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Friction is a force that is around us all the time that opposes relative motion between systems in contact but also allows us to move, which you have discovered if you have ever tried to walk on ice. While a common force, the behavior of friction is actually very complicated and is still not completely understood. We have to rely heavily on observations for whatever understandings we can gain. However, we can still deal with its more elementary general characteristics and understand the circumstances in which it behaves.
Friction
Friction is a force that opposes relative motion between systems in contact.
One of the simpler characteristics of friction is that it is parallel to the contact surface between systems and always in a direction that opposes motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. For example, friction slows a hockey puck sliding on ice. But when objects are stationary, static friction can act between them; the static friction is usually greater than the kinetic friction between the objects.
Kinetic Friction
If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction.
Imagine, for example, trying to slide a heavy crate across a concrete floor&#;you may push harder and harder on the crate and not move it at all. This means that the static friction responds to what you do&#;it increases to be equal to and in the opposite direction of your push. But if you finally push hard enough, the crate seems to slip suddenly and starts to move. Once in motion, it is easier to keep it in motion than it was to get it started, indicating that the kinetic friction force is less than the static friction force. If you add mass to the crate, say by placing a box on top of it, you need to push even harder to get it started and also to keep it moving. Furthermore, if you oiled the concrete, you would find it to be easier to get the crate started and keep it going, as you might expect.
Figure 5.2 is a crude pictorial representation of how friction occurs at the interface between two objects. Close-up inspection of these surfaces shows them to be rough. So when you push to get an object moving, in this case, a crate, you must raise the object until it can skip along with just the tips of the surface hitting, break off the points, or do both. A considerable force can be resisted by friction with no apparent motion. The harder the surfaces are pushed together, such as if another box is placed on the crate, the more force is needed to move them. Part of the friction is due to adhesive forces between the surface molecules of the two objects, which explain the dependence of friction on the nature of the substances. Adhesion varies with substances in contact and is a complicated aspect of surface physics. Once an object is moving, there are fewer points of contact (fewer molecules adhering), so less force is required to keep the object moving. At small but nonzero speeds, friction is nearly independent of speed.
Figure
5.2
Frictional forces, such as ff size 12{f} {}, always oppose motion or attempted motion between objects in contact. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks can skip along the bottom surface. Thus, a force is required just to set the object in motion. Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction free. Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles.
The magnitude of the frictional force has two forms: one for static situations (static friction), the other for when there is motion (kinetic friction).
When there is no motion between the objects, the magnitude of static friction f s f s size 12{f rSub { size 8{s} } } {} is
5.1
fs&#;μsN,fs&#;μsN, size 12{f rSub { size 8{s} } = μ rSub { size 8{s} } N} {}
where μsμs size 12{μ rSub { size 8{s} } } {} is the coefficient of static friction and N N is the magnitude of the normal force, the force perpendicular to the surface.
Magnitude of Static Friction
Magnitude of static friction fsfs size 12{f rSub { size 8{s} } } {} is
5.2
fs&#;μsN,fs&#;μsN, size 12{f rSub { size 8{s} } = μ rSub { size 8{s} } N} {}
where μsμs size 12{μ rSub { size 8{s} } } {} is the coefficient of static friction and N N is the magnitude of the normal force.
The symbol &#; &#; size 12{ = {}} {} means less than or equal to, implying that static friction can have a minimum and a maximum value of μsNμsN size 12{μ rSub { size 8{s} } N} {}. Static friction is a responsive force that increases to be equal and opposite to whatever force is exerted, up to its maximum limit. Once the applied force exceeds fs(max)fs(max) size 12{f rSub { size 8{s \( "max" \) } } } {}, the object will move. Thus
5.3
fs(max)=μsN.fs(max)=μsN. size 12{f rSub { size 8{s \( "max" \) } } =μ rSub { size 8{s} } N} {}
Once an object is moving, the magnitude of kinetic friction f k f k size 12{f rSub { size 8{k} } } {} is given by
5.4
fk=μkN,fk=μkN, size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {}
where μkμk size 12{μ rSub { size 8{K} } } {} is the coefficient of kinetic friction. A system in which fk=μkNfk=μkN size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {}is described as a system in which friction behaves simply.
