Abstract
Initial contact height in contact between a directional rough surface and a sphere is analyzed theoretically. Effects of surface roughness on length measurement with a hemispherical tip are discussed using the results of the above theory and simulational results. Consequently, the followings are clarified. 1) The theoretical value of initial contact height can be approximated by the mean value of the following two theoretical values : One is obtained on the assumption that the distribution of asperity peak intervals is exponential, and the other is obtained on the assumption that the intervals are constant. 2) As the radius of the tip increases, a mean value of measured length increases, and a standard deviation of measured length decreases. Concerning to the roughness of surface finished by the abrasive paper, the mean values and the standard deviation of measured length are proportional with the standard deviation of asperity peak height distribution. 3) The influence of load on the standard deviation of measured length can be neglected at the usual measuring condition. 4) Theoretical analysis can be verified by experimental results.
