Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine http://pih.sagepub.com/ Development and experimental validation of a mathematical model for friction between fabrics and a volar forearm phantom A M Cottenden, D J Cottenden, S Karavokiros and W K R Wong Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 2008 222: 1097 DOI: 10.1243/09544119JEIM406 The online version of this article can be found at: http://pih.sagepub.com/content/222/7/1097 Published by: http://www.sagepublications.com On behalf of: Institution of Mechanical Engineers Additional services and information for Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine can be found at: Email Alerts: http://pih.sagepub.com/cgi/alerts Subscriptions: http://pih.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsReprints.nav Permissions: http://www.sagepub.com/journalsPermissions.nav Citations: http://pih.sagepub.com/content/222/7/1097.refs.html >> Version of Record - Oct 1, 2008 What is This? Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 1097 Development and experimental validation of a mathematical model for friction between fabrics and a volar forearm phantom A M Cottenden1, D J Cottenden1*, S Karavokiros1, and W K R Wong2 1 Department of Medical Physics and Bioengineering, University College London, UK 2 SCA Hygiene Products AB, Gothenburg, Sweden The manuscript was received on 8 February 2008 and was accepted after revision for publication on 9 April 2008. DOI: 10.1243/09544119JEIM406 Abstract: An analytical mathematical model for friction between a fabric strip and the volar forearm has been developed and validated experimentally. The model generalizes the common assumption of a cylindrical arm to any convex prism, and makes predictions for pressure and tension based on Amontons’ law. This includes a relationship between the coefficient of static friction (m) and forces on either end of a fabric strip in contact with part of the surface of the arm and perpendicular to its axis. Coefficients of friction were determined from experiments between arm phantoms of circular and elliptical cross-section (made from Plaster of Paris covered in Neoprene) and a nonwoven fabric. As predicted by the model, all values of m calculated from experimental results agreed within ¡8 per cent, and showed very little systematic variation with the deadweight, geometry, or arc of contact used. With an appropriate choice of coordinates the relationship predicted by this model for forces on either end of a fabric strip reduces to the prediction from the common model for circular arms. This helps to explain the surprisingly accurate values of m obtained by applying the cylindrical model to experimental data on real arms. Keywords: 1 skin, friction, mathematical model, experimental validation INTRODUCTION AND BACKGROUND Wearers of incontinence pads often experience skin damage, soreness, and discomfort in the diaper area [1, 2]. When skin is occluded by (wet) pad materials, the skin becomes over-hydrated, thereby compromising its barrier function and making it susceptible to abrasion damage by friction against the pad and vulnerable to chemical irritation and bacterial colonization [3–5]. In an earlier paper [6], the present authors described the development and validation of a new method for determining the coefficient of friction between volar forearm skin (a commonly used surrogate for diaper area skin) and nonwoven materials of the *Corresponding author: Department of Medical Physics and Bioengineering, University College London, Archway Campus Clerkenwell Building, Highgate Hill, London N19 5LW, UK. email: d.cottenden@ucl.ac.uk JEIM406 F IMechE 2008 kind used to face incontinence pads. The apparatus (see Fig. 1) and the experimental procedure are described in detail in the earlier paper [6] but, in essence, the strip of nonwoven fabric under test is dragged across the volar forearm using a tensometer. A weight (mass m) is attached to the free vertical end of the fabric and the tensometer force F is plotted against displacement. Following the example of Gwosdow et al. [7], the maximum force (Fmax) on the plot is taken to be that needed to overcome static friction and the coefficient of friction is calculated using 2 Fmax m~ ln ð1Þ p mg Equation (1) assumes the arm to be a rigid cylinder and the nonwoven fabric to be inextensible (as in Fig. 1). In spite of these highly unrealistic