This work aims to investigate vibration behavior of rotating roller - a fixed segment friction pair lubricated with pure motor oil and motor oil containing liquid crystal (cholesteryl oleate) additive. Experiments were performed under boundary friction conditions. Mechanical vibrations were registered through the processing and analysis of radial vibration data of the segment, obtained for each lubricant composition under constant roller speed. It is established that vibration level of the segment is reduced at the presence of liquid crystal additive. Theoretical investigations of load-carrying properties of individual layered liquid crystal in a lubricating gap of the film lubrication bearing show a strong increase in load as compared with the equivalent viscous lubricant

Arturas Kilikevicius

Vadim Mokšin

Vladas Vekteris

English

Journal of Vibroengineering

 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
502
773. Investigation of dissipative properties of liquid 
crystalline lubricant layer  
  
Vadim Mokšin
1
, Artūras Kilikevičius
2
, Vladas Vekteris
3
 
Vilnius Gediminas Technical University, Department of Machine Engineering, Lithuania  
E-mail: 1vadim@vgtu.lt, 2akilikevicius@gmail.com, 3vekteris@vgtu.lt 
  
(Received 10 September 2011; accepted 14 May 2012) 
 
Abstract. This work aims to investigate vibration behavior of rotating roller – a fixed segment 
friction pair lubricated with pure motor oil and motor oil containing liquid crystal (cholesteryl 
oleate) additive. Experiments were performed under boundary friction conditions. Mechanical 
vibrations were registered through the processing and analysis of radial vibration data of the 
segment, obtained for each lubricant composition under constant roller speed. It is established 
that vibration level of the segment is reduced at the presence of liquid crystal additive. 
Theoretical investigations of load-carrying properties of individual layered liquid crystal in a 
lubricating gap of the film lubrication bearing show a strong increase in load as compared with 
the equivalent viscous lubricant. 
 
Keywords: liquid crystal, motor oil, friction pair, vibration amplitude.  
 
Introduction  
 
Dissipative properties of lubricants are manifested in both shear and bulk cyclic deformation 
of the lubricant layer [1]. Under conditions of variable pressures, temperatures and other 
parameters of state of the lubricant layer there is a rapid redistribution of components of the 
lubricant, formation and rearrangement of molecular associates and complexes with changes in 
their mutual solubility. The associates, micelles, and other electrically charged colloidal particles 
interact with each other and with the surface. This results in changes in the viscosity, electrical 
conductivity and other properties of the lubricating medium. As the end result, the lubricant 
dissipates the mechanical energy transmitted to it, transforming the energy into heat, sound and 
other forms of energy [1]. 
This process results in the damping effect of the lubricant layer [2], which lowers vibration 
level in machinery and vehicles and thereby reduces dynamic forces acting on the mechanisms. 
Furthermore, dissipation is related to viscous resistance forces that influence the load-carrying 
capacity of the lubricating layer. The dissipative properties of a lubricant are also important in 
other aspects. Service life of the lubricant can be extended by improving their dissipative 
properties. Next, dissipative properties influence lubricant capability to reduce the internal 
energy accumulated during periodic deformations; increase of the density of this energy can lead 
to breakdown.  
It is known that liquid crystals have the fluidity characteristics of a liquid and the elasticity 
characteristics of a crystalline solid (in the direction perpendicular to the flow), and have a 
layered structure. Formation of lubricant layers with the mentioned properties on the surfaces of 
contacting bodies would allow providing simultaneously a high durability, high dissipation 
properties and a low friction coefficient of friction pairs. This can be achieved by introducing 
liquid crystals into lubricants, thus realizing the liquid crystal specific “guest-host” effect, i.e. a 
parallel orientation of lubricant and liquid crystal molecules and formation of liquid crystalline 
lubricant layer. 
Antifriction and anti-wear properties of the liquid crystals are well-studied. These properties 
appear using liquid crystals as lubricant and as lubricant additives [3-5]. It should be mentioned 
that the second approach is more promising in terms of economic considerations. It is known 
that liquid crystals additives to the various lubricants can significantly reduce the friction 
coefficient of lubricated friction pairs. In isolated cases, when twisted nematic liquid crystals are 
 
773. INVESTIGATION OF DISSIPATIVE PROPERTIES OF LIQUID CRYSTALLINE LUBRICANT LAYER. 
VADIM MOKŠIN, ARTŪRAS KILIKEVIČIUS, VLADAS VEKTERIS 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
503
used as additives, maximum reduction of the friction coefficient of friction pairs is reached 5 
times [5], wear of friction surfaces decreases 20 times [5] and friction zone temperature – 2 
times [4] in comparison with pure lubricants. It may be expected that liquid crystals also 
increase dissipative properties of lubricants. However, scientific literature provides no 
information about dissipative properties of lubricant with liquid crystals. 
The present work intends to contribute for improving knowledge on the relationship between 
vibration phenomena and lubrication in friction pairs. This is done by studying how liquid 
crystals additives can affect the mechanical vibration of rotating roller – fixed segment friction 
pair lubricated under boundary lubrication conditions. 
 
