Tribol Lett (2013) 49:301–311
DOI 10.1007/s11249-012-0066-x
ORIGINAL PAPER
Traction Characteristics of Siloxanes with Aryl and Cyclohexyl
Branches
Thomas Zolper • Zhi Li • Manfred Jungk •
Andreas Stammer • Herbert Stoegbauer •
Tobin Marks • Yip-Wah Chung • Qian Wang
Received: 6 September 2012 / Accepted: 1 November 2012 / Published online: 15 November 2012
Ó Springer Science+Business Media New York 2012
Abstract The molecular structures, rheological properties, and friction coefficients of several new siloxane-based
polymers were studied to explore their traction characteristics. The molecular structures including branch content
were established by nuclear magnetic resonance spectroscopy, while the molecular mass distributions were determined by gel permeation chromatography. Density,
viscosity, elastohydrodynamic film formation, and friction
were investigated over a temperature range of 303–398 K.
Film thickness and friction measurements were studied
under the conditions that are representative of boundary,
mixed, and full-film lubrication regimes, aiming at maximizing traction performance and temperature stability by
simultaneous optimization of the size and content of ringshaped branch structures. This study provides quantitative
insight into the effect of siloxane molecular structure on the
tribological performance for traction drive applications
such as continuously variable transmissions.
T. Zolper (&) Y.-W. Chung Q. Wang
Department of Mechanical Engineering, Northwestern
University, Evanston, IL 60208, USA
e-mail: thomaszolper2010@u.northwestern.edu
Z. Li T. Marks
Department of Chemistry, Northwestern University, Evanston,
IL 60208, USA
M. Jungk A. Stammer H. Stoegbauer
Dow Corning GmbH, Rheingaustr. 34, 65201 Weisbaden,
Germany
Y.-W. Chung
Department of Materials Science and Engineering, Northwestern
University, Evanston, IL 60208, USA
Keywords Silicones Synthetic base stocks EHL
friction (traction) Continuously variable transmissions
(CVT) Traction fluids
1 Introduction
Traction drives such as continuously variable transmissions
(CVT) have been in development for decades, leading to an
array of configurations in modern applications. Many
industrial, automotive, and aerospace companies have
investigated different types of traction drives for their
production lines to increase efficiency and reduce transmission components [1–7]. Traction drives such as CVT’s
have been tested in various engine applications for their
potential to improve vehicle performance and extend
engine life by running at the maximum power, or efficiency, at a constant engine speed [8–12]. However,
implementation of traction drives in automotive applications is beset with lingering functional and financial challenges including component weight, durability, and cost.
Traction driven transmissions such as toroidal, conical,
and planetary CVTs, transmit torque from one machine
element to another without the use of gears [5, 13]. Typically torque is transferred through point or line contacts
rather than through the larger surface areas that characterize clutches and brakes [5, 10]. Specially designed
traction fluids are required to transfer torque across a fluid
film while maintaining good surface protection and low
wear [14, 15]. These fluids differ from more generally
lubricated interfaces in the requirements to increase the
interface film friction between the driving and the driven
components.
Elastohydrodynamic (EHD) friction, lEHD, also known
as the traction coefficient is a key performance parameter
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302
in traction fluids. Successful traction fluids should have a
higher EHD friction than normal lubricants while maintaining sufficiently low viscosity at low temperatures to
allow its circulation during start-up and sufficiently high
viscosity at high temperatures to support the designed load
when fully warm-up. Additional requirements include
chemical inertness toward the metal surfaces in contact,
reasonable lubrication properties, and heat dissipation.
Hydrocarbon-based fluids including aliphatic, naphthenic, and cycloalkyl branched hydrocarbon structures
have been tested for traction performance [1, 14–21].
Various natural seed oils, including olive, sesame, canola,
and soybean oil, have also been evaluated for film formation and traction performance [22–26]. Several synthetic
lubricants, including silahydrocarbons, siloxanes, and perfluorinated polyalkylethers, have also been investigated to
examine their tribological performance [27–29]. The
research in this contribution extends previous investigations into the frictional performance of a series of new
polysiloxane materials.
Siloxane-based polymers have silicon–oxygen backbones instead of the carbon–carbon backbones that are
present in hydrocarbons. Siloxanes have been shown to
have greater oxidative stability and lower viscosity temperature dependence than many hydrocarbon polymers
[29–31]. Siloxanes are synthesized by reacting silicon and
methyl chloride to produce dimethylchlorosilanes, which
are hydrolyzed to produce silanols, which then undergo
polymerization to polydimethylsiloxane (PDMS), the
structure of which is shown in Fig. 1a. PDMS is composed
of methyl molecules bonded to the silicon atoms of the
siloxane backbone [30]. Polyphenylmethylsiloxane
(PPMS) has phenyl branches in the places of some methyl
branches (Fig. 1b) and is prepared by copolymerization of
dimethyldichlorosilane with methylphenyldichlorosilane.
Note that incorporation of phenyl branches significantly
increases polysiloxane oxidative stability, and decreases
the molecular flexibility.
The high molecular rigidity noted for the PPMS samples
was augmented by hydrogenation of the phenyl rings to
Fig. 1 Macromolecular
structures of a PDMS and
b PPMS
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Tribol Lett (2013) 49:301–311
produce polycyclohexylmethylsiloxanes (PCMS). Two
samples of PCMS were synthesized from the PPMS samples that exhibited the best traction performance. A sample
of polydiphenylsiloxane (PDPS) with 50 % diphenyl and
50 % phenyl methyl was also procured for film formation
and friction testing. The increased phenyl content of the
PDPS sample increases the molecular rigidity of the fluid
in anticipation of greater traction performance.
The extreme pressures and shear conditions of a traction
drive may subject a traction fluid to very large shear
stresses that can reduce its effectiveness by causing
molecular breakdown. Permanent viscosity breakdown
known as ‘‘molecular scission’’ occurs when the polymers
of a lubricant are mechanically broken into shorter/lower
mass segments by the high shear stresses at a tribological
interface. Siloxanes are being studied because the polysiloxane Si–O bond dissociation enthalpy (460 kJ/mol) significantly exceeds that of the corresponding C–C bond
(348 kJ/mol) in hydrocarbon polymers [32] and has been
shown to give siloxanes greater resistance to permanent chain breakdown than hydrocarbons. Mackenzie and
Jemmett [33] applied shear stresses to siloxanes and concluded that they have a permanent shear threshold that is an
‘‘order of magnitude’’ greater than that of organic
polymers.