Magnitude of Kinetic Friction
The magnitude of kinetic friction fkfk size 12{f rSub { size 8{K} } } {} is given by
5.5
fk=μkN,fk=μkN, size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {}
where μkμk size 12{μ rSub { size 8{K} } } {} is the coefficient of kinetic friction.
As seen in Table 5.1, the coefficients of kinetic friction are less than their static counterparts. That values of μμ size 12{μ} {} in Table 5.1 are stated to only one or, at most, two digits is an indication of the approximate description of friction given by the above two equations.
System Static Frictionμsμs size 12{μ rSub { size 8{s} } } {} Kinetic Frictionμkμk size 12{μ rSub { size 8{K} } } {} Rubber on dry concrete 1.0 0.7 Rubber on wet concrete 0.7 0.5 Wood on wood 0.5 0.3 Waxed wood on wet snow 0.14 0.1 Metal on wood 0.5 0.3 Steel on steel (dry) 0.6 0.3 Steel on steel (oiled) 0.05 0.03 Polytetrafluoroethylene on steel 0.04 0.04 Bone lubricated by synovial fluid 0.016 0.015 Shoes on wood 0.9 0.7 Shoes on ice 0.1 0.05 Ice on ice 0.1 0.03 Steel on ice 0.4 0.02Table
5.1
Coefficients of Static and Kinetic Friction
The equations given earlier include the dependence of friction on materials and the normal force. The direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force. For example, if the crate you try to push (with a force parallel to the floor) has a mass of 100 kg, then the normal force would be equal to its weight, W=mg=(100 kg)(9.80m/s2)=980 NW=mg=(100 kg)(9.80m/s2)=980 N size 12{W="mg"= \( "100""kg" \) \( 9 "." "80"`"m/s" rSup { size 8{2} } \) ="980"N} {}, perpendicular to the floor. If the coefficient of static friction is 0.45, you would have to exert a force parallel to the floor greater than fs(max)=μsN= 0.45(980N)=440Nfs(max)=μsN= 0.45(980N)=440N size 12{f rSub { size 8{S \( "max" \) } } =μ rSub { size 8{S} } N=0 "." "45" times "980"N="440"N} {}to move the crate. Once there is motion, friction is less, and the coefficient of kinetic friction might be 0.30, so that a force of only 290 N, (fk=μkN=0.N=290Nfk=μkN=0.N=290N size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N= left (0 "." "30" right ) left ("980"" N" right )="290"" N"} {}, would keep it moving at a constant speed. If the floor is lubricated, both coefficients are considerably less than they would be without lubrication. Coefficient of friction is a unitless quantity with a magnitude usually between 0 and 1.0. The coefficient of the friction depends on the two surfaces that are in contact.
Take-Home Experiment
Find a small plastic object (such as a food container) and slide it on a kitchen table by giving it a gentle tap. Now spray water on the table, simulating a light shower of rain. What happens now when you give the object the same-sized tap? Now add a few drops of vegetable or olive oil on the surface of the water and give the same tap. What happens now? This latter situation is particularly important for drivers to note, especially after a light rain shower. Why?
Many people have experienced the slipperiness of walking on ice. However, many parts of the body, especially the joints, have much smaller coefficients of friction&#;often three or four times less than ice. A joint is formed by the ends of two bones, which are connected by thick tissues. The knee joint is formed by the lower leg bone (the tibia) and the thighbone (the femur). The hip is a ball (at the end of the femur) and socket (part of the pelvis) joint. The ends of the bones in the joint are covered by cartilage, which provides a smooth, almost glassy surface. The joints also produce a fluid (synovial fluid) that reduces friction and wear. A damaged or arthritic joint can be replaced by an artificial joint (Figure 5.3). These replacements can be made of metals (stainless steel or titanium) or plastic (polyethylene), also with very small coefficients of friction.
