Fretting damage modeling of liner-bearing interaction by combined finite element – discrete element method
Highlights
► A combined method is proposed to analyze the fretting damage behavior. ► The continuous and discontinuous behavior of material under fretting condition is studied. ► The mechanism of fretting damage and its effect factors are discussed. ► A visualization technique is developed to dynamically display cracks and third-body particles.
Introduction
In general, fretting is defined as a small displacement oscillatory motion between two solids in contact. The fretting wear and fretting fatigue may become relevant failure mechanism when two or more solids in contact experience small reciprocating motion. Experimental and analytical investigations have shown that fretting process is a complex combination of science, relating to Tribology, Contact Mechanics, Fatigue; it is affected by 50 different variables [1]. In aeronautic and astronautic industries, fretting damage has been one of the most detrimental damage and it may cause catastrophic consequences.
Fretting damage has been reported and investigated for over 50 years. Scientists and engineers have occupied themselves to develop analytical solution, experimental measurement and numerical algorithm to study fretting problems. Cattaneo [2] and Mindlin [3] proposed independently the first analytical solutions to solve fretting problem; Goryacheva [4] developed an analytical model for fretting wear based on Archard wear equation; Kasarekar modeled the fretting contact between randomly generated three-dimensional rough contacts solving elasticity equations by Fast Fourier Transform [5].
Also, the fretting process has been experimentally evaluated via full scale test or coupon scale test using specially designed test rigs. However, main problems remained in experimental method include: (1) there has been no standard or generally accepted test rig for fretting experiment up to now. As a result, the experimental results obtained from different test rigs cannot be consistent with one another; (2) previous studies found that the evolution of fretting damage behavior was difficult to accurately measure in practice, such as the process of crack initiation and propagation inside specimen and dynamical behavior of third body particles between contact and target surfaces during fretting; also, it was impossible to control each of the different parameters involved without modifying the others.
More recently, with rapid development of multi-core CPU technique, it is possible to study fretting problem by means of numerical algorithm, such as finite element method (FEM), boundary element method (BEM), molecular dynamics (MD), discrete element method (DEM), and so on.
The FEM, based on continuum mechanics, has already been widely used to solve fretting problem. Earlier fretting models built upon earlier finite element models were used to study sliding wear [6], [7] and reciprocating sliding [8]; McColl [9] originally studied fretting wear using a commercial FEM software; Fouvry [10] and Paulin [11] developed finite element models to study fretting wear. In general, the processes of fretting analysis based on FEM can be more or less summarized as follows: (1) modeling contact and target solids to allow them to rub against each other along a given sliding distance under specified loading and boundary condition; (2) using an Archard-type law, the volume of matter that should be removed from material is calculated and the geometry feature is modified according to the loss volume for the next time step. The FEM-based method is able to solve non-linear contact problem with reasonable accuracy and computational efficiency, however, it is lack of capability or qualification to reproduce the discontinuous behavior of material during fretting process. For a FEM-based fretting simulation, the calculated results are strongly dependent on the parameters obtained from the corresponding experiment, such as the initially prescribed crack path and the wear coefficient of materials; the third body particles (debris) are not permitted to be retained in contact zone during fretting calculation. As a result, the FEM is not an ideal tool to solve fretting problem with high fidelity. It is necessary to develop an adequate algorithm to evaluate the discontinuous behaviors during fretting process.
The DEM, originally proposed by Cundall [12], [13] for geotechnical applications, has been an ideal tool to simulate discontinuous, heterogeneous, anisotropic medium behavior. More recently, scientists have successfully used the DEM to study material's fracture, damage, wear behaviors and contact mechanics between rough surfaces [14], [15], [16], [17], [18], [19], [20]. It has been proved that the DEM has a practical potential to simulate the evolution of crack initiation and propagation as well as the behavior of third body particles with high fidelity. However, the DEM is a time consuming algorithm in nature. Therefore, it is merely adopted to simulate assembly systems constructed by a relatively small amount of elements.
Considering the strengths and weaknesses of the FEM and the DEM for solving fretting problem, scientists have developed FE-DE coupled algorithm to solve fretting problem [21]. This algorithm is gaining popularity for problems involving contact modeling.
The aim of our current work is to develop a fundamental method to numerically analyze the fretting problem taking into account the discontinuous behavior of material and the balance between computational efficiency and accuracy. This paper is composed of five sections. In Section 2, a series of non-linear contact analyses are carried out by FEM. The risk position is predicted based on FFD method and FEM simulated results. In Section 3, a discrete element modeling technique is proposed and the microscopic parameters required by DEM are determined and calibrated. In Section 4, a series of DEM simulations are performed. The mechanisms of fretting wear and fatigue are investigated. A crack visualization technique is proposed to display cracks according to their failure mode and/or time dependency. The effect of fretting condition on crack initiation and propagation as well as fretting damage is studied. Section 5 concludes the paper.