The elastohydrodynamic film thickness, h, of lubricants
is modeled with rheological properties, such as atmospheric viscosity, go, and pressure–viscosity index,
a, together with entrainment velocity, U. Equation 1
depicts a simplification of the Hamrock-Dowson [34–36]
equation, where material and geometry parameters are
included in the constant k.
0:53
hoil ¼ kU 0:67 g0:67
0 a
ð1Þ
Increasing the pressure–viscosity index not only
improves the film forming ability of a lubricant but also
increases the EHD friction [21, 37, 38]. High EHD friction
causes efficiency loss in most lubricants, but importantly
gives rise to efficiency gains in traction fluids. Several
researchers have noted correlations between molecular
Tribol Lett (2013) 49:301–311
structure and pressure–viscosity index. Bridgman [39],
ASME [40], Kuss [41], Winer [42], and Jakobsen et al. [43]
measured the viscosity of several siloxanes including
PDMS and PPMS at elevated pressures; they
demonstrated that increasing the phenyl ring content of
siloxanes causes a significant increase in the pressure–
viscosity index. For example, the room temperature
pressure–viscosity index of PPMS 90 (27 GPa-1) is
approximately twice that of PDMS (14 GPa-1) [43].
Hammann [16], Hentschel [17], Muraki [19], DareEdwards [20], and Tsubouchi and Hata [44] show that
compounds with high ring structure branching content, QR,
generally exhibit high EHD friction. Hentschel [17] and
Hata and Tsubouchi [14] attributed the high EHD friction
of certain successful traction fluids to their ability to
molecularly interlock. Dare-Edwards [20] credited performance of traction fluids to the molecular rigidity induced
by the steric hindrance caused by ring branches. Muraki
[19] broadly correlated molecular rigidity to the cycloalkyl
content that Kyotani et al. [45, 46] further connected with
the activation volume.
Gunsel et al. [38] measured the film thickness and
friction coefficient of several different hydrocarbon polymers and determined that the EHD friction coefficient
positively correlates with the pressure–viscosity index [38].
Villegas et al. [47] measured the radius of gyration and
persistence length of alkyl and phenyl branched siloxanes.
Using correlations between structure and conformation
based on a model of Huglin [48], Villegas et al. [47]
concluded that PPMS has a rigid rod configuration in
solution. The rigid rod shape of PPMS differs significantly
from PDMS which is highly flexible with a random distribution [47].
The results of the aforementioned studies indicate how
molecular structure affects properties such as molecular
rigidity, EHD friction, and pressure–viscosity index. A
high density of ring branches on a macromolecule increases its molecular rigidity and promotes a rod-like conformation. The flow characteristics of the rigid rod structures
increase the pressure–viscosity index as well as the EHD
friction coefficient. The sum of the data suggests an optimum direction for further improving the traction performance of siloxane-based traction fluids, and the goal of the
present study is to extend the aforementioned correlations
from natural to synthetic hydrocarbons to siloxane-based
polymer traction fluids.
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2 Siloxane Synthesis and Experimental Procedures
Previous research into the film formation and friction
performance of siloxanes had indicated that increasing
phenyl branch content increases the EHD friction coefficient in addition to improving the Newtonian film formation of siloxane lubricants [29]. This research aims to
further increase the noted EHD friction as well as the
temperature stability of performance. The PDMS and
PPMS examined in this research were provided by Dow
Corning Corporation, and may be procured commercially.
The PDPS sample of 50 % diphenyl and 50 % phenylmethyl content was purchased from Geleste Inc.
2.1 Synthesis of Polycyclohexylmethylsiloxanes
Correlations between the molecular structure and frictional performance led to the synthesis of polycyclohexylmethylsiloxane
(PCMS) branched siloxanes shown in Fig. 2. PCMS was
synthesized at Northwestern University by the catalytic
hydrogenation of the corresponding PPMS derivative using
palladium on activated charcoal as the heterogeneous catalyst (Fig. 2). The reaction was carried out in a pressurized
reactor at 413 K and a H2 pressure of 4.14 MPa with no
solvent. Complete synthesis required approximately 24 h
with several recharges to make up for consumed hydrogen.
The final product was filtered through Celite to remove the
catalyst, and was characterized by NMR spectroscopy and
gel permeation chromatography. Details of the synthesis
are included in the ‘‘Appendix’’.
2.2 Molecular Mass and Structure
Molecular mass distributions of the polysiloxane samples
were measured by gel permeation chromatography (GPC)
using a Waters 2695 Separations Module equipped with a
vacuum degasser, and a Waters 2410 differential refractometer. Data collection and analyses were performed
using ThermoLab Systems Atlas chromatography software
and Polymer Laboratories Cirrus GPC software. Details of
the procedures are listed in the ‘‘Appendix’’.
The PDMS, PPMS, and PCMS molecular structures
were assayed from 1H/13C NMR spectroscopic data using
Varian INOVA 400 or Mercury 400 NMR spectrometers.
Details of the NMR characterization are included in the
Fig. 2 Catalytic hydrogenation
of PPMS to produce PCMS
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‘‘Appendix’’. The degree of polymerization was then calculated from the mass and structural data.
2.3 Density and Viscosity Measurement
A Cannon CT-2000 constant temperature bath was used to
simultaneously measure the density, q, and kinematic viscosity, t, from 303 to 398 K. The density of each siloxane
sample was calculated from precision measurements of the
mass and volume. Cannon–Fenske capillary viscometers
were used to measure kinematic viscosity. The absolute
viscosity, g, was obtained from measurements of the
kinematic viscosity and the density.