Figure
5.3
Artificial knee replacement is a procedure that has been performed for more than 20 years. In this figure, we see the post-op X-rays of the right knee joint replacement. (Credit: Mike Baird, Flickr)
Other natural lubricants include saliva produced in our mouths to aid in the swallowing process and the slippery mucus found between organs in the body, allowing them to move freely past each other during heartbeats, during breathing, and when a person moves. Artificial lubricants are also common in hospitals and doctor's clinics. For example, when ultrasonic imaging is carried out, the gel that couples the transducer to the skin also serves to to lubricate the surface between the transducer and the skin&#;thereby reducing the coefficient of friction between the two surfaces. This allows the transducer to move freely over the skin.
Example
5.1
Skiing Exercise
A skier with a mass of 62 kg is sliding down a snowy slope. Find the coefficient of kinetic friction for the skier if friction is known to be 45.0 N.
Strategy
The magnitude of kinetic friction was given in to be 45.0 N. Kinetic friction is related to the normal force NN size 12{N} {} as fk=μkNfk=μkN size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {}; thus, the coefficient of kinetic friction can be found if we can find the normal force of the skier on a slope. The normal force is always perpendicular to the surface, and since there is no motion perpendicular to the surface, the normal force should equal the component of the skier's weight perpendicular to the slope (see the skier and free-body diagram in Figure 5.4).
Figure
5.4
The motion of the skier and friction are parallel to the slope, so it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is perpendicular (axes shown to left of skier). NN (the normal force) is perpendicular to the slope, and ff (the friction) is parallel to the slope, but ww (the skier's weight) has components along both axes, namely, w &#; w &#; and W // W // . NN is equal in magnitude to w&#;w&#;, so there is no motion perpendicular to the slope. However, ff is less than W//W// in magnitude, so there is acceleration down the slope (along the x-axis).
That is,
5.6
N=w&#;=wcos25º=mgcos25º.N=w&#;=wcos25º=mgcos25º. size 12{N=w rSub { size 8{ ortho } } =w"cos""25" rSup { size 8{ circ } } = ital "mg""cos""25" rSup { size 8{ circ } } } {}
Substituting this into our expression for kinetic friction, we get
5.7
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fk=μkmgcos25º,fk=μkmgcos25º, size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } ital "mg""cos""25" rSup { size 8{ circ } } } {}
which can now be solved for the coefficient of kinetic friction μkμk size 12{μ rSub { size 8{k} } } {}.
Solution
Solving for μkμk size 12{μ rSub { size 8{k} } } {} gives
5.8
μk=fkN=fkwcos25º=fkmgcos25º.μk=fkN=fkwcos25º=fkmgcos25º. size 12{μ rSub { size 8{k} } = { {f rSub { size 8{k} } } over {N} } = { {f rSub { size 8{k} } } over {w"cos""25" rSup { size 8{ circ } } } } = { {f rSub { size 8{k} } } over { ital "mg""cos""25" rSup { size 8{ circ } } } } } {}
Substituting known values on the right-hand side of the equation,
5.9
μk=45.0 N(62 kg)(9.80 m/s2)(0.906)=0.082.μk=45.0 N(62 kg)(9.80 m/s2)(0.906)=0.082. size 12{μ rSub { size 8{k} } = { {"45" "." 0N} over { \( "60"`"kg" \) \( 9 "." "80"`"m/s" rSup { size 8{2} } \) \( 0 "." "906" \) } } =0 "." "084"} {}
Discussion
This result is a little smaller than the coefficient listed in Table 5.1 for waxed wood on snow, but it is still reasonable since values of the coefficients of friction can vary greatly. In situations like this, where an object of mass m m slides down a slope that makes an angle θ θ size 12{θ} {} with the horizontal, friction is given by fk=μkmgcosθfk=μkmgcosθ size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } ital "mg""cos"θ} {}. All objects will slide down a slope with constant acceleration under these circumstances. Proof of this is left for this chapter's Problems and Exercises.
