we suppose the roughness is increasing when friction coefficient is increasing but there some materials have high roughness with a low coefficient of friction
If roughness increases, the friction coefficient increases in case of polymeric materials. In addition, the friction coefficient can decrease if the surface can be hydrophobic.
I don't agree with Mr. Rahman. Because, surface with high roughness has lower contact (noncontinuous contact) with another object compared to that time surface roughness is low. A clear example: you wear "Football Shoes Stock" and walk on the street, you repeatedly slip. Then compare it with flat shoes.
The definition of the coefficient of friction is determined by the known relationship:
u = Ft / Fn
Ft - shear
Fn - Normal force of natovrvane
Coefficient natriene depends on the roughness ma test material. As a large roughness, the greater the coefficient of friction. Furthermore, the coefficient of friction depends on the materiyal between which they are deleted. When uniform coefficient of friction is high. While material if raznordni coefficient is small. In order to reduce the coefficient of friction are used interchangeably special greases or coatings.
I am not sure what friction coefficient you have in mind. However, in the pavement tire interface roughness may increase frictional properties. There, we are dealing with two components of friction adhesion and hysteresis . Roughness increase hysteresis and consequently friction
Depending on the material, the roughness will affect the friction differently. For example in asphaltic roads, initially the roughness is high and over time is decreasing, but the peak maximum friction is reached after some erosion - that is the friction increases a little before it starts to decrease duo to aging effects. You can check some more details in my publication here: Article Mapping Asphaltic Roads’ Skid Resistance Using Imaging Spectroscopy
La corellation rugositè facteur de frottement n'est pas toujours verifièe puisque la topographie rugeuse peut se comporter des fois comme source d'abrasion et donc augmenter le fottement ou au contraire les debris d'usure s'y incrustent et selon leur nature pourront jouer le ròle de lubrifiants dimiinuant aisi le facteur de frottement .
Et la rugositè, du moment qu'elle forme des micro-sculptures qui faciliteront l'èvacuation des dèbris d'usure ,contribueront donc à la diminution du COF.
It depends entirely on the lubrication mechanism, in many cases if it applies that having a higher surface roughness has a higher coefficient of friction as in this exampleArticle The influence of surface roughness on friction and wear of m...
But other factors of the material must be taken, such as whether the surface is soft or hard or hydrophilic or hydrophobic, to have a better study of the material.