2.4 Film Thickness Measurement
A PCS thin-film tribometer was used to measure elastohydrodynamic lubricant film thickness from 303 to 398 K
±1 K. A polished AISI 52100 steel ball of 19.050 mm
diameter is partly immersed in the test fluid and pressed
against an optically transparent glass disk. The respective
Young’s moduli of the glass disk and steel ball are 75 and
210 GPa resulting in a maximum Hertzian pressure of
0.54 GPa under a 20 N load [38]. The disk has a 500 nm
thick silica spacer layer allowing measurement of lubricant
film thicknesses with a precision up to 1 nm for films under
30 nm, and within 5 % for film thicknesses [30 nm
[49, 50]. The r.m.s. roughness of the steel ball and glass
disk are 14 and 5 nm, respectively. The composite roughness, Rqc, is approximately 15 nm.
Film thickness measurements were undertaken in nominally pure rolling conditions with the disk velocity, U1,
varying from 0.020 to 4.35 m/s. In nominally pure rolling,
the ball was completely driven by the disk. Additional
measurements were made with the ball attached to a motordriven shaft to allow independent variation of the ball
velocity U2. This arrangement allowed additional film
thickness measurements at different slide-to-roll ratios, R,
ranging from pure rolling (R = 0) to pure sliding (R = 2)
as defined in Eq. 2.
R¼
Slidingspeed
jU1 U2 j
¼
Entrainment speed ðU1 þ U2 Þ=2
ð2Þ
2.5 Friction Measurement
The friction coefficients, l, of the test fluids were measured
on the same PCS instrument. Friction was also measured
from 303 to 398 K, with temperature controlled to ±1 K
for each test in the temperature sequence. Friction tests
were conducted using a 19.050 mm diameter AISI 52100
steel ball applied to a steel disk. The respective surface
roughness of the disk and ball were about 30 and 5 nm. The
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Young’s moduli of the steel ball and steel disk are both
210 GPa, resulting in a maximum Hertzian pressure of
0.82 GPa under a load of 20 N. The composite surface
roughness is calculated to be approximately 30 nm.
A new steel ball and a new disk track were used for
every test in the film formation and friction measurements.
The reservoir, ball carriage, disk, and ball were thoroughly
cleaned with isopropyl alcohol and hexane, and then
allowed to dry before each test. The friction coefficient was
measured at a fixed slide-to-roll ratio of R = 0.50 while the
disk velocity was varied from 0.025 to 5.00 m/s. The radial
position of the ball used in the friction tests was varied
from 42 to 44 mm to minimize the contribution of a spin
component to the overall friction measurements. Since all
friction measurements were made at these radii, the precision was within 3 % for friction measurements. It should
be pointed out that the use of the parallel-axis ball and disk
interface for friction measurement may induce minor
inaccuracies; however, this does not affect the results of
relative comparisons for the best result selection [51].
3 Results
3.1 Molecular Mass and Structure
Table 1 lists the fluid types and molecular mass distributions for all of the traction fluids tested. Data from the
NMR measurements confirm that the PDMS samples have
100 % methyl branching. Two samples of PPMS have
10 % phenyl methyl branch content and the remaining two
have 50 and 90 % phenyl methyl branch content, respectively. The two PCMS samples were synthesized from the
PPMS samples with high phenyl methyl branch content
and, therefore, have 50 and 90 % cyclohexyl methyl
branch content, respectively. The samples are named for
their percent phenyl (PPMS), cyclohexyl (PCMS), and
diphenyl (PDPS) branch content. Two samples with the
same branch content are alphabetized by increasing viscosity. Therefore, the higher viscosity 10 % phenyl branched siloxane is termed PPMS 10-B.
3.2 Density and Viscosity
Table 1 lists the density and viscosity of the polysiloxanes
at 303, 348, and 398 K. The density and viscosity of all
samples increase with molecular mass for lubricants with
the same branch content. Density increases with phenyl
content but decreases slightly when the PPMS samples are
hydrogenated to synthesize PCMS. The viscosity of
siloxanes increases with increasing phenyl and cyclohexyl
content at a given molecular mass. Hydrogenation of
PPMS to produce PCMS causes a significant increase in the
Tribol Lett (2013) 49:301–311
Table 1 Molecular mass,
density, viscosity, and
activation energy for
polysiloxanes with varying
branch structures and contents
305
Sample
PDMS
Molecular
mass (g/mol)
Density (g/cm3)
303 K
348 K
398 K
303 K
348 K
398 K
Viscosity (mPa-s)
Activation
energy (kJ/mol)
32,000
0.96
0.92
0.88
937.0
423.3
213.2
PPMS 10-A
8,180
0.97
0.93
0.89
91.8
40.3
19.8
16
PPMS 10-B
26,600
0.99
0.94
0.90
443.3
202.4
98.0
16
2,690
1.05
1.01
0.98
125.7
38.5
15.8
23
PPMS 50
15
PPMS 90
1,990
1.07
1.04
1.00
472.1
68.7
21.8
33
PCMS 50
2,820
1.01
0.98
0.96
746.7
125.0
39.6
31
PCMS 90
2,090
1.03
1.00
0.97
19,800
1,523
242.1
47
PDPS 50
1,560
1.09
1.07
1.03
559.2
59.0
16.5
35
viscosity at room temperature, increasing with phenyl
content.
The Andrade–Eyring equation (Eq. 3) is used to calculate the activation energy of the lubricants, where E is the
activation energy, R is the universal gas constant, and T is
the temperature [52]. The low-shear viscosity reference gR
is calculated by fitting a line to the measured viscosity data
and taking the limit to infinite temperature [52].
E
g0 ðT Þ ¼ gR eRT
ð3Þ
The activation energy calculated over the entire
temperature range is also shown in Table 1. The addition
of phenyl branches decreases the temperature stability of
viscosity that siloxanes, especially PDMS, are known for
[29–31]. The hydrogenation of the phenyl rings to
cyclohexyl structures significantly increases the activation
energy. In general, activation energy increases as the
branch content and the hydrogen content of branches
increases.
