Article...( Manuscript received 28 October 2015; accepted 27 May 2016; published 15 September 2016 ) ( Presented at the International Tribology Conference Tokyo 2015, 16-20 September,

Tribology Online, 11, 5 (2016) 601-607. ISSN 1881-2198

DOI 10.2474/trol.11.601

Copyright © 2016 Japanese Society of Tribologists 601

Article

Influence of Dewettability on Rubber Friction Properties with Different Surface

Roughness under Water/Ethanol/Glycerol Lubricated Conditions

Toshiaki Nishi*, Kenta Moriyasu, Kenichi Harano and Tsuyoshi Nishiwaki

Institute of Sport Science, ASICS Corporation 6-2-1 Takatsukadai, Nishi-ku, Kobe, Hyogo 651-2271, Japan

*Corresponding author: [email protected]

( Manuscript received 28 October 2015; accepted 27 May 2016; published 15 September 2016 ) ( Presented at the International Tribology Conference Tokyo 2015, 16-20 September, 2015 )

In the material designing process of footwear outer-soles, a grip property of rubber is of crucial importance under water or oil lubricated condition. In general, contact states between rubber and floors under lubricated conditions are influenced by various factors, i. e. viscosity of a lubricant, sliding velocity, normal force, surface roughness and wettability between the two substrates. It has been said that lubrication conditions can be distinguished based on Stribeck curves, which are described by the relationship between Sommerfeld numbers and dynamic friction coefficients. Wettability under the static condition is estimated by the spreading coefficient, which is used to evaluate the energy balance of interface free energies at a triple line. The purpose of this study is to investigate influences of surface free energies, viscosities, sliding velocities and surface roughnesses on dynamic friction coefficients of rubber under lubricated conditions. The influences of spreading coefficients on the behaviors of Stribeck curves and the relationship between dewetting velocities and dynamic friction coefficients are also discussed. Keywords: shoe, footwear, rubber, surface free energy, interfacial free energy, spreading coefficient, surface roughness, Stribeck curve, Sommerfeld number, dewetting velocity

1. Introduction

Recently, the fatalities rate caused by slip-and-fall related accidents in Japan has been getting increased and the accidents become more serious. In various situations, risks of slip-and-fall related accidents get high on wet floors [1]. Therefore, accurate grip designing of footwear plays important role to prevent these accidents.

Shoe-sole mainly consists of a mid-sole and an outer-sole. Commonly, an outer-sole is composed of rubber, i. e. butadiene rubber, styrene butadiene rubber and so on. To improve the grip property of footwear, it is general to design compositions of rubber and tread patterns [2].

It has been said that lubricant condition between two substrates makes influence on friction force generation [3]. The lubricated conditions can be classified into boundary lubrication, mixed lubrication and fluid lubrication based on the Stribeck curve. Lubrication conditions change from boundary lubrication to fluid lubrication with increase of Sommerfeld numbers, which are calculated from lubricant viscosities, sliding velocities and mean contact pressure. It has been also reported that behaviors of the Stribeck curves depend on

surface roughnesses of the substrates. However, given that various rubbers are composed to design the practical outer-sole, it is not sufficient to consider influence of rubber material properties on the Stribeck curve. In fact, some researchers have reported that interaction between rubber and a floor in real contact area dominantly effects on an adhesion term of friction [4-6]. For instance, phenomenological physical models for adhesive friction under unlubricated condition have been proposed based on crack propagation at interfaces and molecular-scale phenomena such as molecular chain attachments and mechanical deformations [5,6]. According to these models, the adhesion component depends on surface free energies of rubber and a floor material. It has been also reported that static friction coefficients have positive correlations to surface free energies with halogenated polyethylene under unlubricated condition [7]. Additionally, surface free energies have an influence on wettability between rubber and a floor [8]. With regard to lubricated condition, it has been experimentally reported that static and dynamic friction coefficients of rubber are influenced by surface free energies [9,10].

As mentioned above, friction force between rubber

Toshiaki Nishi, Kenta Moriyasu, Kenichi Harano and Tsuyoshi Nishiwaki

Japanese Society of Tribologists (http://www.tribology.jp/) Tribology Online, Vol. 11, No. 5 (2016) / 602

and a floor under lubricated condition depends on the Sommerfeld numbers, surface roughnesses and surface free energies. However, in the theory of Stribeck curves, the effect of surface free energies has not been considered yet.

The purpose of this study is to clarify influences of viscosities, sliding velocities, surface roughnesses and surface free energies on dynamic friction coefficients of rubber. To consider lubricant conditions, the behaviors of Stribeck curves and the influences of dewetting velocities are also discussed.

