Abstract
The paper presents a dry friction model considering plastic interactions described by the Oxley equations. The model differs clearly from those published by Oxley due to the fact that it includes a statistical analysis of rough surface interactions. The contact of a single asperity is analyzed in a 3D—not 2D—space. The results of this analysis are further extended to the contact of two rough-surfaces by accomplishment of an appropriate summing (integration) of individual elementary forces of friction and pressure occurring in discreet contacts. In the case of papers based on the Oxley model, their authors analyze the contact of a single asperity with a plane and thus compute the macroscopic friction coefficient. On the basis of the achieved mathematical model of dry friction, the friction force was determined and consequently, the friction coefficient. In order to verify theoretical speculations, an experimental test was carried out in the system consisting of a steel disk with a galvanized coating and a steel pin. The results of experimental tests comply with the solutions achieved via a computer simulation. The resistance to motion results mainly from plastic deformations, which in turn result in adhesion tacking. Among investigated galvanic coatings, the highest motion resistance was revealed by a nickel coating, whereas the lowest one was revealed by a silver coating.
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Abbreviations
- a :
-
Radius of the area of contact
- A′:
-
Area of a single plastic contact
- A n :
-
Nominal contact area
- A r :
-
Real contact area
- b, \({\nu }\) :
-
Parameters of bearing surface curve
- c :
-
Approach of the mating surfaces for bearing surface curve (measured fromthe highest asperity)
- d :
-
Mutual overlapping of maximum asperities
- f :
-
Relative strength of connections
- h :
-
Mutual overlapping of two given asperities
- k :
-
Shear strength of the deformed material (shear yield stress)
- m :
-
Linear density of profile heights (number of peaks per 1mm of theprofile)
- n :
-
Density of asperities of contacting areas
- N :
-
Normal force
- N R :
-
Number of profile peaks over the 10 mm section
- p :
-
Pressure
- P :
-
Elementary force between two asperities
- P z :
-
Elementary normal force (normal force on a single asperity)
- P x :
-
Elementary friction force (friction force on a single asperity)
- r :
-
Parameter of mutual asperity overlapping
- r max :
-
Border parameter of asperity penetration
- R :
-
Radius of hemispherical asperity
- R a :
-
Arithmetic mean deviations of roughness profile
- R max :
-
Maximum roughness height
- R q :
-
Quadratic mean deviations of roughness profile
- R t :
-
Sum of the curvature radii of contacting asperities
- S :
-
Standard deviation of asperity heights
- S m :
-
Mean spacing of profile irregularities
- T :
-
Friction force
- t p :
-
Bearing ratio (relative reference length of profile)
- z :
-
Height of asperity measured from the mean of asperity heights
- \({\delta }\) :
-
Separation distance of asperities along the normal to the contactpoint
- \({\varepsilon }\) :
-
Relative approach for bearing surface curve
- \({\phi }\) (z):
-
Distribution function of asperity heights
- \({\tau }\) :
-
Shear strength of the interfacial film
- \({\mu }\) :
-
Coefficient of friction
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Jedynak, R., Sułek, M. Numerical and Experimental Investigation of Plastic Interaction Between Rough Surfaces. Arab J Sci Eng 39, 4165–4177 (2014). https://doi.org/10.1007/s13369-014-1026-6
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DOI: https://doi.org/10.1007/s13369-014-1026-6