3.3 Film Thickness
Figures 3 and 4 illustrate the measured (symbols) and
calculated (lines) film thickness of selected fluids as a
function of entrainment speed at temperatures of 303, 348,
and 398 K. For simplicity, Eq. 1 is used for the calculation
of the EHL film thickness for the cases investigated here
without considering the effects of roughness. Previous
research by the authors provides supporting film thickness
data for PDMS and PPMS samples not included here [29].
High molecular mass samples of PDMS and PPMS were
previously found to exhibit non-Newtonian shear-thinning
behavior, which enables slip and limits the EHD friction
coefficient for a given fluid [29, 53–55]. Therefore, the
fluids under analysis are highly branched with relatively
lower molecular mass to prevent shear-thinning.
Figure 3a, b illustrate the film forming ability of PPMS
and PCMS, respectively. The film thicknesses of the
samples were calculated using Eq. 1 with the measured
viscosity and pressure–viscosity indices at the test
Fig. 3 Measured (symbols) and calculated (lines) film thickness vs.
entrainment speed for a PPMS 50 and b PCMS 50 at 303 K
(triangles), 348 K (squares), and 398 K (diamonds)
temperatures (Fig. 3a). The hydrogenation of PPMS to
produce PCMS increases the viscosity and the pressure–
viscosity indices sufficient to increase film thickness significantly even though the two samples have the same
branch content and degree of polymerization. However,
Fig. 3b illustrates that the higher activation energy of
PCMS simultaneously causes a greater decrease in the
viscosity and the pressure–viscosity index with increasing
temperature, resulting in a greater variation of film
thickness.
Figure 4a, b illustrates the film thickness of PCMS 90
and PDPS 50, respectively. The high viscosity of PCMS 90
at 303 K contributes to film thicknesses that exceed the
measurement capability of the test instrumentation, so data
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Table 2 Pressure–Viscosity indices for PDMS, PPMS, PCMS, and
PDPS at 303, 348, and 398 K
Sample
Pressure–Viscosity index (GPa-1)
303 K
348 K
398 K
PDMS
15.0
14.8
14.6
PPMS 10-A
15.5
14.1
13.0
PPMS 10-B
PPMS 50
15.5
23.7
14.1
17.8
13.0
12.8
PPMS 90
27.0
20.2
14.5
PCMS 50
34.2
27.8
16.7
PCMS 90
–
33.7
17.8
PDPS 50
38.8
27.2
17.2
3.4 Friction Coefficient
Fig. 4 Measured (symbols) and calculated (lines) film thickness vs.
entrainment speed for a PCMS 90 and b PDPS 50 at 303 K
(triangles), 348 K (squares), and 398 K (diamonds)
at that temperature are not presented. The samples exhibit
the logarithmic slope of approximately 0.67 when modeled
by the Hamrock-Dowson equation, which is characteristic
of Newtonian fluids. Neither the PCMS nor the PDPS
exhibit the shear-thinning behavior that is characteristic of
typical high mass polysiloxanes, indicating that they
remain Newtonian over the entire entrainment speed range.
Table 2 summarizes the pressure–viscosity indices for
PDMS, PPMS, PCMS, and PDPS that were interpolated
from high pressure viscometric data [39–43, 56, 57] using
the procedure described by Zolper et al. [29]. The high
pressure–viscosity index exhibited by highly branched
PPMS that has been noted by Bridgman [39], AMSE [40],
Kuss [41], Winer [42], and Jakobsen et al. [43] is also
found here in the PCMS and PDPS samples.
As expected, the pressure–viscosity indices of the
PCMS samples are higher than those of PPMS because of
the increased dimensions and flexibility of the cyclohexyl
versus phenyl branches. The PDPS also exhibits higher
pressure–viscosity indices than PPMS because of the
increased density of phenyl branching groups. This effect is
attributed to the increased molecular rigidity caused by
bulky, rigid branches. These findings are in agreement with
the observed effects of ring structures on the pressure–
viscosity indices of hydrocarbons and polysiloxanes
reported by Kuss [58], Jakobsen et al. [43], Tammai and
Kyotani [59], and Gunsel et al. [38].
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Friction and film thickness measurements were carried out
for the same lubricants using the same entrainment speed
range at R = 0.5 and temperatures of 303, 348, and 398 K.
Such common thermal and dynamic conditions allow the
film thickness and friction coefficient data to be crossplotted to determine the friction coefficient as a function of
the lubrication regime [29, 38]. PCMS 90 was found to be
too viscous to test at 303 K, but at higher temperatures the
performance was measurable. Figures 5, 6 and 7 illustrate
the cross-plots of film thickness and friction coefficient that
were made for the fluids under investigation.
Figure 5 shows the variation of friction coefficient as a
function of film thickness at T = 303 K and R = 0.5. A
high viscosity PDMS reference is included in the figures to
provide a performance baseline. Previous investigations
showed that PDMS maintains nearly constant EHD friction
with increasing viscosity over the range of 10–1,000 cSt, at
a constant load, slide-to-roll ratio, and temperature [29].
Figure 5a illustrates that the introduction of phenyl branches in PPMS causes a significant increase in EHD friction
over that of PDMS. Furthermore, hydrogenation of PPMS
to PCMS causes a substantial increase in the EHD friction.
Figure 5b illustrates the EHD friction of polysiloxanes with
high phenyl branch contents. PPMS 90 have higher EHD
friction than PPMS 50, as would be expected from the
increase in pressure–viscosity index. Note that while the
diphenyl branched siloxane (PDPS 50) has higher phenyl
branch content; it exhibits slightly lower EHD friction than
PPMS 90. This suggests that projection of friction performance from the molecular structure only can yield unexpected results.
The lower friction of PDPS 50 in comparison to that of
PPMS 90 illustrates the difficulty in ascribing EHD friction
solely to molecular rigidity. The phenomenon lends credence to Hentchel’s [17] hypothesis that EHD friction is
partly influenced by interlocking molecular asperities of
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307
Fig. 7 PPMS 90 Variation of friction coefficient vs. film thickness at
R = 0.5 and 303 K (triangles), 348 K (squares), and 398 K
(diamonds)
Fig. 5 Friction coefficient vs. film thickness at R = 0.5 and 303 K
for a PPMS 50 and PCMS 50 and b PPMS 90 and PDPS 50,
compared with that of PDMS
Fig. 6 Friction coefficient vs. film thickness at R = 0.5 and 398 K
for a PPMS 50 and PCMS 50 and b PPMS 90 and PCMS 90,
compared with that of PDMS
the test fluids. Hentschel [17] argued that effective traction
fluids have molecular structures with ‘‘pockets’’ that he
hypothesized could interlock with the asperities of other
molecules.
