Normalising tactile friction

Finger pad friction varies significantly between individuals due to personal differences and environmental effects. For this reason, comparison of the absolute friction values becomes non-informative and is rarely reported in literature. This work investigates whether friction data can be normalised to correlate between individuals. A set of textured samples were tested by 10 volunteers in dry sliding conditions with a range of normal loads up to 4 N. A reference smooth sample was used for each participant to normalise the dataset. The proposed approach allows to eliminate one of the unknown parameters, e.g., finger pad ridge contact area function, and discuss the data with respect to other variables.


Introduction
The physical properties of a product surface can be perceived by humans through active touch and tactile exploration of the surface by the finger pad. An important requirement for texture discrimination is a relative sliding movement between the finger pad and a surface [1]. Resulting friction and normal forces serve as a stimulus, which activate groups of mechanoreceptors located just below the skin surface. Surface textures can be designed to modify this frictional behaviour with the aim to enhance the product tactile perception or improve its handling performance by making it more sticky or slippery. For research and development purposes texture design might be validated by friction experiments. The experimental data could, however, easily result to a very broad set of friction values when compared between individuals [2][3][4]. The variance is partially caused by change in the operational conditions and partially by differences in the finger pad structure from person to person. Therefore, it is not possible to compare finger pad friction data quantitatively between studies, nor to validate texture designs in a generic way based on friction experiments involving multiple persons. Normalisation of the finger pad friction could allow to compare those results and evaluate the contact conditions at the scale of the finger padtexture interaction.
Contact with a finger pad depends on phenomena occurring at multiple length scales. On the macro scale the finger pad deforms producing a near-elliptical shaped gross contact A g . As suggested by conventional Hertzian model [5], gross contact area is expected to increase with the normal load to the power of 2/3. However, experimental results show that gross contact area follows a power function of the normal load A g = k•F m with the reported exponents m ranging from 0.1 to 0.5 [6][7][8][9], suggesting the influence of other parameters. Naturally, people have a different size of the fingertip and, therefore, the finger pad radius differs from person to person. Moreover, the inclination of the finger relative to the surface influences the resulting fingertip radius. Dzidek et al. [8] measured the finger pad gross contact areas at angles of 30 and 45 degrees to the surface. Best power function fits maintained similar exponents m ≈ 0.36, while the reduction in contact area was associated with a decrease in coefficient k. Another influencing parameter, the effective elastic modulus of the skin, is related to finger deformation. At low normal loads, the gross contact area is restricted by harder outer skin layers, while at higher loads, finger pad deformation is restrained by the distal phalanx bone [6,8].
At the meso scale, the finger padsurface interaction involves deformation of the fingerprint ridges, which form a characteristically shaped contact region. Hereinafter it is also referred to as a ridge contact area. A fingerprint structure has an approximate spacing of 350-600 µm between the ridges with respective heights of 40-100 µm [7,[10][11][12]. Ridge contact area is often assumed to represent the real contact area in contact with smooth flat surfaces [9,13,14]. It remains a fraction of the gross contact area with reported values between 0.1 and 0.7 depending on the normal load [3,9,12,13]. Ridge contact area follows a similar power function as gross contact i.e., A fr = k•F m , but with a different coefficient and exponent. The exponents reported in literature are generally higher that those calculated for the gross contact and vary from 0.2 to 0.7 [6,8,9,15]. A few contact models were proposed for the prediction of the finger ridge contact [8,12]. However, they require skin elasticity and fingerprint topography data for the estimation.
The micro-scale is considered in this work for contact with surface features, that have smaller dimensions than the fingerprint ridge at least by one order of magnitude. In this case the ridge is supported along its width by multiple asperities and the sum of their contacts defines the real contact area. Without reliable methods to measure the real contact area, only comparative analysis can be performed, e.g. based on friction measurements with designed and deterministic textures. Given the predominantly adhesive nature of the finger pad friction [16][17][18], introduction of surface texture allows to reduce and limit the real contact area, which allows to study the contact mechanics on the microscale [7,12,17]. Nevertheless, to predict friction for an individual, one requires to know the contact area at meso scale, interfacial shear strength and effective elastic modulus of the skin at microscale.
Coefficient of friction is rarely compared between volunteers due to its variation based on personal and environmental differences [19,20]. Veijgen et al. [21] reported a linear relationship between corneometer hydration values and dynamic friction coefficient. Arvidsson et al. proposed to normalise the friction measurements with the moisture level from the corneometer [22]. They observed the linear increase of the friction coefficient with the rise in skin hydration level for the same sample and finger. Moreover, the data between several participants was compared after linear normalisation of the friction coefficients, based on the ratio between mean total and mean individual values.
The aim of the current work is to investigate whether tactile friction against textured surfaces can be compared between individuals after data normalisation with respect to discussed variables. This approach is designed thus to normalise finger pad friction measurements with the intention of analysing mechanistic factors in comparative studies of tactile friction. The method that is used in the current work is original for skin friction and based on experimental work that uses deterministic surface textures and a smooth reference sample.