Section snippets
FE modeling
In our research, the ‘shaft-bearing-liner’ assembly is modeled in the global coordinate system. A constant radial force Fr and different fretting amplitudes δapp are employed during FEM simulation. Fig. 1 shows the geometrical and physical model of this assembly.
In order to improve the computational efficiency, the initial ‘shaft-bearing-liner’ assembly model (Fig. 1) is simplified, and the equivalent loading and boundary conditions are employed. The simplified FE model is plotted in Fig. 2(a).
Rebuild the sub-model by DEM
In general, metallic material has a polycrystalline structure, which is made up of a large quantity of grains on a microscopic scale [1]. As a result, we rebuild the sub-model extracted from the initial FE model by means of assemblies of cylinder-like elements with unit thickness. The DE model and its loading/ boundary conditions are represented in Fig. 4.
Crack damage analysis
The accumulated crack number and crack distribution in the degradable model are used as critical quantities for the investigation of fretting damage caused by cracks; corresponding numerical results are presented in Fig. 11, Fig. 12, Fig. 13. Furthermore, for the sake of clarity, a crack visualization technique is developed to display cracks in the degradable model according to their failure modes and time dependency. In Fig. 11(a), we use blue lines to represent cracks formed by tensile
Conclusion and prospects
This paper presents a methodology to study the fretting damage behavior by combined FE-DE method based on FFD method and CBDM. The inter-element contact constitutive model as well as its microscopic parameters are determined and calibrated in order to reproduce continuous and discontinuous behaviors of material in DEM simulation. A crack visualization technique is developed to display cracks according to their failure mode and/or time dependency. Three non-dimensional parameters are introduced
Acknowledgments
This project was partially supported by the China Aviation Science Fund Project under grant No.2011ZB08002. The authors would like to acknowledge the anonymous reviewers for their invaluable suggestions that helped improve the manuscript, and thank Dr. Shuyan Hu and Mr. Shuo Liu for improvement in the grammar of the manuscript. Finally, thanks are due to Prof. Yunbo Shen and Mr. Bin Ouyan for useful discussion of the results presented here.
References (38)
- et al.
Modeling of fretting wear evolution in rough circular contacts in partial slip
International Mechanical Sciences
(2007) - et al.
Simulation sliding wear with finite element method
Tribology International
(1999) Numerical simulations of mild wear using updated geometry with different step size approaches
Wear
(2001)- et al.
Finite element simulation and experimental validation of fretting wear
Wear
(2004) - et al.
A global-local wear approach to quantify the contact endurance under reciprocating-fretting sliding conditions
Wear
(2007) - et al.
Finite element modeling of fretting wear surface evolution
Wear
(2008) - et al.
Modeling third body flows with a discrete element method-a tool for understanding wear with adhesive particles
Tribology International
(2007) - et al.
Discrete element method (DEM) modeling of fracture and damage in the machining process of polycrystalline SiC
Journal of the European Ceramic Society
(2009) - et al.
Normal contact between rough surfaces by the discrete element method
Tribology International
(2012) - et al.
A discrete element model to investigate sub-surface damage due to surface polishing
Tribology International
(2008)
Discrete element method to simulate continuous material by using the cohesive beam model
Computer Methods in Applied Mechanics and Engineering
Discrete element method to simulate continuous material by using the cohesive beam model
Computer Methods in Applied Mechanics and Engineering
New method for simulating fracture using an elastically uniform random geometry lattice
International Journal of Engineering Science
Stress–strain relationship for granular materials based on the hypothesis of best fit
International Journal of Solids and Structures
The third body approach: a mechanical view of wear[J]
Wear
Sul contatto di due corpi elastici: distribution locale degli sforzi
Rend Accad Naz Lincei
Compliance of elastic bodies in contact
Journal of Applied Mechanics—ASME
Wear in partial slip contact
Journal of Tribology—the ASME
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2017, Journal of Materials Processing TechnologyCitation Excerpt :Rojek et al. (2005) simulated the process of sand filling cavity with the two-dimensional FE-DE coupling approach. Li et al. (2013) proposed a FE-DE method to analyze the fretting damage behavior of the bearing. However, the finite element analysis used in above method is only limited to the strength problem of elastic deformation, but not involved the research in coupling deformation process of discrete body with plastic deformation body.
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2017, Mechanism and Machine TheoryCitation Excerpt :Because of multi-contact conditions, the contact algorithm must be robust and studies are conducted on a part of the entire bearing. Some authors associate the FEM and multibody methods for fatigue analysis [25,26]. In order to understand wear mechanisms leading to damage, a dynamic modeling of the entire component including cage and rings is required.