The discrepancy between PPMS 90 and PDPS 50 may
suggest that an optimum number of molecular pockets and
asperities for a traction fluid may augment the EHD friction
contribution of molecular rigidity. PPMS 90 contain about
45 % phenyl branch rings (asperities) and 55 % methyl
branch groups (voids) along its length. In contrast, PDPS
50 has about 75 % phenyl branch rings (asperities) and
25 % methyl branch groups (voids) along its length. The
additional phenyl asperities of PDPS 50 may decrease the
likelihood of interlocking of neighboring molecules, thus
limiting EHD friction.
Figure 6 shows the variation of friction coefficient as a
function of film thickness at T = 398 K and R = 0.5. The
data for PDMS and PPMS at low film thicknesses illustrate
the transition from boundary to full-film lubrication. At
high temperatures, the films are thinner, so that boundary
friction is visible on the left of the figures. The friction then
decreases with increasing entrainment speed until the film
thicknesses, a product of entrainment speed, exceed the
composite roughness of the disk and ball. PPMS samples
exhibit a steady increase in EHD friction as the phenyl
branch content is increased [29]. This phenomenon continues in the PCMS samples.
The friction coefficient of the PPMS samples decreases
more significantly as temperature is increased. The PCMS
samples exhibit the greatest stability of performance over
the temperature range tested; they offer higher friction than
PPMS with the same branch content at room temperature
(Fig. 5). Moreover, the hydrogen saturation of PPMS to
produce PCMS causes a substantial increase in viscosity as
well as film formation and EHD friction coefficient. When
the temperature is raised to 398 K, PCMS still offers higher
friction relative to the PPMS samples which exhibit significantly greater temperature dependence (Fig. 6). At
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higher temperatures, the PDMS reference sample exhibits
stable friction as film thickness increases while the friction
of PCMS and PPMS generally decreases.
As film thickness increases, the lubrication regime k
transitions from boundary to mixed and finally full-film
lubrication (conservatively, k ¼ hc Rqc [ 3) [60]. The
lubrication regimes are associated with distinct changes in
friction, with EHD friction occurring in the full-film regime
[60]. Figure 7 illustrates where the boundary and mixed
frictional regimes intersect with the EHD frictional regime
for PPMS 90 over the test temperature range. The limiting
EHD friction coefficient is just outside the mixed lubrication
regime, and represents the shear stress sustained by the fluid
film with minimum influence from the effects of shear
heating [26, 38]. Gunsel et al. [38] and Biresaw and Bantchev
[26] determined the limiting EHD friction coefficient of
several mineral oils and seed oils at R = 0.5 and similar
loads to those studied here. Figure 7 illustrates how the
limiting EHD friction is determined from the intersection of
lines of measured EHD friction at the transition from mixed
to full-film lubrication.
Table 3 compiles the limiting EHD friction coefficients for
the polysiloxanes tested herein over the temperature range
studied. In most cases, a clear transition from mixed lubrication to full-film lubrication (k ¼ 3) is visible in the cross-plots
of film thickness and friction coefficient. In some cases, such
as the low temperature PPMS 90 data (Fig. 7), friction in the
boundary and mixed lubrication regimes is not measureable
due to the thick film formation at low speeds. In such cases, the
limiting EHD friction was approximated by extrapolating the
EHD friction to the intersection of mixed and full-film friction
data based on high temperature data as illustrated in Fig. 7.
Figure 8 depicts the relationship between the ring-shaped
branch content and the limiting EHD friction coefficient for
PPMS and PCMS. Both datasets are compared to the limiting
EHD friction of PDMS with no ring branch content. It is
evident that as phenyl branch content increases, the overall
EHD friction increases (Fig. 8a). Hydrogenation of the
phenyl rings to cyclohexyl groups causes a substantial
increase in the limiting EHD friction (Fig. 8b). PCMS also
has higher temperature stability of EHD friction than does
PPMS. These results extend the correlation between ring
branch content and EHD friction first noted by Hammann
[16], Hentschel [17], Muraki [19], Dare-Edwards [20], and
Tsubouchi and Hata [44] to siloxane-based lubricants.
Figures. 9 and 10 depict the pressure–viscosity index
data of Table 2 plotted against the limiting EHD friction
coefficient of Table 3. The data indicate a general positive
correlation between the two properties. For the PPMS
samples, there is a strong correlation between pressure–
viscosity index and limiting EHD friction coefficient
(Fig. 9).
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The correlation between pressure–viscosity and limiting
EHD friction is not as distinct when examined for all of the
samples tested (Fig. 10). Nevertheless, a trend can be largely drawn at individual temperatures to relate pressure–
viscosity index to the limiting EHD friction coefficient.
The findings support the observations made by Gunsel
et al. [38] and Biresaw and Bantchev [26] for mineral oils
and seed oils, respectively.
Table 3 Limiting elastohydrodynamic friction coefficients for
PDMS, PPMS, PCMS, and PDPS at R = 0.5 and temperatures of
303, 348, and 398 K
Sample
Elastohydrodynamic friction coefficient
303 K
348 K
398 K
PDMS
0.042
0.018
0.007
PPMS 10-A
0.051
0.022
0.016
PPMS 10-B
0.052
0.024
0.016
PPMS 50
0.077
0.062
0.035
PPMS 90
0.093
0.074
0.052
PCMS 50
0.105
0.098
0.086
PCMS 90
–
0.118
0.110
PDPS 50
0.092
0.083
0.075
Fig. 8 Limiting EHD friction coefficient vs. ring branch content
at R = 0.5 and 303 K (triangles), 348 K (squares), and 398 K
(diamonds) for a PPMS and b PCMS
Tribol Lett (2013) 49:301–311
309
3.
