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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 . Introduction 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 R eff Ceff 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 r 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]. tg 0.04 0.03 0.02 1 2 3 4 0.01 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. Cp 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 RA 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. R Rad C 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 AT Basic algorithm spectral Im procedure analysis Quality q Classification 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 [2]: 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 appropriate. 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 interval 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 (3.5) for x x i , x i 1 Among the parameters that define the spline Sx 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 ' ' (3.6) ' 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]. y artificial X1 points Xm 0 x Figure.8. Artificially created points on the splines Conclusions 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. References 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, http://www.patentstorm.us/ 6. Cubic Spline Interpolation, http://www.physics.utah.edu/~detar/phys6720/handouts/cubic_spline/cubic_spline/node1.html Address 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- mail: dpeev@uni-ruse.bg. 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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