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					Höhere Werkstofftechnik: Tribologie                                                                                     Friction




                                                                                                  Werkstofftechnik
                                                                                      Materials Science & Engineering




                                                       Friction




                                    Friction        Universität Duisburg-Essen
                        1 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




                                                                                                  Werkstofftechnik
                                                                                      Materials Science & Engineering


                   Friction is the force that opposes the relative motion or tendency of such
                   motion of two surfaces in contact.




                     Friction can be understood as
                              - introduction
                              - transformation and
                              - dissipation
                     of mechanical energy.

                     All single processes can be with and without changes of the involved
                     materials structure and properties
                                    Friction        Universität Duisburg-Essen
                        2 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                       Friction




                                                                                                    Werkstofftechnik
                                                                                        Materials Science & Engineering


                   Friction is the force that opposes the relative motion or tendency of such
                   motion of two surfaces in contact.
                   Friction depends on the scale and the aspect you look at it




                    atomic level
                                                                                        roughness (asperity) level
                                                microstructural level




                     crystal lattice level
                                                                                   surface profile (bulk) level
                                     Friction         Universität Duisburg-Essen
                         3 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




                                                                                                    Werkstofftechnik
                                                                                        Materials Science & Engineering



                   Friction




                   static friction (stiction)
                   dynamic friction (kinetic friction)

                   sliding friction e.g. journal, thrust bearing, hip joint
                   rolling friction e.g. wheels, ball bearing, gear tooth, knee joint
                   spinning friction e.g. drilling

                   dry friction                 solid-solid contact
                   fluid friction               solid - liquid or gas separates - solid
                   boundary friction            solid - thin film in between - solid
                   mixed friction               mixture of above
                                     Friction         Universität Duisburg-Essen
                         4 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                       Friction




                                                                                                    Werkstofftechnik
                                                                                        Materials Science & Engineering



                   Friction
                   static friction μs (stiction)
                   dynamic friction μd (kinetic friction)


                   I: μs > μd:

                   II: μd ≠ const: stick-slip; the counterbody
                   starts und stops because of e.g. agitation
                   from outside, agitation of characteristic
                   frequency by asperities; counterbody breaks
                   away and stops again (e.g. squealing if tires)

                   III: μs < μd:


                                     Friction         Universität Duisburg-Essen
                         5 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




                                                                                                    Werkstofftechnik
                                                                                        Materials Science & Engineering


                   Friction is a force that resists the sliding or rolling
                   of one solid object over another
                   Friction can be understood as
                            - introduction
                            - transformation and
                            - dissipation
                   of mechanical energy.

                   All single processes can be with and without changes of the involved
                   materials structure and properties

                   Dry friction has two (to three) major contributions coming from
                            - adhesion between contact materials                      μad
                            - plastic deformation of contact materials                    μdef
                            - elastic hysterisis                                               μhys
                            - (particle entrappment)
                                                   the system are
                   NOTICE: Particles not leaving Universität Duisburg-Essennot contributing to wear!
                                    Friction
                         6 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                       Friction




                                                                                                    Werkstofftechnik
                                                                                        Materials Science & Engineering


                   Introduction of Mechanical Energy
                   via the real area of contact (s.a. Chapter 4)




                    1 apparent area of contact (geometrical locations of all possible
                    contacts, e.g. Hertzian contact area)
                    2 contour area (contact area generated by roughness)
                    3 real area of contact (sum of all real physical contact areas)
                                    Friction          Universität Duisburg-Essen
                        7 www.uni-due.de/wt      Lotharstr 1, 47057 Duisburg, Germany




                                                                                                    Werkstofftechnik
                                                                                        Materials Science & Engineering


                   Transformation of Energy
                    Through every contact a different amount of energy is dissipated
                    depending on the locally and time-depending acting mechanisms of
                    friction



                                               μdef                                               μad




                                    Friction          Universität Duisburg-Essen
                        8 www.uni-due.de/wt      Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                           Friction




                                                                                                        Werkstofftechnik
                                                                                            Materials Science & Engineering


                   Transformation of Energy
                    Through every contact a different amount of energy is dissipated
                    depending on the locally and time-depending acting mechanisms of
                    friction




                                               μad         μdef               μdef             μhys




                                    Friction              Universität Duisburg-Essen
                        9 www.uni-due.de/wt          Lotharstr 1, 47057 Duisburg, Germany




