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steel ball contact under water lubrication conditions
Tribology International 44 (2011) 757–763
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Friction properties of PVA-H/steel ball contact under water lubrication conditions Keisuke Mamada a, Hiroyuki Kosukegawa b, Vincent Fridrici c, Philippe Kapsa c, Makoto Ohta d,n a
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8577, Japan Graduate School of Engineering, Tohoku University, Sendai 980-8577, Japan c Laboratoire de Tribologie et Dynamique des Syste mes, UMR CNRS 5513, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France d Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan b
a r t i c l e i n f o
abstract
Article history: Received 15 February 2010 Received in revised form 3 November 2010 Accepted 30 December 2010 Available online 19 January 2011
An in vitro biomodel with mechanical properties similar to those of human soft tissues is useful to learn skills for clinical practice of medical doctors or dentists (for instance for suturing oral mucosa). Poly (vinyl alcohol) hydrogel (PVA-H) with good mechanical strength and low surface friction has potential for use in such a biomodel for surgical trainings. The friction properties of biomodels and medical devices are an important factor for reproducing the natural feel of human soft tissue. However, while the low surface friction of PVA-Hs is well known, the effects of PVA factors such as concentration, polymerization, and saponification on the friction properties have not been clarified. In this study, five kinds of PVA-H samples with different properties were prepared, and ball-on-disk friction tests were carried out using a stainless steel ball, the same material as that of a surgical scalpel blade. Furthermore, the contact areas between the PVA-H sample and the ball were evaluated by measurement of the contact radii. Results showed that the friction coefficients of various PVA-Hs varied despite their similar contact areas. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Sliding friction Hydrogel Lubrication Adhesion
1. Introduction Adjusting the force to which soft tissues are subjected during surgical operations such as touching, cutting, or suturing may play an important role in patient treatment. With recent advances in medical technology, the importance of surgical training and simulations in the acquisition of specialized skills has grown. A biomodel material with geometries and mechanical properties similar to those of human soft tissue greatly enhances surgical training [1,2]. However, several characteristics of conventional models (most of them being made of silicone) are different from those of real soft tissue. Therefore, the development of novel biomodels, which approximate real soft tissue is an important issue for improving the quality of training situations. While several researchers have developed haptic devices by using virtual reality systems to realize realistic training situations [3,4], the role of practice models remains important because trainers can get hands-on experience with such models. Poly (vinyl alcohol) hydrogel (PVA-H) has been used as a functional biomodel material because of its proper feel, mechanical properties (Young’s modulus in the 10 kPa to 1 MPa range), and low surface friction (lower than 0.05 depending on contact
n
Corresponding author. Tel./fax: + 81 22 217 53 09. E-mail address: ohta@biofluid.ifs.tohoku.ac.jp (M. Ohta).
0301-679X/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2010.12.014
conditions) [5]. This hydrogel has good transparency and good mechanical strength [6]. Additionally, its mechanical properties can be flexibly controlled by changing the factors of PVA such as concentration, polymerization, and saponification [7]. We have previously measured dynamic viscoelastic properties of several kinds of PVA-Hs and attempted sensory evaluations with wellexperienced dental surgeons for the development of a PVA-H oral mucosa model [8]. The results showed correlations between viscoelasticities and the surgeons’ evaluations (for instance, an intermediate value of G0 of 20 kPa leading to the best evaluation of surgeons for suturing and pushing), and several PVA-H models received higher evaluations than a conventional model made of silicone. Meanwhile, the evaluation of PVA-Hs prepared by changing PVA factors varied despite the similar elasticity. This demonstrated that consideration of the other mechanical properties such as friction and fracture properties was necessary to evaluate the ability of an oral mucosa model to approximate actual oral mucosa. The reproduction of friction properties of human soft tissue may be an important issue for biomodeling because the responses of mechanical sliding contact between medical devices and soft tissue contribute to the reality of surgical situations. Several researchers have performed tribological studies of PVA-Hs [5,9,10], revealing their excellent low surface friction (lower than 0.05 depending on contact conditions). Cha et al. prepared PVA-Hs with low water contents and showed the strong increase in wear volume with increase in friction coefficient. Pan et al. prepared PVA-Hs using physiological saline as
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the solvent and carried out ball-on-disk friction tests with different lubricant media. The results revealed the effects of lubricants on the friction properties. Such studies deal with the application of PVA-H to artificial cartilage and total joint replacement materials, and thus researchers need to investigate friction characteristics under various test conditions, in particular with high load, to approximate in vivo conditions. Meanwhile, we need to investigate the friction behaviors present in a comprehensive lubrication regime to understand the friction characteristics due to the PVA factors. Then we can evaluate in vitro biomodels and pursue the reality of human soft tissue by changing the characteristics of PVA-Hs. In the present study, we measured the friction of several PVA-Hs to elucidate the effect of concentration, polymerization, and saponification of PVA. Furthermore, using stainless steel as a representative material of a surgical scalpel blade for the counterbody of these friction tests, we undertook fundamental investigation of friction properties, which would contribute to the characteristics of cutting.
2. Materials PVA powder (JAPAN VAM & POVAL Co. Ltd.) was dissolved in aqueous dimethyl sulfoxide (DMSO) (Toray Fine Chemicals Co. Ltd.) mixed solvent by heating for 2 h at 100 1C. The PVA solution was poured into an acrylic mold with a thickness of 12 mm and a diameter of 88 mm. It was then gelated by cooling for 24 h at a temperature below 20 1C. In this study, five kinds of PVA-H samples were prepared with various parameters as shown in Table 1. C represents the weight concentration of PVA powder in the solvent. PVA contains both hydrophilic and hydrophobic
groups (Fig. 1), and the saponification value (SV [mol%]) and the degree of polymerization (DP) are defined by the following equations: SV ¼
x 100 xþy
ð1Þ
DP ¼ x þy
ð2Þ
where x and y represent the number of hydrophilic and hydrophobic group units, respectively. F17/10 was defined as the standard sample in this study, and the parameters of each sample were determined with reference to the dynamic viscoelasticities: dynamic storage modulus G0 , which indicates the elasticity of the material, and dynamic loss modulus G00 , which indicates the viscosity of the material. One sample (F17/18) had higher elasticity (Young’s modulus of 350 kPa), and the three other samples (F10/12, M17/12, and M100 /17) with lower DP and/or SV showed elasticity similar (around 50 kPa for Young’s modulus) to that of the standard sample (Fig. 2(a)). Meanwhile, the viscosity of the four samples with similar elasticity showed different frequency dependences (Fig. 2(b)). A stainless steel ball (AISI 410) with a diameter of 10 mm was used as the counterbody. The average surface roughness Ra was less than 0.01 mm. Before the tests, the ball was cleaned in acetone and ethanol, and was then rinsed with distilled water, in order to remove all the solvents.
