Friction Wear and Lubrication of Materials
Homework # 5
Bill Beckman
1)
Friction Lecture by Prof. Manoj Harbola, Department of Physics, IIT Kanpur
http://www.youtube.com/watch?v=na90uKzc9JY
Frictional force can be between any two surfaces and opposes tendency of motion
Coulomb friction – between dry surfaces
Wet friction – between surfaces with liquid between them
Friction force increases until Fmax is reached (static friction), at which point the component can
be moved (kinetic friction). In practice friction force reduces after Fmax, however stays
relatively stationary. Coulomb found the following, where N is the normal force opposing the
body (mass x gravity), µs is coefficient of static friction, µk is coeff of kinetic friction:
Friction is independent of the area of contact
Examples of mass pulley system on an incline ramp of 30° were covered (frictionless as well as
with friction). Because of friction of 0.4, a smaller mass can hold the system in equilibrium. On
the other hand, the mass can be increased to a point where the maximum friction force is
opposing pulling the mass up the inclined plane. Ultimately a range of 7.68 kg < mass < 42.32
kg for the static friction coefficient of 0.4 would allow the system to be static and in
equilibrium.
Second example of mass on inclined plane with a force applied (600 N, 500 N, 100 N) on the
block at an angle to the sureface. Depending on force applied, either the static or kinetic
frictional value must be used. The frictional force due to 600 N and 500 N would allow the
block to remain stationary, which the direction of frictional force switched. However for F=100
N the frictional for and force on the block wouldn’t keep the block from sliding down the
surface.
Dry thrust bearing (cylinder fixed on wall with torque applied). Different frictional forces due to
torque will occur at varying radius of the cylinder. Therefore integrating over the radius results
in the following maximum frictional torque is:
Belt Friction over a pulley is also discussed where maximum frictional force and tension per
angle can be found. Integrating both sides shows the tension is related to the exponential of
the frictional component.
2) Adhesion of Coating Lecture by Prof. Chattopadhyay, Department of Mechanical
Engineering, IIT Kharagpur
http://www.youtube.com/watch?v=HQ8OJw4ICyE
“Adhesion – It is the state in which two surfaces are held together by internal forces which may
consist of valance forces or interlocking forces or both”
Types of Bonding Force: Vander Waal Bonding, Electrostatic Forces, Chemical
Attachment/Bonding, Mechanical Interlocking
Theoretical Adhesion and Actual Adhesion.
Practical Adhesion = Theoretical Adhesion – Internal Stress+/-Method Specific (error in
measurement)
Assessment of Coating Adhesion: Adhesion of a coating to a substrate can be assessed by
bending the specimen. Prefered to have the bending follow the path of the substrate all the
way around the bend (up to 180 degrees). Ductility between coating and substrate may be
different and the coating could separate from the substrate. Large values of theta that the
coating remains attached means good adhesion has been achieved. Conversely, low values of
theta means bad adhesion. These values of theta can ultimately be indexed for guide of
coating.
Experimental Assessment of Adhesion: Force of separation or how much energy must be
expended to force separation of coating from substrate can be indexed
Indentation test (hardness tester like Rockwell) can be used to leave an impression on the
surface that will vary based on the adhesion between the coating and substrate. Coating
indentation may follow bulk material indentation, however coating is typically harder than
substrate meaning the bulk material deforms more. It is possible that cracks will form in the
coating (poor adhesion) around the area of the indenter. The diameter where the coating
cracks (D = Crack Diameter) is also indexed against load P for reference (P vs D graphs).
Thickness, application temperature, process (gas phase etc) can all have an effect on coating
adhesion.
Scratch Test (with finger nail or sharp knife) is another test for adhesion. Typically done with
stylus having a Diamond Brake tip with thickness of 200 micro-meter and a 120 degree angle.
Cohesion of coating and adhesion. Scratch track and scratch channel is important to determine
coating failure as well. The adhesive strength F can be found by:
Where Lc is the critical load, R is the tip radius of the indenter, and a is the contact radius.
2) Project
The intent of my project will be to focus on friction contact influences on vibration behavior. Many
engineering applications either rely on or have a bi-product of vibrational damping due to contact
between two or more surfaces. Damping by frictional contact between surfaces reduces the relative
motion between components having a benefit on component vibration.
One that immediately comes to mind is vibrational damping of turbine or compressor blading. Gaspath
airfoil structures can be sensitive to system rotational speeds and upstream structures. Designing
components that have natural frequencies out of the system operating range can have adverse effects
on other system metrics. Typically stiffening a component to increase its natural frequency outside of
the expected operating range means undesirable additional mass. However blade or vane vibrational
excitation could result in excessive high cycle fatigue (HCF) loading that can lead to premature failure or
blade loss.
