Home Page of Professor Q. Jane Wang

FFT-Based Computational Contact Mechanics

Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. However, rough surfaces, complicated materials, and intertwined fields make modeling and simulations difficult and time consuming.  The mathematical nature of the relationship between an excitation and a body response is either in the form of a convolution or correlation, or partial differential equations, solvable by means of a Fourier-transform algorithm, thus converting a tedious integration operation into multiplication accompanied by Fourier and inverse Fourier transforms with a great computational efficiency.   Both computational accuracy and efficiency are crucial to involving contact mechanics as a module in the digital twins for components and systems under contact and relative motion. Built on this, Professor Wang’s group created the first and a series of efficient and accurate fast Fourier transform (FFT) methods for computational contact mechanics and frictional heat transfer of rough surfaces and engineering materials, enabling fast simulation of microscopic solid asperity interaction in macroscopic contact and frictional heating, which are the basis and a backbone of computational mechanotribology. 

It is important to note that different contact types require different convolution theorems and thus different FFT algorithms, and with these, even the influence coefficients (ICs) from the 0-order shape function are sufficient to an achieve high accuracy in most cases.  Her group compared different contact types with different convolution theorems in signal processing and quantified the mathematical nature of point-contact, line-contact, and nominally flat-flat contact problems of rough surfaces. Each convolution theorem must be properly used to model one particular type of contact problem. Based on this understanding, her team has developed a tree of accurate algorithms for solving rough-surface contact problems precisely and efficiently, including 1) discrete-convolution and fast-Fourier-transform (DC-FFT) with one time domain extension for non-periodic point-contact problems, which was the ground-breaking work of this series, and the discrete-convolution and fast-Fourier-transform algorithm (DC-FFT) without domain extension for plain-strain cylindrical-contact problems; 2) continuous-convolution and Fourier-transform (CC-FT) for periodic (or infinite) contact problems; 3) discrete convolution with duplicated padding and FFT (DCD-FFT), discrete-continuous convolutions and FFT (DC-CC-FFT), and discrete convolution with IC summation and FFT (DCS-FFT) for 3D line-contact problems that are periodic (or infinite) in one direction but non-periodic in the other direction; 4) a uniform DCSS-FFT (the added S means IC summation in the other direction as well) and non-uniform DCS-FFT method for solving large-scale contact problems; 5) discrete-convolution-correlation and FFT (DCR-FFT) for contact problems involving eigenstrain-containing materials; and 6) frequency response function and influence-coefficient conversion (FRF-IC) for contact problems involving layered materials, anisotropic elastic materials, and viscoelastic polymers, or those subjected to multi-fields. From 6), her team derived two set of extended Hertz formulae for contacts of coated surfaces and an approach for non-destructive thin-film property determination. The frequency-domain operation enables the FFT-based method to solve more and wider physical problems related to contact, benefiting from transforming partial differential equations into the frequency domain. The figure here summarizes the FFT algorithms and the application fields in a tree. The roots of this tree are the essential analytical solutions to mechanics and physical problems in the forms of integral equations with Green’s functions, which lead to ICs, or in the form of partial differential equations, which lead to frequency response functions. These FFT-based methods have been widely used in the research communities worldwide (e.g., INSA Lyon, France; Tsinghua U., China; NIT, India; U. Leeds, UK, U. Freiburg, Germany,  EPFL, Switzerland). These FFT-based methods make tough and tedious issues simpler and many engineering problems solvable in a reasonable time.

These theories and methods have supported her group on the development of industrial application software sets for simulation-based powertrain-drivetrain component R&D, now used in Caterpillar, ExxonMobil, Ford, GM, Mazda, NSK, Timken, TimkenSt, and Valvoline, as well as Mazda, Nissan and NSK in Japan, either in company-wide design platform or standing alone design/analysis software. The application of this method group in her work with BRP US has contributed to the global launch of BRP’s new generation of Evinrude E-TEC engines in 2014.