4.
Fig. 9 Limiting EHD friction coefficient vs. pressure–viscosity index
at R = 0.5 for all PPMS samples
5.
6.
Fig. 10 Limiting EHD friction coefficient vs. pressure–viscosity
index at R = 0.5 and 303, 348, and 398 K for PDMS (squares),
PPMS 10 (diamonds), PPMS 50 (green circles), PPMS 90 (purple
circles), PCMS 50 (green triangles), PCMS 90 (purple triangles), and
PDPS (crosses) (Color figure online)
4 Conclusions
Several siloxanes with various types and percentages of
ring branch structures were evaluated in terms of their
traction performance. The PPMS, PDPS, and PCMS samples were compared to a PDMS sample through rheological, film formation, and friction testing. The results of this
study indicate that a polysiloxane lubricant can exhibit
broad traction performance depending on its length, branch
content, and branch structure. The major findings are as
follows:
1.
2.
Polysiloxanes with a high content of aryl and cycloalkyl ring structures have higher EHD friction than
polysiloxanes without ring branch structures, such as
PDMS. For polysiloxanes with the same ring content,
larger cycloalkyl branches (PCMS) increase EHD
friction more than aryl branches (PPMS).
There appears to be an optimum density of ring
branches to maximize the contribution of molecular
interlocking to EHD friction [14, 17]. The optimum
may be approached by PPMS 90 and PCMS 90 but
exceeded by PDPS 50.
Increasing polysiloxane ring branch density and ring
branch dimensions causes an increase in molecular
rigidity, resulting in a rigid rod-like conformation [47]
which contributes to high pressure–viscosity index as
well as high EHD friction.
Polysiloxanes with the same percentage branch density
exhibit higher and more temperature stable EHD
friction with larger, more flexible ring structures
(cyclohexyl) than do polysiloxanes with smaller, more
rigid rings (phenyl).
The viscosity and pressure–viscosity indices of highly
branched polysiloxanes decrease significantly with
increasing temperature, in accord with the correlation
between activation energy and pressure–viscosity
index observed by Roelands [61], Jakobsen et al.
[43], Spikes [62], Aderin [63], and Gunsel et al. [38].
A positive correlation exists between pressure–viscosity index and the limiting EHD friction coefficient for
all polysiloxanes investigated. The observed correlation is greater in materials with the same type of
branch structures.
The correlations of branch content to traction performance as well as the noted invariance of pressure–viscosity
with respect to degree of polymerization [29, 41–43] suggest that the viscosity may be reduced by reducing degree
of polymerization [64]. As long as the branch type and
content remains the same, the species of polysiloxane
species examined herein are expected to maintain similar
traction performance regardless of degree of polymerization. Therefore, viscosity dominated phenomenon, such as
film formation and fluid circulation, may be varied for
different applications while maintaining reasonably high
EHD friction.
Acknowledgments The authors thank Dow Corning Corporation
for support of this research.
Appendix: Synthesis and Experimental Procedures
Synthesis of PCMS
The procedure for the synthesis of PCMS 50 was also
representative for the synthesis of PCMS 90. All chemical
reactions were carried out in oven-dried flasks under N2
unless otherwise noted. All reagents and catalysts were
obtained from commercial vendors and used as received. A
100 mL Parr Micro Reactor equipped with a Teflon reaction vessel, a pressure gauge, an H2 inlet, and a mechanical
stirrer was used, and heating was charged with
123
310
poly(phenylmethylsiloxane) PPMS 50 (10 mL) and 10 %
Palladium on Charcoal (1 g). After sealing and purging the
reaction vessel with H2, the reactor was heated to 413 K
with vigorous stirring and 4.14 MPa H2 (Fig. 2). During
the course of the reaction, the H2 pressure was renewed
when it fell below 3.45 MPa. The reaction was kept stirring
until the pressure became constant. The reactor was then
cooled to room temperature and the pressure released to the
atmosphere. After carefully opening the reactor, the black
residue was dissolved with hexanes, filtered through Celite,
and the solvent was removed in vacuo. The obtained clear
oil was dried under high vacuum overnight to provide pure
product.
NMR Experimental Details
1
H NMR spectra were recorded on Varian Inova
(500 MHz) spectrometers. Chemical shift values (d) were
expressed in ppm using signal of solvent residue as the
internal standard (CHCl3 at 7.26 ppm). 13C NMR spectra
were recorded on Varian Inova (125 MHz) spectrometers
and were expressed in ppm using solvent as the internal
standard (CDCl3 at 77.16 ppm). The results are as follows.
PCMS 50. 1H NMR (CDCl3): d 1.74 (m), 1.20 (m), 0.55
(m), 0.09 (m), 0.08 (m) 0.05 (m), 0.01 (m), -0.02 (m). 13C
NMR (CDCl3): d 28.03, 28.01, 27.99, 27.96, 27.87, 27.70,
27.63, 27.59, 27.57, 27.49, 27.12, 26.81, 26.76, 26.71,
26.67, 26.65, 2.09, 2.05, 1.97, 1.95, 1.52, 1.46, 1.38, 1.33,
1.30, 1.24, -2.14, -2.19, -2.24, -2.32.
PCMS 90. 1H NMR (CDCl3): d 1.72 (m), 1.20 (m), 0.56
(m), 0.09 (m), 0.10 (m) 0.03 (m), -0.01 (m), -0.02 (m).
13
C NMR (CDCl3): d 28.03, 28.02, 27.99, 27.95, 27.90,
27.74, 27.72, 27.69, 27.60, 27.18, 27.16, 27.14, 26.88,
26.83, 26.81, 26.68, 2.10, -1.93, -2.02, -2.10, -2.36.
