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英语毕业论文代写 Determine The Number Of Asperity Peaks

The modified 3-point peak criterion with a peak threshold value (M3PP criterion)

In 1995 Bhushan and Poon [9] proposed a modified 3-point peak (M3PP) criterion. They defined an asperity peak as a point higher than its two neighbour points (the same as in [8] for the 3PP), but with the additional criteria that the height difference Δzi between the two neighbouring points and the peak point must be greater than a pre-defined peak-threshold value (see Figure 2). They proposed a peak-threshold value of 10% Rq for smooth surfaces (Rq < 0.05 µm), and threshold values below 10% Rq for rougher surfaces (Rq > 0.05 µm) [4].

A 3-point peak with peak-threshold value criteria (M3PP) on a 2D profile must therefore satisfy the following criteria:

zi > zi-1, zi+1,

with the additional conditions

zi > m

min (Δz1,i, Δz2,i) > peak-threshold value.

The asperity-peak radius β is again calculated in the same way as for the 3PP, but with satisfactory additional peak-threshold-value criteria, as described.

2. Experimental details

2.1 Specimen geometry and the surface roughness

Stainless-steel 100Cr6 cylindrical discs with five different roughnesses were prepared for the purpose of this research. The dimensions of the cylindrical discs were Φ 24 mm x 8 mm. The specimens were initially cut from a steel rod and then machined to the desired geometry. The surface hardness of the steel specimens was 63 ± 1 HRC, measured with a microhardness tester (Leitz Miniload, Wild Leitz GmbH, Wetzlar, Germany).

The different roughnesses were obtained with a sequence of grinding and polishing steps to achieve values of Ra in the range between 0.003 µm and 0.70 µm using a surface-grinding machine (RotoPol-21with RotoForce-3 module, Struers, Denmark).

The surface-roughness parameters were measured using a stylus-tip profiler (T8000, Hommelwerke GmbH, Schwenningen, Germany) according to the DIN 4768 standard. Eight measurements in different directions were performed on each specimen and the surface parameters Ra and Rq were determined. The average values of the roughness parameters together with their standard deviations were calculated for every surface-roughness condition. The results are presented in Table 1. It is clear that measurements of the roughness, even in different directions, had relatively low standard deviations, i.e., below 5%, which is negligible compared to the distinctive differences among the five selected roughness ranges.

Table 1: Values of Ra and Rq for different surface roughnesses.

Surface condition

Ra, µm

Rq, µm

Roughness 1

0.003 ± 0.001

0.004 ± 0.001

Roughness 2

0.032 ± 0.001

0.041 ± 0.001

Roughness 3

0.073 ± 0.003

0.094 ± 0.008

Roughness 4

0.190 ± 0.006

0.249 ± 0.011

Roughness 5

0.644 ± 0.016

0.843 ± 0.020

2.2 Measurements of the surface profiles for an analysis of the asperity-peak properties

For the analysis of the asperity-peak properties, additional surface profiles needed to be measured, using the same stylus profiler. Namely, the data from profiles used for the surface-roughness measurements could not be used for the asperity-peak analysis due to the different measuring lengths that were used; these are required for measurements of the surface roughness according to DIN 4768. This would lead to different lateral resolutions Δx, since the same number of data points are always recorded on different measuring lengths. However, for the purpose of this study, the same Δx is needed for all the profiles; otherwise different lateral resolutions would lead to different asperity-peak parameter properties [4, 9, 10, 19].

A lateral resolution Δx = 0.1875 µm was selected for our measurements and can be achieved with most contact and optical profilers [28] and also with AFMs [29]. Table 2 presents the selected measuring conditions for a determination of the asperity-peak properties, valid for all the surface-roughness conditions used.

Table 2: Profile measuring conditions for all the surface roughnesses.

Measuring length




Δx resolution


Measuring speed






Samples of each surface roughness were measured six times in different directions to obtain the representative 2D profiles for an analysis of the asperity-peak properties. Figure 4 shows a representative profile for every surface roughness.

Figure 4: Surface profiles for the asperity-peak analysis of the average roughness values a) Ra = 0.003 µm, b) Ra = 0.032 µm, c) Ra = 0.073 µm, d) Ra = 0.190 µm and e) Ra = 0.644 µm. Different scales are used for the z axis in order to obtain a clearer presentation of the profiles’ topography characteristics.

Prior to the surface-profile analysis, each profile was filtered using a Gaussian filter in order to eliminate the effect of profile tilt.

In addition to the 3PP, 5PP and 7PP criteria, a modified criterion with a variation of the peak-threshold value in the z-direction was also used in this work. However, this was only applied to the 3PP criterion, i.e., to form the M3PP criterion. Accordingly, different peak-threshold values were used for the asperity-peak identification. These were selected in the range proposed by Bhushan and Poon [9] in a sequence of five different Rq values, as presented in Table 3. The 3PP criterion is thus actually the M3PP with a 0% Rq peak-threshold value (Table 3).

Table 3: Peak-threshold values for the 3PP and M3PP criteria for different surface-roughness conditions and peak-threshold values.