Mathematical study 
 
To understand the rheological properties of layered (smectic) crystals the model shown in 
Fig. 1 was proposed [6]. According to this model layers of liquid crystals are separated by 
porous walls connected by springs. Newtonian fluid flowing along the layers is not influenced 
by walls, but in direction normal to the wall fluid experiences a resistance from walls. 
Resistance value is proportional to the normal pressure gradient. 
 
 
 
Fig. 1. Model of the smectic liquid crystal: p – pressure, x, y – coordinates, u, v – components of the 
velocity 
 
If x-axis coincides with flow direction and y-axis is normal to the surface of layers of liquid 
crystal (Fig. 1), continuity, momentum and flow equations for the two-dimensional flow of the 
liquid crystal in the film lubrication bearing gap can be expressed as follows [1]: 
 
,0=
∂
∂
+
∂
∂
y
v
x
u
 (1) 
,0
2
2
2
2
=
′∂
′∂
′−







∂
∂
+
∂
∂
+
∂
∂
−
x
w
F
y
u
x
u
x
p
µ  (2) 
,0
2
2
2
2
=′+







∂
∂
+
∂
∂
+
∂
∂
− F
y
v
x
v
y
p
µ  (3) 
,
1
4
4
2
2
x
w
k
y
w
Ev
y
w
v
x
w
uF
′∂
′∂
−
′∂
′∂
=





′−
′∂
′∂
′+
′∂
′∂
′=′
λ
 (4) 
 
 
773. INVESTIGATION OF DISSIPATIVE PROPERTIES OF LIQUID CRYSTALLINE LUBRICANT LAYER. 
VADIM MOKŠIN, ARTŪRAS KILIKEVIČIUS, VLADAS VEKTERIS 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
504
where u and v are x and y components of the velocity of the lubricant, x, y, x’, y’ are coordinates, 
p is the pressure, µ is the viscosity, λ is the permeation coefficient of the layer, w’ is the 
displacement of the lubricant layer, k is coefficient in force dimension [7], E is the modulus of 
elasticity, F’ is the volume force function established according the principle of minimum 
energy. 
These equations can be transformed into non-dimensional form [8]: 
 
* *
* *
0,
u v
x y
∂ ∂
+ =
∂ ∂
 (5) 
* 2 *
* *2
0,
p u
x y
∂ ∂
− + =
∂ ∂
 (6) 
*
*
*
0,
p
F
y
∂
− + =
∂
 (7) 
* * * 2 * 4 *
* * * *
* * * *2 *4
,
w w p w w
F N u v v M K
x y y y x
 ∂ ∂ ∂ ∂ ∂
= + − = = − 
∂ ∂ ∂ ∂ ∂ 
 (8) 
 
where 
( ) 2* * * * * */ ,  / , / , , / , ,ap p HvBx x B y y H u u U v h h H p
UH UBµ
−
= = = = = =  * / ,w w H=  H 
is the thickness of lubricant layer at the entrance of wedge, B is the length of analyzed area of 
lubricant layer, h is the thickness of lubricant layer, M, N and K are parameters characterizing 
specific effects (elastic compression of the layers, flow through the layer and elastic bending of 
the layer) occurring when the liquid crystals are used as lubricant.    
 
2 4
2 5
, , ,
EH H kH
M N K
UB B UBµ µλ µ
= = =  (9) 
*
* *
*
,yy yy
w
p p M
y
σ τ
∂
= − + = − +
∂
 (10) 
 
where σ* is the normal stress, τ* is the shear stress. 
Eqs. (5-7) can be transformed into single-variable equation, which contains single 
independent variable – non-dimensional flow function Ψ [8]: 
 
*
*
*
,u
y
∂Ψ
=
∂
 
*
*
*
.v
x
∂Ψ
= −
∂
 (11) 
2 * 4 *
*2 *4
.N
x y
∂ Ψ ∂ Ψ
=
∂ ∂
 (12) 
 
After designating: 
 
( )
4
* * *
0*
, ,
N
N x y y
x
ξ η= = −  (13) 
 
the flow function can be expressed as follows: 
 