Software download

Related Publications

1. Liu, S., Wang, Q., and, Liu, G., 2000, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses,” Wear, Vol. 243, pp. 101-111. https://www.sciencedirect.com/science/article/pii/S0043164800004270.
2. Liu, S. and Wang, Q., 2002, “Studying Contact Stress Fields Caused by Surface Tractions with a Discrete Convolution and Fast Fourier Transform Algorithm,” ASME Journal of Tribology, Vol. 124, pp. 36-45. https://doi.org/10.1115/1.1401017.
3. Chen, W. W., Liu, S. B., and Wang, Q., 2008, “Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces,” Journal of Applied Mechanics, Vol. 75, 011022-1-11. https://doi.org/10.1115/1.2755158.
4. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York. https://sites.northwestern.edu/qianwang/interfacial-mechanics/
5. Wang, Q., Sun, L., Zhang, X., Liu, S., and Zhu, D., 2020, “FFT-Based Methods for Computational Contact Mechanics,” Frontiers in Mechanical Engineering. 6:61. https://doi.org/10.3389/fmech.2020.00061.
6. Sun, L., Wang, Q., Zhao, N., and Zhang, M., 2021, “Discrete Convolution and FFT Modified with Double Influence-Coefficient Superpositions (DCSS-FFT) for Contact of Nominally Flat Heterogeneous Materials Involving Elastoplasticity,” Computational Mechanics, Vol. 67, pp 989–1007. https://doi.org/10.1007/s00466-021-01980-z.

Computational Contact Micromechanics

Materials are complicated in structures and defects; it is nearly impossible, or inefficient, to involve a time-consuming procedure in the analysis of a tribological interface. Professor Wang and co-workers have done a series of ground-breaking work of computational contact micromechanics and created an integrated modeling system for contact of materials involving eigenstrains, or inelastic strains.  Computational contact micromechanics starts from Love-Mindlin’s theories of strain nuclei, Yu-Sanday’s analytical Galerkin vectors, extends Eshelby’s equivalent-inclusion method (EIM) to numerical EIM, or NEIM, solves core solutions to eigenstrain induced fields in terms of analytical influence coefficients, and converts material inhomogeneities into equivalent eigenstrains subjected to contact and frictional loading. Inhomogeneities such as reinforcements, coatings, thermal mismatch, impurities, defects, voids, inclusions, residual strains, contact plasticity and thermal strains are all unified into the same mathematic formulation system for the fields caused by eigenstrains in a contact setting.  The integration of the core analytical equations is resolved into three-dimensional convolutions and correlations, and the computation-method development has resulted in a novel discrete-convolution-correlation (DCR)-FFT algorithm.  This unified approach has been extended to materials joined with imperfect interfaces. Moreover, her recent cross-field analogy theory for elasticity, chemical diffusion, heat transfer, and electromagnetics, has further extended the NEIM concept and Galerkin vectors to the fields of thermal, diffusion, and electromagnetics for inhomogeneous materials.

These theories and methods have supported her group on the development of industrial application software sets for materials and component R&D, now used in Timken and TimkenSteel in their company-wide design platforms.

Software download: half-space contact micromechanics; Join half-space eigenstrain problems