Materials
Surface texture designs were selected based on our previous studies [23,24] with the aim to represent three distinctive contact states, i.e., contact with asperity features, full contact with a texture valley and a gradual transition between the two. This approach allows to estimate microscale deformation based on friction measurements. Therefore, three respective textured surfaces and a non-textured reference were used in this study. All textures consist of square packed evenly distributed asperities (Fig. 1). Textures S100 and S200 have spherical asperities with a lateral spacing of 100 and 200 µm respectively. Bumps have the same tip radius of 27 µm and height of 22 µm. Sample E200 consists of ellipsoidal asperities placed with a spacing of 200 µm between each other. Ellipsoids have a minor and major lengths of 50 and 100 µm respectively. The ellipsoidal texture also had the highest feature height of 47 µm. Flat reference samples had an average roughness of 70 nm. The surface topography was obtained with a 3D LED confocal microscope S neox (Sensofar, Spain).
Textures were replicated on a silicone rubber to promote a compliant adhesive contact and prohibit a rise of the deformation friction. Samples were produced by taking a 2 mm thick imprint from a textured embossing roll with commercial silicone rubber ALPA-SIL 97071-3 (CHT Group, Germany). It has a Shore-A hardness of 45 and an estimated Young's modulus of 1.5 MPa. Silicone was cut into equal pieces of 50 × 50 mm and glued to polycarbonate mounting plates using a silicone rubber adhesive Sil-Poxy™ (Smooth-on, USA). Texture features were aligned to perform sliding parallel to the vertical direction of Fig. 1. Therefore, elliptical texture was moved along the major asperity radius to reduce deformation friction component.
Samples were wet wiped with tissues soaked in acetone and alcohol and rinsed with demineralised water. Prior to the friction measurements the samples were put in a vacuum chamber for at least 12 h to prevent possible rubber swelling.

Friction measurements
Friction measurements were performed with a setup designed by Klaassen et al. [19]. The equipment was customised for finger pad sliding tests. The instrument consists of a chamber with a lead screw driven linear stage, which carries a balancing lever with a loadcell on one end and a counterweight on the other (Fig. 2). The hand is placed on a stage palm up with an index finger positioned on a 30-degree wedge. The sample plate attached to the transducer is lowered on top of a finger pad while the normal load is set with a static weight. An additional motor was mounted on a stage to set the sensitivity drift correction, control the lever lowering speed and lock its position angle during carriage return.
Measurements were performed in-vivo with a test group of 10 adult and healthy volunteers (8 males and 2 females), represented within the ages range of 25-55. Before the experiment, the test procedure was thoroughly explained to each participant and an informed consent was taken. Each participant had his own set of four samples. Sample order was randomised and tested within the same day per person.
The tests were carried out in an ambient environment with the temperature and humidity being measured. Prior to performing measurements with each sample, a participant was asked to wash hands with a soap and air dry them for 15 min. Afterwards an index finger pad skin hydration level was taken with a Corneometer CM 825 (Courage + Khazaka GmbH, Germany). At the first load of 0.2 N three preliminary strokes were performed to form a sweat and sebum layer on the surface.
The sample was moved from a subject's body with a constant velocity of 2 mm/s and a total sliding distance of 20 mm. Initial acceleration was set to 2 mm/s 2 to ensure that it does not affect the dynamic friction. After each stroke, the sample was lifted, and the stage was returned to its starting position. The normal load was increased during the measurement series, starting from 0.2 N and followed by the load range from 0.5 N to 4 N with a step of 0.5 N. This decision was made to reduce the variation of the contact area due to the visco-elastic behaviour of the finger pad and conserve the time needed for full finger shape restoration. Three consecutive strokes were performed for each normal load.