Take-Home Experiment
An object will slide down an inclined plane at a constant velocity if the net force on the object is zero. We can use this fact to measure the coefficient of kinetic friction between two objects. As shown in Example 5.1, the kinetic friction on a slope fk=μkmgcosθfk=μkmgcosθ size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } ital "mg""cos"θ} {}. The component of the weight down the slope is equal to mgsinθmgsinθ size 12{ ital "mg""sin"θ} {} (see the free-body diagram in Figure 5.4). These forces act in opposite directions, so when they have equal magnitude, the acceleration is zero. Writing these out,
5.10
f k = Fg x f k = Fg x size 12{f rSub { size 8{k} } = ital "Fgx"} {}
5.11
μkmgcosθ=mgsinθ.μkmgcosθ=mgsinθ. size 12{μ rSub { size 8{k} } ital "mg""cos"θ= ital "mg""sin"θ} {}
Solving for μkμk size 12{μ rSub { size 8{k} } } {}, we find that
5.12
μk=mgsinθmgcosθ=tanθ.μk=mgsinθmgcosθ=tanθ. size 12{μ rSub { size 8{k} } = { { ital "mg""sin"θ} over { ital "mg""cos"θ} } ="tan"θ} {}
Put a coin on a book and tilt it until the coin slides at a constant velocity down the book. You might need to tap the book lightly to get the coin to move. Measure the angle of tilt relative to the horizontal and find μkμk size 12{μ rSub { size 8{K} } } {}. Note that the coin will not start to slide at all until an angle greater than θ θ size 12{θ} {} is attained since the coefficient of static friction is larger than the coefficient of kinetic friction. Discuss how this may affect the value for μkμk size 12{μ rSub { size 8{K} } } {} and its uncertainty.
We have discussed that when an object rests on a horizontal surface, there is a normal force supporting it equal in magnitude to its weight. Furthermore, simple friction is always proportional to the normal force.
Making Connections: Submicroscopic Explanations of Friction
The simpler aspects of friction dealt with so far are its macroscopic (large-scale) characteristics. Great strides have been made in the atomic-scale explanation of friction during the past several decades. Researchers are finding that the atomic nature of friction seems to have several fundamental characteristics. These characteristics not only explain some of the simpler aspects of friction&#;they also hold the potential for the development of nearly friction-free environments that could save hundreds of billions of dollars in energy which is currently being converted (unnecessarily) to heat.
Figure 5.5 illustrates one macroscopic characteristic of friction that is explained by microscopic (small-scale) research. We have noted that friction is proportional to the normal force but not to the area in contact, a somewhat counterintuitive notion. When two rough surfaces are in contact, the actual contact area is a tiny fraction of the total area since only high spots touch. When a greater normal force is exerted, the actual contact area increases, and it is found that the friction is proportional to this area.
Figure
5.5
Two rough surfaces in contact have a much smaller area of actual contact than their total area. When there is a greater normal force as a result of a greater applied force, the area of actual contact increases, as does friction.
But the atomic-scale view promises to explain far more than the simpler features of friction. The mechanism for how heat is generated is now being determined. In other words, why do surfaces get warmer when rubbed? Essentially, atoms are linked with one another to form lattices. When surfaces rub, the surface atoms adhere and cause atomic lattices to vibrate&#;essentially creating sound waves that penetrate the material. The sound waves diminish with distance, and their energy is converted into heat. Chemical reactions that are related to frictional wear can also occur between atoms and molecules on the surfaces. Figure 5.6 shows how the tip of a probe drawn across another material is deformed by atomic-scale friction. The force needed to drag the tip can be measured and is found to be related to shear stress, which will be discussed later in this chapter. The variation in shear stress is remarkable (more than a factor of 10 12 10 12 size 12{"10" rSup { size 8{"12"} } } {} ) and difficult to predict theoretically, but shear stress is yielding a fundamental understanding of a large-scale phenomenon known since ancient times as friction.