GPC Experimental Details
The chromatographic equipment consisted of a Waters
2695 Separations Module equipped with a vacuum degasser, and a Waters 2410 differential refractometer. The
separation was made with two (300 9 7.5 mm) Polymer
Laboratories PLgel 5 lm Mixed-C columns (molecular
weight separation range of 200–2,000,000), preceded by a
PLgel 5 lm guard column (50 9 7.5 mm). The analyses
were performed using certified grade THF flowing at
1.0 mL/min as the eluent, and the columns and detector
were both heated to 35 °C. The samples were prepared in
THF at about 0.5 % w/v solids, solvated about 2 h with
occasional shaking, and transferred to autosampler vials
without filtering. An injection volume of 100 lL was used
and data were collected for 25 min. Data collection and
analyses were performed using ThermoLab Systems Atlas
chromatography software and Polymer Laboratories Cirrus
123
Tribol Lett (2013) 49:301–311
GPC software. Molecular weight averages were determined relative to a calibration curve (3rd order) created
using the polystyrene standards covering the molecular
weight range of 580–2,300,000.
References
1. Haseltine, M.: Design and Development of Fluids for Traction
and Friction Type Transmissions. Society of Automotive Engineers, Warrendale (1971)
2. Loewenthal, S., Rohn, D., Anderson, N.: Advances in Traction
Drive Technology. Society of Automotive Engineers, Warrendale
(1983)
3. Coy, J.J., Townsend, D.P., Coe, H.H.: Results of NASA/Army
transmission research. DTIC Document (1987)
4. Boos, M., Mozer, H.: Ecotronic: The Continuously Variable Zf
Transmission (CVT). Society of Automotive Engineers, Warrendale (1997)
5. Kluger, M.A., Fussner, D.R.: An Overview of Current CVT
Mechanism, Forces, and Efficiencies. Society of Automotive
Engineers, Warrendale (1997)
6. Birch, S.: Audi takes CVT from 15th century to 21st century.
Automotive Engineering International 1 (2000)
7. Yamada, S., Nakamura, G., Amiya, T.: Shear properties for thin
films of star and linear polymer melts. Langmuir 17(5),
1693–1699 (2001)
8. Chau, K., Chan, C.: Emerging energy-efficient technologies for
hybrid electric vehicles. Proc. IEEE 95(4), 821–835 (2007)
9. Kamal, W.: Improving energy efficiency-the cost-effective way
to mitigate global warming. Energy Convers. Manage. 38(1),
39–59 (1997)
10. Heilich, F.W., Shube, E.E.: Traction Drives: Selection and
Application. Dekker, New York (1983)
11. Carbone, G., Mangialardi, L., Mantriota, G.: A comparison of the
performances of full and half toroidal traction drives. Mech.
Mach. Theory 39(9), 921–942 (2004)
12. Poulton, M.L.: Fuel Efficient Car Technology. Computational
Mechanics Publications, Southampton (1997)
13. Patil, H.: An experimental study on full toroidal continuously
variable transmission system. Int. J. Adv. Des. Manuf. Technol.
5(1), 19–23 (2012)
14. Hata, H., Tsubouchi, T.: Molecular structures of traction fluids in
relation to traction properties. Tribol. Lett. 5(1), 69–74 (1998)
15. Tsubouchi, T., Hata, H., Yoshida, Y.: Optimisation of molecular
structure for traction fluids. Lubr. Sci. 16(4), 393–403 (2004)
16. Hammann, W., Schisla, R., Groenweghe, L., Gash, V.: Synthetic
fluids for high capacity traction drives. ASLE Trans. 13(2),
105–116 (1970)
17. Hentschel, K.: The influence of molecular structure on the frictional behaviour of lubricating fluids. J. Synth. Lubr. 2(2),
143–165 (1985)
18. Hentschel, K.H.: The influence of molecular structure on the
frictional behaviour of lubricating fluids 2: low coefficients of
traction. J. Synth. Lubr. 2(3), 239–253 (1985)
19. Muraki, M.: Molecular structure of synthetic hydrocarbon oils
and their rheological properties governing traction characteristics.
Tribol. Int. 20(6), 347–354 (1987)
20. Dare Edwards, M.: A novel family of traction fluids deriving
from molecular design. J. Synth. Lubr. 8(3), 197–205 (1991)
21. Cecil, R., Pike, W., Raje, N.: Development of methods for
evaluating traction fluids. Wear 26(3), 335–353 (1973)
Tribol Lett (2013) 49:301–311
22. Ohno, N., Shiratake, A., Kuwano, N., Hirano, F.: Behavior of
some vegetable oils in EHL contacts. Tribol. Ser. 32, 243–251
(1997)
23. Cloesen, C., Kabuya, A., Bozet, J.: The optical EHD method
applied to the study of ageing of biodegradable oils. J. Synth.
Lubr. 15(1), 1–12 (1998)
24. Adhvaryu, A., Biresaw, G., Sharma, B.K., Erhan, S.Z.: Friction
behavior of some seed oils: biobased lubricant applications. Ind.
Eng. Chem. Res. 45(10), 3735–3740 (2006)
25. Biresaw, G., Bantchev, G.: Effect of chemical structure on filmforming properties of seed oils. J. Synth. Lubr. 25(4), 159–183
(2008)
26. Biresaw, G., Bantchev, G.B.: Elastohydrodynamic (EHD) traction properties of seed oils. Tribol. Trans. 53(4), 573–583 (2010)
27. Jones Jr, W., Jansen, M., Gschwender, L., Snyder Jr., C., Sharma,
S., Predmore, R., Dube, M.: The tribological properties of several
silahydrocarbons for use in space mechanisms. J. Synth. Lubr.
20(4), 303–315 (2004)
28. Gschwender, L., Snyder Jr, C.E., Sharma, S.K., Fultz, G.W.: High
speed civil transport (HSCT) hydraulic fluid development. Tribol.
Trans. 45(2), 185–192 (2002)
29. Zolper, T., Li, Z., Chen, C., Jungk, M., Marks, T., Chung, Y.,
Wang, Q.J.: Lubrication properties of poly-alpha-olefin and
polysiloxane lubricants: molecular structure-tribology relationships. Tribol. Lett. (2012). doi:10.1007/s11249-012-0054-1
30. Ziegler, M., Fearon, F.: Silicon-Based Polymer Science: A
Comprehensive Resource, Advances in Chemistry Series, 224.