Data processing
The forces were measured with a 6-axis Mini40 transducer (Schunk, Germany) at a sampling rate of 100 Hz. The load cell has a resolution of 6 mN and 2 mN in the normal and tangential directions respectively.
A MATLAB script was used to extract the forces and friction coefficient during sliding. That was performed to ensure that initial rising slope, which corresponds to the finger pad deformation, does not influence the results. A high wavelength noise of 0.5 Hz introduced by the guide bearing was removed from the signal. It is recognisable due to the pitch distance of the lead screw of 4 mm and a number of shaft revolutions per second with a chosen speed. Notably, removing of the specific wavelength does not influence the mean value, but reduces signal deviations. The data from the consecutive measurements at each normal load were used to find the arithmetic mean and standard deviation.

Calculation
A minimum dataset that can be used for normalisation consists of friction measurements performed for a single person at a range of normal loads. At least two tested samples are required: a textured sample of interest and a smooth surface to serve as a reference. The obtained data is represented by two friction force functions of the normal load F f ref (F) and F ftex (F) for the reference and the textured samples respectively.
The following assumptions are taken for further analysis: With the given assumptions, the measured friction force with a flat sample can be used as a control reference. It can be approximated as a power function of the normal load as F f ref (F) ≈ kF m , where k and m are the power-law coefficient and exponent, respectively. Power law fit approximation is performed to reduce calculation errors caused by the deviation of the normal loads during measurements.
The friction data for the surface of interest can be represented as a unitless real contact area fraction. This designation is chosen instead of a neutral "normalised coefficient of friction" to emphasize the fundamental meaning behind the obtained values. Considering that the interfacial shear strength τ remains constant for the dataset, the contact area ratio r can be found as a quotient of the friction coefficients or friction forces: where the F ftex (F) is the measured friction force for the textured sample and F f ref (F) is a power fit function for the flat reference. Plotting the contact ratio against the normal load allows to evaluate contact area development and compare it between datasets. However, with a variation of ridge contact area between individuals, the same normal load corresponds to a different ridge pressure. To compare the contact area development at the micro scale, the data can be plotted as a function of the mean ridge pressure. It cannot be found numerically without additional measurements, but it can be substituted by a ratio of the normal and tangential forces. Given that the mean ridge pressure is a function of the normal load as p fr (F) = F/A fr (F), friction data from a reference surface can be used to obtain a dimensionless force ratio:  Plotting contact area ratio as a function of the force ratio r Influence of the effective elastic modulus is generally removed by normalisation of the mean ridge contact pressure by effective elastic modulus or maximum pressure [12,25,26]. With those values unknown, the axis can be normalised by a p fr /τ value, which corresponds to a specific contact area ratio. Use of the deterministic surfaces allows to define the value as a force ratio, at which real contact area fraction for two textures is equal. This step allows to compare experimental data with a contact model and discuss the initial assumptions.

Environmental and corneometer measurements
Measurements with volunteers were performed at different days and times of the day. Room temperature was kept at 22 ± 0.5 • C through the measurements. Average relative humidity of 58 ± 5% was calculated across participants. Corneometer measurements however, varied significantly between individuals (Fig. 3). Most of the volunteers had skin hydration levels with the values between 40 and 60 arbitrary units (AU), which relates to a normal skin condition [27], with subjects V1 and V3 showing extreme values around 30 and 80 AU. For most of the participants skin hydration remained relatively stable during four friction measurement series with a standard deviation below 10 AU. Higher variance during the series can be noticed for V4 and V9, however no specific trend was observed.