Figure
5.6
The tip of a probe is deformed sideways by frictional force as the probe is dragged across a surface. Measurements of how the force varies for different materials are yielding fundamental insights into the atomic nature of friction.
PhET Explorations: Forces and Motion
Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration versus time. Draw a free-body diagram of all the forces, including gravitational and normal forces.
Figure
5.7
Forces and Motion
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In vivo frictional properties of human skin and five materials, namely aluminium, nylon, silicone, cotton sock, Pelite, were investigated. Normal and untreated skin over six anatomic regions of ten normal subjects were measured under a controlled environment. The average coefficient of friction for all measurements is 0.46±0.15 (p<0.05). Among all measured sites, the palm of the hand has the highest coefficient of friction (0.62±0.22). For all the materials tested, silicone has the highest coefficient of friction (0.61 ±0.21), while nylon has the lowest friction (0.37±0.09).
Frictional properties of human skin depend not only on the skin itself, its texture, its suppleness and smoothness, and its dryness or oiliness (Lodén, ), but also on its interaction with external surfaces and the outside environment. Investigation of skin frictional properties is relevant to several research areas, such as skin physiology, skin care products, textile industry, human friction-dependent activities and skin friction-induced injuries.
Frictional properties of the skin surface may become an objective assessment of skin pathologies. It has been shown that frictional properties can reflect the chemical and physical properties of the skin surface and thus depend on the physiological variations as well as pathological conditions of skin (Lodén et al., ; Lodén, ; Comaish and Bottoms, ; Eisner et al., ; Cua et al., ). The measurement of skin friction may be useful in studying the progress of individual disease processes in skin (Comaish and Bottoms, ). Lodén et al. () found experimentally that the friction of skin with dry atopic subjects was significantly lower than that for the normal skin.
Skin frictional data have been used to evaluate skin care and cosmetic products (El-Shimi, ). Friction of skin forms an integral part of tactile perception and plays an important role in the objective evaluation of consumer-perceptible skin attributes (Wolfram, and ). Cosmetic products, which aim at conferring smoothness to the skin, are thought to perform their function by depositing sufficient amounts of desirable ingredients leading to a perceptible change in the adhesion and friction properties of skin. Some experiments (Nacht et al., ; El-Shimi, ; Gerrard ; Hills et al., ; Highley et al., ) investigated friction changes induced by hydration and emollient application and the correlation with perceived skin feel. The changes in skin friction coefficient immediately after product use are inversely proportional to the subjective after-feel of "greasiness", that is, the higher the increase in skin friction coefficient, the less greasy the product is perceived (Nacht et al., ). In textile industry, skin friction to clothing materials may be related to sensation, comfort or fabric cling (Kenins, ).
Skin friction properties are also relevant to some friction-dependent functions, such as grasping, gripping and locomotion (Cua et al., ; Johansson and Cole, ; Smith and Scott, ). An understanding of these properties is very important in the design of handles, tools, controls and shoes. Buchholz et al. () investigated the frictional properties of human palmar skin and various materials, using a two-fingered pinch grip and studying the effects of subjects, materials, moisture and pinch force. Taylor and Lenderman () measured the coefficient of static friction between finger tips and aluminium (0.6) and found the value dropped by at least 75% when the surfaces were covered with soap. Foot-insole friction was investigated to study the characteristics of locomotion and damage to the foot skin.
The investigation of the skin frictional properties is also helpful in understanding skin friction-induced injuries (Naylor, ; Sulzberger et al., ; Dalton, ; Armstrong, ; Akers, ). The injurious effects of friction on the skin and the underlying tissues can be divided into two classes, those without slip and those with slip. The former may rupture the epidermis and occlude blood and interstitial fluid-flows by stretching or compressing the skin. The latter adds an abrasion to this damage. Research showed that the skin shear force, produced by frictional force combining with pressure, is effective in occluding skin blood flow (Bennett et al., ; Zhang and Roberts, ; Zhang et al., ). Repetitive rubbing causes blistering and produces heat which may have uncomfortable and injurious consequences.