assumptions, coefficients of friction measured using the authors’ Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 1098 A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong Fig. 2 A diagram of the arm. It is assumed that the arm is a prism over the length considered. The major variables and functions are illustrated 2 MATHEMATICAL MODEL The new mathematical model characterizes the system in terms of the following quantities, many of which are illustrated in Fig. 2: Fig. 1 The set-up used by the authors in an earlier paper [6]: (a) shows the equipment in use, while (b) shows the assumed geometry, where the circle represents a cross-section of the arm new method [6] agreed remarkably well with values measured using a mathematically simpler but experimentally more difficult method in which fabric samples were dragged over regions of the volar forearm that could be well approximated as flat. Measurements were made on the wet and dry volar forearms of five young women using three different nonwoven materials. The correlation coefficient for the two methods was 0.95. The purpose of the work described in the current paper was to extend the mathematical model to address convex prisms of arbitrary cross-section and to explain why the earlier model produced such accurate values for coefficients of friction in spite of its obviously unrealistic assumptions. (a) the shape of the arm immediately before initial slippage, described in terms of a polar function R(h) around an arbitrary coordinate centre within the arm: as shown in Fig. 2, first contact between the vertical hanging fabric and the arm is taken as h 5 0 and the loss of contact near the tensometer is taken as h 5 H; (b) the tension in the fabric at an angle of h, T(h): from Fig. 2 it follows that T(0) 5 mg and T(H) is the tension in the fabric between the tensometer and the arm; (c) the element of normal reaction force from the arm at an angle h, denoted dN; (d) the element of angle through which the arm surface turns when h R h + dh, denoted dx (Fig. 3). 2.1 Assumptions The present model makes certain assumptions on both the arm geometry and the physical mechanisms at play. A diagram of the geometry (including relevant variables) is shown in Fig. 2. The assumptions are as follows. 1. The arm is a strictly convex prism at the instant of slip. It is assumed that contact between the fabric Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 JEIM406 F IMechE 2008 Mathematical model for friction between fabrics 1099 tangent of the angle between that function’s graph and the x axis, and considering Fig. 3 it follows that dR dx~dh{d tan{1 dl 1 dR ~dh{d tan{1 RðhÞ dh ð3Þ Fig. 3 The angular change on the arm surface for a change of dh in coordinates. The tangential are length l is defined as R(h)dh and the skin is maintained all around the curve r 5 R(h);h g [0,H]. 2. Amontons’ law is obeyed. The friction force at the instant of slip locally obeys Amontons’ law, Ff 5 mN, where Ff is the friction force, N is the normal force, and m is the coefficient of static friction. m is assumed not to vary with N. m is also assumed not to vary intrinsically with fabric tension. 3. Total slip occurs when each location is at its local maximum loading. Neither real arms nor real fabrics are inextensible. As deformation and stretching will occur, this will act anomalously to load the arm over some of the arc of contact and to unload other parts, in turn meaning that some locations will reach the limit of the shear they can support before others. Local slip or creep will occur in these regions. This assumption implies that local creep will simply act to remove regions of anomalous loading without causing general slip. This ensures that it is locally true that dF f 5 mdN when general slip occurs. If the coefficient of dynamic friction were equal to the static coefficient, then the system would certainly behave this way. It should be noted that it is not necessary to assume that the arm does not deform as it is loaded, nor is it assumed that the fabric does not stretch. The sole condition on arm deformation is that whatever occurs does not cause any concavity. 