Related Publications

1. Liu, S. and Wang, Q., 2005, “Elastic Fields Due to Eigenstrains in a Half-space,” ASME Journal of Applied Mechanics, Vol. 72, pp. 871-878. https://doi.org/10.1115/1.2047598
2. Chen, W., W., Zhou, K., Keer, L. M., and Wang, Q., 2010, “Modeling Elasto-plastic Indentation on Layered Materials Using the Equivalent Inclusion Method,” International Journal of Solids and Structures, doi:10.1016/j.ijsolstr.2010.06.011, Vol. 47, 2841–2854.
3. Zhou, K., Chen, W. W., Keer, L. M., Ai, X., Sawamiphakdi, K., Glaws, P., and Wang, Q., 2011, “Multiple 3D Inhomogeneous Inclusions in a Half Space under Contact Loading,” Mechanics of Materials, Volume 43, Issue 8, pp. 444-457. https://doi.org/10.1016/j.mechmat.2011.02.001.
4. Liu, S., Jin, X., Wang, Z., Keer, L.M., and Wang, Q., 2012, “Analytical Solution for Elastic Fields Caused by Eigenstrains in A Half-Space and Numerical Implementation Based on FFT,” International Journal of Plasticity, Vol. 35, pp. 135–154. http://dx.doi.org/10.1016/j.ijplas.2012.03.002.
5. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York. https://sites.northwestern.edu/qianwang/interfacial-mechanics/
6. Li, D., Wang, Q., Zhang, M., Hegedu, P., and Glaws, P., 2022, “Deformation and stress in materials with inhomogeneity/void under contact loading,” Mechanics Research Communications. https://www.sciencedirect.com/science/article/pii/S0093641322000118
7. Shi, X., Wang, Q., and Wang, L., 2019, “New Galerkin-Vector Theory and Efficient Numerical Method for Analyzing Steady-State Heat Conduction in Inhomogeneous Bodies Subjected to a Surface Heat Flux,” Journal of Applied Thermal Engineering, Vol. 161, 113838. https://doi.org/10.1016/j.applthermaleng.2019.113838
8. Zhang, X. and Wang, Q., 2022, “A Unified Analogy-Based Computation Methodology from Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing,” ASME Open Journal of Engineering, invited, Inaugural issue. https://doi.org/10.1115/1.4053910.

Computational Friction Heat Transfer, Electrical Contacts, and Electro-Thermomechanical Interfaces

Frictional heating, produced by asperity rubbing, material transform, and viscous dissipation, is a serious problem because accumulated heat can trigger a chain of events from thermal growth, junction expansion, to scuffing of surfaces and seizure failure of interfaces.  Heat partition between the interactive surfaces and heat source on each surface are distributed and location dependent, affected by the level of asperity rubbing and the velocity of the relative motion. Furthermore, electrical current can subject the interfaces to stronger stress and thermal fields. Professor Wang’s group pioneered deterministic and fast computations of frictional thermomechanical interfaces and electro-thermomechanical interfaces formed by engineered surfaces via the DC-FFT algorithm and the frequency-domain solutions.  Models for interfacial heat transfer and thermomechanical fields in rough surface under contact elastoplasticity, layered materials, materials with inhomogeneities, and viscoelastic polymers, as well as TEHL, have also been developed, and the modeling systems have been applied in industrial product developments and defense equipment research. 