Different types of dampers can exist in systems. Under-platform damping of turbine blading has been
investigated greatly, while other cantilevered static structures also have damping effects. Typical
damping systems in compressor or fan blades utilize wire ribbon at the tip of the system to provide a
non-linear damping and coupled stiffening to adjacent blading. Under platform turbine blade dampers
rely on centrifugal loads to seat the damper against adjacent blades. There are typically two directions
of vibration to be concerned with damper contact, tangential motion between blade to blade, and radial
motion. Because of the complex nature of the system, optimizing a damper is typically done for one
critical mode or resonance. However understanding, modeling, and optimizing the effect of the dry
friction damper can be rather challenging. Stiffness, friction, stick or slip conditions, damper rolling are
all inputs that must be taken into consideration for damper effectiveness and resulting harmonic
response. Numerous dynamic friction models exist including Valanis, LuGre, Dahl, Bristle model and
others.
I plan to research dry friction dampers likely with a focus on turbomachinery applications, however may
not be limited to this. Material combination, energy dissipation, or modeling of the system could be
explored as an impact to natural frequency of the components in question. Possible other areas to
research are stick vs slip regimes where component vibration frequencies can vary greatly. System
frequency variation is a challenging subject as frictional sticking or slipping can occur very rapidly, or be
completely dependent on a specific operating point and boundary conditions.
References:
Palm III, William J. (2007). Mechanical Vibration : John Wiley & Sons, Inc.
Voldřich, J. (2009). Modelling of lthe three-dimensional friction contact of vibrating elastic bodies with
rough surfaces. Applied and Computational Mechanics 3 (2009) 241-252.
https://otik.uk.zcu.cz/bitstream/handle/11025/1912/acm_vol3no1_p23_pdf_a.pdf?sequence=1
Půst, L., Pešek, L., Radolfová, A. (2011). Various types of dry friction characteristics for vibration
damping. Engineering MECHANICS, Vol.18, 2011, No.3/4, p.203–224.
http://www.engineeringmechanics.cz/pdf/18_3_203.pdf
Tolephih, M. (2007). The Micro-Slip Damper Stiffness Effect on the Steady-State Characteristics of
Turbine Blade. Nahrain University, College of Engineering Journal (NUCEJ) Vol. 10, No.1, 2007
pp.27-36. http://www.iasj.net/iasj?func=fulltext&aId=28926
Giridhar, R. K., Ramaiah, P. V., Krishnaiah, G., and Barad, S. G. (2012). Gas Turbine Blade Damper
Optimization Methodology. Hindawi Publishing Corporation, Advances in Acoustics and
Vibration, Volume 2012, Article ID 316761, 13 pages, doi:10.1155/2012/316761
Lopez, I, Busturia J.M., Nijmeijer, H. (2003). Energy dissipation of a friction damper. Journal of Sound
and Vibration 278 (2004) 539-561. http://www.mate.tue.nl/mate/pdfs/4576.pdf
Berger, E.J. (2012). Friction modeling for dynamic system simulation. CAE Laboratory, Department of
Mechanical, Industrial, and Nuclear Engineering, University of Cincinnati.
http://www.mae.virginia.edu/NewMAE/wp-content/uploads/2012/10/berger_amr.pdf
Abouelsoud, A. A., Ahmed, J. A. (2009). Amplitude Estimate of Stick-Slip Vibration. 3rd International
Conference on Integrity, Reliability and Failure, Porto/Portugal, 20-24 July 2009.
http://paginas.fe.up.pt/clme/IRF2009/PROCEEDINGS/PAPERS/P0343.pdf
Liang, Jin-Wei, Feeny, Brian (2005). Wavelet Analysis of Stick-Slip Signals in Oscillators with Dry-Friction
Contact. Journal of Vibration and Acoustics 127 (2) 139-143 (2005).
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=11&ved=0CCsQFjAAOAo
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Zhang, Y. (2006). MULTI-ASPERITY BASED FRICTION MODELLINGAND HAPTIC RENDERING IN
VIRTUALENVIRONMENTS. BEING A THESIS SUBMITTED FOR THE DEGREE OFDOCTOR OF
PHILOSOPHYINTHE UNIVERSITY OF HULL. http://www.academia.edu/181641/Multiasperity_based_friction_modelling_and_haptic_rendering_in_virtual_environments