2.2 At the point of slippage all forces are in equilibrium. In particular ð2Þ at h. The derivative of a function is equal to the JEIM406 F IMechE 2008 ð4Þ where the last equality in equation (3) follows by identifying a tangential arc length l with R(h)dh. Substituting this result into equation (2) produces d 1 dR tan{1 dN ~T ðhÞdh 1{ dh RðhÞ dh ð5Þ By assumption, at the point of slippage dFf 5 mdN. Further, it is clear that the tension T(h) comprises the deadweight mg and the total frictional force accrued between the fabric and arm up to the angle h, i.e. T ðhÞ~mgzFf ðhÞ ð6Þ ? dT ~dFf where Ff(h) is the integral of dFf between 0 and h. Combining equations (5) and (6) and Amontons’ law, a closed equation for the system can be written dT d 1 dR {1 ~T ðhÞdh 1{ tan m dh RðhÞ dh ð7Þ This can easily be solved by separation of variables to give T ðhÞ~T ð0Þexp mh{m tan {1 1 dR RðhÞ dh h ! ð8Þ 0 hence ! 1 dR H {1 T ðHÞ~mg exp mH{m tan RðhÞ dh 0 ð9Þ by applying the boundary conditions mentioned at the start of this section. A solution dN ~T ðhÞdx d 1 dR {1 tan dx~dh 1{ dh RðhÞ dh 2.3 Choice of coordinate centre As equation (9) will be the most regularly used the free choice of coordinate centres will be used to simplify it. If the coordinate centre is chosen to be Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 1100 A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong d [arc length]2 5 (Rdh)2 + dR2, hence sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dR2 dh d ½arc length~ RðhÞ2 z dh 1 dN P ðhÞ~ h i1=2 dh 2 2 w RðhÞ zR0 ðhÞ ð12Þ From equation (6) and Amontons’ law it follows that dT 5 mdN at the point of slip, hence Fig. 4 the point of intersection of perpendicular bisectors to tangents to R(h) at h 5 0, h 5 H (see Fig. 4) then by definition dR dR ~ ~0 dh 0 dh H Substituting this result into equation (9) greatly simplifies it by making both the upper and lower limits of the integral in the exponent vanish T ðHÞ~mg expðmHÞ ð10Þ This is identical with the expression connecting T(H) and mg on a cylinder [7]. It is frequently more useful to rearrange this equation to give m in terms of the other variables m~ 2.4 dN 1 dT ~ dh m dh If the centre of coordinates is taken as the intersection of the perpendicular bisectors to the tangents to the arm at h 5 0, H then the relationship between the forces on either end of the fabric strip simplifies significantly 1 T ðH Þ ln H mg 2 2 0 2 3 00 6RðhÞ z2R ðhÞ {RðhÞR ðhÞ7 P ðhÞ~4 h i3=2 5T ðhÞ 2 2 0 w RðhÞ zR ðhÞ ð13Þ immediately before slip occurs. It is important to recall that if this expression is used for general values of h then the complete form of T(h) (equation (8)) must also be used: the simplified version (equation (10)) applies only to h 5 0 or h 5 H. 3 3.1 EXPERIMENTAL VALIDATION Materials The mathematical model was investigated experimentally using two model arms made from Plaster of ð11Þ Pressure If the normal force is known at any point around the surface of the arm then the pressure can be calculated. If the width of the fabric strip is w and the pressure P P ðhÞ~ 1 dN w d½arc length The arc length of the arm can be determined easily by considering Pythagoras’ theorem Fig. 5 Model arms were constructed from Plaster of Paris wrapped around with Neoprene. The join in the Neoprene was avoided in all experiments Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 JEIM406 F IMechE 2008 Mathematical model for friction between fabrics Fig. 8 Fig. 6 An optical micrograph of the test fabric used in all experiments Paris covered with a layer (1 mm thick) of Neoprene (Fig. 5). One arm was circular (diameter, 66 mm) and the other elliptical (major and minor axes, 67 and 45 mm). It was not the intention to imitate accurately the shape or mechanical properties of real arms or the friction behaviour of real skin. Rather the need was for prisms of well-defined cross-section that could be made easily. All friction experiments were conducted with strips of a spunlaid, thermal-calendered polypropylene material with area density 17 g/m2 and fibre diameter 30 mm (see Fig. 6), denoted fabric A in the earlier study [6]. Strips were 30 mm wide and 450 mm long. 3.2 Method With the cylindrical arm, experiments were run for starting arc of contact H0 5 63.5u, 76u, 90u, 111.5u, 131.5u (see Fig. 8 later). Similarly, a range of H0 values were used with the elliptical prism arm (H0 5 70u, 80u, 90u, 105u, 120u) with the major axis at 0u, 90u, and 135u to the horizontal (Fig. 7). All experiments were run with masses m 5 10 g, 30 g, 1101 The angle of contact, H approaches p/2 as the displacement of the cross-head increases 50 g, and 70 g (Fig. 