Related Publications

1. Liu, S., Wang, Q., and, Liu, G., 2000, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses,” Wear, Vol. 243, pp. 101-111. https://www.sciencedirect.com/science/article/pii/S0043164800004270.
2. Liu, S. and Wang, Q., 2001, “A Three-Dimensional Thermomechanical Model of Contact between Non-Conforming Rough Surfaces,” ASME Journal of Tribology, Vol. 123, pp. 17-26. https://doi.org/10.1115/1.1327585.
3. Liu, S., Wang, Q., Rodgers, M., Keer, L. M., and Cheng, S. H., 2002, “Temperature Distributions and Thermoelastic Displacements in Moving Bodies,” Computer Modeling in Engineering and Sciences, 3, pp. 465-481. TSP_CMES_26606 (1).pdf
4. Liu, S. and Wang, Q., 2003, “Transient Thermoelastic Stress Fields in a Half-space,” ASME Journal of Tribology, Vol. 125, pp. 33-43. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1069.2605&rep=rep1&type=pdf
5. Martini, A., Liu, S., and Wang, Q., 2005, “Transient Three-Dimensional Solution for Thermoelastic Displacement Due to Surface Heating and Convective Cooling,” ASME Journal of Tribology, Vol. 127, pp. 750-755. https://doi.org/10.1115/1.1924574.
6. Kim, W.-S. and Wang, Q., 2006, “Numerical Computation of Surface Melting at Imperfect Electrical Contact between Rough Surfaces,” Proceedings of the 2006 IEEE Holm Conference, pp. 81-88.
7. Kim, W.-S., Wang, Q., Liu, S., and Asta, M., “Simulation of Steady and Unsteady Surface Temperatures under Sliding Imperfect Electrical Contact between Rough Surfaces,” Proceeding of the 23^rd International Conference on Electric Contacts, pp. 226-231.
8. Chen, W. W. and Wang. Q., 2008, “Thermomechanical Analysis of Elasto-Plastic Bodies in a Sliding Spherical Contact and the Effects of Sliding Speed, Heat Partition, and Thermal Softening,” Journal of Tribology, Vol. 130, pp. 041402-1-10. https://doi.org/10.1115/1.2959110.
9. Chen, W., W., Wang, Q., and Kim, W., 2009, “Transient Thermomechanical Analysis of Sliding Electrical Contact of Elasto-Plastic Bodies, Thermal Softening and Melting Inception,” Journal of Tribology, Vol. 131, pp. 021406-1-10. https://doi.org/10.1115/1.3084214.
10. Liu, Z., Pickens, III D., He, T., Zhang, X., Liu, Y., Nishino, T., and Wang, Q., 2019, “A Thermal Elasto-Hydrodynamic Lubrication Model for Crowned Rollers and its Application on Apex Seal-Housing Interfaces,” Journal of Tribology, Vol. 141, https://doi.org/10.1115/1.4042503.
11. He, T., Wang, Q., Zhang, X., Liu, Y., Li, Z., Kim, H. J., and Park, S., 2021, “Modeling Thermal-Visco-Elastohydrodynamic Lubrication (TVEHL) Interfaces of Polymer-Based Materials,” Tribology International, 154, 106691, https://doi.org/10.1016/j.triboint.2020.106691.
12. Shi, X., Wang, L., Zhou, Q., and Wang, Q., 2018, “A Fast Approximate Method for Heat Conduction in an Inhomogeneous Half Space Subjected to Frictional Heating,” Journal of Tribology, Vol. 140 (4), 041101, https://doi.org/10.1115/1.4038953.
13. Zhang, X. and Wang, Q., 2022, “A Unified Analogy-Based Computation Methodology from Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing,” ASME Open Journal of Engineering, invited, Inaugural issue. https://doi.org/10.1115/1.4053910.
14. Zhang, X., Wang, Q., He, T., Liu, Y., Li, Z., Kim, H., Park, S.,  2022, “Fully Coupled Thermo-Viscoelastic (TVE) Contact Modeling of Layered Materials Considering Frictional and Viscoelastic Heating,” Tribology International. Vol. 170, June, 107506, https://doi.org/10.1016/j.triboint.2022.107506.

Computational Contact Thermo-Viscoelasticity and TVEHL

Professor Wang and co-workers have developed a novel modeling system for transient and steady-state thermoviscoelastic (TVE) responses of a polymer-based material as a layer, a substrate, or the entire body, considering imperfect material interfaces, subjected to sliding/rolling, frictional heating, and lubrication. This group of the work have resulted in novel analytical transient and steady-state viscoelastic frequency response functions (FRFs) derived from our elastic solutions with imperfect interfaces. Instead of using the integration form of the creep function, viscoelastic modulus is directly incorporated into the viscoelastic FRFs by a novel time-space frequency transform that links the time-related frequency and sliding velocity  with the space-related frequency number. The solutions are so formulated that fast numerical techniques, such as our discrete convolution-fast Fourier transform (DC-FFT) algorithm, can be incorporated for computation efficiency. The design parameters like layer thickness, material viscoelastic and heat-transfer properties, creep functions, sliding velocity, and the degree of interface imperfection, as well as lubricant properties, are all included in the models. The TVE models have been extended to lubrication models, such as thermo-viscoelasto-hydrodynamic lubrication (TVEHL), for the interfaces of components made of polymer-based materials. The research has resulted in several maps for the design of contact-lubrication interfaces of polymer-based materials.

These theories and methods have supported her group on the development of industrial application software sets for materials and component R&D, now used in GM.