3. Methods Table 1 List of PVA-H samples.
3.1. Friction test
Notation
SV (mol%)
DP
C (wt%)
F17/18 F17/10 F10/12 M17/12 M10/17
98.4 98.4 98.2 96.6 94.5
1700 1700 1000 1700 1000
18 10 12 12 17
SV: saponification value; DP: degree of polymerization; C: concentration.
Fig. 1. Chemical structure of PVA.
The friction coefficients of PVA-Hs were measured using a ballon-disk rotating home-built tribometer (Fig. 3) under various conditions as shown in Table 2. The PVA sample was fixed on the moving part of the tribometer, and distilled water was put on the surface of the sample, so that the contact area is always surrounded by water. The stainless steel ball was loaded to the sample with a constant normal load. The sample was rotated at a constant sliding speed (V) in one direction for 30 s and turned in the opposite direction every 30 s. The mean friction force in whole measurement time was subtracted from the measured friction force, and the value was defined as the real friction force. The average of the absolute value was used for the calculation of friction coefficient; the friction coefficient (m) was obtained by dividing the average friction force (F) by the normal load (FN).
500 F17/10
M17/12
M10/17
F10/12
F17/18
15
300
G" [kPa]
G' [kPa]
400
20 F17/18
200
F17/18 M10/17
10
M17/12 F17/10 F10/12
5
100 4 PVA-Hs with near elasticity
0 10-1
100 101 Freq. [Hz]
102
0 10-1
100 101 Freq. [Hz]
102
Fig. 2. Dynamic viscoelasticities of PVA-H samples at various frequencies: (a) dynamic storage modulus G0 and (b) dynamic loss modulus G00 (temperature: 20 1C, Ave.7 SD of three samples).
K. Mamada et al. / Tribology International 44 (2011) 757–763
759
0.05 Weight for normal load
Seesaw arm
F17/18 F10/12 M10/17
Strain gage Weight for balance
Sample in acrylic case
Ball
Distilled water
Revolving stage
Friction coefficient [-]
0.04
F17/10 M17/12
0.2 N
0.03
0.02
0.01 Fig. 3. Schematic diagram of the ball-on-disk tribometer.
0.00
Table 2 Conditions of friction tests. Sample
Normal load (N)
F17/18
0.1–1.0
4 PVA-Hs
0.1, 0.2, 0.3
10 Sliding speed (mm/s) (rpm)
50 Sliding speed [mm/s]
100
Fig. 5. Friction coefficients of PVA-H samples at a constant normal load of 0.2 N (Ave. 7SD of 2 samples).
10(4), 50(20), 100(40)
4.0 F17/18 F10/12 M10/17
Contact radius [mm]
3.0
F17/10 M17/12
2.0
1.0
0.0 0.1 Fig. 4. Measured friction force of a PVA-H (F17/10) versus measurement time (normal load: 0.2 N, sliding speed: 50 mm/s).
3.2. Measurement of contact radius When a ball is loaded to the surface of a PVA-H sample, the contact circle can be observed from the bottom of the sample. Pictures of the contact circle were taken using an optical microscope (SZH-ILLC2, OLYMPUS Co.) to measure the contact radius. A picture of grid paper was taken with the same focus distance, and the picture was used for calibrating the distance on the obtained pictures. Measurements were carried out for five kinds of PVA-Hs with the same load conditions as shown in Table 2.
4. Results Fig. 4 shows the time dependence of measured friction force in a certain condition. The dependence obviously follows the sliding velocity pattern. The friction coefficients (m) of PVA-Hs calculated from the measured friction forces are shown in Fig. 5. The values of m are in a range from 0.01 to 0.04. Except at low sliding speed, the sample with high elasticity (F17/18) shows the lowest friction coefficient. Meanwhile, the sample M100 /17 with low DP and low SV shows a higher friction coefficient than those of other samples.
0.2
0.3 0.5 Normal load [N]
0.7
1.0
Fig. 6. Measured contact radii of PVA-H samples at various normal loads.
The contact radii of each sample are shown in Fig. 6. The contact radius increases with increase in normal load in all cases. The sample with high elasticity (F17/18) has the smallest contact radius. According to Amontons–Coulomb’s friction law, frictional force does not depend on the apparent contact area. However, the apparent contact area should be equal to the real one when the sample has a smooth surface. Concerning the PVA-H sample used in this study, the surface was smooth, and thus the effect of the smallest contact area can explain why the sample shows the smallest friction coefficient. Meanwhile, four samples with similar elasticity show similar contact radii. The maximum difference against the standard sample (F17/10) was 3.9% (M100 /17, 0.3 N). Therefore, the contact area in static contact is consequently considered as the same for the four samples with similar elasticity.
