impedance approaches to motor oils

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					                     IMPEDANCE APPROACHES TO MOTOR OILS

                                               Darin Iv. Peev

     Abstract: In this paper are investigated variety of concepts and methods for impedance characterization of
motor oils. Their abilities to estimate the lubricant properties and to detect chemical composition changes are
analyzed. The general impedance methods and complex electrochemical impedance spectroscopy (EIS)
techniques are discussed. A detail survey of Differential Impedance Analysis (DIA) is conducted. The virtues and
the disadvantages of these concepts are listed.

    Key words: Differential Impedance Analysis, Motor Oil, Quality Control .


   One of the important machine maintenance tasks is the determination of the
accurate oil change intervals. Using an oil beyond its effective useful life can lead to
an excessive friction and machine wear. Also the effect of the increased heat and
decreased performance can cause component failure and therefore to high cost losses.
On the other hand too frequent oil changes result to extra expenses, inappropriate
material consumption and eventually to environmental changes.
    Normally the mileage criterion is used to determine the oil change interval. But this
criterion is often hard to formulate objectively because of the various factors such as
work conditions, machine health, outside environment etc. Also the unforeseen
conditions can dramatically reduce the oil life. A fuel dilution, water or coolant
contamination, high temperatures and revolutions would make the oil unusable far
before the mileage criterion is fulfilled.
    One possible solution is the utilization of the known laboratory oil tests. The used
oil samples are examined and the standard characteristics such as total acid/base
number, viscosity and amount of oxidation products indicate the condition of the
lubricant. But these methods normally require at least twenty-four hour time and are
very resource consuming. For this reason the systems for fast oil condition estimation
find a wide application.
   The paper is dedicated to the comparison of the different electrical impedance
methods and particularly to a Differential Impedance Analysis [2] of motor oils.
    Results and Discussion
    1. Capacitive and resistive conductance method
    Usually the electrical characteristics of the oil are extracted measuring the complex
Impedance of an electrochemical cell. Between the two parallel electrodes of the cell is
the lubricant which acts as a dielectric medium. Therefore the impedance typically has
a resistance-capacitive character and generally can be expressed by an equivalent
circuit composed of a parallel combination of capacitance Ceff and resistance Reff
(fig.1). Several versions of the method are based on the relative permittivity. As the
relative dielectric constant of water is around   rwater
                                                               81 and more than decade
                                                  fresh  oil
bigger than the constant of the fresh motor oil  r            4.5, the presence of water
can be easily detected. The ethylene glycol which is widely used as an automotive
antifreeze has   glycol  37 and also strongly affect the relative permittivity of the oil.

                                              R eff


                                   Figure.1.Equivalent circuit

    Some systems use an empirical dependency of dielectric constant from the driving
distance [4]. After certain threshold value is exceeded an alarm for oil change is turned
on. The change of this parameter is not more then 10% at the whole driving range so
the precision is controversial.

                            oil

                                                                 distance, km

            Figure.2. Dependency of the dielectric constant from the driving distance

   The resistive part of the impedance is highly affected by the soot and metal
particles percentage and could partake in the analysis.

   Other method is to measure the quality factor (Q-factor) or loss tangent             tg [1].
                             0.02           1 2 3 4


                                       20   40    60   80 100
                                                 Frequency, kHz

        Figure.3. Loss tangent dependence on the presence of mechanical impurities

    It is found that the loss tangent increases depending on the presence of mechanical
impurities as is shown on the fig 3. The curves 1 to 4 indicate the purification through
a filter with an increasing density [1].
   In this method no frequency dependence is considered and it relies only on four
values – Ceff and Reff of fresh and drain oil.
   2. Applying Electrochemical Impedance Spectrometry (EIS)
    That is the second stage of the oil analysis systems. According to the method one
or more hypothetical equivalent models are determined and after model validation one
of them is chosen. Another way is to build the model knowing some information about
the electrochemical nature of the oil-electrode system. Two possible models are shown
on the figures 4, 5. In the first the R1 and R 2 represent the charge transfer resistance
at the two electrodes, while the      Cd1 and Cd 2 characterize the double layer
capacitance at the electrodes [5]. The R bulk is the bulk layer resistance of the
lubricant. The C p is a physical capacitance of the sensor.


                                C D1                   CD2
                                         R BULK

                                R1                     R2

                               Figure. 4.Equivalent model

    If the frequency range is extended – 1mHz to 10MHz and the measurement is very
precise the second model could be used (fig.5). It was developed by M. Smiechowski
[3] and take into account the relaxations of surfactant micelles in the solution, the
double layer on the electrode, charge transfer, materials adsorbing on the electrode
surface and impedance associated with diffusion. In the quoted study is analyzed the
value of the R BULK depending on the TAN (total acid number) and TBN (total base
number) values of the certain oil. In such a way it could be developed a tabular register
consisted of combinations of values of the equivalent model and the known
exploitation characteristics of the certain oil brand (such as viscosity).

                           CB        C BULK

                                                   CPE A      CPE DL

                           RB        R BULK                    W
                                                                       R CT
                                    BULK          INTERFACE

                           Figure.5.Extended equivalent model

   As the equivalent models have several groups of components each of them could
serve as a recognition element for the oil condition analysis. Because of the frequency
dependence estimation of the system response is considered more promising results
can be expected in this method.
   3. Differential Impedance Analysis
    The DIA analysis as opposed to EIS does not require an initial working hypothesis
and the information about the object is extracted from the experimental data [2]. The
DIA applies the algorithm of the scanning local analysis. The used local estimator,
called Local Operating Model (LOM) is shown on fig.6. The effective time constant
T = RC is also regarded as a LOM’s parameter [2]. The characterization of the oil is
based on the temporal or spectral analysis of the effective time-constant
                   
  lg T  F lg T f , where T f is the period of the stimulus signal.