Friction measurements
All friction tests exhibited a steady motion without a notable stickslip effect. As anticipated, the calculated friction coefficients varied greatly between volunteers. The difference between the highest and the lowest values for the equivalent samples and normal loads reaches a factor of 4. Flat reference samples showed reduction of friction with increase of the applied normal load, reaching the range of 0.9-2.5 at 4 N (Fig. 4a). Textured samples S200 and E200 exhibited significantly lower coefficient of friction at low normal loads as observed on Fig. 4b and c. However, friction increased with the applied normal loads and stabilised in value ranges of 1.1-2.0 and 0.7-1.3 for S200 and E200 respectively. The lowest friction coefficient was observed for the highest density texture S100 and remained independent of normal load at respective values of 0.35-1.0 (Fig. 4d).
Volunteers can be arranged in descending order by the coefficient of friction for the specific texture and the normal load. However, only the order for the flat reference sample remains consistent for every normal load. The comparison between 0.5 N and 3 N normal loads is presented on Fig. 5. The sorting order for the textured samples does not follow the same trend. High friction with a reference surface for the specific volunteer does not imply that the same holds true for the textured surfaces.

Power law fit
The best power law function fit was determined for each volunteer based on the reference friction measurements from Fig. 4a. The power law equation for the coefficient of friction μ was represented as a function of normal load F as: μ(F) = k•F m− 1 , where k and m are the power-law coefficient and the load index respectively [16]. Consequently, friction force can be represented as F f ref (F) = k•F m . The only three data points which were considered as outliers belong to V1 at 2.0 N, 2.5 N and 3.0 N and stand out from the rest of the curve (Fig. 4a), therefore they were excluded for the best fit calculation. The comparison of the found functions are provided below in the Table 1. Coefficient of determination R 2 was used to evaluate the success of the power fits and was above 0.8 for most of the curves. The exponents for the friction forces fits lay in the range from 0.58 to 0.89, while the latter was obtained from the poor fit for V9. Interestingly, the highest values for the exponent correspond to the subjects with the lowest skin hydration: V3, V6, V8.

Normalisation of friction forces
Obtained power fits are used to normalise the friction data using Eq.
(1). The resulted graphs are shown on Fig. 6. With this representation the influence of the interfacial shear strength is eliminated, and the contact area development can now be compared between textures and volunteers. The highest contact area ratios are shared by subjects V3, V4 and V5, who have previously shown various hydration levels and friction coefficients. For V3, who had the lowest corneometer readings, it indicates a smaller ridge contact area.  according to the Eq. (2). After plotting the graphs, the change of the trend for the texture E200 shown on Fig. 7b became evident for all volunteers. It consists of two parts: initial slope comparable to results of S100 on Fig. 7c and subsequent change of inclination similar to S200 Fig. 7a. On the contrary, surface S100 has a linear trend for all participants. Normalised data for texture S200 show the largest variation. Volunteers V3, V4 and V5 have a calculated real contact ratio above 1 (Fig. 7a), which contradicts the second initial assumption. Interestingly, for two of these participants, V3 and V5, the contact area growth rate decreases around the value of 1.2.

Direct comparison of the absolute friction values between volunteers
provides little insight about the origin of the observed differences. Contact conditions for each person differ based on their unique index finger pad structure and skin properties [8]. Even if friction measurements are performed at the same normal load on the macro-scale, at the asperity level the ridge contact pressure differs, as it remains inversely proportional to each individual's ridge contact area. Furthermore, interfacial shear strength cannot be considered constant for all volunteers. The values reported in literature vary between 1 kPa and 1.2 MPa for various anatomical locations and materials in contact [4,[28][29][30].
In this work comparison of the friction results between volunteers is performed by utilising designed deterministic surfaces [24]. The contact with the textured surfaces can be divided in general, into three distinctive stages. At low normal loads, the skin is fully supported by asperities resulting in a reduced real contact area. With increase of the normal load, the skin micro-deformation exceeds the texture height and comes in contact with the lower surface. This increases the real area of contact and ultimately leads to a transition from the asperity contact state to full contact. This transition is characterised by an increase in friction coefficient. Finally, the contact stabilises at full contact state and further rise of the contact area becomes negligible. The effect of contact transition was discussed by other researchers [7,12,31] and an approach to model it was proposed in our previous work [23].
All three contact states are observed for the textured surfaces. Textures S200 and E200 display an increase in friction coefficient as skin deforms and comes in a contact with a texture valley (Fig. 4b, c). Elliptic texture E200 has a higher equivalent asperity radius and height, therefore, it can support higher load before contact transition starts. It also showed the lowest coefficient of friction across all subjects at normal loads below 1 N. That confirms the initial asperity contact state, considering that the feature density for E200 texture is lower than that  . 6. Calculated contact area ratio as a function of normal load grouped by texture: S200 (a), E200 (b), S100 (c).

