INNOVA Research Journal, ISSN 2477-9024  
Enero-Abril, 2019). Vol. 4, No.1 pp. 9-20  
(
DOI: https://doi.org/10.33890/innova.v4.n1.2019.795  
URL: http://revistas.uide.edu.ec/index.php/innova/index  
Correo: innova@uide.edu.ec  
Medición de las vibraciones del motor utilizando mezclas de combustible de  
aceite vegetal reciclado y diesel. Un análisis matemático y computacional  
Measurement of engine vibrations using fuel blends of recycled vegetable oil  
and diesel. A mathematical and computational analysis  
Marcos Gutiérrez  
Tablet School-Escuela de Ciencias y Centro de Investigación Científica, Ecuador  
Autor para correspondencia: marcosgutierrez@tablet-school.com  
Fecha de recepción: 15 de agosto de 2018 - Fecha de aceptación: 01 de diciembre de 2018  
Resumen: Las vibraciones del motor de combustión interna son un indicador de su estabilidad y  
condición mecánica. Las vibraciones del motor que resultan del movimiento alternativo y giratorio de  
sus partes también dependen de la calidad del proceso de combustión y las propiedades del  
combustible. La presente investigación se centra en el efecto de las propiedades y la concentración de  
la mezcla de combustible de diesel y aceite vegetal reciclado en el nivel de vibración del motor debido  
al proceso de combustión. Las vibraciones del motor se recopilaron con los acelerómetros de un  
dispositivo de comunicación móvil, para luego determinar el nivel de vibración resultante del motor y  
su espectro de frecuencia mediante transformadas de Fourier rápidas. En este procedimiento llevado a  
cabo con cada uno de los combustibles probados, las propiedades como el número de cetano y el punto  
de inflamación se encontraron como aquellas que tienen influencia en el nivel de vibración del motor.  
El propósito de la presente investigación es cuantificar el nivel de vibración producido por diferentes  
concentraciones de la mezcla de combustible de diesel y aceite vegetal reciclado, dependiendo de sus  
propiedades y en comparación con el diesel puro. De esto, se concluye que la estabilidad del motor  
con respecto a su nivel de vibración debido al proceso de combustión, puede controlarse de acuerdo  
con las propiedades del combustible.  
Palabras clave: diésel; aceite vegetal reciclado; número de cetano; punto de inflamación; vibraciones  
del motor  
Abstract: Vibrations of the internal combustion engine are an indicator of its stability and mechanical  
condition. The vibrations of the engine resulting from reciprocating and rotating movement of its parts  
also depend on quality of combustion process and properties of the fuel. The present research focuses  
on the effect of the properties and concentration of the fuel blend of diesel and recycled vegetable oil  
on the vibration level of the engine due to the combustion process. The vibrations of the engine were  
collected with accelerometers of a mobile communication device, to then determine the resulting  
vibration level of the engine and its frequency spectrum by means of fast Fourier transforms. In this  
procedure carried out with each of the tested fuels, the properties such as the cetane number and the  
flash point were found as those that have influence on the vibration level of the engine. The purpose  
of the present investigation is to quantify the level of vibration produced by different concentrations of  
the fuel blend of diesel and recycled vegetable oil, depending on their properties and compared to pure  
diesel. From this, it is concluded that the stability of the engine in regard to its level of vibration due  
to the combustion process, can be controlled according to the properties of the fuel.  
Key words: diesel; vegetable recycled oil; cetane number; flash point; engine vibrations  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Introduction  
The study of alternative and ecological fuel blends, mainly aims to reduce the pollutant  
emissions compared with the use of neat diesel. At the same time, for sustainable use of a fuel  
blend as an energy source for internal combustion engines, it must have properties and  
characteristics that keep or improve the engine parameters such as performance, fuel  
consumption, durability and stability. As the quality of the combustion is conditioned by the  
cetane number and flash point of the fuel, the present research focuses on determining of the  
effect of these properties on the engine vibration level.  
The vibrations on the internal combustion engine are the result of unbalanced forces of  
the rotational and reciprocating parts; as well as cyclic variations of pressure inside of the engine  
cylinders, which depend on the rotation velocity, fuel supply and quality of the combustion  
process [1]. There are identified two types of engines vibrations: torsional and longitudinal. The  
torsional vibrations have an effect over the engine crankshaft, because of the pressure fluctuation  
coming from the fuel combustion and engine loads; while the longitudinal ones, have an effect  
over the engine block and mountings, because of the rotary and alternating components [2]. The  
present research considers the effect of the fuel properties and the quality of the combustion on  
the total end engine vibration resulting from the torsional and longitudinal engine vibrations.  
