Experimental validation of FEM for frictional contacts.
Piscan, Iuliana ; Janssens, Thierry ; Predincea, Nicolae 等
Abstract: Experimental validation of FEM is required to assure
accurate results and to be able to update FE models, such that their
simulation can be trusted and used in design. Here, the correlation
between experimental results, coming from a flat on flat frictional
contact on a tribometer, with its simulation in Ansys Workbench is
discussed and validated. The validation is performed for two commonly
used materials, viz. PVC and AI, and the normal load and displacement
dependency of the frictional behaviour is also taken into account. It is
shown that, by using appropriate inputs and an optimised representation
of the non-linear frictional behaviour, an accurate frictional contact
simulation is obtained
Key words: friction, contact, FEM, normal load, displacement
1. INTRODUCTION
Friction is unavoidably present in many mechanical systems. Their
performance is considerably influenced by contact stiffness parameters
which are determining the behaviour of their intrinsic connections such
as flat on flat contacts or bolted connections. Stiffness effects on the
performance of mechanical systems are due to the influence of
deformations on static and fatigue strength, wear resistance, efficiency
(friction losses), accuracy, dynamic/vibration stability, and
manufacturability (Rivin, 1999). In function of its application,
friction can be desirable e.g. in brakes, clutches and friction drives
or undesirable in bearings, slides and joints. In both cases, it is
important to be able to characterize and control the frictional
behaviour in order to assure a good performance of the system.
The study of contact problems with friction has been the subject of
numerous experimental investigations for hundreds of years and recently
numerous computational investigations have been performed. One of the
first investigations concerns a plane contact problem in full sliding
(Muskhelishvili, 1966) in which the frictional stress is linearly
proportional to the contact pressure. A frictional contact with stick
and slip is considered in Galin, 1980. In numerous practical cases the
frictional stress is a nonlinear function of pressure.
Although expansive research has been done, there are still many
unknowns related to friction phenomena. In dry sliding contacts, the
friction coefficient depends on various factors such as the applied
load, surface topography, sliding velocity, temperature, elastic and
plastic properties. The dependence of the friction coefficient on these
factors is treated in numerous technical journals (Bengisu & Akay,
1997; Kalker, 1975). The research elaborated by Bowden and Tabor, 1964
had an important role in the study of friction. They demonstrated that
the static friction between two sliding surfaces is significantly
influenced by the real area of contact. Their general conclusion was
that the friction force consists of forces due to adhesion and
mechanical deformations.
The characterization of friction depends significantly on the
accuracy of experimental measurements. The frictional behaviour is
generally a characteristic of the system, and not only of the materials
in contact, therefore no single test can describe all types of
frictional situations (Blau, 2001).
Furthermore, studies have been made in relating the friction
coefficient to contact parameters and relevant operating conditions
through theoretical modelling (Greenwood & Tripp, 1967; Greenwood
& Williamson, 1966) though the most significant sources of guidance
to practical values are experimental investigations.
2. FRICTIONAL CONTACTS IN FEM
The formulations of contact elements within FEM were developed in
the 1970's. In our days, commercial FE-programs use contact models
such as node to node which are typically used to model point-to-point
contact applications, node to surface, which connects the nodes of the
surface to the elements of the other surface. In industrial applications
(seals, metal-forming processes), due to the occurrence of large
deformations, non-linear behaviour and large relative motion between the
participating contact members a surface to surface formulation is
advised to be used.
The main advantages of a 3D-FE model are (1) the proper utilization
of correct geometry (dimensions, surface topography, degrees of freedom)
and (2) the ability to calculate stresses and deformations in the entire
body. 3D-FE models have a major disadvantage. Due to the very fine mesh
they require high processing times for rough surfaces.
With the increased capabilities of digital computers, numerical
methods became the main focus of researchers. Several formulations have
been proposed to treat frictional contact problems using the Finite
Element Method (FEM) (Karnopp, 1985; Kikuchi & Oden, 1988).
Contact problems in FEM programs consist of two general classes:
rigid-to-flexible and flexible-to-flexible. The flexible-to-flexible is
the more common contact problem. In this case, both (or all) contacting
bodies are deformable (i.e., have similar stiffness). An example of a
flexible-to-flexible contact is bolted connections.