D.A. Sergachev et al.
for S100. High density texture S100 remains in asperity contact for all volunteers, which is represented in consistently low friction coefficient across all normal loads (Fig. 4d). The difference between samples is depicted on Fig. 8 for a single volunteer. Interestingly, the texture related trends are independent from the volunteer that tested the samples and can be described in a similar way. Fig. 7. Calculated contact area ratio as a function of pressure ratio grouped by texture: S200 (a), E200 (b), S100 (c).

Reference value for normalisation
The validity of using a reference sample for normalisation can be judged by examining the results for the textured surfaces E200 and S100 more closely. E200 showed the lowest coefficient of friction for all participants at normal loads below 1 N. However, at higher loads, friction increased due to the transition to full contact state. The trends for the two textured surfaces E200 and S100 can be compared to estimate a point of intersection, at which friction coefficient and, therefore, contact area ratio become equal for those surfaces. On Fig. 8 such intersection can be observed at 1 N normal load. On the normalised graph this point should correspond to the same contact area ratio value for all participants.
For the linear elastic case, the intersection of those functions corresponds to a specific deformation. Fig. 9 shows the matching values for two volunteers, at which friction coefficient and, therefore, contact area ratio becomes equal for those surfaces. Due to the differences in ridge contact area and elastic modulus of the skin, normal load at those points significantly vary between volunteers. Table 2 represents the values for the equivalent point for each participant. The mean contact area fraction for the volunteers averages at 0.37. However, participants V3, V5 and V8 deviate further from the rest with the values above 0.43.
The high deviation from other results for these participants indicates a contradiction to the taken assumptions. Therefore, normalisation of their data could be unrepresentative. Interestingly, both volunteers V3 and V8 showed the lowest skin hydration values. Moreover, participants V3 and V5 showed contact area ratio larger than 1 on Fig. 7a. This is a probable case if those volunteers had high fingerprint ridge roughness which led to a reduced contact area with a reference sample.

Normalisation by the point of reference
Considering that a linear elastic case can be applied for small skin deformations, each dataset is normalised by the intersection point discussed above, which corresponds to a mean contact ratio value of 0.37. This point of intersection can be clearly defined both for the friction results and a contact model, which allows to apply the same normalisation approach and oppose the assumptions. This operation allows to eliminate the remaining personal differences from the graphs on Fig. 7.
The convergence of the data for the textured surfaces E200 and S100 means that deformation on the asperity scale remains proportional to pressure for all volunteers. Notably, on Fig. 10c volunteers V3, V5 and V8 show higher values than other participants. As discussed above, skin roughness and low skin hydration resulted in reduced friction against reference samples introducing error to the normalised results.

Comparison with numerical model
A boundary element method (BEM) was used to calculate a contact area ratio for a micro-scale case. The contact was assumed as a halfspace linear elastic problem. Skin was assumed ideally flat, while the texture topography was obtained from confocal measurements. Contact area ratio can be plotted against normalised pressure to represent a function of surface topography. In this case effective elastic modulus chosen for the simulation becomes irrelevant. Normally ridge pressure is normalised by the Young's modulus or pressure at maximum contact. To compare the model with experimental results the data is normalised by the point of intersection for two textures E200 and S100.
After the normalisation of pressure, the total deformation range can be compared to experimental results on Fig. 11. The modelled results are fit to the frictional data as r is a contact area ratio function obtained from the numerical model and p fr is a mean ridge contact pressure normalised by the reference point. Interestingly, the linear fit does not change with texture or participant. It suggests that coefficient of friction is proportional to pressure. This behaviour is best explained by the interfacial shear strength relation to pressure proposed by Adams et al. [28]. They proposed that in the Fig. 9. Intersection of the calculated contact area ratio trends for textures S100 and E200.