American Chemical Society, Washington (1990)
31. Rochow, E.: Silicon and Silicones. Springer, Berlin (1987)
32. Lewis, G.: The atom and the molecule. J. Am. Chem. Soc. 38(4),
762–785 (1916)
33. Mackenzie, K., Jemmett, A.: Polymer shear stability. Wear
17(5–6), 389–398 (1971)
34. Hamrock, B., Dowson, D.: Isothermal elastohydrodynamic
lubrication of point contacts. Part I theoretical formulation.
ASME Trans. (1975)
35. Hamrock, B., Dowson, D.: Isothermal elastohydrodynamic
lubrication of point contacts. Part II ellipticity parameter results.
ASME Trans. (1975)
36. Hamrock, B., Dowson, D.: Ball Bearing Lubrication: The Elastohydrodynamics of Elliptical Contacts. National Aeronautics
Space Administration, Lewis Research Center, Cleveland (1981)
37. LaFountain, A.R., Johnston, G.J., Spikes, H.A.: The elastohydrodynamic traction of synthetic base oil blends. Tribol. Trans.
44(4), 648–656 (2001)
38. Gunsel, S., Korcek, S., Smeeth, M., Spikes, H.: The elastohydrodynamic friction and film forming properties of lubricant base
oils. Tribol. Trans. 42(3), 559–569 (1999)
39. Bridgman, P.: Viscosities to 30,000 Kg/Cm. Proc. Am. Acad.
Arts Sci. 77(4), 117–128 (1949)
40. A. S. M. E: Viscosity and Density of Over 40 Lubricating Fluids
of Known Composition at Pressures to 150,000 Psi and Temperatures to 425 F. American Society of Mechanical Engineers,
New York (1953)
41. Kuss, E.: Viskositats-Druckverhalten von flussigen MethylPhenylmethyl- und Cyclohexylmethyl-Siloxeanen. Erdol und
Kohle-Erdgas-Petrochemie vereinigt mit Brennstoff-Chemie
27(8), 416–422 (1974)
42. Winer, W.O.: A Study of the Elastohydrodynamic Lubrication
and High Pressure Rheological Behavior of a Series of Silicone
Fluids. Georgia Institute of Technology, Atlanta (1972)
311
43. Jakobsen, J., Sanborn, D., Winer, W.: Pressure viscosity characteristics of a series of siloxane fluids. ASME Trans. Ser. F J.
Lubr. Technol. 96, 410–417 (1974)
44. Tsubouchi, T., Hata, H.: Study on the fundamental molecular
structures of synthetic traction fluids: part II. Tribol. Int. 28(5),
335–340 (1995)
45. Kyotani, T., Yamaha, T., Tamai, Y., Aoyama, S.: Relation
between shear relaxation and molecular structure of lubricating
oils. Tribol. Trans. 28(3), 374–380 (1985)
46. Kyotani, T., Yoshitake, H., Ito, T., Tamai, Y.: Correlation
between flow properties and traction of lubricating oils. Tribol.
Trans. 29(1), 102–106 (1986)
47. Villegas, J., Olayo, R., Cervantes, J.: Effect of side groups on the
conformation of a series of polysiloxanes in solution. J. Inorg.
Organomet. Polym. 13(4), 205–222 (2003)
48. Huglin, M.B.: Light Scattering from Polymer Solutions. Academic Press, Waltham (1972)
49. Smeeth, M., Spikes, H., Gunsel, S.: Boundary film formation by
viscosity index improvers. Tribol. Trans. 39(3), 726–734 (1996)
50. Guangteng, G., Spikes, H.: Boundary film formation by lubricant
base fluids. Tribol. Trans. 39(2), 448–454 (1996)
51. Liu, Y., Wang, Q., Bair, S., Vergne, P.: A quantitative solution
for the full shear-thinning EHL point contact problem including
traction. Tribol. Lett. 28(2), 171–181 (2007)
52. Van Krevelen, D., Hoftyzer, P.: Newtonian shear viscosity of
polymeric melts. Die Angewandte Makromolekulare Chemie
52(1), 101–109 (1976)
53. Dyson, A., Wilson, A.: Film Thicknesses in Elastohydrodynamic
Lubrication by Silicone Fluids. Prof Eng Publishing, Suffolk
(1965)
54. Bair, S.: A rough shear-thinning correction for EHD film thickness. Tribol. Trans. 47(3), 361–365 (2004)
55. Chapkov, A., Bair, S., Cann, P., Lubrecht, A.: Film thickness in
point contacts under generalized Newtonian EHL conditions:
numerical and experimental analysis. Tribol. Int. 40(10–12),
1474–1478 (2007)
56. Bair, S., Qureshi, F.: The generalized Newtonian fluid model and
elastohydrodynamic film thickness. J. Tribol. 125(1), 70–75
(2003)
57. Bair, S., Qureshi, F.: The high pressure rheology of polymer-oil
solutions. Tribol. Int. 36(8), 637–645 (2003)
58. Kuss, E.: Extreme values of the pressure coefficient of viscosity.
Angew. Chem. Int. Ed. Engl. 4(11), 944–950 (1965)
59. Tamai, Y., Kyotani, T.: Estimation of flow activation volumes of
synthestic ester lubricants. J. Jpn. Petroleum Ind. 25, 281–285
(1982)
60. Spikes, H., Olver, A.: Basics of mixed lubrication. Lubr. Sci.
16(1), 1–28 (2003)
61. Roelands, C., Vlugter, J., Watermann, H.: The viscosity temperature pressure relationship of lubricating oils and its correlation with chemical constitution. ASME J. Basic Eng. 85, 601–606
(1963)
62. Spikes, H.: A thermodynamic approach to viscosity. Tribol.
Trans. 33(1), 140–148 (1990)
63. Aderin, M., Johnston, G., Spikes, H., Caporiccio, G.: The elastohydrodynamic properties of some advanced non hydrocarbonbased lubricants. Lubr. Eng. 48(8), 633–638 (1992)
64. Dawkins, J.V., Hemming, M.: Universal calibration procedures in
gel permeation chromatography. Examination of poly (dimethyl
siloxane) in a theta solvent. Die. Makromol. Chem. 155(1), 75–89
(1972)
123