In lower-limb prosthetic socket and orthotic design, achieving a proper load transfer is the key issue since the soft tissues, such as those of the stump, which are not suited for loading, have to support the body weight as well as other functional loads. Skin and prosthetic device forms a critical interface, at which skin friction is an important determinant in the mechanical interactional properties. Friction plays significant roles in supporting the load and in causing discomfort or skin damage (Zhang, ; Zhang et al., ). To optimise frictional actions, there is a requirement to understand adequately the friction properties between the skin and its contact surface.
In spite of its importance, there is however a paucity of knowledge about the frictional properties of skin and those materials used in prosthetic and orthotic devices. The objective of this study is to investigate the friction properties of skin in contact with those materials, and the variation of friction with load magnitudes, rotation speeds, anatomical sites and subjects.
Skin frictional force was measured using Measurement Technologies Skin Friction Meter (Aca-Derm Inc., California), described in details by Elsnau (). The main part of the meter is a hand-held probe unit, including a DC motor, a rotating Teflon disk probe and rotary position transducer. When resting on the skin surface, the rotating disk probe contacts with skin and the torque resulting from frictional force can be measured. The normal force cannot be monitored, but depends on the relative position of the rotary probe to the base plate. The normal force applied to the probe is assumed to be constant, if only the weight of the probe unit is applied and the relative position of the rotary probe to the base plate is unchanged. However the weight supported by the base plate or by the sensing area depends on the geometry and stiffness of the soft tissue and the underlying bone in the measurement sites.
The Friction Meter is used in this investigation had two improvements. First, normal force was monitored by an additional spring balance. A critical factor in the accurate and consistent measurement of the coefficient of friction is the normal force applied. In this study, a spring balance (capacity 1 kg) was connected to the hand-held probe, as shown in Fig. 1. The base plate did not contact the skin surface. The weight applied to the skin surface can be read from the spring balance. A high accuracy electronic balance (AS200, OHAUS) was used to validate the accuracy of the spring balance reading. In 20 trials with application of an intended load of 100 grams, results showed that the weight recorded ranged from 93 to 108 grams, with an average 100.5±4.7 grams.
The second improvement was made on the sensing surface, using a plane-ended annulus instead of a solid plane or a hemispherical shape. The pressure distribution in the sensing surface will affect the frictional torque - the product of the force and the distance to the centre.
In practice, the pressure distribution on the sensing surface varies with the geometry and the stiffness of the soft tissues and the underlying bone. An annular surface applying the load over the annulus can eliminate the error caused by the load distribution. In this study, all the probe sensing surfaces were annular with an outer diameter of 16mm and an inner diameter of 10mm.
Five (5) materials, namely, aluminium, nylon, silicone (soft liner material for trans-tibial suction sockets), cotton sock (often worn with a prosthesis) and Pelite (soft liner material for lower limb prostheses) were measured. The sensing surfaces of aluminium and nylon were machined with fine turning. An annular disk of silicone, cotton sock or Pelite was glued on the tip of the metal probe.
Ten (10) normal subjects, age from 19 to 40, with no visible signs of skin diseases, voluntarily participated in this investigation. For each subject, 6 anatomical sites, namely the palm of hand (PH), dorsum of the hand (DH), anterior side of the forearm (AF), posterior side of the forearm (PF), middle anterior leg (AL), and middle posterior leg (PL) were investigated. The skin was untreated but clean. Since the skin frictional properties may be affected by the ambient environment, all experiments were carried out in a room with controlled temperature of 20-24°C, and relative humidity of 55-65%. The subjects were required to enter the test room for at least 20 minutes before the tests. During the test period, they were asked to sit down and stay relaxed.