Related Publications

1. Chen, W. W., Wang, Q., Zhang, H., and Luo, X., 2011, “Semi-Analytical Viscoelastic Contact Modeling of Polymer-Based Materials,” Journal of Tribology, Vol. 133, 041404-1-10. https://doi.org/10.1115/1.4004928.
2. Yu, H., Zhe L., Jiang, B., Poldneff, M., Burkhart, C., Liu, W. K., and Wang, Q., 2015, “Determination of the Viscoelastic Interfacial Properties between Silica and SNR-Based Materials via a Semi-Empirical Approach,” Mechanics of Materials, Vol. 80, Part A, pp. 1–12. http://www.sciencedirect.com/science/article/pii/S0167663614001744.
3. Yu, H., Zhe, L., and Wang, Q., 2013, “Viscoelastic-Adhesive Contact Modeling: Application to the Characterization of the Viscoelastic Behavior of Materials,” Mechanics of Materials, Vol. 60, pp 55-65. http://dx.doi.org/10.1016/j.mechmat.2013.01.004.
4. Zhang, X., Wang, Q., and He, Tao, 2020, “Transient and Steady-State Viscoelastic Contact Responses of Layer-Substrate Systems with Interfacial Imperfections,” Journal of the Mechanics and Physics of Solids, Vol. 145, 104170, https://authors.elsevier.com/a/1byGO57Zjx1Y2.
5. He, T., Wang, Q., Zhang, X., Liu, Y., Li, Z., Kim, H. J., and Park, S., 2021, “Modeling Thermal-Visco-Elastohydrodynamic Lubrication (TVEHL) Interfaces of Polymer-Based Materials,” Tribology International, 154, 106691, https://doi.org/10.1016/j.triboint.2020.106691.
6. He, T., Wang, Q., Zhang, X., Liu, Y., Li, Z., Kim, H., and Park, S., 2021, “Visco-Elastohydrodynamic Lubrication of Layered Materials with Imperfect Layer-substrate Interfaces,” International Journal of Mechanical Sciences, Vol. 189, 105993, https://doi.org/10.1016/j.ijmecsci.2020.105993.
7. Zhang, X., Wang, Q., He, T., Liu, Y., Li, Z., Kim, H., Park, S.,  2022, “Fully Coupled Thermo-Viscoelastic (TVE) Contact Modeling of Layered Materials Considering Frictional and Viscoelastic Heating,” Tribology International.

AI-Assisted Design and Data-Technology Supported Property/Performance Predictions

Professor Wang is among the first to implement AI and data technologies in tribology.  Her group developed an AI-assisted method for worn surface simulation, in 2002, which only requires a small number of wear tests, from which worn surfaces are measured at a finite number of time intervals in the wear process. An artificial neural network (ANN) was built and trained with the statistical parameters obtained from the measurements. The trained ANN was then used to predict the wear-dependent statistical parameters for any surfaces in the group. With the original statistical parameters of the unworn surface and their variation due to wear predicted by ANN, the simulation process can generate the corresponding 3-D worn surface with respect to a desired duration within the wear process.

Her group has also developed a science-based data-driven optimization approach for engine-bearing surface design. The data driven approach constructed the bearing design space, and the Pareto optimization and sensitivity analysis methods helped analyze the data and provide insight to the design. The most influential parameter for the optimal bearing surface design for energy-efficient lubrication performance was identified and the optimized design was achieved.  This work has assisted Ford engineers in a new product development and resulted in a software package for their R&D.  

In addition, lubricant property prediction formulas have been obtained through an approach of integrated MD simulation and experimental measurements, supported by data analyses.  These formulas have been provided to Valvoline for new product design and analysis. Properties of anode metals in solid-state batteries have been determined through analyzing the data obtained from using a simulation-experiment approach, and the results well agree with published measurement data. 