2) and there were five repeats for each mass, for each of three fabric test pieces for the cylindrical arms and two test pieces for the elliptical prism. The tensometer (Model MTT170, Dia-Stron, USA) cross-head speed was 150 mm/min. In each experiment the tensometer force F was plotted against cross-head displacement, and the first maximum in the graph – corresponding to initial slippage between the fabric and the arm – was used to calculate the coefficient of static friction. For H 5 p/2 the calculation is simple because F 5 T(H) and H does not change with cross-head displacement. For H ? p/2 two corrections have to be made. 1. Cross-head displacement. As the cross-head moves away from the arm the angle of contact changes (shown in Fig. 8): H decreases with crosshead displacement for H0 . p/2, and increases for H0 , p/2. By application of trigonometry, and taking the cross-head displacement DL to be large compared to the distance l (Fig. 8) Q~tan {1 l0 tan Q0 l0 zDL where Q and Q0 are defined in Fig. 8. As Q 5 p/2 – H and Q0 5 p/2 – H0 p l0 tan½ðp=2Þ{H0 H~ {tan{1 2 l0 zDL Fig. 7 Orientations for elliptical prism arms JEIM406 F IMechE 2008 ð14Þ For the test configuration, l0 5 100 mm and DL ( 3 mm which corresponds to angular shifts of less than 1u for all experiments. As these corrections would cause an error in m calculations of less than 1 per cent they are neglected in presenting the results. Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 1102 A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong Fig. 9 Example graphs of F against displacement: (a) corresponds to m 5 70 g and H 5 90u; (b) corresponds to m 5 30 g and H 5 63.5u. The oscillations are thought to be attributable to repeated stick and slip between the fabric and the Neoprene 2. Resolution of F. If H ? p/2 then T(H) ? F. Rather, by resolving forces, F 5 T(H)cosQ 5 T(H)sinH. Equations (10) and (11) can therefore be rewritten as F ~mg expðmHÞ sinH ð15Þ 1 F mðF,m,HÞ~ ln H mg sinH ð16Þ The maximum force (Fmax) on the plot of force against displacement was used to calculate the coefficient of static friction using equation (16). 3.3 Results Example plots of F against displacement are shown in Fig. 9 for experiments on the cylindrical arm. The plot for H0 5 90u averages to a horizontal line, while that for H0 5 63.5u increases with displacement, as expected from equation (15). Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 JEIM406 F IMechE 2008 Mathematical model for friction between fabrics Fig. 10 Example graphs of ln(T(H)/mg) against H for the cylindrical arm (a) and each orientation of the elliptical prism (b)–(d). The four point and line styles correspond to the four different applied weights in newtons. For (a) 0.57 , m , 0.66, 0.96 , R2 , 0.98; for (b) 0.52 , m , 0.60, 0.91 , R2 , 0.96; for (c) 0.61 , m , 0.62, 0.94 , R2 , 0.98; for (d) 0.56 , m , 0.64, 0.93 , R2 , 0.98 Plots of ln(T(H)/mg) against H are given for an example data set for the cylindrical arm (Fig. 10(a)) and each orientation of the elliptical prism (Figs 10(b) to (d)). The gradient in each case is m (from equation (10)). In all, 36 m values were obtained by linear regression: 0.91 , R2 , 0.99 for 35 (R2 5 0.78 for the other fit; it was not clear why this correlation was weaker). As predicted by the model, the graphs in Fig. 11 show little systematic variation of m with m. There was some variation of m between data sets (¡8 per cent), but no more than could be explained by variablity between samples of the Neoprene and the fabric. 4 1103 DISCUSSION The mathematical model predicts that m should be invariant with H, with m, and with the crosssectional shape of the model arm (subject to a JEIM406 F IMechE 2008 careful choice of coordinate centre) provided it is convex across the whole area of nominal contact with the fabric. This has now been experimentally confirmed. The agreement between model and experiments implies that, at least for the majority of the pressure range involved here, Amontons’ law holds to a good approximation. The agreement with Amontons’ law can be further elucidated by considering Fig. 11, which shows a steady increase in m with m for each sample data set, in contradiction with the model. However, the increase is small compared to the scatter in the data, and moreover represents a variation in m of less than 5 per cent across the experimental mass range. This is likely