5. Discussion 5.1. Lubrication regime The Stribeck curve can show the condition of lubrication. The vertical axis is the friction coefficient, and the horizontal axis is a
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single parameter: ZV/P. In this parameter, Z, V, and P represent viscosity of the lubricating liquid (1.002 10 3 Pa s for distilled water), sliding speed and contact pressure, respectively. The contact area (A) can be calculated as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ A ¼ 2pR R R2 a2 where R is the radius of the ball (5 mm) and a the contact radius. Then, the contact pressure (P) between the stainless steel ball and PVA-Hs can be calculated by dividing the normal load by the contact area. The single parameter of the Stribeck curve is calculated for each PVA-H sample and the results are shown in Fig. 7. By comparing the Stribeck curves, the lubrication conditions of four PVA-Hs (F17/10, F10/12, M17/12 and M100 /17) appear to be hydrodynamic lubrication at high sliding speed (as friction coefficient increases with an increase in ZV/P). Meanwhile, the four PVA-Hs at low speed and the sample with high elasticity (F17/18) may show conditions intermediate between mixed lubrication and hydrodynamic lubrication (minimum value of friction coefficient). The equation of minimum lubrication thickness (hmin) in the contact between the ball and plane is given as follows [11]: 0:65 hmin ZV FN 0:21 ¼ 2:80 ð4Þ EuR R EuR2 The equivalent elastic modulus (E0 ) is calculated as follows: 1 1 1n21 1n22 ¼ þ ð5Þ Eu 2 E1 E2
where E1 and n1 are the elastic modulus and Poisson’s ratio of PVA-Hs, respectively. And, E2 and n2 represent those of stainless steel (AISI410). With reference to Eq. (4), the minimum lubrication thickness increases with a decrease in FN, an increase in V, and a decrease in E0 . Increase in fluid film thickness induces an increase in the friction coefficient in hydrodynamic lubrication. The effects of load and velocity for the friction properties are discussed in the following sections. 5.2. Load dependence Fig. 8 shows the evolution of friction coefficients of PVA-Hs versus load. At high speed and low load, the friction coefficients of all PVA-Hs decrease when load is increased. This is explained by a decrease in the fluid film thickness. Meanwhile, at low speed (10 mm/s), the relationship is not clear concerning four PVA-Hs with similar elasticity. This is attributed to the fact that the contact between the stainless steel ball and the surface of PVA-H is induced by a decrease in the fluid film: the intermediate condition between mixed and hydrodynamic lubrication. Concerning the sample with high elasticity (F17/18), it seems that the lubrication condition is mixed lubrication at low speed (10 mm/s) and high load. At low speed and low load, F17/18 shows load dependence the same as that of the hydrodynamic lubrication. However, in the mixed lubrication condition, the values of friction coefficients and the Stribeck curves are different for the four PVAHs having the same elasticity (Fig. 7). Thus, the friction properties under these conditions may include other factors such as adhesion force involved in the contact (for the four samples of PVA-H with the same elasticity, even with the same contact area, differences in surface chemistry can modify the adhesion force with the counterbody). The effects of adhesion force are investigated by comparing measured contact radii and theoretical values in the following paragraph. According to Hertzian theory, the contact radius (ah) between two elastic solids can be calculated by the following equation [12]: 3FN R 1=3 ð6Þ ah ¼ 4E E* is determined as follows: 1n21 1n21 1 ¼ þ E E1 E2
Fig. 7. Friction coefficients of PVA-H samples versus a single parameter based on Stribeck theory: V/P (Ave. 7 SD of 2 samples).
ð7Þ
The theoretical contact radii of two PVA-Hs (F17/18, F17/10) are calculated using the values in Table 3. The results are shown in Table 4 and Fig. 9 with the measured contact radii. By comparing these results, it can be seen that the theoretical values are smaller than the measured ones. The relative error (Eh for Hertz/measured between the calculated contact radius with
F17/18
F17/18/Adhesion
F17/10
F10/12
M17/12
M10/17
0.015
10 mm/s
0.010
Friction coefficient [-]
Friction coefficient [-]
0.020 0.035 M10/17 100 mm/s
0.025
M17/12 F17/10 F10/12
0.015
F17/18 F17/18/Adhesion
0.005 0.0
0.2
0.4 0.6 0.8 Normal load [N]
1.0
1.2
0.005 0.0
0.2
0.4 0.6 0.8 Normal load [N]
1.0
1.2
Fig. 8. Load dependences of friction coefficients at a constant sliding speed of (a) 10 mm/s and (b) 100 mm/s (Ave. 7 SD of 2 samples).
K. Mamada et al. / Tribology International 44 (2011) 757–763
are defined by Eq. (8), and the adhesive force is obtained in each theory when the total relative error shows the minimum value. By this processing, the best value of adhesive force can be calculated to have the best fit between the measured results and the theoretical values. Then, the surface energy (w) of the PVA-H samples in the contact area is calculated by the estimated adhesion force. Concerning F17/18, the total relative error in the JKR theory is smaller than that in the DMT theory, as shown in Table 4, and the estimated surface energy for the DMT theory is much higher. Therefore, it seems that the measured data follow the JKR theory (Fig. 9). When the result is applied to F17/ 10 as well (Fig. 9), the value of the estimated adhesion force is smaller than that of F17/18. The ratio of the adhesion force of F17/18 to the total applied force is about 25% for the lowest load. The friction coefficient (m0 ) including the effect of adhesion force is defined by the following equation, and the calculated values are shown in Fig. 8.
Hertzian theory ah and the measured contact radius am) defined by Eq. (8) decreases with an increase in normal load. In the Hertzian theory, only compressive stress can exist in the contact area. If the elastic solids have a surface energy, the real applied load is larger than the normal load. Therefore, the contact radius is also larger than the Hertzian one. Eh ¼
ah am 2 am
ð8Þ
Meanwhile, there are two kinds of theories of elastic contact, which considers the existence of surface energy: the Johnson– Kendall–Roberts (JKR) theory [13] and the Derjaguin–Muller– Toporov (DMT) theory [14]. The JKR theory can be applied generally for soft solids with a large radius and high adhesion, and the DMT theory can be applied for rigid solids with a small radius and low adhesion. The adhesion force (F0) and contact radii (aj for JKR theory, ad for DMT theory) are calculated by following equations:
761
mu ¼
F FN þ F0
ð13Þ
JKR theory F0 ¼
3 pwR 2
ð9Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=3 3R FN þ2F0 þ 2 F0 ðFN þF0 Þ aj ¼ 4E
3.0
F17/10
ð10Þ
F17/18
F0 ¼ 2pwR ad ¼
ð11Þ
1 3RðFN þ2F0 Þ 4E
1=3 ð12Þ
where w is surface energy per unit contact area. In this study, the estimation of adhesion force is carried out for two samples (F17/ 18 and F17/10) using Excel solver (Microsoft Co. Ltd.) as follows: the relative errors (Ej for JKR/measured, Ed for DMT/measured)
Contact radius [mm]
DMT theory 2.0
Measured
1.0
Hertz theory JKR theory
Table 3 Elastic moduli (E), Poisson’s ratios (n) and curvature radii (R) of PVA-H samples and a stainless steel. Material
Elastic modulus (Pa)
Poission’s ratio
Curvature radius (mm)
PVA-HF17/18 PVH-HF17/10 Stainless steel AISI410
350 103 50 103 200 109
0.5 0.5 0.3
– – 5
DMT theory 0.0 0.0
0.2
0.4
0.6 0.8 Normal load [N]
1.0
Fig. 9. Comparison between measured and theoretical contact radii with 3 kinds of theories: Hertz, JKR, and DMT theory. JKR: Johnson–Kendall–Roberts, DMT: Derjaguin–Muller–Toporov.