Related Publications

1. Ao, Y., Wang, Q., and Chen, P., 2002, “Simulating the Worn Surface in a Wear Process,” Wear, 252, pp.37-47. https://doi.org/10.1016/S0043-1648(01)00841-9.
2. Liu, P., Yu, H., Ren, N., Lockwood, F. E., and Wang, Q., 2015, “Pressure-Viscosity Coefficient of Hydrocarbon Base Oil through Molecular Dynamics Simulations,” Tribology Letters, Vol. 65, paper 34. http://link.springer.com/article/10.1007%2Fs11249-015-0610-6.
3. Lu, J., Wang, Q., Ren, N., and Lockwood, F., 2019, “Correlation between Pressure-Viscosity Coefficient and Traction Coefficient of the Base Stocks in Traction lubricants: A Molecular Dynamic Approach,” Tribology International, Vol. 134, pp, 328–334. https://doi.org/10.1016/j.triboint.2019.02.013.
4. Gu, T., Wang, Q., Gangopadhyay, A., and Liu, Z., 2020, “Journal Bearing Surface Topography Design Based on Transient Lubrication Analysis,” Journal of Tribology. DOI: 1115/1.4046289, https://doi.org/10.1115/1.4046289.
5. Zhang, X., Wang, Q., Harrison, K. L., Roberts, S. A, and Harris, S. J., 2020, “Pressure-Driven Interface Evolution in Solid State Lithium Metal Batteries,” Cell Reports Physical Science, Vol. 1 (2), 100012, https://doi.org/10.1016/j.xcrp.2019.100012.
6. Ahmed, J., Shi, J., Lu, J, Ren, N., Lockwood, F., and Wang, Q., 2021, “A Novel Method for Fluid Pour-Point Prediction by Molecular Dynamics Simulations,” Tribology Transactions, Vol. 64, 4, pp. 721-729,  http://dx.doi.org/10.1080/10402004.2021.1910391.

Mixed Lubrication Modeling and Simulation

Mixed lubrication, with both fluid and asperity contact pressures, is a regime between full-film and boundary lubrication regimes, encountered in all machinery. Numerical modeling requires precise and efficient determination of fluid-asperity and asperity-asperity interactions. Prof. Wang and co-workers developed the first precise method to solve multi-asperity fluid-solid interaction for lubricant flow through the interface channel with interactive roughness asperities, enabling efficient integration of FFT-based contact mechanics with Reynolds equation to model mixed asperity contact and elastohydrodynamic lubrication, key to the simulation of interface failure. Over the years, Professor Wang and co-workers have developed rough-surface differential schemes and accurate expressions of fluid-asperity interaction. Combining these with the models for computational contact mechanics/micromechanics,  the team has built numerical tools for  mixed-lubrication simulation of parts of materials with contact elastoplasticity, viscoelasticity, and inhomogeneities like coatings, particles, and defects, with applications in industries for gear, bearing, materials, and lubricant manufacturing.  The team has conducted wide ranges of mixed-lubrication analyses of machined and patterned surfaces and discovered the principles for roughness/texture design to promote lubrication and reduce friction.  More on surface designs for low friction and high contact fatigue resistance can be found in Science of Tribological Interface. 

These theories and methods have supported her group on the development of industrial application software sets for component and lubricant R&D, now used in Baker Hughes, Caterpillar, Eaton, Exxon Mobil, GM, Mazda, NSK, and Valvoline, either in company-wide design platforms or as standing-alone design/analysis software. 