Table 2
Normal loads at which contact area ratio for two surfaces S100 and E200 becomes equal. presence of a thin organic film, such as sebum layer, the interfacial shear strength τ is not a constant, but a linear function of the real contact pressure p r as follows: τ = τ 0 + αp r , where τ 0 is the intrinsic interfacial shear strength and α is a pressure coefficient. For textured surfaces average real contact pressure is expected to be several times higher, which leads to higher interfacial shear strength for the same normal load. Interestingly, the volunteer data lies within a small range of normalised ridge pressure values. The participants experienced a similar range of skin micro-deformations, even though the personal differences were prominent. For this to hold true, the higher skin elastic modulus must be accompanied by a corresponding increase in ridge pressure and vice versa, which can be achieved by the deformation of fingerprint ridges. This could explain why perception of surface textures is closely related to texture dimensions and similar textures receive uniform ratings [32,33].

Assumptions and limitations
The validity of the assumptions taken in Section 3 can be discussed  based on the observed datasets. The first assumption states that fingerprint ridge contact area as a function of normal load does not change during the test series for a given individual. Environmental conditions remained stable during each test series, and measurements were performed at least 15 min after the hands cleaning procedure, which is in agreement with literature. Acclimatisation time between 10 and 30 min is considered sufficient for the skin to reach a steady state [4,19,[34][35][36]. Based on results obtained, a change in the ridge contact area function occurred for participant V9. It was represented in a deviation of corneometer readings prior to the test with E200 and resulted in a noticeable divergence from the general trend (Fig. 7b). For most of the volunteers the skin hydration level remained stable during the measurement procedure. However, one should exercise caution if the experiments are performed across several days.
The second assumption states that real contact area for a reference sample approaches ridge contact area at all normal loads. It can be considered viable if skin and surface roughness is negligible or at least one of the surfaces is compliant. In the current study, the combination of silicone rubber material with a relatively low surface average roughness allows to satisfy the assumption. Power law fit exponents are close to the theoretical exponent of 2/3, predicted for adhesive contact and experimental values from other studies [6,13,28,37]. With increase of the reduced Young's modulus or surface roughness, real contact area reduces leading to errors during normalisation procedure as it was observed with the participants V3, V5 and V8.
The third assumption considers that the friction force is based purely on adhesion. For the dry finger pad sliding against smooth surfaces, adhesion is considered to be a predominant component of friction [16][17][18]. Tomlinson et al. [38] reported a 10% deformation term for the triangular ridged surfaces with the heights over 250 µm. Moreover, they found an interlocking term to become considerable for surfaces with heights above 40 µm. Textures used in this study were designed to minimise interlocking and have smaller feature sizes. However, the interfacial shear strength seems to be dependent on pressure as discussed by Adams et al. [28]. It leads to overestimation of contact area fraction after normalisation, which increases linearly with pressure and does not change with participant.

Conclusions
• Normalisation of the frictional data allows to reduce one of the unknown personal variables: function of the ridge contact area, reduced Young's modulus or interfacial shear strength. Furthermore, the results can be normalised to dimensionless values to compare the contact area development on the microscale. The resulted graphs confirm interfacial shear strength relation to contact pressure. • All subjects experienced the same contact states with the tested textures, despite the personal differences, contact area and skin hydration levels. • This suggests that deformation of the skin on the microscale is independent of the skin elasticity due to the fingerprint ridge pattern. In other words, the change of the skin Young's modulus is closely related to the reduction of the ridge contact area and, therefore, increase of the ridge pressure, leading to comparable displacement values.

Ethics approval and consent to participate
The procedures performed in the current study were approved by the Natural Sciences and Engineering Sciences Ethics committee, University of Twente, Enschede. The measurements were carried out in compliance with COVID19 government regulations active during that time.
All subjects provided a written informed consent. None of the experiments were invasive or harmful physiologically or psychologically. All data was stored anonymously, and the participants had the right to quit at any time if they so wished.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.