a result of changes in the interacting Neoprene and nonwoven surfaces as the pressure increases, and corresponds to a small departure from Amontons’ law. The oscillatory stick–slip behaviour seen in Fig. 9 is caused by the inability of the smaller dynamic friction Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 1104 A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong Fig. 11 Graphs showing the variation of m with mass corresponding to the graphs in Fig. 10. m is calculated for all {F, H, m} groups and all are plotted against m. The horizontal lines denote the mean of all m, and the mean m for each mass is shown as a large square. Letters (a)–(d) correspond to those in Fig. 10 force to maintain the deformation caused by the static friction force at the point of slip. As the ‘yield force’ (and so surface deformation before slip occurs) is proportional to the normal force, the magnitude of the stick–slip oscillation would be expected to increase with m, as was indeed observed. Inspection of Fig. 10 shows that the spread of data from experiments with different masses is of the same order as the spread of data from replicates of experiments with the same mass, leading to variations in m of ¡8 per cent for each configuration. This is very similar to the spread of m values between configurations. This degree of variation is consistent with the likely variations of material properties, within a given sample and between samples. These results also provide the opportunity to address some related issues. 4.1 Robustness of the m values In practice, it is simplest to conduct experiments with H 5 90u as F 5 T(H) and H0 5 H for all displacements. Given that it is difficult to fix H exactly in experiments on real arms, it is important to establish how sensative the m value derived from an experiment is to inaccuracies in H. If the coefficient of friction calculated on the basis of measured values of F and m, and an (inaccurately) ~, and the difference assumed H 5 p/2 is denoted m ~ and the true m (calculated using the between m correct H 5 p/2 + DH) is denoted D~ m then the fractional error is D~ m mðF,m,ðp=2ÞÞ{mðF,m,ðp=2ÞzDHÞ ~ ~ m mðF,m,ðp=2ÞzDHÞ Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 JEIM406 F IMechE 2008 Mathematical model for friction between fabrics 1105 From equation (16) it follows that to first order in DH D~ m LH mðF,m,p=2Þ ~{DH ? ~ m mðF,m,p=2Þ D~ m fmðF,m,ðp=2ÞÞ=p=2g{f1=½p=2 tanðp=2Þg ~DH ~ m mðF,m,ðp=2ÞÞ D~ m 2DH ~ ~ m p ð17Þ as 1/tan(p/2) 5 0. This means that if an error less than 5 per cent were required, then the angular deviation would have to be less than 4.5u. In practice, a 4.5u deviation from horizontal is easy to detect by eye: the potential error introduced by inaccurate angle measurement is small, making the method suitable for routine and frequent use. 4.2 Variation of pressure with h It is worth considering pressure and shear stress sf (owing to friction) around the arc of contact. As dFf ~mdN ~ ? sf : ~ m dN w d½arc length 1 dFf w d½arc length ? sf ~mP where the last step used equation (13), and w is the width of the fabric strip. In this context, discussing pressure is equivalent to discussing shear stress. In Fig. 12 calculated pressure is plotted against h for each of the three ellipse orientions used in these experiments. It is interesting and important to note that for each orientation (w) the pressure at h 5 0 is the same for high m (1.3) and low m (0.3), that is P(0) depends only on arm geometry and applied weight (Fig. 2). Equation (13) makes it clear that P(h) is determined by the product of a geometrical prefactor and the local tension. Equation (9) shows that ln T(h) 5 mg(h): a low m leads to a slow increase in T, while a larger m causes rapid increase (compare parts (a) and (b) in Fig. 12). This increase is significantly modulated by the geometry for low m values, even causing an almost uniform pressure for the ellipse with a horizontal major axis. However, for large m, P increases very rapidly with h so that local pressure at h 5 p/2 is 5–10 times larger than the initial pressure. This result underlines the potential for serious skin damage to occur if wet incontinence pads are removed carelessly. For example, if a wet pad is JEIM406 F IMechE 2008 Fig. 12 Graphs of pressure against h (calculated using equation (13)) at two values of m for ellipses of the dimensions used in these