The vibrations are mainly understood as mechanical effects, which can be controlled by  
attenuators [3]; for this reason, another methods and researches are carried out, in order to  
analyze this phenomenon in a more detailed way. One of the investigations in special determined  
that the irregular torque on the engine cylinders are produced by unequal fuel injection in each  
cylinder. The control of the fuel injection improves the exactitude of the delivered fuel quantity,  
allowed to reduce the level of vibration up to 92% [4].  
One of the applied techniques is non-intrusive, which allows measuring of the engine  
vibrations without interrupting functionalities of either process [5]. With this technique, the data  
of the vibrations measurements, can be collected during the combustion process. It allows also  
distinguishing and analyzing of the effects of different fuel types.  
The method to construct the frequencies spectrum and evaluate the vibration level of the  
engine was performed by means of the fast Fourier Transforms (FFT) [6]. This method consists  
of discomposing the resulting signal of the acceleration spectrum in individual components of a  
sinusoidal wave in order to get a frequency spectrum [7]. In this way it is possible to visualize  
the value of the dominant frequencies corresponding to rotation and ignition process of the  
engine. The relationship between the frequencies of these two processes is expressed as a  
function of the engine rotation speed and the number of cylinders [8, 9]. It means that in case of  
a four-cylinder and four-stroke engine the frequency values corresponding to the ignition are  
equal to the double of the rotation frequency of the engine. Any additional excitation source, for  
example the effect of the concentration of the fuel blend, is evidenced with the apparition of  
addition dominant frequencies in the spectrum.  
The studies of engine vibrations with different types and concentrations of biodiesel,  
beside of valuation of engine stability, show also the capacity of a determined type of biodiesel  
to be burned, and its ability to keep or improve the engine performance [6, 10]. Engine  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
measurements, regarding engine performance and vibrations using biodiesel based on animal fat  
[
11], show that with increase of biodiesel in the fuel blend there is an increase in the cylinder  
pressure, with the consequently growing engine vibrations.  
Other investigations testing different concentrations of biodiesel based on recycled  
vegetable palm oil blended with neat diesel, affirm that the engine vibration level decreases when  
the biodiesel concentration is higher in the blend, because of a higher combustion capacity [10].  
While in the investigation, where the fuel blend was preheated [12, 13], the vibrations were  
reduced, because of the solved issues regarding the higher viscosity, improving the performance  
of a process like pumping, atomization or combustion.  
The biodiesel of the present research, based on recycled vegetable palm oil, was obtained  
by means of transesterification with methanol and heterogeneous catalysators like calcium oxide  
(CaO). This kind of catalysators was selected because of their reusability, lower water  
requirement during the process and easier separation of methyl esters from glycerol [14].  
Furthermore, the resulting methyl esters are more volatile compared with the esters resulting  
from the transesterification with ethanol. The choice of ethanol obeys to the fact that the  
methanol is more reactive and economic; however, it is more toxic and comes from non-  
renewable sources, in comparison with ethanol, which comes from starch or sucrose components  
[
15].  
The problems to solve in order to produce and implement alternative ecological fuels are  
not limited to reduce pollutant emissions and fuel consumption; for this reason, in the present  
research, it is considered that the engine stability can be controlled, by managing the fuel  
properties, which influence the combustion quality, such as the cetane number and the flash  
point. A higher cetane number reduces the ignition delay avoiding the combustion in later stages  
and sudden pressure rises; while a lower flash point allows the combustion process at lower  
cylinder pressure and temperature. The goal is to determine the effect of these properties of the  
fuel blend from recycled vegetable palm oil biodiesel for the engine vibration level, compared  
with neat diesel. In this way it is possible to control engine stability with a more ecological fuel.  
Materials and Methods  
Material and Equipment  
Five types of fuels were characterized. The first one consists of neat diesel, and the other  
four consist of a blend with the 5, 10, 15 and 20% concentration of recycled vegetal palm oil  
with 95, 90, 85 and 80% of neat diesel respectively. The oil was processed by means of  
transesterification with calcium oxide, because of more environmentally friendly process [14].  
The blend with diesel was carried out by agitation, without any additional reactive, equipment or  
processes.  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Table 1.Fuel properties.  