Table 4 Estimated theoretical contact radii and adhesion forces between PVA-H (F17/18) and a stainless steel ball. Normal load (N)
0.0 0.1 0.2 0.3 0.5 0.7 1.0
Contact radius Measured (mm)
Hertz (mm)
Relative error (Hertz/measured)
JKR (mm)
Relative error (JKR/measured)
DMT (mm)
Relative error (DMT/measured)
1.27 1.45 1.61 1.85 2.04 2.30
0.00 0.95 1.18 1.36 1.60 1.79 2.02
0.06 0.03 0.02 0.02 0.01 0.01
0.92 1.29 1.48 1.63 1.85 2.02 2.24
0.00030 0.00039 0.00018 0.00002 0.00004 0.00068
1.16 1.34 1.48 1.60 1.78 1.94 2.14
0.00316 0.00026 0.00009 0.00160 0.00224 0.00465
Total relative error Adhesion force (N) Surface energy (J/m2) JKR: Johnson–Kendall–Roberts; DMT: Derjaguin–Muller–Toporov.
1.2
0.00160 0.024 1.017
0.01200 0.192 6.126
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K. Mamada et al. / Tribology International 44 (2011) 757–763
0.04
0.04 0.1 N
0.3 N M17/12
0.03
F17/10 F10/12
0.02 F17/18
0.01
0.00
Friction coefficient [-]
Friction coefficient [-]
M10/17 M10/17
0.03 M17/12 F17/10
0.02
F10/12 F17/18
0.01
0.00 0
20
40 60 80 100 Sliding speed [mm/s]
120
0
20
40 60 80 100 Sliding speed [mm/s]
120
Fig. 10. Velocity dependence of friction coefficients at a constant normal load of (a) 0.1 N and (b) 0.3 N (Ave. 7 SD of 2 samples).
The application of adhesion force affects the load dependence, and it can be seen that the dependence is shifted to follow the Stribeck curve. Though the adhesion force would not be effective on the sliding properties in hydrodynamic lubrication, it must affect the friction from the boundary to the mixed lubrication under low load and low speed conditions in this study. 5.3. Velocity dependence Fig. 10 shows the velocity dependences of friction coefficients of PVA-Hs. The friction coefficients increase with an increase in sliding speed. The dependence corresponds to that of the calculated minimum lubrication thickness and follows the Stribeck curve in hydrodynamic lubrication. Concerning the sample with low DP and low SV (M100 /17), the friction coefficient shows a larger velocity dependence than that of the other samples. The measured contact areas do not show any significant differences among the four PVA-Hs with similar elasticity. Therefore, the higher value of friction coefficient of M100 /17 at high speed may be induced by the lower DP and/or SV, which modify the hydrophilicity of the rubbing surface and the viscoelasticities of the materials. The interaction of M100 /17 with water is lower than that of the other samples because of the lower ratio of the hydrophilic group on the surface. Consequently, the high friction may result from the diminished lubrication property [15–17]. However, in hydrodynamic lubrication, the hydrophilicity of the surface would not affect the friction because the counterbody contacts the sample via the fluid water film [18]. Meanwhile, the inner crystalline structure variations should be considered. PVA-Hs are believed to consist of crystalline and amorphous regions. The crystalline regions are formed mainly by hydrogen bonds on the hydrophilic groups, while the amorphous regions include flexible chains without hydrogen bonds. Decrease in polymerization induces decreased entanglement of the chains, and decreased saponification induces an increase in the amorphous regions [19]. The amorphous regions may act as a damper and consequently affect the viscous property. Concerning the four PVA-Hs with similar elasticity, the effect of DP and/or SV on the characteristics of the bulk material appears as a variety of viscosities, and the frequency dependence is similar to the velocity dependence of friction coefficients (Figs. 2 and 10). The viscous component of materials affects the deformation of the counterpart: the lag of deformation is increased with an increase in the viscosity (or the sliding speed). Though the viscoelasticities contribute to the friction with contact [20–22], it is believed that the bulk properties do not affect the friction in hydrodynamic lubrication. However, the effect could not be neglected for the four soft PVA-Hs (F17/10: E 50 103 Pa) because of the large
deformation and the very low friction. Thus, differences in velocity dependence may be induced by the resistance force via the fluid water film. The above discussions can possibly explain the different friction characteristics among PVA-Hs with different PVA factors and is supported by the evaluation of the counterpart in the sliding contact. Additional tests and analyses with considerations of the possibility of other mechanisms are essential to elucidate the effect of PVA factors on the friction properties.
6. Conclusion Friction tests of PVA-Hs with different PVA factors such as concentration, polymerization, and saponification were carried out using a stainless steel ball as the counterbody. The different friction coefficients were shown to be due to the PVA factors though the contact areas showed similar values. Velocity dependence varied. Hydrophilicity of the rubbing surface and viscoelasticities of the bulk material were discussed for the explanation of these differences. These results indicate that the PVA factors affect the friction properties and that the effect should be considered in order to reproduce the responses of human soft tissue in sliding contact.