                                                                                                        Werkstofftechnik
                                                                                            Materials Science & Engineering



                   Transformation by Adhesion
                   μad depends on the shear strength of the contact materials and their
                   tendency to adhere to each other. This can be described in the simplest
                   case by (Bowdon&Tabor)
                         τ
                   μ ad = m
                          H

                    τm = shear strenght ~
                    1/3 Rm
                    H = Hardness of contact
                    material
                                                                    Sikorsky 1963



                                    Friction              Universität Duisburg-Essen
                       10 www.uni-due.de/wt          Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                         Friction




                                                                                                      Werkstofftechnik
                                                                                          Materials Science & Engineering



                   Transformation by Adhesion
                   μad depends on the shear strength of the contact materials and their
                   tendency to adhere to each other. This can be described in the simplest
                   case by (Bowdon&Tabor)
                                              τm = shear strenght in contact ~ 1/3 Rm
                          τm
                   μ ad =                     H = Hardness of contact material
                           H
                    incorporating the tendency for adhesion by the free surface energy γad
                    within a Hertzian contact spot with a radius of a/2 (Rabinowicz)
                             τm                1           with γ ad      = γ 1 + γ 2 − γ 1, 2
                    μ ad =
                              H 1 − 2γ ad cot ϑ             and ϑ the attacking angle
                                          a
                                        H
                                          2
                                    Friction            Universität Duisburg-Essen
                       11 www.uni-due.de/wt        Lotharstr 1, 47057 Duisburg, Germany




                                                                                                      Werkstofftechnik
                                                                                          Materials Science & Engineering



                   Work of adhesion γad
                   γ ad = γ 1 + γ 2 − γ 1, 2




                                                             from Zum Gahr (1985)



                                                                                              γ1,2
                                    Friction            Universität Duisburg-Essen
                       12 www.uni-due.de/wt        Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                      Friction




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Transformation by Deformation
                   The tranformation by deformation can be brought about by
                                                          μpl: ploughing deformation of the surface
                   μdef shear deformation of
                                                          (similar to chipping but without loss of
                   the material below the
                                                          material; the ploughed volume is just
                   contact
                                                          shifted to the edges of the groove)




                                    Friction        Universität Duisburg-Essen
                       13 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Transformation by Deformation

                                                       The shear deformation γ has ist maximum
                                                       at the surface and decreases with the
                                                       distance form the surface z by an e-
                                                       function; thus τ and γ follow:
                                                       γ ( z ) = γ m e − cz
                                                      τ ( z ) = τ m 1 − e − cγ
                     By integrating the product of τ and γ (work of plastic deformation)
                     along z on gets (Rigney):                               τ      τ
                     Ac = area of contact                          2 ln(1 + 0 ) − 0
                                                            Aτ               τm τm
                     τ0 = max. shear stress         μ def = c 0
                     in contact                              F                 τ0 2
                                                                          N           ln(1 − (        ) )
                                                                                                 τm
                                    Friction        Universität Duisburg-Essen
                       14 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                      Friction




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Transformation by Deformation
                                 FN
                                                   This contribution to friction depends on the
                          FT                       contact geometry and the adhesive forces
                   z0                ϑ             within the contact area:
                                                                       8        z
                                                              μ ad + arcsin 0
                               for spheres (Hisakado) μ pl =          3π       2R
                                                                       8         z
                                                             1 − μ ad    arcsin 0
                                                                      3π        2R
                                                2        μ
                                                  cot ϑ + ad (1 + cos ecϑ )
                     for cones (Brookes) μ pl = π          2
                                                         2                          45° < ϑ < 75°
                                                      1 − μ ad cot ϑ
                                                               π
                                                         cot ϑ + μ ad (1 + 2 secϑ )
                    for pyramids (Hisakado)       μ pl =
                                                              3 − μ ad cot ϑ

                                     Friction        Universität Duisburg-Essen
                        15 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Transformation by elastic Hysteresis and Damping
                   Another contribution to
                   friction is brough about by                                             Hertzian
                   the fact that the elastic                                               Contact
                   deformation of materials                                                Cylinder on Plane

                   might not be fully reversible.
                   Thus the areas under the
                   loading and unloading stress-
                   strain or contact force
                   displacement curves are not
                   identical. The remaining                                                            Hertzian
                   integral represents the                                                             Contact
                                                                                                       Ball on Plane
                   dissipated (elastic) work of
                   deformation (hatched areas).