Fuel properties  
Diesel  
95% diesel  
with 5%  
recycled  
vegetable  
palm oil  
90% diesel  
with 10%  
recycled  
vegetable  
palm oil  
85% diesel  
with 15%  
recycled  
vegetable  
palm oil  
80% diesel  
with 20%  
recycled  
vegetable  
palm oil  
Density API 60°F  
3
5.3  
34.5  
65.4  
34.5  
67.4  
33.7  
69.5  
33.9  
70.1  
Flash point [°C]  
62.3  
Kinematic viscosity [cSt]  
4.02  
51.8  
4.35  
51.98  
4.55  
51.25  
4.75  
50.37  
5.03  
50.20  
Cetane Number [-]  
Lower heating value [MJ  
4
2.7817  
42.6389  
42.2469  
42.5648  
42.5632  
/
kg]  
Characterization of neat diesel and different concentrations of biodiesel. Source: Authors  
The vibration measurement was performed with neat diesel and with each of the  
characterized fuel blends on an engine equipped with a common rail system. The goal is to find  
the concentration and the properties of the biodiesel, that provides the same or a better engine  
performance and stability, compared with the use of neat diesel.  
Table 2. Engine specification.  
Displacement  
2999 cc  
Fuel injection system  
Fuel type  
Common rail direct injection  
Diesel  
4
Number of cylinders  
Number of valves  
Power  
16  
134 hp @ 3600 rpm  
294 Nm @ 1400-3000 rpm  
Torque  
Specification of the test engine. Note  
The vibrations were registered with accelerometers of a communication mobile device,  
by means of a non-intrusive measurement. The collected data is the result of the individual  
accelerations in each orthogonal axis, X, Y and Z; afterward the resulting acceleration is  
calculated. The data were registered in format *.txt, in order to be exported into a spreadsheet for  
the construction of the frequencies spectrum by fast Fourier transforms (FFT).  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Table 3. Linear accelerometers specification.  
0
.009575196 [m/s2]  
Resolution  
Accuracy  
±1.1%  
Measurement range max.  
Power  
19.61 [m/s2]  
0.13 mW  
Specification of the linear accelerometers of the mobile communication device. Note  
Experimental procedure  
The vibrations measurement was registered over the valves cover on the top of the engine  
see Fig. 1), at different speeds without load, with each of the characterized fuels. As for the  
(
conditions under load, more fuel needs to be burned, and as a consequence the vibration level of  
the engine increases, it is necessary, firstly, to determine the possible level of vibration that can  
be obtained under conditions that are not too severe to engine, avoiding to put it in risk of  
damage. Secondly, it is necessary to guarantee, that the fuel blends of this research will not  
compromise the safety and durability of the engine, by means of corrosion effects and lubricity  
ability of the fuel injection components.  
Figure 1. Measurement process and data processing of the engine vibrations.  
Mathematical formulation  
The registered accelerations in each orthogonal axis X, Y and Z were used to calculate the  
resulting accelerations, in order to analyze and to determine the effect of the properties of each  
fuel type on the vibration level of the engine.  
푅 = √푎 2 + 푎 2 + 푎 2  
(1)  
푥
푦
푧
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
R: Resulting acceleration  
ax, ay, az: Acceleration values in the orthogonal axis  
To calculate the engine vibration level and to represent it as a function of a unique  
amplitude value, the root mean square acceleration was calculated with each calculated resulting  
acceleration.  
ꢀ1  
ꢂꢃꢀ ꢂꢃ⋯ꢃꢀ푛ꢂ  
ꢂ
푅ꢀ푀푆 = ꢁ  
(2)  
ꢄ
ARMS: Root mean square acceleration  
R1, R2, Rn: Resulting accelerations in the selected measured range  
n: Number of data in the selected measurement range  
Finally, the frequency spectrum was calculated by means of fast Fourier transforms on a  
spreadsheet, according to the following mathematical formulation:  
ꢇ
ꢅ
2휋푖( )푘  
ꢄ−ꢅ  
푘ꢈ0  
퐶푗 =  
∑
푣 푒  
푘
푛
(3)  
ꢆꢄ  
Cj: Vector of the FFT function  
k: Additive index from 0 to n-1  
v: Output vector  
i: Imaginary unit  
j: Harmonic number from 0 to n/2  
Measurements and Evaluation  
The performed measurements were carried for about 10 seconds at four different engine  
rotation speeds and with each of the five characterized fuels. From the 20000 registered  
measurement points, the range with the higher stability at the measured regime was selected.  
