Friction is a complex phenomenon that depends on many parameters.Despite this,we still rely on and describe friction in the vast majority of cases with a single value,namely,the coefficient of friction(µ),as firs...Friction is a complex phenomenon that depends on many parameters.Despite this,we still rely on and describe friction in the vast majority of cases with a single value,namely,the coefficient of friction(µ),as first proposed by Amontons in 1699.Later,Coulomb introduced a two-parameter description by separating the adhesive and load-dependent terms.However,experimental evidence that determines under what conditions either of the two historical models is more appropriate has not been investigated in detail.In particular,to take full advantage and achieve better accuracy with the two-parameter equation,the real contact area must be well characterized to determine the constant adhesive component sufficiently and accurately.In this study,we performed sliding experiments and measured friction,but at the same time,we also measured the real contact area with sub-micron lateral resolution,which allowed us to design a two-parameter(Coulomb-type)friction equation.We compared these results with the historical friction models of Amontons and Coulomb to better understand the actual differences between them and how this corresponds to the linearity between the friction force and the normal force,which is a key assumption in the more common and simpler Amontons relation.A strong scaling effect of roughness was observed,as well as the related nonlinearity between the normal load,friction,and real contact area.Under high loads and roughnesses,the one-or two-parameter friction descriptive models differed from experiments by only a few percent,and the variation among them was small in the same range.However,for very low roughnesses and loads(close to the nanoscale region),the two-parameter Coulomb model was required for any relevant friction prediction due to the strong adhesive contribution,while the one-parameter description was not appropriate.展开更多
We propose a model based on extreme value statistics(EVS) and combine it with different models for single-asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load...We propose a model based on extreme value statistics(EVS) and combine it with different models for single-asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load and the friction force on a rough interface. We determine that, when the summit distribution is Gumbel and the contact model is Hertzian, we obtain the closest conformity with Amonton’s law. The range over which Gumbel distribution mimics Amonton’s law is wider than that of the Greenwood–Williamson(GW) model. However, exact conformity with Amonton’s law is not observed for any of the well-known EVS distributions. Plastic deformations in the contact area reduce the relative change in pressure slightly with Gumbel distribution. Interestingly, when elasto-plastic contact is assumed for the asperities, together with Gumbel distribution for summits, the best conformity with Amonton’s law is achieved. Other extreme value statistics are also studied, and the results are presented. We combine Gumbel distribution with the GW–McC ool model, which is an improved version of the GW model, and the new model considers a bandwidth for wavelengths α. Comparisons of this model with the original GW–McCool model and other simplified versions of the Bush–Gibson–Thomas theory reveal that Gumbel distribution has a better conformity with Amonton’s law for all values of α. When the adhesive contact model is used, the main observation is that there is some friction for zero or even negative applied load. Asperities with a height even less than the separation between the two surfaces are in contact. For a small value of the adhesion parameter, a better conformity with Amonton’s law is observed. The relative pressure increases for stronger adhesion, which indicates that adhesion-controlled friction is dominated by load-controlled friction. We also observe that adhesion increases on a surface with a lower value of roughness.展开更多
文摘Friction is a complex phenomenon that depends on many parameters.Despite this,we still rely on and describe friction in the vast majority of cases with a single value,namely,the coefficient of friction(µ),as first proposed by Amontons in 1699.Later,Coulomb introduced a two-parameter description by separating the adhesive and load-dependent terms.However,experimental evidence that determines under what conditions either of the two historical models is more appropriate has not been investigated in detail.In particular,to take full advantage and achieve better accuracy with the two-parameter equation,the real contact area must be well characterized to determine the constant adhesive component sufficiently and accurately.In this study,we performed sliding experiments and measured friction,but at the same time,we also measured the real contact area with sub-micron lateral resolution,which allowed us to design a two-parameter(Coulomb-type)friction equation.We compared these results with the historical friction models of Amontons and Coulomb to better understand the actual differences between them and how this corresponds to the linearity between the friction force and the normal force,which is a key assumption in the more common and simpler Amontons relation.A strong scaling effect of roughness was observed,as well as the related nonlinearity between the normal load,friction,and real contact area.Under high loads and roughnesses,the one-or two-parameter friction descriptive models differed from experiments by only a few percent,and the variation among them was small in the same range.However,for very low roughnesses and loads(close to the nanoscale region),the two-parameter Coulomb model was required for any relevant friction prediction due to the strong adhesive contribution,while the one-parameter description was not appropriate.
文摘We propose a model based on extreme value statistics(EVS) and combine it with different models for single-asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load and the friction force on a rough interface. We determine that, when the summit distribution is Gumbel and the contact model is Hertzian, we obtain the closest conformity with Amonton’s law. The range over which Gumbel distribution mimics Amonton’s law is wider than that of the Greenwood–Williamson(GW) model. However, exact conformity with Amonton’s law is not observed for any of the well-known EVS distributions. Plastic deformations in the contact area reduce the relative change in pressure slightly with Gumbel distribution. Interestingly, when elasto-plastic contact is assumed for the asperities, together with Gumbel distribution for summits, the best conformity with Amonton’s law is achieved. Other extreme value statistics are also studied, and the results are presented. We combine Gumbel distribution with the GW–McC ool model, which is an improved version of the GW model, and the new model considers a bandwidth for wavelengths α. Comparisons of this model with the original GW–McCool model and other simplified versions of the Bush–Gibson–Thomas theory reveal that Gumbel distribution has a better conformity with Amonton’s law for all values of α. When the adhesive contact model is used, the main observation is that there is some friction for zero or even negative applied load. Asperities with a height even less than the separation between the two surfaces are in contact. For a small value of the adhesion parameter, a better conformity with Amonton’s law is observed. The relative pressure increases for stronger adhesion, which indicates that adhesion-controlled friction is dominated by load-controlled friction. We also observe that adhesion increases on a surface with a lower value of roughness.