For each test, 5 trials were repeated. The coefficient of friction was calculated as the ratio of frictional force to the normal force (µ=F/N). The mean value and standard deviation were calculated with T-test statistical analyses.
Various normal forces were applied to investigate the effect of load on the coefficient of friction. Various probe rotation speeds from 25rpm to 62.5rpm were used to investigate the effect of speed.
Table 1 gives the coefficients of kinetic friction at 6 skin sites with 5 materials for 10 subjects. Each datum comprises mean and standard deviation obtained from the 5 tests. The load applied was 100 grams (average pressure of 80kPa) and the probe rotation speed was 25rpm (average linear speed of 1m/min). The 'Mean' on the right column means the average coefficient of friction between one material and one site of skin for all subjects. The 'mean' on the bottom row for each material shows the average value of this material on all the measured sites for each subject. The 'MEAN' on the bottom row of the table means the average coefficient of friction between all the measured sites and all materials for each subject.
In all the measurements, the coefficient of friction ranged from 0.24 to 1.26, and the average value for all tests was 0.46±0.15 (p<0.01). The coefficients of friction with different materials and at different anatomical sites are shown in Table 2 and Table 3. The highest coefficient of friction of skin was found over the site of the palm of the hand with the silicone. The palm of the hand has the highest coefficient of friction in all the sites measured. Of all the materials tested, the silicone shows the highest coefficient of friction.
Fig. 2 shows the change in coefficient of friction with the normal force applied to the skin surface in the 10 trials. The results show there is a slight decrease in coefficient of friction with an increase of the load. When the load increases from 25 grams to 100 grams, the average coefficient of friction was decreased by 9.5±6% (p<0.05).
Fig. 3 displays the effect of the probe rotation speed on the coefficient of friction in the 8 trials. The coefficient of friction increases slightly with an increase of the rotation speed. When the rotation speed increased from 25rpm to 62.5rpm, the coefficient of friction increased by 7±2% (p<0.05).
Skin frictional properties have been reported by several groups, and the results show they varied with interface materials, subjects, anatomical sites, ambient environment and skin conditions (Naylor, ; Comaish et al., ; Highley et al., ; El-Shimi, ; Nacht et al., ; Cua et al., ). The data reported in this study are particularly relevant to prosthetics and orthotics. These results provide the information needed for better understanding of the biomechanics of load transfer at the body support interface. The coefficient of friction obtained will be used in the computational biomechanical models of the load transfer characteristics between the human body and its supporting devices (Zhang, ; Zhang and Mak, ; Zhang et al., ).
The findings in this investigation are in agreement with previous reports. The coefficients of friction reported for skin were generally within the range of 0.1-1.3 (Wolfram, ). In general, the coefficient of friction decreases with increasing load, especially in the range of a small load (El-Shimi, ; Comaish et al., ). The effect of rotation speed was noted to be negligible over the range examined 3.6 - 585rpm (El-Shimi, ).
Frictional forces can be generated via two actions, one from the "ploughing" action, and the other one from the force required to overcome adhesion between the two surfaces. The former produces friction forces due to the mechanical interlocking of surface roughness elements. The latter generates friction forces due to dissipation when the atoms of one material are plucked out of the attractive range of their counter-parts on the material surface. The relative contribution from these two mechanisms depends on the physical and chemical properties of the contact surfaces. Generally speaking pairs of materials will compatible properties will have a larger friction if the second part is the major contributor. This may be the reason why silicone has the highest friction among the test materials.
The high coefficient of friction found in the palm of the hand may also be related to the fact that this is very rarely sweat free (Comaish et al., ). Thus the physiological state of the skin at any one time must have a profound effect. Other geometric features such as the epidermal ridges may play an important part.
The first author thanks the Hong Kong Polytechnic University for a postdoctoral research fellowship. Help from the undergraduate students in the BSc (Hons) programme in Prosthetics and Orthotics is appreciated.
References:
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