Related Publications

1. Liu, Y., Wang, Q., Hu, Y., Wang, W., and Zhu, D., 2006, “Effects of Differential Schemes and Mesh Density on EHL Film Thickness in Point Contacts,” ASME Journal of Tribology, Vol. 128, pp. 641-653. https://doi.org/10.1115/1.2194916.
2. Liu, Y., Wang, Q., Zhu, D., Wang, W., and Hu, Y., 2009, “Effects of Differential Scheme and Viscosity Model on Rough-Surface Point-Contact Isothermal EHL,” Journal of Tribology, Vol.131, Iss.4, pp. 044501-1-5, https://doi.org/10.1115/1.2842245.
3. Zhu, D. and Wang, Q., 2013, “Effect of Roughness Orientation on the EHL Film Thickness,” Journal of Tribology, 135 (3), 031501-1-9. doi:10.1115/1.4023250.
4. Zhu, D., Ren, N., and Wang, Q., 2009, “Pitting Life Prediction Based on 3-D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress Calculation,” Journal of Tribology, Vol. 131/ 041501-1.
5. Liu, Y., Wang, Q., Krupka, I., Hartl, M., and Bair, S., 2008, “The Shear-Thinning Elastohydrodynamic Film Thickness of a Two-Component Mixture,” Journal of Tribology, Vol. 130, pp. 021502-1-7. https://doi.org/10.1115/1.2842298.
6. Ren, N., Zhu, D., Chen, W. W., Liu, Y., and Wang, Q., 2009, “A Three-Dimensional Deterministic Model for Rough Surface Line-Contact EHL.” Journal of Tribology, Vol. 131, pp. 011501-1-9, https://doi.org/10.1115/1.2991291.
7. Ren, N., Zhu, D., Chen, W. W., and Wang, Q., 2010, “Plasto-Elastohydrodynamic Lubrication (PEHL) in Point Contact,” Journal of Tribology, Vol. 132, 031501-1, DOI: 10.1115/1.4001813.
8. Zhu, D. and Wang, Q., 2011, “Elastohydrodynamic Lubrication (EHL): A Gateway to Interfacial Mechanics – Review and Prospect,” Journal of Tribology, Vol. 133, 041001-1-14. https://doi.org/10.1115/1.4004457.
9. Liu, Z., Pickens, III D., He, T., Zhang, X., Liu, Y., Nishino, T., and Wang, Q., 2019, “A Thermal Elasto-Hydrodynamic Lubrication Model for Crowned Rollers and its Application on Apex Seal-Housing Interfaces,” Journal of Tribology, Vol. 141, doi: 10.1115/1.4042503.
10. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York. https://www.crcpress.com/Interfacial-Mechanics-Theories-and-Methods-for-Contact-and-Lubrication/Wang-Zhu/p/book/9781439815106.
11. Liu, S., Wang, Q., Chung, Y. W., and Berkebile, S., 2021, “Lubrication-Contact Interface Conditions and Novel Mixed/Boundary Lubrication Modeling Methodology,” Tribology Letters, 69:164. https://doi.org/10.1007/s11249-021-01515-w.

Computational Frictional Contact of Multi-Layered Materials

Multilayer coatings are often seen in surface engineering for surface modifications. Optimal design of the multilayered materials requires the understanding of their mechanical behaviors based on deformation and stress analyses. The frequency response functions (FRFs) of the displacement and stress fields in multilayered materials under unit normal and shear loadings are the analytical cores for solving the contact of such materials. Professor Wang and co-worker have successfully derived these functions by utilizing the Papkovich-Neuber potentials and appropriate boundary conditions. Two matrix equations containing unknown coefficients in the FRFs are established by following the structure rules, and then the closed-form FRFs written in a recurrence format are established. A fast numerical semi-analytical model based on the derived FRFs and DC-FFT is further developed for investigating the elastic contact of multilayered materials with any desired material design. Methods for solving fretting contact problems and EHL of multilayered materials have also been developed.

Related Publications

Yu, C., Wang, Z., and Wang, Q., 2014, “Analytical Frequency Response Functions for Contact of Multilayered Materials,” Mechanics of Materials, Vol. 76, pp. 102–120.

Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York.

CMP Simulation

In a chemical-mechanical planarization (CMP) system, the contact between a polishing pad and a wafer is critical for achieving high-quality planar surface finish. Professor Wang’s group has developed a deterministic  model for the interface a rough bi-layer pad and a wafer. Homogenized or equivalent material properties were obtained and utilized for modeling each layer.  The simulated pad-wafer contact areas were compared with the results from optical contact measurements for model verification. The application region of the bi-layered model was determined, and a map for the use of the bi-layer contact model was generated. In addition, a collaborative research has resulted in a mixed three-dimensional soft elastohydrodynamic lubrication  model with asperity contact for CMP simulation. A set of simulation code has been delivered to Cabot R&D.

Software download (to come)

Related publications

Jin, X., Keer, L. M., and Wang, Q., 2005, “A Three Dimensional EHL Simulation of CMP: Theoretical Framework of Modeling,” Journal of the Electrochemical Society, v 152, pp. G7-G15.