2. Experimental methods

2.1. Sample preparation To clarify the influences of surface free energy and

viscosity on rubber friction under lubricated condition, the solutions containing water (ion-exchanged with REP343RB; Toyo Seisakusyo Kaisha, Ltd.), ethanol (Wako 1st grade; Wako Pure Chemical Industries, Ltd.) and glycerol (Wako 1st grade; Wako Pure Chemical Industries, Ltd.) were prepared. Mixture ratio among water, ethanol and glycerol were controlled to change surface free energies and viscosities as shown in Table 1. The total surface free energies of the lubricants were measured by using a contact angle meter (DMs-401; Kyowa Interface Science Co., Ltd.) based on a pendant drop method. Dispersion and polar components of the surface free energies were calculated from the total free energies and the contact angles between the lubricants and a polytetrafluoroethylene plate on the basis of the Kaelble-Uy theory [11]. The viscosities of the lubricants were measured with an Ostwald viscometer (2370-03-10; Climbing Co., Ltd.).

To consider the influence of surface roughness on

rubber friction under lubricated condition, surface roughnesses of rubber specimen and a floor were controlled by polishing with wet abrasive paper #100, #600, #2000 or #15000. Silica-filled isoprene rubber and marble were selected as the rubber specimen and the floor material, respectively. The roughnesses were measured with a laser microscope (VK-X110; Keyence Corporation). Based on the theory of Kaelble and Uy [11], the surface free energies of rubber and the marble floor were calculated from the contact angles of water (ion-exchanged with REP343RB; Toyo Seisakusyo Kaisha, Ltd.) and diiodomethane (Wako 1st grade; Wako Pure Chemical Industries, Ltd.). The surface roughnesses and the surface free energies are listed in Table 2. The initial elastic modulus of the isoprene rubber is 4.00 MPa.

2.2. Experiment apparatus Figure 1 shows an overview of the experiment

system for measuring friction force. A dead-weight typed friction tester (HEIDON 14; Shinto Scientific Co., Ltd.) was used and dynamic friction coefficients of hemispherical isoprene rubber (ϕ = 25 mm) on the marble plate were measured under water/ethanol/glycerol lubricated conditions for three

Table 1 Compositions, viscosities and surface free energies of lubricants

Table 2 Surface roughnesses and surface free energies of the floor and the rubber

LubricantFloor

Rubber

Load cell

Friction force

Normal load

Fig. 1 Experimental system

Influence of Dewettability on Rubber Friction Properties with Different Surface Roughness under Water/Ethanol/Glycerol Lubricated Conditions


times in each condition. Dynamic friction coefficient was calculated from an average of friction force in the steady states. Normal force and sampling rate were 1.96 N and 1.0 kHz, respectively. Sliding velocities were set to 1.0, 5.0, 10.0 and 100.0 mm/s. The atmosphere temperature and moisture were controlled within 24.0-25.0°C and 61-65%RH, respectively.

Sommerfeld numbers were calculated to consider lubricant conditions in the Striveck curves [3]. Sommerfeld numbers are defined as ηVs/P, where η is lubricant viscosity, Vs is sliding velocity and P is pressure. Pressure is defined as mean pressure based on Hertz contact theory [12].

2.3. Wettability evaluation In order to evaluate an influence of wettability

between the rubber and the floor on rubber friction under lubricated conditions, wettability was estimated by a spreading coefficient S. The spreading coefficient is equivalent with the energy balance of the interface free energies at the triple line as shown in Fig. 2 and obtained from the following formula;

RF RL FLS (1)

2 2d d p pij i j i j (2)

where, ij is the interface free energy between material

i and material j [9]. Subscripts R, F and L denote rubber, floor and lubricant, respectively. d

i and pi are the

dispersion and polar components of surface free energy of material i, respectively [11]. Spreading coefficients under each lubricated condition are listed in Table 3.

3. Results

Figure 3 shows influences of spreading coefficients on dynamic friction coefficients at Vs = 10.0 mm/s. Lubricants (ii), (v) and (viii) are collected to confine the viscosities within 49.3-58.6 mPa·s. Negative relationships between spreading coefficients and dynamic friction coefficients were confirmed regardless of surface roughnesses. It is confirmed that increase of surface roughnesses made dynamic friction coefficients higher at the same spreading coefficients.