experiments. The three lines correspond to the three orientatations used, described by the angle w of the major axis to the horizontal (Fig. 7). The two values of m correspond to typical values between a nonwoven and wet skin (m 5 1.3, part (a)), and a non-woven and dry skin (m 5 0.3, part (b)), found by the authors in a previous in vivo study of volar forearm skin [6] pulled from beneath a supine user such that it is in contact with an arc of the buttocks, the skin near where the pad loses contact will experience shear stresses far higher than the average values. The situation will be still worse than suggested by this model, as the normal pressure is not only caused by the force in the pad, but is supplemented by the patient’s weight. ACKNOWLEDGEMENTS The authors acknowledge with thanks SCA Hygiene Products AB, the Engineering and Physical Sciences Research Council, and the General Hospital of Rhodes who funded the work. Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 1106 A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong REFERENCES 1 Schnelle, J. F., Cruise, P. A., Alessi, C. A., Samarrai, N. A., and Ouslander, J. G. Individualised nighttime incontinence care in nursing home residents. Nursing Res., 1998, 47(4), 197–204. 2 Brown, D. S. Diapers and underpads. Part 1: skin integrity outcomes. Ostomy Wound Mgmnt, 1994, 40, 20–22, 24–6, 28. 3 Lyder, C. H., Clemes-Lowrance, C., Davis, A., Sullivan, L., and Zucker, A. Structured skin care regimen to prevent perineal dermatitis in the elderly. J. Enterostomal Therapy Nursing, 1992, 19(1), 12–16. 4 Berg, R. W. Etiology and pathophysiology of diaper dermatitis. Adv. Dermatology, 1988, 3, 75–98. 5 Ersser, S. J., Getliffe, K., Voegeli, D., and Regan, S. A critical review of the inter-relationship between skin vulnerability and urinary incontinence and related nursing intervention. Int. J. Nursing Stud., 2005, 42, 823–835. 6 Cottenden, A. M., Wong, W. K. R., Cottenden, D. J., and Farbrot, A. Development and validation of a new method for measuring friction between skin and nonwoven materials. Proc. IMechE, Part H: J. Engineering in Medicine, 2008, 222(H5), 791–803. 7 Gwosdow, A. R., Stevens, J. C., Berglund, L. G., and Stolwijk, J. A. J. Skin friction and fabric sensation in neutral and warm environments. Textile Res. J., 1986, 56, 574–580. DL m N P R(h) T(h) w h H DH H0 l APPENDIX m Notation F Ff Fmax g g(h) h l l0 L experimentally measured force applied to the nonwoven frictional force at a location experimentally measured force required to initiate slippage gravitational field strength an unknown function of h vertical distance between the point of loss of contact between the nonwoven and the arm phantom, and the tensometer cross-head arc length around the surface of the arm phantom initial distance between the point of last contact between the nonwoven and arm phantom, and the cross-head distance at slippage between the point of last contact between the , m , Dm sf Q Q0 x nonwoven and arm phantom, and the cross-head distance moved by the tensometer cross-head to cause slippage mass of the dead weight hung on the nonwoven normal force exerted by the arm phantom pressure of the nonwoven against the arm phantom radius of the arm (from an arbitrary coordinate centre) at the angle h tension in the nonwoven at the angle h width of the nonwoven strip angle (measured from an arbitrary coordinate centre) from the point of first contact between nonwoven and arm phantom value of h at which the nonwoven parts from the arm phantom difference between the assumed value of H and the actual value value of H at which an experiment was set up distance between the initial loss of contact between the nonwoven and arm phantom and the final one coefficient of static friction between the nonwoven test material and the arm phantom value of m calculated owing to an incorrect estimation of H difference between the true value of m and the value calculated owing to an incorrect estimation of H frictional shear stress at the interface between the nonwoven and arm phantom angle of depression or elevation of the fabric strip from horizontal at the point of slippage initial angle of depression or elevation of the fabric strip from horizontal angle by which the surface of the arm phantom has changed between one location and another Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011 JEIM406 F IMechE 2008