                                     Friction        Universität Duisburg-Essen
                        16 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                      Friction




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Transformation by elastic Hysteresis and Damping
                   The 2nd contribution stem form the fact that the
                   deformation velocities during loading an                            µFN
                   unloading are not equal, which generates some                         FT
                   additional damping (especially under impact;
                   most pronounced for polymers, which sometimes
                   show entropy-elastic behaviour).



                                               e.g. for energy-elastic                         penetration depth δ
                                                   materials (metals,
                                                            ceramics)




                                    Friction         Universität Duisburg-Essen
                       17 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Dissipation of Mechanical Energy

                   The dissipation of mechnical energy ca be understood as
                           - thermal process (mechanical equivalent of heat)
                           - absorption of energy
                                   - excitation of phonos and electrons
                                   - elastic hysteresis (e.g. entropy-elastic polymers)
                                   - distortion of lattice
                                   - generation and motion of dislocations, vacancies
                                   - phase transformation
                                   - tribochemical reations
                           - emission of energy




                                    Friction         Universität Duisburg-Essen
                       18 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                      Friction




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Dissipation of Mechanical Energy

                   The dissipation of mechnical energy ca be understood as
                           - thermal process (mechanical equivalent of heat)
                           - absorption of energy
                           - emission of energy
                                   - heat conduction
                                   - heat radiation
                                   - emission of phonons (luminiscense)
                                   - emision of electrons or ions
                                   - emission of sound




                                    Friction         Universität Duisburg-Essen
                       19 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Dissipation of Mechanical Energy

                   The dissipation of mechnical energy ca be understood as
                           - thermal process (mechanical equivalent of heat)
                           - absorption of energy
                           - emission of energy
                   The mechanical equivalent of heat is defined as the product of stress and
                   strain; which is the integral under the stress-strain curve
                   For friction it it the product of shear stress τ and shear strain γ, which can
                   be derived by (Rigney)                              τ0
                                                                                       ( z0 − z )
                                                                                   k
                                                                   2 z0
                                               τγ = τ 0γ 0               e z0 + z
                                                                  z0 + z   k = coefficient of cold
                                                                                       working under e.g. cold
                                                                                       rolling
                                    Friction         Universität Duisburg-Essen
                       20 www.uni-due.de/wt     Lotharstr 1, 47057 Duisburg, Germany




                                                                                                                              10
Höhere Werkstofftechnik: Tribologie                                                                                      Friction




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Dissipation of Mechanical Energy

                   Notice: if τ0/k ≈ 10 the product τγ decreases by a factor of 40 between
                   z=z0 and z=2z0

                   Thus, the gradient is very steep and the zone affected by heat must be
                   very small




                                     Friction        Universität Duisburg-Essen
                        21 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Rolling Friction
                   The coefficient of friction under rolling is smaller than under sliding.

                   Reason: The contact points or areas are moving normal to each other and
                     not tangential (which causes the shear stresses)




                    But rolling friction is not „zero“!




                                     Friction        Universität Duisburg-Essen
                        22 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




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Höhere Werkstofftechnik: Tribologie                                                                                      Friction




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Rolling Friction
                    Coefficient of Friction
                    Surfaces                    Rolling Friction µr                    Kinetic Friction µk or µd
                    Train wheel on steel        0.001                                  0.1
                    track
                    Ordinary car tire on dry    0.015                                  0.8
                    pavement
                    Truck tire on dry           0.006-0.01                             0.8
                    pavement




                                     Friction        Universität Duisburg-Essen
                        23 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




                                                                                                   Werkstofftechnik
                                                                                       Materials Science & Engineering



                   Rolling Friction
                   Coefficient of rolling friction is not „zero“!

                   Reason: The Hertzian contact area under rolling consists of two zones:
                   1) zone with no relative motion between body and counterbody
                   2) zone with relative motion of a very small stroke, slip or slippage; static
                      and dynamic (kinetic) friction (!)

                   2) is brought about the differences in contact stiffness/compliance (shape
                      or Youngs-moduli) of the contacting bodies (Reynolds 1876, Heathcote
                      1921, Carter 1926, Poritsky 1950)




                                     Friction        Universität Duisburg-Essen
                        24 www.uni-due.de/wt    Lotharstr 1, 47057 Duisburg, Germany




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