To compare the relationships between viscosities and dynamic friction coefficients, dynamic friction coefficients at Vs = 10.0 mm/s are plotted against viscosities in Fig. 4. To eliminate the influence of spreading coefficients, lubricants (iv), (v) and (vi) are collected. It is confirmed that dynamic friction coefficients got decreased with increase of viscosity. In the range of η = 58.6-187.9 mPa·s, dynamic friction coefficients got increased with surface roughnesses. On the other hand, in the range of η = 1.06 mPa·s, the influence of surface roughnesses was small.

Fig. 2 Triple line

Table 3 Spreading coefficients under each condition

Lubricant Spreading coefficient, mJ/m2 (i) −44.4 (ii) −27.9 (iii) −24.2 (iv) −14.1 (v) −13.9 (vi) −16.8 (vii) 7.8 (viii) 4.0 (ix) −11.9

Fig. 3 Influence of spreading coefficients on dynamic friction coefficients at Vs = 10.0 mm/s under lubricated conditions: lubricants (ii), (v) and (viii)

Fig. 4 Influence of viscosities on dynamic friction coefficients at Vs = 10.0 mm/s under lubricated conditions: lubricants (iv), (v) and (vi)



Influence of sliding velocities on dynamic friction coefficients under the condition of lubricant (v) is shown in Fig. 5. It is confirmed that dynamic friction coefficients had a negative correlation to sliding velocities, and that dynamic friction coefficients got increased with increase of surface roughnesses of rubber regardless of sliding velocities.

Judging from Figs. 4 and 5, it is confirmed that dynamic friction coefficient depended on sliding velocity and viscosity of the lubricant. Therefore, dynamic friction coefficients of rubber (2) under all conditions of sliding velocities and lubricants are plotted against Sommerfeld numbers in Fig. 6. The difference of spreading coefficients is denoted by red to yellow colored symbols. Dynamic friction coefficients had a negative correlation to Sommerfeld numbers at Sommerfeld number = 10−11-10−8 m. According to comparison of lubricants (ii) and (viii), it is confirmed that increase of spreading coefficient made dynamic friction coefficients lower in the range of Sommerfeld number = 10−9-10−8 m. Same tendencies of influence of spreading coefficients on dynamic friction coefficients were obtained at Sommerfeld number = 10−11-10−8 m.

Because of the negative correlation between Sommerfeld numbers and dynamic friction coefficients, it can be said that the lubrication condition was mixed lubrication at Sommerfeld number = 10−11-10−8 m. Therefore, it is considered that spreading coefficients have a crucial role to determine dynamic friction coefficients under mixed lubricated condition.

4. Discussion

As mentioned in the previous chapter, dynamic friction coefficients depended on viscosities, sliding velocities and surface roughnesses. Based on the theory of Striveck curves, it has been reported that real contact area gets increased with decrease of Sommerfeld numbers and/or increase of surface roughnesses under mixed lubricated condition [3]. In addition, dynamic friction coefficients had negative correlation to spreading coefficients under mixed lubricated condition. This result explains that spreading coefficients have influence on wetting behavior between rubber and a floor. Some researchers have reported that behavior of liquid film between rubber and a floor on static condition is based on wettability and viscosity [13-18]. Hence, once rubber has a real contact with a floor under lubricated condition, the real contact area gets increased due to dewetting effect, which relates to spreading coefficient and viscosity [18]. In other words, it is considered that dewetting velocity makes influence on rubber friction under lubricated condition. In this chapter, to clarify the influence of spreading coefficients on dynamic friction coefficients, the relationship between dewetting velocities and dynamic friction coefficients is discussed.

Dewetting velocity Vd was derived based on the following formula [18];

2

dR min

SV

E h (3)

where, S is the spreading coefficient, ER is the elastic modulus of the rubber, η is the lubricant viscosity and hmin is the minimum film thickness. Based on elastohydrodynamic lubrication, the minimum film thicknesses were calculated from the following formulas [19];

min min xh H R (4) 0.65 0.21

min 7.43 (1 0.85exp( 0.31 ))H U W k (5)

s

x

VU

E'R

(6)

2x

wW

E'R (7)

ak

b (8)

2 2R F

R F

1 12

E' E E

(9)

where, Rx is the radius to sliding direction, E’ is the

Fig. 5 Influence of sliding velocities on dynamic friction coefficients under lubricated condition: lubricants (v)

Fig. 6 Relationships among Sommerfeld numbers, spreading coefficients and dynamic friction coefficients of rubber (2)



synthetic elastic modulus of the rubber and the floor, w is the normal load, a is the radius of ellipse to rectangular direction, b is the radius of ellipse to sliding direction, EF is the elastic modulus of the floor, νR is the Poisson ration of the rubber and νF is the Poisson ration of the floor. Due to the circular contact between the rubber and the floor, k = 1. Based on ER << EF, formula (9) is described as the following formula;