Yu, C., Wang, Z., Sun, F., Lu, S., Keer, L. M., and Wang, Q., 2013 “A Deterministic Semi-Analytical Model for the Contact of a Wafer and a Rough Bi-Layer Pad in CMP,” ECS Journal of Solid State Science and Technology, Vol. 2 pp. 368-374. http://jss.ecsdl.org/content/2/9/P368.full.pdf

Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York.

https://www.crcpress.com/Interfacial-Mechanics-Theories-and-Methods-for-Contact-and-Lubrication/Wang-Zhu/p/book/9781439815106

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Computational Conformal-Contact Interfacial Mechanics and TEHL

A conformal interface is formed by a concave and a convex surface of nearly the same geometry, and the clearance between the two is provided by tolerance. A journal bearing set is a good example of the the conformal-contact elements, and the interface is under contact and sliding, subjected to a long pass of surface interaction and vulnerable to scuffing and seizure. Professor Wang’s group has developed the first mixed-TEHL model set for journal-bearing types of conformal interfaces and applied it to the rock-drilling bit design for Baker Hughes. The modeling system considers the effects of roughness, heat transfer, elasticity, and journal-thrust bearing coupling. Her group has also developed R&D codes for automotive ICE engine bearings (used in Ford and GM) and a vehicle pump system with the ability to do surface design. 

Related Publications

1. Shi, F. and Wang, Q., 1998, “A Mixed-TEHD Model for Journal Bearing Conformal Contacts, Part I: Model Formulation and Approximation of Heat Transfer Considering Asperity Contacts,” ASME Journal of Tribology, Vol. 120, pp. 198-205.
2. Shi, F. and Wang, Q., 1998, “A Method of Influence Functions for Thermal Analyses of Tribological Elements,” Tribology Transactions, Vol. 41, 350-358.
3. Wang, Q., Shi, F. and Lee, S., 1998, “A Mixed-TEHD Model for Journal Bearing Conformal Contacts, Part II: Contact, Film Thickness, and Performance Analyses,” ASME Journal of Tribology, Vol. 120, pp. 206-213.
4. Wang, Y., Zhang, C., Wang, Q., and Lin, C., 2002, “A Mixed-TEHD Analysis and Experiment of Journal Bearings under Severe Operating Conditions,” Tribology International, Vol. 35, pp 395-407.
5. Wang, Y., Wang, Q., and Lin, C., 2003, “Mixed Lubrication of Coupled Journal-Thrust-Bearing Systems Including Mass Conserving Cavitation,” ASME Journal of Tribology, Vol. 125, pp. 747-755.
6. Xiong, S. and Wang, Q., 2012, “Steady-State Hydrodynamic Lubrication Modeled with the Payvar-Salant Mass Conservation Model,” Journal of Tribology, Vol. 134 / 031703-1-16. http://asmedl.org/journals/doc/JOTRE9-ft/vol_134/iss_3/031703_1.html.
7. Ma, X., Wang, Q., Lu, X., and Mehta, V., 2018, “A Transient Hydrodynamic Lubrication Model for Piston/Cylinder Interface of Variable Length,” Tribology International, Vol. 118, pp. 227-239. http://www.sciencedirect.com/science/article/pii/S0301679X17304504
8. Ma, X., Lu, X., Mehta, V. S., and Wang, Q., 2019, “Piston Surface Design to Improve the Lubrication Performance of a Swash Plate Pump,” Tribology International, Vol. 132, pp. 275-28. https://doi.org/10.1016/j.triboint.2018.12.023.
9. Gu, T., Wang, Q., Xiong, S., Liu, Z., Gangopadhyay, A., and Lu, Z., 2019, “Profile Design for Misaligned Journal Bearings Subjected to Transient Mixed-Lubrication,” Journal of Tribology. 141(7): 071701, https://doi.org/10.1115/1.4043506
10. Gu, T., Wang, Q., Gangopadhyay, A., and Liu, Z., 2020, “Journal Bearing Surface Topography Design Based on Transient Lubrication Analysis,” Journal of Tribology. DOI: 1115/1.4046289, https://doi.org/10.1115/1.4046289.