                                Figure.6. Local operating model

    The method doesn’t rely on any equivalent circuit model or hypothesis about the
oil degradation mechanisms. The mathematical model or algorithm of this technique is
given on the figure.7 It involves the components of complex impedance as a function
of frequency, calculation the effective time-constant, converting the analysis to a
spectral form, extracting the basic parameters of the specter as initial values for the
further analysis (m, s, h values – peaks, coombs etc.), calculating the quality factor of
the used oil toward to a fresh oil, categorize the used oil sample into one of the n-
quality categories. The oil’s quality is estimated in respect to its lubricating ability. As
the main purpose of the oil is to reduce the wear of the friction surfaces the DIA
method estimates the real exploitation characteristics of the oil.

           Re        DIA    T Spectral AT                  Basic
                     algorithm                                    spectral
           Im                    procedure

                                 Quality      q
                                  factor                                     Result
                                                       function      (within n - categories)
                   (m, s, h)    estimation

                               Figure.7. Mathematical model

   The impedance of the LOM can be presented by :

                                     R               RT
       ZLOM  j  R ad                     j                                (3.1)
                                1  T2   2
                                                   1  2 T 2
    The calculation of the effective time-constant for specific frequency is based on
       T  dL eff  dR e                                                (3.2)

      where L eff is the effective inductance, R e - the real part of the impedance

    As the T  can vary within several decades the form   lg T is more
    The conversion the analysis from temporal to spectral representation the scope of
values for  is separated into k-equal intervals   . For the first, second and n-th
interval the  corresponds to the following conditions :

        min  i   min  
        min    i   min  2                                            (3.3)
        min n  1  i   min  n 
   The amplitude for the i-th interval is :

       Ai   const .K i                                                     (3.4)

      where K i is the number of time-constant values which belong to the i-th
   The values A1   , A 2   … , A k   at the Y-axis and the values  i at the X-axis
form a spectral histogram.
   The artificially extension of the experimental points can be achieved through a
cubic splines interpolation [6]. This interpolation is a piecewise continuous curve,
passing through a set of m control points. That makes m-1 intervals between them. The
curve satisfy the table of control points x i , y i  , for the i  1,..., m . There is a separate
cubic polynomial for each interval, each with its own coefficients:

        Si x   a i x  x i 3  bi x  x i 2  ci x  x i   d i
        for x  x i , x i 1 

    Among the parameters that define the spline Sx  are some conditions that depend
on the user’s choice. If the curves are so called “natural” splines then the conditions
are :

        S1' x1   0, S'm 1 x m   0
         '               '
       where x 1 and x m are the two endmost points; S1' and S'm 1 are the

       second derivatives at the first and the last interval

   The artificially created points could be chosen on each spline at regular intervals
between the control points (fig.8).
   The extended number of experimental points improves the density of the histogram
both at the amplitude and the time-constant axis [2].

                                  X1           points

                              0                                            x

                           Figure.8. Artificially created points on the splines

   The capacitive and resistive conductance method has simplicity and the connection
between the condition of the oil and the system output is straightforward. As the oil
covers more mileage the dielectric permittivity increases and this indicates the oil
deterioration. The results are unreliable. The method provides an information only in a
qualitative manner.
    Applying Electrochemical Impedance Spectrometry could lead to more promising
results as it extracts maximum impedance information of the lubricant. The equivalent
models have several groups of components and using additional measurements of
certain exploitation characteristic empirical connections could be found. The result of
the analysis has a quantitative significance.
    The Differential Impedance Analysis has higher information potential, it does not
require an initial working hypothesis and the information about the model’s structure
is extracted from the experimental data. As the method offers structural identification
the more objective results are achievable. It could estimate the oil’s quality directly
from the lubricating characteristic. This ensures the knowledge of the oil’s lubricating
ability which is significant for exploitation.
    1. B. Dikarev, Conduction currents and dielectric properties of engine oils, Seoul, Korea, 1997
    2. D. Vladikova, The technique of the differential impedance analysis, part 1-2, Proceedings of the
International Workshop “Advanced Techniques for Energy Sources Investigation and Testing”, Sofia,
Bulgaria, 2004.

   3. M. Smiechowski, Electrochemical characterization of lubricants for microfabricated sensor
applications, PhD Thesis, Department of Chemical Eng., Case Western Reserve University, 2005.

    4. W. Kim, Development of a coil-typed oil senor system for the automobile engine oil on the
dielectric constant, Chungnam, Korea.

   5. On-line oil condition sensor system for rotating and reciprocating machinery, Patient number:
US 7 043 402 B2,

    6. Cubic Spline Interpolation,

   Master of Communications Darin Ivanov Peev, Department of Electronics, University of
Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria, tel. +359 82 888 246, gsm. +359 886 11 35 34, e-

   The study was supported by contract № BG051PO001-3.3.04/28, "Support for the
Scientific Staff Development in the Field of Engineering Research and Innovation”.
The project is funded with support from the Operational Programme "Human
Resources Development" 2007-2013, financed by the European Social Fund of the
European Union.

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