### Abstract

An easily programmed method is proposed for translating the rms height (R_{q}) and rms slope (Δ_{q}) determined using a profile measuring instrument, into more readily interpreted measures of functional severity such as the density of plastic contacts or the mean real contact pressure. The method involves estimation from the ratio R_{q}/Δq, of the exponent k of an assumed power function relation between the profile spectrum and the spatial frequency. Having estimated k, the mean square curvature is computed analytically and used together with Rq and Aq to determine the three input variables needed for the Greenwood-Williamson (GW) microcontact model The GW model is then used to compute, as a function of the separation of two rough surfaces, the contact density, the plastic contact density, the mean load per unit area and the mean load per unit of real contact area. The mean square curvature estimated in this manner is compared to the directly measured mean square curvature for 12 distinct surface types. The values compared quite favorably (within 25 percent) for three of the specimens which included a bearing ball and the ground inner ring rolling path of a cylindrical roller bearing. The discrepancies exceeded a factor of 3 for three other specimens. The microcontact model output computed using both measured and estimated mean square curvature values showed that some output variables, e.g., plastic contact density, are more discrepant than the estimated and measured curvature values. Other output variables of the microcontact model, in particular, the mean real pressure, attenuate the discrepancies. The mean real pressures computed using the calculated and measured curvatures, were within 30 percent for all but three specimens. The maximum discrepancy observed was 55 percent. The results are sufficiently encouraging and the methodology so easy to apply, to commend the practice of routinely supplementing profile measurement data with microcontact model output.

Original language | English (US) |
---|---|

Pages (from-to) | 264-270 |

Number of pages | 7 |

Journal | Journal of Tribology |

Volume | 109 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1987 |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Surfaces and Interfaces
- Surfaces, Coatings and Films

### Cite this

*Journal of Tribology*,

*109*(2), 264-270. https://doi.org/10.1115/1.3261349

}

*Journal of Tribology*, vol. 109, no. 2, pp. 264-270. https://doi.org/10.1115/1.3261349

**Relating profile instrument measurements to the functional performance of rough surfaces.** / McCool, John I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Relating profile instrument measurements to the functional performance of rough surfaces

AU - McCool, John I.

PY - 1987/1/1

Y1 - 1987/1/1

N2 - An easily programmed method is proposed for translating the rms height (Rq) and rms slope (Δq) determined using a profile measuring instrument, into more readily interpreted measures of functional severity such as the density of plastic contacts or the mean real contact pressure. The method involves estimation from the ratio Rq/Δq, of the exponent k of an assumed power function relation between the profile spectrum and the spatial frequency. Having estimated k, the mean square curvature is computed analytically and used together with Rq and Aq to determine the three input variables needed for the Greenwood-Williamson (GW) microcontact model The GW model is then used to compute, as a function of the separation of two rough surfaces, the contact density, the plastic contact density, the mean load per unit area and the mean load per unit of real contact area. The mean square curvature estimated in this manner is compared to the directly measured mean square curvature for 12 distinct surface types. The values compared quite favorably (within 25 percent) for three of the specimens which included a bearing ball and the ground inner ring rolling path of a cylindrical roller bearing. The discrepancies exceeded a factor of 3 for three other specimens. The microcontact model output computed using both measured and estimated mean square curvature values showed that some output variables, e.g., plastic contact density, are more discrepant than the estimated and measured curvature values. Other output variables of the microcontact model, in particular, the mean real pressure, attenuate the discrepancies. The mean real pressures computed using the calculated and measured curvatures, were within 30 percent for all but three specimens. The maximum discrepancy observed was 55 percent. The results are sufficiently encouraging and the methodology so easy to apply, to commend the practice of routinely supplementing profile measurement data with microcontact model output.

AB - An easily programmed method is proposed for translating the rms height (Rq) and rms slope (Δq) determined using a profile measuring instrument, into more readily interpreted measures of functional severity such as the density of plastic contacts or the mean real contact pressure. The method involves estimation from the ratio Rq/Δq, of the exponent k of an assumed power function relation between the profile spectrum and the spatial frequency. Having estimated k, the mean square curvature is computed analytically and used together with Rq and Aq to determine the three input variables needed for the Greenwood-Williamson (GW) microcontact model The GW model is then used to compute, as a function of the separation of two rough surfaces, the contact density, the plastic contact density, the mean load per unit area and the mean load per unit of real contact area. The mean square curvature estimated in this manner is compared to the directly measured mean square curvature for 12 distinct surface types. The values compared quite favorably (within 25 percent) for three of the specimens which included a bearing ball and the ground inner ring rolling path of a cylindrical roller bearing. The discrepancies exceeded a factor of 3 for three other specimens. The microcontact model output computed using both measured and estimated mean square curvature values showed that some output variables, e.g., plastic contact density, are more discrepant than the estimated and measured curvature values. Other output variables of the microcontact model, in particular, the mean real pressure, attenuate the discrepancies. The mean real pressures computed using the calculated and measured curvatures, were within 30 percent for all but three specimens. The maximum discrepancy observed was 55 percent. The results are sufficiently encouraging and the methodology so easy to apply, to commend the practice of routinely supplementing profile measurement data with microcontact model output.

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UR - http://www.scopus.com/inward/citedby.url?scp=0023330995&partnerID=8YFLogxK

U2 - 10.1115/1.3261349

DO - 10.1115/1.3261349

M3 - Article

AN - SCOPUS:0023330995

VL - 109

SP - 264

EP - 270

JO - Journal of Tribology

JF - Journal of Tribology

SN - 0742-4787

IS - 2

ER -