2 2 2R F R

R F R

1 1 12~

E' E E E

(10)

In Table 4, minimum film thicknesses under each condition are listed. Figure 7 shows influences of dewetting velocities on dynamic friction coefficients of rubber (2) under all conditions of sliding velocities and lubricants. It is confirmed that dynamic friction coefficients had positive correlations to dewetting velocities. In case of Vs = 100.0 mm/s, increase of dynamic friction coefficients got started at 100 mm/s of dewetting velocity. On the other hand, in case of Vs = 1.0, 5.0 and 10.0 mm/s, increase of dynamic friction coefficients got started at 10−2 mm/s of dewetting velocity. These results explain that the lubricants at the rubber/floor interfaces were squeezed out with increase of dewetting velocity, and that the dependency of dewetting velocity depended on sliding velocities. Figure 8 shows a model of dewetting behavior at an edge of real contact area between rubber and a floor

during friction under lubricated condition. The real contact area gets increased in case that dewetting velocity gets increased. At the same time, the interface between rubber and a floor is wetted by sliding effect. In fact, the shape of real contact area depends on dewetting and sliding velocities [20]. Therefore, it is considered that the magnitude relationship between dewetting and sliding velocities determines the contact condition.

In order to clarify the influence of both dewetting and sliding velocity, normalized dewetting velocity was defined as a ratio of dewetting velocity to sliding velocity. In Fig. 9, dynamic friction coefficients of rubber (2) under all friction conditions are plotted

Table 4 Minimum film thicknesses under each condition, μm

Lubricant Sliding velocity, mm/s

1.0 5.0 10.0 100.0 (i) 0.0050 0.014 0.023 0.10 (ii) 0.076 0.22 0.34 1.5 (iii) 0.16 0.46 0.72 3.2 (iv) 0.0056 0.016 0.025 0.11 (v) 0.077 0.22 0.34 1.5 (vi) 0.16 0.46 0.73 3.3 (vii) 0.0054 0.015 0.024 0.11 (viii) 0.068 0.19 0.31 1.4 (ix) 0.16 0.45 0.71 3.2

Fig. 7 Influences of dewetting velocities and sliding velocities on dynamic friction coefficients of rubber (2)

Fig. 8 Model of dewetting behavior at an edge of real contact area between rubber and a floor during friction under lubricated condition

Fig. 9 Relationship between normalized dewetting velocities and dynamic friction coefficients of rubber (2)



against normalized dewetting velocities. It is confirmed that dynamic friction coefficients had positive correlation to normalized dewetting velocities regardless of sliding velocities, and that most of results were plotted on one curve. These results explain that the real contact area between the rubber and the floor gets increased with increase of normalized dewetting velocities. Interestingly, increase of dynamic friction coefficients did not get started at Vd/Vs = 100, but at Vd/Vs = 10−3. It is possible that the normalized dewetting velocities might be estimated lower than the true values, because the minimum film thicknesses around the real contacts were thinner than the calculated minimum film thicknesses in consequence of surface roughness. Figure 10 shows the influence of normalized dewetting velocities on dynamic friction coefficients of the rubber with different surface roughnesses under all friction conditions. It is confirmed that dynamic friction coefficients had positive correlation to normalized dewetting velocities regardless of surface roughnesses, and that the increasing rates of dynamic friction coefficients against normalized dewetting velocities got decreased with increase of surface roughnesses. Therefore, it is considered that dynamic friction coefficients of rubber depends on not only normalized dewetting velocities but also surface roughnesses. It is concluded that consideration of normalized dewetting velocities and surface roughnesses is important in the material design process of footwear outer-soles.

5. Conclusions

Based on above experimental results, following conclusions are obtained. 1) Dynamic friction coefficients of rubber depend on

viscosities, spreading coefficients, sliding velocities and surface roughnesses.

2) Behaviors of Stribeck curves are influenced by spreading coefficients.

3) There is a positive correlation between dynamic friction coefficients and normalized dewetting velocities, which depends on surface roughnesses.

References

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Fig. 10 Dynamic friction coefficients of the rubber with different surface roughnesses plotted against normalized dewetting velocity



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Article...( Manuscript received 28 October 2015; accepted 27 May 2016; published 15 September 2016 ) ( Presented at the International Tribology Conference Tokyo 2015, 16-20 September,