This paper describes a modification of the theoretical model presented by Nakahara for estimating the static friction coefficient of the contact between rough surfaces and a boundary film. The theoretical model is modified from Halling's friction model for soft thin metallic films. The effective hardness in Halling's model is transposed with a new model, which is modified from Bhattacharya–Nix's equation for a conical indenter, in order to apply it to a spherical indenter on the basis of Johnson's cavity model. Nakahara's model takes into consideration the effect of pressure on the shear strength of the boundary film, which was suggested by Briscoe et al., and it can elucidate the effects of the following factors on the friction coefficient: apparent contact pressure, film thickness, the three parameters of roughness in Greenwood–Williamson's model, and the ratio of film bulk hardness to substrate hardness.
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