Tactile perception of randomly rough surfaces

Abstract

Most everyday surfaces are randomly rough and self-similar on sufficiently small scales. We investigated the tactile perception of randomly rough surfaces using 3D-printed samples, where the topographic structure and the statistical properties of scale-dependent roughness were varied independently. We found that the tactile perception of similarity between surfaces was dominated by the statistical micro-scale roughness rather than by their topographic resemblance. Participants were able to notice differences in the Hurst roughness exponent of 0.2, or a difference in surface curvature of 0.8 [Formula: see text] for surfaces with curvatures between 1 and 3 [Formula: see text]. In contrast, visual perception of similarity between color-coded images of the surface height was dominated by their topographic resemblance. We conclude that vibration cues from roughness at the length scale of the finger ridge distance distract the participants from including the topography into the judgement of similarity. The interaction between surface asperities and fingertip skin led to higher friction for higher micro-scale roughness. Individual friction data allowed us to construct a psychometric curve which relates similarity decisions to differences in friction. Participants noticed differences in the friction coefficient as small as 0.035 for samples with friction coefficients between 0.34 and 0.45.

Figure 1

(a) Color-coded representation of the height of the nine samples, blue indicates valleys and red crests. Each row shows surfaces with the same topographic structure and Hurst roughness exponents of $H=0.4$, $H=0.6$, and $H=0.8$. Close inspection of the images reveals more spatial detail for lower Hurst exponents, that is a higher roughness amplitude at small length scales. The color scale bar refers to height in mm. (b) Cross section with height details for the first 20 mm of the upper edge of the top three images in (a). While there is a strong resemblance between the topographic profiles, the fine structure has lower amplitude for higher Hurst exponents. (c) Height correlation values for different distances report the rms roughness at different length scales.

Figure 2

Photograph of the tactile exploration experiment with three of the 3D printed samples mounted on top of the force sensor.

Figure 3

Results of the ordinal three-dimensional scaling analysis of participants’ decisions on perceived similarity. Data points represent surfaces, with colors representing one of three topographic structures and symbols the small-scale roughness (square $H=0.4$, triangle $H=0.6$, circle $H=0.8$). (a, b) Similarity in visual perception (Experiment 1). (c, d) Similarity in tactile perception through tapping touch (Experiment 2). (e, f) Similarity in tactile perception through sliding touch (Experiment 3).

Figure 4

Dimension 1 of the MDS results plotted versus the root-mean-square (rms) curvature of the surfaces for (a) visual, (b) tapping touch, and (c) sliding touch perception. (d) Average coefficient of friction (CoF) plotted versus the rms surface curvature. The coefficient of friction is averaged for each sample over all trials of all participants. Data points represent surfaces, with colors representing one of three topographic structures and symbols the small-scale roughness (square $H=0.4$, triangle $H=0.6$, circle $H=0.8$).

Figure 5

Psychometric curves showing the proportion of expected similarity decisions as function of the stimulus intensity. (a–c) The stimulus intensity $S=\left|D_{left,ref},-,D_{right,ref}\right|$ is calculated as difference in perceived distance as predicted by the metric $D_{i,j}$ between left or right sample and the reference for the three experiments. (d) The stimulus intensity $S=\left|\left|{\mu }_i,-,{\mu }_{\mathit{ref}}\right|,-,\left|{\mu }_j,-,{\mu }_{\mathit{ref}}\right|\right|$ is calculated from the coefficients of friction measured for each trial and participant. The psychometric functions are modeled by a Weibull sigmoid (a) $R=0.93$, (b) $R=0.59$ (c) $R=0.68$, (d) $R=0.93$.

Figure 6

The plot shows the performance of different perceptual spaces in explaining the experimental data as a function of the number of dimensions for all our experiments. The error bars indicate standard deviations computed using tenfold cross-validation.