Institut für Technische Mechanik
On self-excited vibrationsdue to sliding friction between moving bodies
Hartmut Hetzler
www.kit.edu
• Motivation, considered class of systems• a general formulation• example: rotating Timoshenko annulus• Conclusion
7th ISVCS, Zakopane, 2009
2 | Hartmut Hetzler | On self-excited vibrations due to sliding friction …
Motivation
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vehicle brakes
band saws grinding tools
usually:• particular application
structural models• specific formulation
shaft seals
Abstract system generic formulation for
- results generally valid?- further effects?- parameters
• systems of continua• relative motion• sliding friction contacts• spatially fixed contact zone
3 | Hartmut Hetzler | On self-excited vibrations due to sliding friction …
System Description
Normal contact
• Lagrange Multipliers: „ideal bodies“ kinematic constraint
• Penalty formulation:„contact layer“ contact stiffness
Hamilton‘s Principle (for open systems)
normal contact tangential contactsliding friction
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Spatial frame, linearized system
linearized contact contributions
• Eulerian coordinates of intermediate configuration
• rigid body motion relates
• small vibrations about transport motion Linearization
referenceintermediateconfiguration
final configuration
system border
Spatial descriptionrigid body motion
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Contact
Kinematics
surface normal
friction direction
gap vector
normal distance
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Contact
Normal contact
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Contact
Friction
Linearization,
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Contact
orientation of friction vector contact pressure
stiffnessdamping
Friction […]
stiffness
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Contact contributions
normal contact
normal contact • stiffness• symmetric,
pos. semidefinite
• no discretization• no structural model
• damping and „stiffness“• damping: symmetric,
positive semidefinitegrows with 1/v
• stiffness: non-symmetric
friction
frictional contact
parametersparameters
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Example: rotating Timoshenko ring
pad
beam
• rotating circular Timoshenko beam• friction pads as Winkler foundation• Eulerian description• simple model for brake squeal
4 field variables
data:
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Stability of steady-state
unstable
stable
Gyroscopic influence
discretization
Flutter-type instability
unstable
damped gyroscopic circulatory system
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Stability of trivial solution
friction contribution to dampingimportant at low relative speeds
gyroscopic terms have significant effect
Theorem of Thomson&Tait does not apply to circulatory systems!
Influence of and
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Contact stiffness
(Sherif: Investigation on effect of surface topography…on squeal generation, Wear, 2004 )
new
worn
Constitutive contact model • Greenwood&Williamson• surface statistics
long padshort pad
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Conclusion
Abstract problem
• generic form of perturbation equations• physical meaning of the contributions• no discretization / no structural model• systematic way to formulate contributions
Example: moving Timoshenko-Ring
• rotating timoshenko-ring• strong influence of transport motion and
„friction damping“• contact stiffness shows strong influence
microcmechanics of contact need to be considered
Thank you for your attention!
15 | Hartmut Hetzler | On self-excited vibrations due to sliding friction …