qian Wang
Keyword(s):  
Heat Conduction ◽  
Half Space ◽  
Frictional Heating ◽  
Three Dimensional ◽  
Frictional Heat ◽  
Three Dimensional Model ◽  
Equivalent Inclusion Method ◽  
Influence Coefficients ◽  
Parametric Studies ◽  
Combined Algorithm

This paper reports a new three-dimensional model for heat conduction in a half-space containing inhomogeneities, applicable to frictional heat transfer, together with a novel combined algorithm of the equivalent inclusion method (EIM) and the imaging inclusion approach for building this model. The influence coefficients (ICs) for temperature and heat flux are obtained via converting the frequency response function (FRF) and integrating Green's function. The model solution is based on the discrete convolution and fast Fourier transform (DC-FFT) algorithm using the ICs, convenient for solving problems involving multiple elliptical inhomogeneities with arbitrary orientations. A group of parametric studies are conducted for understanding the thermal fields in the inhomogeneous half-space due to surface frictional heating, influenced by the properties of the inhomogeneity, its depth, and orientation.

Three-Dimensional Dry/Wet Contact Analysis of Multilayered Elastic/Plastic Solids With Rough Surfaces

2005 ◽  
Vol 128 (1) ◽  
pp. 18-31 ◽  
Author(s):  
Shaobiao Cai ◽  
Bharat Bhushan
Keyword(s):  
Contact Area ◽  
Microelectromechanical Systems ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Multilayered Structure ◽  
Contact Analysis ◽  
Maximum Displacement ◽  
Elastic Plastic ◽  
Surface Displacements ◽  
Dry And Wet Conditions

Friction/stiction and wear are among the main issues in microelectromechanical systems (MEMS/NEMS) devices having contact interfaces. Relevant parameters, i.e., layers thickness, need to be optimized. The contact analyses of multilayered structure under both dry and wet conditions are necessary to optimize these parameters. This study presents a first attempt to perform three-dimensional contact analysis of multilayered solids with rough surfaces in both dry and wet conditions. The surface displacements and contact pressure distributions are obtained based on variational principle with fast Fourier transform scheme. The effective hardness is modeled and plays a role when the local displacement meets the maximum displacement criterion. Simulations are performed to obtain the contact pressures, fractional total contact area, fractional plastic contact area, surface/subsurface stresses. Relative meniscus forces are obtained with the presence of an ultrathin liquid film for different loads and layers properties. These contact statistics and meniscus forces are analyzed to study the effects of layer-to-substrate ratios of stiffness and hardness, and the layers thickness of rough, two-layered elastic/plastic solids. The methods to decrease friction/stiction and wear are investigated, and the optimum layer parameters are identified.

Damping in Lap Joints Due to Partial and Full Micro-Slip Using a Three Dimensional Elastic Contact of Rough Surfaces

2008 ◽  
Author(s):  
K. Farhang ◽  
A. Sepehri ◽  
D. Segalman ◽  
M. Starr
Keyword(s):  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Elastic Interaction ◽  
Lap Joints ◽  
Joint Interface ◽  
Flat Surfaces ◽  
Mechanical Joints ◽  
Statistical Sense ◽  
Scale Roughness

Energy dissipation in mechanical joints occurs as a result of micro-slip motion between contacting rough surfaces. An account of this phenomenon is especially challenging due to the vast differences in the length and time scale differences between the macro-mechanical structure and the micron-scale events at the joint interface. This paper considers the contact between two nominally flat surfaces containing micron-scale roughness. The rough surface interaction is viewed as a multi-sphere elastic interaction subject to a periodic tangential force. It combines the Mindlin’s formulation [1, 2] for the elastic interaction of two spheres with the Greenwood and Williamson’s [3] statistical approach for the contact of two nominally flat rough surfaces so as to develop a model for multi-sphere problem in which sphere radii, contact load and the number of spheres in contact can only be known in a statistical sense and not deterministically.

Validation of the Stress Predictions in Rolling EHL Contacts Having In-Line Roughness Using the Inverse Method

2006 ◽  
Vol 128 (4) ◽  
pp. 745-752 ◽  
Author(s):  
C. J. Hooke ◽  
K. Y. Li
Keyword(s):  
Fluid Flow ◽  
Inverse Method ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Plane Flow ◽  
Preliminary Results ◽  
Rolling Contacts ◽  
Out Of Plane ◽  
Transverse Roughness

Using modern EHL programs it is relatively simple to determine the pressures and clearances in rough EHL contacts. The pressures may then be used to calculate the subsurface stresses in the two contacting components. However, the results depend on the assumptions made about the fluid’s rheology. While it is possible to measure the clearances using interferometric techniques, measurement of either the pressures or stresses is extremely difficult. However it is these, rather than the clearances, that determine the life of the contact. In previous papers the authors have described how the inverse method may be used to validate the stress predictions for contacts with transverse roughness. This type of contact has fluid flow in only one plane and it remained necessary to check the results for more general rough surfaces where the flow is three-dimensional. Accordingly, the inverse method is extended, in this paper, to a situation where out-of-plane flow is significant. The paper describes the approach and presents some preliminary results for rolling contacts.

Reduced Rough-Surface Parametrization for Use With the Discrete-Element Model

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Stephen T. McClain ◽  
Jason M. Brown
Keyword(s):  
Heat Transfer ◽  
Rough Surface ◽  
Surface Characterization ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Three Dimensional ◽  
Element Model ◽  
Discrete Element ◽  
Diameter Distribution ◽  
Discrete Element Model

The discrete-element model for flows over rough surfaces was recently modified to predict drag and heat transfer for flow over randomly rough surfaces. However, the current form of the discrete-element model requires a blockage fraction and a roughness-element diameter distribution as a function of height to predict the drag and heat transfer of flow over a randomly rough surface. The requirement for a roughness-element diameter distribution at each height from the reference elevation has hindered the usefulness of the discrete-element model and inhibited its incorporation into a computational fluid dynamics (CFD) solver. To incorporate the discrete-element model into a CFD solver and to enable the discrete-element model to become a more useful engineering tool, the randomly rough surface characterization must be simplified. Methods for determining characteristic diameters for drag and heat transfer using complete three-dimensional surface measurements are presented. Drag and heat transfer predictions made using the model simplifications are compared to predictions made using the complete surface characterization and to experimental measurements for two randomly rough surfaces. Methods to use statistical surface information, as opposed to the complete three-dimensional surface measurements, to evaluate the characteristic dimensions of the roughness are also explored.

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