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Friction properties of PVA-H/steel ball contact under water lubrication conditions Keisuke Mamada a, Hiroyuki Kosukegawa b, Vincent Fridrici c, Philippe Kapsa c, Makoto Ohta d,n a
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8577, Japan Graduate School of Engineering, Tohoku University, Sendai 980-8577, Japan c Laboratoire de Tribologie et Dynamique des Syste mes, UMR CNRS 5513, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France d Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan b
a r t i c l e i n f o
abstract
Article history: Received 15 February 2010 Received in revised form 3 November 2010 Accepted 30 December 2010 Available online 19 January 2011
An in vitro biomodel with mechanical properties similar to those of human soft tissues is useful to learn skills for clinical practice of medical doctors or dentists (for instance for suturing oral mucosa). Poly (vinyl alcohol) hydrogel (PVA-H) with good mechanical strength and low surface friction has potential for use in such a biomodel for surgical trainings. The friction properties of biomodels and medical devices are an important factor for reproducing the natural feel of human soft tissue. However, while the low surface friction of PVA-Hs is well known, the effects of PVA factors such as concentration, polymerization, and saponification on the friction properties have not been clarified. In this study, five kinds of PVA-H samples with different properties were prepared, and ball-on-disk friction tests were carried out using a stainless steel ball, the same material as that of a surgical scalpel blade. Furthermore, the contact areas between the PVA-H sample and the ball were evaluated by measurement of the contact radii. Results showed that the friction coefficients of various PVA-Hs varied despite their similar contact areas. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Sliding friction Hydrogel Lubrication Adhesion
1. Introduction Adjusting the force to which soft tissues are subjected during surgical operations such as touching, cutting, or suturing may play an important role in patient treatment. With recent advances in medical technology, the importance of surgical training and simulations in the acquisition of specialized skills has grown. A biomodel material with geometries and mechanical properties similar to those of human soft tissue greatly enhances surgical training [1,2]. However, several characteristics of conventional models (most of them being made of silicone) are different from those of real soft tissue. Therefore, the development of novel biomodels, which approximate real soft tissue is an important issue for improving the quality of training situations. While several researchers have developed haptic devices by using virtual reality systems to realize realistic training situations [3,4], the role of practice models remains important because trainers can get hands-on experience with such models. Poly (vinyl alcohol) hydrogel (PVA-H) has been used as a functional biomodel material because of its proper feel, mechanical properties (Young’s modulus in the 10 kPa to 1 MPa range), and low surface friction (lower than 0.05 depending on contact
n
Corresponding author. Tel./fax: + 81 22 217 53 09. E-mail address: ohta@biofluid.ifs.tohoku.ac.jp (M. Ohta).
0301-679X/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2010.12.014
conditions) [5]. This hydrogel has good transparency and good mechanical strength [6]. Additionally, its mechanical properties can be flexibly controlled by changing the factors of PVA such as concentration, polymerization, and saponification [7]. We have previously measured dynamic viscoelastic properties of several kinds of PVA-Hs and attempted sensory evaluations with wellexperienced dental surgeons for the development of a PVA-H oral mucosa model [8]. The results showed correlations between viscoelasticities and the surgeons’ evaluations (for instance, an intermediate value of G0 of 20 kPa leading to the best evaluation of surgeons for suturing and pushing), and several PVA-H models received higher evaluations than a conventional model made of silicone. Meanwhile, the evaluation of PVA-Hs prepared by changing PVA factors varied despite the similar elasticity. This demonstrated that consideration of the other mechanical properties such as friction and fracture properties was necessary to evaluate the ability of an oral mucosa model to approximate actual oral mucosa. The reproduction of friction properties of human soft tissue may be an important issue for biomodeling because the responses of mechanical sliding contact between medical devices and soft tissue contribute to the reality of surgical situations. Several researchers have performed tribological studies of PVA-Hs [5,9,10], revealing their excellent low surface friction (lower than 0.05 depending on contact conditions). Cha et al. prepared PVA-Hs with low water contents and showed the strong increase in wear volume with increase in friction coefficient. Pan et al. prepared PVA-Hs using physiological saline as
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the solvent and carried out ball-on-disk friction tests with different lubricant media. The results revealed the effects of lubricants on the friction properties. Such studies deal with the application of PVA-H to artificial cartilage and total joint replacement materials, and thus researchers need to investigate friction characteristics under various test conditions, in particular with high load, to approximate in vivo conditions. Meanwhile, we need to investigate the friction behaviors present in a comprehensive lubrication regime to understand the friction characteristics due to the PVA factors. Then we can evaluate in vitro biomodels and pursue the reality of human soft tissue by changing the characteristics of PVA-Hs. In the present study, we measured the friction of several PVA-Hs to elucidate the effect of concentration, polymerization, and saponification of PVA. Furthermore, using stainless steel as a representative material of a surgical scalpel blade for the counterbody of these friction tests, we undertook fundamental investigation of friction properties, which would contribute to the characteristics of cutting.
2. Materials PVA powder (JAPAN VAM & POVAL Co. Ltd.) was dissolved in aqueous dimethyl sulfoxide (DMSO) (Toray Fine Chemicals Co. Ltd.) mixed solvent by heating for 2 h at 100 1C. The PVA solution was poured into an acrylic mold with a thickness of 12 mm and a diameter of 88 mm. It was then gelated by cooling for 24 h at a temperature below 20 1C. In this study, five kinds of PVA-H samples were prepared with various parameters as shown in Table 1. C represents the weight concentration of PVA powder in the solvent. PVA contains both hydrophilic and hydrophobic
groups (Fig. 1), and the saponification value (SV [mol%]) and the degree of polymerization (DP) are defined by the following equations: SV ¼
x 100 xþy
ð1Þ
DP ¼ x þy
ð2Þ
where x and y represent the number of hydrophilic and hydrophobic group units, respectively. F17/10 was defined as the standard sample in this study, and the parameters of each sample were determined with reference to the dynamic viscoelasticities: dynamic storage modulus G0 , which indicates the elasticity of the material, and dynamic loss modulus G00 , which indicates the viscosity of the material. One sample (F17/18) had higher elasticity (Young’s modulus of 350 kPa), and the three other samples (F10/12, M17/12, and M100 /17) with lower DP and/or SV showed elasticity similar (around 50 kPa for Young’s modulus) to that of the standard sample (Fig. 2(a)). Meanwhile, the viscosity of the four samples with similar elasticity showed different frequency dependences (Fig. 2(b)). A stainless steel ball (AISI 410) with a diameter of 10 mm was used as the counterbody. The average surface roughness Ra was less than 0.01 mm. Before the tests, the ball was cleaned in acetone and ethanol, and was then rinsed with distilled water, in order to remove all the solvents.