The frictional contact problem involves two distinct states: slip
and stick. In the fundamental Coulomb friction model, two contacting
surfaces can undergo the tangential force to a value of the magnitude
along their contact interface before starting to slide. This state is
known as sticking [F.sub.t] < [mu] x [F.sub.n]. In the Coulomb
friction model an equivalent tangential force [F.sub.t] is defined,
where the sliding on the contact surface begins as a fraction of the
normal load [F.sub.n], [F.sub.t] = [mu] x [F.sub.n], where p represents
the friction coefficient, defined as a material property. Sliding
between the two surfaces occurs when the tangential force is exceeded
[F.sub.t] > [mu] x [F.sub.n]. Fig. 1. represents the Coulomb
frictional model.
Frictional contact problems produce asymmetric stiffness matrices
due to the existence of a tangential force. Using an asymmetric solver
is more computationally expensive than a symmetric solver for each
iteration. For this reason, ANSYS uses a symmetrization algorithm by
which most frictional contact problems can be solved using solvers for
symmetric systems. Frictional effects and normal contact conditions are
included through Lagrange multipliers or penalty terms.
[FIGURE 1 OMITTED]
3. INTERPRETATION OF THE RESULTS
The FEA in Ansys Workbench consists of two bodies of each 100x15x15
mm, making contact in one face. The upper body is constrained such that
it can not move in two of its side planes and the lower body is
constrained by two frictionless planes, as well a normal load and a
remote displacement are applied to simulate the actual experiment. This
simulation is performed for two materials, viz. PVC and A1, and for 5
loads (23, 40, 75, 92, 109 N).
The results of the experimental data are used as an input for the
simulations in Ansys Workbench. For each load a set of breakpoints is
chosen with their corresponding friction coefficient. These breakpoints
represent the displacement input for the lower body. For PVC, 10
equidistant points are used going from 0 till 20 [micro]m and for Al 6
optimised points are used from 0 till 6 [micro]m. This optimisation of
point distribution is done based on the fact that for a higher curvature
or lower radius of curvature for the non-linear behaviour, the density
of points should be higher to have a more accurate linear piece wise
representation of the original virgin curve. In this way a lower amount
of breakpoints results into the same accuracy needing less simulation
time.
The experimental results are used as a reference to compare the
results of the FE simulations. As a first comparison the frictional
force in function of the sliding distance is plot and compared with the
friction force coming from the experiments, see Fig. 2. The frictional
force coming from the simulations is slightly lower for all loads and
have the same trend as the original virgin curve. This difference can be
due to the lack of the memory effect, called the non-local memory in
hysteresis behaviour, in the FE simulation. Each simulation, for each
consecutive displacement, starts from zero until it found a numerical
solution close to the input displacement coming from the 10 equidistant
points for PVC and the 6 optimised points for Al. Improvements of the
simulation consist of using the results of each simulation for each
following displacement respectively, taking the local stiffness instead
of the global stiffness into account. The simulation time can
drastically be reduced by applying this alternative implementation
method.
Another result of the simulation is the contact pressure, which is
function of the tangential displacement or sliding distance. One would
expect when no displacement is present that the pressure in the contact
is equal to the applied load divided by the contact area. Since here, as
in all contacts, the stiffness is normal load dependent for both the
tangential and normal stiffness; the pressure in the contact has a
similar hysteretic behaviour.
4. CONCLUSION
Using appropriate inputs and an optimised representation of the
non-linear frictional behaviour, an accurate frictional contact
simulation is obtained, taking the normal load and displacement
dependency of the frictional behaviour into account through experimental
correlation. The model can be improved in calculation time by using a
step wise implementation starting from the previous results for each
displacement respectively.
[FIGURE 2 OMITTED]
5. ACKNOWLEDGEMENTS
The work has been funded by the Sectoral Operational Programme
Human Resources Development 2007-2013 of the Romanian Ministry of
Labour, Family and Social Protection through the Financial Agreement
POSDRU/88/1.5/S/60203 and POSDRU/88/1.5/S/61178. Thanks go to the
Department of Mechanical Engineering from the K.U. Leuven, which made it
possible to perform the experiments.
6. REFERENCES
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