Effects of bearing surfaces on lap joint energy dissipation Page: 3 of 9
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Figure 1: Schematic of Jointed Beam Specimen
Each experiment was performed according to the procedure
outlined in a later section. An impact hammer was used to
excite the structure, and the dynamic response was
measured. The excited beam exhibits response amplitudes
characterized by monotonic decay, and the first mode shape
resembles the schematic shown in Figure 2. In addition the
locations where washers were added in some of the
experiments are shown by capital letters.
Figure 2: First Excited Modal Shape of the Beam
In the first experiment the friction effects on dynamic
response corresponding to the absence of any washers at A
and B was investigated. This configuration established the
greatest possible bearing area where micro-slip can
potentially occur. The second experiment involved placing
large diameter washers at A and B in the lap joints. This
diminishes the bearing area where micro-slip can occur. The
third experiment involved placing small diameter washers at
A and B. This further diminishes the bearing area where
micro-slip can occur.
In order to predict the characteristic behavior in frictional
joints an accurate frictional model is required. There have
been numerous models proposed ranging from static to
dynamic models based on phenomenological and non-
phenomenological observations of sliding friction. Most of
the existing models use classical friction. These are
acceptable for high velocity applications, but for low velocity
applications these models are not sufficient. In this paper we
consider two friction models for the mathematical simulation
of the experimental results.
The first model considered to represent friction in the lap
joints is the Dahl model (Dahl, 1976). The DahI model, which
was developed to simulate control systems with friction, was
constructed with reference to the stress-strain curve in
classical mechanics. The friction force in this model is only a
function of the displacement and the sign of the velocity.
Therefore, the model is considered to be rate independent
and as a result does not capture the Stribeck effect (Gaul
and Nitsche), a rate dependent phenomenon. The model
does not account for stiction.
The second friction model considered to describe the friction
in the bolted lap joints is the LuGre model (Olsson, et al.r
1998). The LuGre model (Lund-Grenoble) combines the
effects of the Dahl model and the bristle model (Haessing
and Friedland, 1991) and has more parameters than the
Dahl model. Therefore, it should have the potential to model
joint friction more accurately. This model accounts for both
the Stribeck effect and stiction.
In the following sections we (1) quantitatively describe the
principles associated with the energy dissipation in the
micro-slip domain, (2) describe the experimental
configuration and the testing and data analysis procedures
used for the experiments, (3) describe the two damping
models and an approximate finite element model created to
simulate the experimental findings, and (4) present the
experimental and analytical results. Finally, conclusions and
recommendations for future investigations are offered.
PRINCIPLES OF ENERGY DISSIPATION IN
MICRO-SLIP
Structures with lap joints display higher damping than
analogous structures with monolithic construction in place of
lap joints because friction occurs in lap joints. This friction
can be modeled in many different ways; however, for the
purpose of this discussion, consider Coulomb friction.
Coulomb friction can be explained using the simple model in
Figure 3.
q
x
Figure 3: Simple Coulomb Friction Model
Friction occurs at the interface between the block and the
rigid surface. P is an external lateral force, and q the normal
force acting on a rigid block. No displacement occurs, in
Coulomb friction, when P < qp, , where p, is the coefficient
of static friction. However, once P exceeds the limiting
Coulomb static friction force, q ,, sliding commences and
the friction restoring force becomes P q= q,, where 9d is
the coefficient of dynamic friction. Typically, > d .
Therefore, Coulomb friction prevents motion form occurring
until an adequate tangential force is realized and then
opposes that force once motion occurs. When sliding
occurs, energy is dissipated in the system. The
phenomenon described here is macro-friction because
motion occurs over the entire contact surface between the
rigid block and the rigid surface that supports it. Before
sliding commences no energy is dissipated. After sliding
starts, energy is dissipated because of friction. The amount
of energy dissipated is proportional to the normal force.
In the case of lap joints, high normal loads applied by
connecting bolts limit relative motions between components.
The schematic in Figure 4a shows a lap joint in the beam
tested in this investigation. As the beam vibrates, it bends.
The beam bending causes generation of shear stresses on
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Kess, H. R. (Harold R.); Rosnow, N. J. (Nathan J.) & Sidle, B. C. (Brian C.). Effects of bearing surfaces on lap joint energy dissipation, article, January 1, 2001; United States. (https://digital.library.unt.edu/ark:/67531/metadc927329/m1/3/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.