3. Methods Table 1 List of PVA-H samples.
3.1. Friction test
Notation
SV (mol%)
DP
C (wt%)
F17/18 F17/10 F10/12 M17/12 M10/17
98.4 98.4 98.2 96.6 94.5
1700 1700 1000 1700 1000
18 10 12 12 17
SV: saponification value; DP: degree of polymerization; C: concentration.
Fig. 1. Chemical structure of PVA.
The friction coefficients of PVA-Hs were measured using a ballon-disk rotating home-built tribometer (Fig. 3) under various conditions as shown in Table 2. The PVA sample was fixed on the moving part of the tribometer, and distilled water was put on the surface of the sample, so that the contact area is always surrounded by water. The stainless steel ball was loaded to the sample with a constant normal load. The sample was rotated at a constant sliding speed (V) in one direction for 30 s and turned in the opposite direction every 30 s. The mean friction force in whole measurement time was subtracted from the measured friction force, and the value was defined as the real friction force. The average of the absolute value was used for the calculation of friction coefficient; the friction coefficient (m) was obtained by dividing the average friction force (F) by the normal load (FN).
500 F17/10
M17/12
M10/17
F10/12
F17/18
15
300
G" [kPa]
G' [kPa]
400
20 F17/18
200
F17/18 M10/17
10
M17/12 F17/10 F10/12
5
100 4 PVA-Hs with near elasticity
0 10-1
100 101 Freq. [Hz]
102
0 10-1
100 101 Freq. [Hz]
102
Fig. 2. Dynamic viscoelasticities of PVA-H samples at various frequencies: (a) dynamic storage modulus G0 and (b) dynamic loss modulus G00 (temperature: 20 1C, Ave.7 SD of three samples).
K. Mamada et al. / Tribology International 44 (2011) 757–763
759
0.05 Weight for normal load
Seesaw arm
F17/18 F10/12 M10/17
Strain gage Weight for balance
Sample in acrylic case
Ball
Distilled water
Revolving stage
Friction coefficient [-]
0.04
F17/10 M17/12
0.2 N
0.03
0.02
0.01 Fig. 3. Schematic diagram of the ball-on-disk tribometer.
0.00
Table 2 Conditions of friction tests. Sample
Normal load (N)
F17/18
0.1–1.0
4 PVA-Hs
0.1, 0.2, 0.3
10 Sliding speed (mm/s) (rpm)
50 Sliding speed [mm/s]
100
Fig. 5. Friction coefficients of PVA-H samples at a constant normal load of 0.2 N (Ave. 7SD of 2 samples).
10(4), 50(20), 100(40)
4.0 F17/18 F10/12 M10/17
Contact radius [mm]
3.0
F17/10 M17/12
2.0
1.0
0.0 0.1 Fig. 4. Measured friction force of a PVA-H (F17/10) versus measurement time (normal load: 0.2 N, sliding speed: 50 mm/s).
3.2. Measurement of contact radius When a ball is loaded to the surface of a PVA-H sample, the contact circle can be observed from the bottom of the sample. Pictures of the contact circle were taken using an optical microscope (SZH-ILLC2, OLYMPUS Co.) to measure the contact radius. A picture of grid paper was taken with the same focus distance, and the picture was used for calibrating the distance on the obtained pictures. Measurements were carried out for five kinds of PVA-Hs with the same load conditions as shown in Table 2.
4. Results Fig. 4 shows the time dependence of measured friction force in a certain condition. The dependence obviously follows the sliding velocity pattern. The friction coefficients (m) of PVA-Hs calculated from the measured friction forces are shown in Fig. 5. The values of m are in a range from 0.01 to 0.04. Except at low sliding speed, the sample with high elasticity (F17/18) shows the lowest friction coefficient. Meanwhile, the sample M100 /17 with low DP and low SV shows a higher friction coefficient than those of other samples.
0.2
0.3 0.5 Normal load [N]
0.7
1.0
Fig. 6. Measured contact radii of PVA-H samples at various normal loads.
The contact radii of each sample are shown in Fig. 6. The contact radius increases with increase in normal load in all cases. The sample with high elasticity (F17/18) has the smallest contact radius. According to Amontons–Coulomb’s friction law, frictional force does not depend on the apparent contact area. However, the apparent contact area should be equal to the real one when the sample has a smooth surface. Concerning the PVA-H sample used in this study, the surface was smooth, and thus the effect of the smallest contact area can explain why the sample shows the smallest friction coefficient. Meanwhile, four samples with similar elasticity show similar contact radii. The maximum difference against the standard sample (F17/10) was 3.9% (M100 /17, 0.3 N). Therefore, the contact area in static contact is consequently considered as the same for the four samples with similar elasticity.