773. INVESTIGATION OF DISSIPATIVE PROPERTIES OF LIQUID CRYSTALLINE LUBRICANT LAYER. 
VADIM MOKŠIN, ARTŪRAS KILIKEVIČIUS, VLADAS VEKTERIS 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
505
( ).* ηξΨ f
N
=  (14) 
 
Function f(η) must satisfy the following requirement [7]: 
 
( ) .0
4
1
=


 ′−+′′′ fff ηη  (15) 
 
Physical quantities expressed in new variables are presented as follows [8]: 
 
( ) ( ) ( )* * * *, , , , 2 .
2
yy
V W
u f v w W V f f W
M N
η ξ
η τ η η
ξ
′
′ ′ ′′= = − = = = − =  (16) 
 
Solutions of the last equations:  
 
,
2
1
2
1
,
2
1
222 










+−=′





−−





−−=
ηη
π
ηηη
erfWerferfW  (17) 
 
where erf is the error function. 
After reduction of Eq. (14) and Eq. (16) to the form of Eq. (7) and further integration with 
respect to the variable η, the pressure can be determined:  
 
( ).
22
1 ** ξ
η
FerfNp +





−=  (18) 
 
It can be obtained from Eq. (6) after its transformation, determining the derivative ξ∂∂ /*p  
and then equating it to zero:  
 
,
22
1*
CerfNp +





−=
η
 (19) 
 
where C is the constant obtained from boundary conditions. 
It is obtained from Eqs. (16) and (17): 
 
.
2
1
2
1*




+−=
η
τ erfNyy  (20) 
 
In accordance with Eq. (10) it is possible to obtain stress value:  
 
.
2
1*
CNyy +−=σ  (21) 
 
In case of conventional viscous fluid: 1* −≈yyσ  [1]. It can be stated that in the case of large 
values of permeation parameter (for example N = 104) there can be a 200-fold difference [8] in 
load-carrying capability of conventional lubricant (oil) layer and liquid crystal layer. 
 
773. INVESTIGATION OF DISSIPATIVE PROPERTIES OF LIQUID CRYSTALLINE LUBRICANT LAYER. 
VADIM MOKŠIN, ARTŪRAS KILIKEVIČIUS, VLADAS VEKTERIS 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
506
Experimental procedure  
 
Despite the unique lubricating [5] and load-carrying properties of individual liquid crystals, 
their use as a lubricant is limited. The main reasons are high cost of liquid crystals and their 
temperature-dependent phase behavior. Therefore use of liquid crystals and oil mixtures are 
more promising approach for practical application of liquid crystals in real tribological systems. 
However dissipative properties of such systems are not studied yet. 
Vibration behavior of friction pair was investigated using a computerized tribometer [9]         
(Fig. 2). Steel friction pair rotating roller – fixed segment (Fig. 2a) was used under the boundary 
lubrication conditions. The segment was vertically loaded and oil bath lubricated. Known values 
of radial load can be applied in the tested friction pair through a lever 4 and a load unit 6 with a 
screw-spring system (not shown in Fig. 2).  
Semi-synthetic mineral motor oil (SAE 10W/30) with and without liquid crystalline additive 
was used to lubricate friction pair. Cholesteryl oleate (oleic acid (unsaturated) cholesteryl ester) 
C45H78O2 which exhibits smectic and twisted nematic phases was used as oil additive. Properties 
of liquid crystal can be described as follows: molecular weight 651.1, melting point 44 – 47 ºC. 
Concentration of liquid crystal in oil was 2 v/v %.   
The mixtures of oil and liquid crystal were prepared as follows: oil and liquid crystal were 
simultaneously heated up to the melting point of the liquid crystal, mixed and cooled down to 
the room temperature.  
Other conditions of the experiment were as follows: rotational speed of the roller – 320 rpm 
(frequency 5.3 Hz), sliding velocity – 0.82 m/s, load force – 1000 N (contact pressure is equal  
to 5 MPa).    
A piezoelectric accelerometer (Brüel & Kjær mod. 4375, 0.1 – 16500 Hz useful range,         
55 kHz resonance frequency) attached to the segment measured radial vibration of the segment. 
Brüel & Kjær LAN-XI Type 3660-D data acquisition hardware was used. The measured signal 
is amplified and filtered with low band pass filter at a 2 Hz cutoff frequency. Measured 
acceleration signal was double integrated using computer. Data analysis was performed with the 
aid of Brüel & Kjær Pulse Reflex software. 
 
 
a) 
 
                                                        b)                                                     c) 
Fig. 2. Scheme of friction pair (a) and top view of a tribometer (b, c): 1 – roller, 2 – segment, 
3 – accelerometer, 4 – load lever, 5 – lubricant bath, 6 – load unit, Nl – load force, Ffr – friction force 
 
