ABSTRACT
For a “sphere-on-¨at” elastic contact, which is known as the Hertzian elastic contact model, this friction coe²cient can be expressed as
39.1 Introduction and DeŸnition of Low Friction ............................. 39-1 39.2 Low Friction Coatings and Mechanisms of Lubrication ..........39-3
39.3 Coating Processing Routes .......................................................... 39-14 39.4 Key Applications ........................................................................... 39-14 Acknowledgments .................................................................................... 39-15 References .................................................................................................. 39-15
m t p a=
o R E
L3 4
⎝
⎜
⎞
⎠
⎟
+ (39.2)
where R is the sphere radius E is the equivalent (composite) Young’s modulus
Instead of the Amontonian Ÿrst law of friction, where μ is independent of L, the Bowden and Tabor analysis for Hertzian contacts predicts
˜us, when contact deformation is elastic, the friction coe²cient will decrease with increasing normal load (or mean Hertz pressure). ˜e linear relationship between L−1/3 and μ (Equation 39.2) has been experimentally veriŸed for a number of low friction coatings, including diamond-like nanocomposite (DLN) [2], MoS2/Sb2O3/Au [3], and ultrananocrystalline diamond (UNCD, unpublished) (see Figure 39.2). For thin and so§ coatings, the pressure is primarily supported by the substrate and increasing the substrate modulus and hardness will decrease the contact area for a given normal load. ˜us,
the ideal scenario for achieving low friction is to have an elastically stiµ and hard substrate support the normal load and keep the contact area small, while the surface coating provides shear accommodation and reduces junction strength, until the substrate begins to yield and plastically deform.