5. Discussion 5.1. Lubrication regime The Stribeck curve can show the condition of lubrication. The vertical axis is the friction coefficient, and the horizontal axis is a
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single parameter: ZV/P. In this parameter, Z, V, and P represent viscosity of the lubricating liquid (1.002 10 3 Pa s for distilled water), sliding speed and contact pressure, respectively. The contact area (A) can be calculated as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ A ¼ 2pR R R2 a2 where R is the radius of the ball (5 mm) and a the contact radius. Then, the contact pressure (P) between the stainless steel ball and PVA-Hs can be calculated by dividing the normal load by the contact area. The single parameter of the Stribeck curve is calculated for each PVA-H sample and the results are shown in Fig. 7. By comparing the Stribeck curves, the lubrication conditions of four PVA-Hs (F17/10, F10/12, M17/12 and M100 /17) appear to be hydrodynamic lubrication at high sliding speed (as friction coefficient increases with an increase in ZV/P). Meanwhile, the four PVA-Hs at low speed and the sample with high elasticity (F17/18) may show conditions intermediate between mixed lubrication and hydrodynamic lubrication (minimum value of friction coefficient). The equation of minimum lubrication thickness (hmin) in the contact between the ball and plane is given as follows [11]: 0:65 hmin ZV FN 0:21 ¼ 2:80 ð4Þ EuR R EuR2 The equivalent elastic modulus (E0 ) is calculated as follows: 1 1 1n21 1n22 ¼ þ ð5Þ Eu 2 E1 E2
where E1 and n1 are the elastic modulus and Poisson’s ratio of PVA-Hs, respectively. And, E2 and n2 represent those of stainless steel (AISI410). With reference to Eq. (4), the minimum lubrication thickness increases with a decrease in FN, an increase in V, and a decrease in E0 . Increase in fluid film thickness induces an increase in the friction coefficient in hydrodynamic lubrication. The effects of load and velocity for the friction properties are discussed in the following sections. 5.2. Load dependence Fig. 8 shows the evolution of friction coefficients of PVA-Hs versus load. At high speed and low load, the friction coefficients of all PVA-Hs decrease when load is increased. This is explained by a decrease in the fluid film thickness. Meanwhile, at low speed (10 mm/s), the relationship is not clear concerning four PVA-Hs with similar elasticity. This is attributed to the fact that the contact between the stainless steel ball and the surface of PVA-H is induced by a decrease in the fluid film: the intermediate condition between mixed and hydrodynamic lubrication. Concerning the sample with high elasticity (F17/18), it seems that the lubrication condition is mixed lubrication at low speed (10 mm/s) and high load. At low speed and low load, F17/18 shows load dependence the same as that of the hydrodynamic lubrication. However, in the mixed lubrication condition, the values of friction coefficients and the Stribeck curves are different for the four PVAHs having the same elasticity (Fig. 7). Thus, the friction properties under these conditions may include other factors such as adhesion force involved in the contact (for the four samples of PVA-H with the same elasticity, even with the same contact area, differences in surface chemistry can modify the adhesion force with the counterbody). The effects of adhesion force are investigated by comparing measured contact radii and theoretical values in the following paragraph. According to Hertzian theory, the contact radius (ah) between two elastic solids can be calculated by the following equation [12]: 3FN R 1=3 ð6Þ ah ¼ 4E E* is determined as follows: 1n21 1n21 1 ¼ þ E E1 E2
Fig. 7. Friction coefficients of PVA-H samples versus a single parameter based on Stribeck theory: V/P (Ave. 7 SD of 2 samples).
ð7Þ
The theoretical contact radii of two PVA-Hs (F17/18, F17/10) are calculated using the values in Table 3. The results are shown in Table 4 and Fig. 9 with the measured contact radii. By comparing these results, it can be seen that the theoretical values are smaller than the measured ones. The relative error (Eh for Hertz/measured between the calculated contact radius with
F17/18
F17/18/Adhesion
F17/10
F10/12
M17/12
M10/17
0.015
10 mm/s
0.010
Friction coefficient [-]
Friction coefficient [-]
0.020 0.035 M10/17 100 mm/s
0.025
M17/12 F17/10 F10/12
0.015
F17/18 F17/18/Adhesion
0.005 0.0
0.2
0.4 0.6 0.8 Normal load [N]
1.0
1.2
0.005 0.0
0.2
0.4 0.6 0.8 Normal load [N]
1.0
1.2
Fig. 8. Load dependences of friction coefficients at a constant sliding speed of (a) 10 mm/s and (b) 100 mm/s (Ave. 7 SD of 2 samples).
K. Mamada et al. / Tribology International 44 (2011) 757–763
are defined by Eq. (8), and the adhesive force is obtained in each theory when the total relative error shows the minimum value. By this processing, the best value of adhesive force can be calculated to have the best fit between the measured results and the theoretical values. Then, the surface energy (w) of the PVA-H samples in the contact area is calculated by the estimated adhesion force. Concerning F17/18, the total relative error in the JKR theory is smaller than that in the DMT theory, as shown in Table 4, and the estimated surface energy for the DMT theory is much higher. Therefore, it seems that the measured data follow the JKR theory (Fig. 9). When the result is applied to F17/ 10 as well (Fig. 9), the value of the estimated adhesion force is smaller than that of F17/18. The ratio of the adhesion force of F17/18 to the total applied force is about 25% for the lowest load. The friction coefficient (m0 ) including the effect of adhesion force is defined by the following equation, and the calculated values are shown in Fig. 8.
Hertzian theory ah and the measured contact radius am) defined by Eq. (8) decreases with an increase in normal load. In the Hertzian theory, only compressive stress can exist in the contact area. If the elastic solids have a surface energy, the real applied load is larger than the normal load. Therefore, the contact radius is also larger than the Hertzian one. Eh ¼
ah am 2 am
ð8Þ
Meanwhile, there are two kinds of theories of elastic contact, which considers the existence of surface energy: the Johnson– Kendall–Roberts (JKR) theory [13] and the Derjaguin–Muller– Toporov (DMT) theory [14]. The JKR theory can be applied generally for soft solids with a large radius and high adhesion, and the DMT theory can be applied for rigid solids with a small radius and low adhesion. The adhesion force (F0) and contact radii (aj for JKR theory, ad for DMT theory) are calculated by following equations:
761
mu ¼
F FN þ F0
ð13Þ
JKR theory F0 ¼
3 pwR 2
ð9Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=3 3R FN þ2F0 þ 2 F0 ðFN þF0 Þ aj ¼ 4E
3.0
F17/10
ð10Þ
F17/18
F0 ¼ 2pwR ad ¼
ð11Þ
1 3RðFN þ2F0 Þ 4E
1=3 ð12Þ
where w is surface energy per unit contact area. In this study, the estimation of adhesion force is carried out for two samples (F17/ 18 and F17/10) using Excel solver (Microsoft Co. Ltd.) as follows: the relative errors (Ej for JKR/measured, Ed for DMT/measured)
Contact radius [mm]
DMT theory 2.0
Measured
1.0
Hertz theory JKR theory
Table 3 Elastic moduli (E), Poisson’s ratios (n) and curvature radii (R) of PVA-H samples and a stainless steel. Material
Elastic modulus (Pa)
Poission’s ratio
Curvature radius (mm)
PVA-HF17/18 PVH-HF17/10 Stainless steel AISI410
350 103 50 103 200 109
0.5 0.5 0.3
– – 5
DMT theory 0.0 0.0
0.2
0.4
0.6 0.8 Normal load [N]
1.0
Fig. 9. Comparison between measured and theoretical contact radii with 3 kinds of theories: Hertz, JKR, and DMT theory. JKR: Johnson–Kendall–Roberts, DMT: Derjaguin–Muller–Toporov.