773. INVESTIGATION OF DISSIPATIVE PROPERTIES OF LIQUID CRYSTALLINE LUBRICANT LAYER. 
VADIM MOKŠIN, ARTŪRAS KILIKEVIČIUS, VLADAS VEKTERIS 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
507
Results and discussion  
 
Fig. 3 shows vibration amplitudes of the segment as function of test time. Amplitude spectra 
are presented in Fig. 4. Comparison of the results in Fig. 4a with those in Fig. 4 b indicates that 
vibration level is much smaller in low frequency range (less than 5 Hz) when oil with liquid 
crystal additive is used to lubricate friction pair. It was shown in [10] that friction process 
mainly affect vibration of friction pairs in the frequency range (0.25 – 0.75)fb, where fb is 
rotational frequency. Fig. 4 confirms that noticeable differences in vibration, due to change in 
lubricant composition, are related to vibration in the 2 – 4 Hz frequency range. The root mean 
square (RMS) values of vibration amplitude are presented in Fig. 5. It is possible to notice 
appreciable difference in vibration of the segment when motor oil with liquid crystalline additive 
was used to lubricate friction pair. 
 
 
                                          a)                                                                                  b) 
Fig. 3. Segment vibration amplitude as function of test time: a)  friction pair is lubricated with motor oil,       
b) friction pair is lubricated with motor oil containing liquid crystalline additive   
 
 
                                            a)                                                                                   b) 
Fig. 4. Segment vibration amplitude spectra: a) friction pair is lubricated with motor oil, b) friction pair is 
lubricated with motor oil containing liquid crystalline additive   
 
Conclusions  
 
1. In the case of large values of permeation parameter the load-carrying capacity of liquid 
crystal layer can be more than 200-fold larger than in the case of oil. 
 
773. INVESTIGATION OF DISSIPATIVE PROPERTIES OF LIQUID CRYSTALLINE LUBRICANT LAYER. 
VADIM MOKŠIN, ARTŪRAS KILIKEVIČIUS, VLADAS VEKTERIS 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
508
 
Fig. 5. RMS amplitude of the segment as function of lubricant composition 
 
2. Liquid crystalline additive only affects the vibration of friction pair in low frequency range 
of 2 – 4 Hz. 
3. Upon increasing the dissipativity of motor oil by the introduction of 2 v/v % cholesteryl 
oleate additive, the RMS amplitude of segment was reduced from 3.14×10-7 mm to 2.84×10-7 
mm as compared with value obtained using motor oil without liquid crystal additive.    
 
References 
 
[1] Vekteris V. Adaptive Tribological Systems. Vilnius: Technika, 1996. 
[2] Serrato R., Maru M. M., Padovese L. R. Effect of lubricant viscosity grade on mechanical vibration 
of roller bearings. Tribology International, Vol. 40, Issue 8, 2007, p. 1270 – 1275. 
[3] Carrion F.-J., Martinez-Nicolas G., Iglesias P., Sanes J., Bermudez M.-D. Liquid crystals in 
tribology. International Journal of Molecular Sciences, Vol. 10, Issue 9, 2009, p. 4102 – 4115. 
[4] Mokšin V., Vekteris V. Research of tribological properties of mineral motor oil with cholesteryl 
stearate additive. Solid State Phenomena, Vol. 147-149, 2009, p. 552 – 557. 
[5] Kupchinov B. I., Rodnenkov V. G., Yermakov S. F. An Introduction into Tribology of Liquid 
Crystals, Gomel: MPRI NASB, Informtribo, 1993. 
[6] Orsay Group on Liquid Crystals On some flow properties of smectics A. Le Journal de Physique 
Colloques, Vol. 36, No. C1, 1975, p. 305 – 313.    
[7] De Gennes P. G., Prost J. The Physics of the Liquid Crystals. Oxford: Oxford University Press, 
1995. 
[8] Tichy J. A., Rhim Y. A theory for the lubrication of layered liquid crystals. Journal of Tribology, 
Vol. 111, Issue 1, 1989, p. 169 – 174. 
[9] Vekteris V., Mokšin V. Initial investigations of computerized tribometer. Measurements, Vol. 2, 
2000, p. 16 – 19.  
[10] Smirnov V. A. Equipment Vibrodiagnostics Examples. Nizhny Novgorod: Inkotes, 2006. 
 


Investigation of dissipative properties of liquid crystalline lubricant layer

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Investigation of dissipative properties of liquid crystalline lubricant layer

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