Table 4 Estimated theoretical contact radii and adhesion forces between PVA-H (F17/18) and a stainless steel ball. Normal load (N)
0.0 0.1 0.2 0.3 0.5 0.7 1.0
Contact radius Measured (mm)
Hertz (mm)
Relative error (Hertz/measured)
JKR (mm)
Relative error (JKR/measured)
DMT (mm)
Relative error (DMT/measured)
1.27 1.45 1.61 1.85 2.04 2.30
0.00 0.95 1.18 1.36 1.60 1.79 2.02
0.06 0.03 0.02 0.02 0.01 0.01
0.92 1.29 1.48 1.63 1.85 2.02 2.24
0.00030 0.00039 0.00018 0.00002 0.00004 0.00068
1.16 1.34 1.48 1.60 1.78 1.94 2.14
0.00316 0.00026 0.00009 0.00160 0.00224 0.00465
Total relative error Adhesion force (N) Surface energy (J/m2) JKR: Johnson–Kendall–Roberts; DMT: Derjaguin–Muller–Toporov.
1.2
0.00160 0.024 1.017
0.01200 0.192 6.126
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0.04
0.04 0.1 N
0.3 N M17/12
0.03
F17/10 F10/12
0.02 F17/18
0.01
0.00
Friction coefficient [-]
Friction coefficient [-]
M10/17 M10/17
0.03 M17/12 F17/10
0.02
F10/12 F17/18
0.01
0.00 0
20
40 60 80 100 Sliding speed [mm/s]
120
0
20
40 60 80 100 Sliding speed [mm/s]
120
Fig. 10. Velocity dependence of friction coefficients at a constant normal load of (a) 0.1 N and (b) 0.3 N (Ave. 7 SD of 2 samples).
The application of adhesion force affects the load dependence, and it can be seen that the dependence is shifted to follow the Stribeck curve. Though the adhesion force would not be effective on the sliding properties in hydrodynamic lubrication, it must affect the friction from the boundary to the mixed lubrication under low load and low speed conditions in this study. 5.3. Velocity dependence Fig. 10 shows the velocity dependences of friction coefficients of PVA-Hs. The friction coefficients increase with an increase in sliding speed. The dependence corresponds to that of the calculated minimum lubrication thickness and follows the Stribeck curve in hydrodynamic lubrication. Concerning the sample with low DP and low SV (M100 /17), the friction coefficient shows a larger velocity dependence than that of the other samples. The measured contact areas do not show any significant differences among the four PVA-Hs with similar elasticity. Therefore, the higher value of friction coefficient of M100 /17 at high speed may be induced by the lower DP and/or SV, which modify the hydrophilicity of the rubbing surface and the viscoelasticities of the materials. The interaction of M100 /17 with water is lower than that of the other samples because of the lower ratio of the hydrophilic group on the surface. Consequently, the high friction may result from the diminished lubrication property [15–17]. However, in hydrodynamic lubrication, the hydrophilicity of the surface would not affect the friction because the counterbody contacts the sample via the fluid water film [18]. Meanwhile, the inner crystalline structure variations should be considered. PVA-Hs are believed to consist of crystalline and amorphous regions. The crystalline regions are formed mainly by hydrogen bonds on the hydrophilic groups, while the amorphous regions include flexible chains without hydrogen bonds. Decrease in polymerization induces decreased entanglement of the chains, and decreased saponification induces an increase in the amorphous regions [19]. The amorphous regions may act as a damper and consequently affect the viscous property. Concerning the four PVA-Hs with similar elasticity, the effect of DP and/or SV on the characteristics of the bulk material appears as a variety of viscosities, and the frequency dependence is similar to the velocity dependence of friction coefficients (Figs. 2 and 10). The viscous component of materials affects the deformation of the counterpart: the lag of deformation is increased with an increase in the viscosity (or the sliding speed). Though the viscoelasticities contribute to the friction with contact [20–22], it is believed that the bulk properties do not affect the friction in hydrodynamic lubrication. However, the effect could not be neglected for the four soft PVA-Hs (F17/10: E 50 103 Pa) because of the large
deformation and the very low friction. Thus, differences in velocity dependence may be induced by the resistance force via the fluid water film. The above discussions can possibly explain the different friction characteristics among PVA-Hs with different PVA factors and is supported by the evaluation of the counterpart in the sliding contact. Additional tests and analyses with considerations of the possibility of other mechanisms are essential to elucidate the effect of PVA factors on the friction properties.
6. Conclusion Friction tests of PVA-Hs with different PVA factors such as concentration, polymerization, and saponification were carried out using a stainless steel ball as the counterbody. The different friction coefficients were shown to be due to the PVA factors though the contact areas showed similar values. Velocity dependence varied. Hydrophilicity of the rubbing surface and viscoelasticities of the bulk material were discussed for the explanation of these differences. These results indicate that the PVA factors affect the friction properties and that the effect should be considered in order to reproduce the responses of human soft tissue in sliding contact.
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