From this selection, only 256 points were used to calculate the root mean square accelerations;  
while by means of the fast Fourier transforms, the frequency spectrums were obtained. As the  
lowest engine frequency at 1000 rpm is equal to 16.6 Hz, there is no necessity that the frequency  
spectrum has a resolution higher than the 256 selected points.  
The resulting root mean square acceleration and the frequency spectrum with the use of  
the neat diesel in each one of the engine velocities during the test, determines the engine  
condition and becomes the reference point to compare the effect that have the fuel properties on  
the base of recycled vegetable palm oil. Once the frequency spectrum of the engine running with  
neat diesel is obtained and excluding the frequencies and amplitude values from the rotation and  
ignition of the engine, it is considered that every variation with reference to this reference point,  
is an effect of the concentration and properties of the tested fuel blend.  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Results  
The figure 2 shows the development of the engine vibrations at different engine speeds.  
At each engine speed and with each of the fuel types 256 measured points are represented. It is  
observed, that higher peak values take place at 3000 rpm and particularly with the fuel blend of  
2
0% recycled vegetable palm oil and 80% neat diesel.  
Figure 2. Development of the engine vibrations with each fuel type at different engine speeds.  
The resulting vibration level, expressed as a function of the root mean square  
accelerations (see Fig. 3), determine that the engine stability depends on the concentration of  
biodiesel in the blend and on the engine rotation speed; in the present research the higher  
vibration level corresponds to the blend with 20% recycled vegetable palm oil at 3000 rpm.  
However, from the 3000 upwards, with the blend of 5% oil and 95% neat diesel, the engine  
vibration level is lower, even compared with the values corresponding to use of neat diesel. The  
fuel blend that shows a more stable vibration level along the whole engine rotation speed range,  
is the blend of 15% oil and 85% neat diesel.  
Figure 3. Root mean square accelerations at different engine speeds with each characterized fuel type.  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
In each frequency spectrum the frequencies corresponding to the engine rotation and fuel  
ignition are identified. The resulting spectrum when using neat diesel is the reference and any  
additional amplitude in the spectrum, a range equal or higher to the ignition frequency, it is  
considered as the effect of the cetane number and the flash point of the fuel blend. The variations  
of amplitudes in a frequencies range lower than the frequencies of the ignition and rotation speed  
of the engine, must be considered as a mechanical instability.  
Table 4. Engine Frequencies.  
Engine rotation speed [rpm]  
Frequency of rotation [Hz]  
Frequency of ignition [Hz]  
1
2
3
000  
000  
000  
16.6  
33.3  
50  
33.3  
66.6  
100  
4
000  
66.6  
133.3  
Frequencies corresponding to the rotation and ignition of a 4-cylinder and 4-stroke engine.  
Figure 4. Frequency spectrum with each fuel type at 1000 rpm.  
Figure 5. Frequency spectrum with each fuel type at 2000 rpm.  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Figure 6. Frequency spectrum with each fuel type at 3000 rpm.  
Figure 7. Frequency spectrum with each fuel type at 4000 rpm.  
Discussion  
The engine vibrations are the result of the lineal, rotational and reciprocating movement  
of its parts. The main indicator of vibrations at a determined frequency is an amplitude. In the  
vibrational analysis it is analyzed the natural and resonance frequency. The first one is the ability  
of an element to vibrate under the force action; while the second one occurs when an excitation  
source or an additional force influences on the system at a frequency equal to the natural one  
[
16]. In the present research, are identified the frequencies and amplitudes corresponding to the  
engine rotation at fuel ignition, with use of neat diesel as a reference point, in order to analyze  
the effect of the values of the cetane number and flash point in each concentration of the fuel  
blend with recycled vegetable palm oil.  
The changes in the amplitude values, corresponding to the frequency ranges of the  
ignition and subsequent processes, are analyzed separately in order to identify the effect of the  
fuel properties for the engine stability, considering the effects of an earlier ignition or any delay  
in the combustion process in the values that the amplitude can reach. The vibrations are more  
intensive during the ignition than during the combustion process, because the higher vibration  
amplitude is a result of the rapid pressure change inside the cylinder during the ignition [16].  
Based on this information, it can be affirmed that a lower amplitude at the frequency  
corresponding to the fuel ignition, means a gradual, uniform and smoother combustion process,  
without sudden pressure rises in the cylinder.  
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INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Comparing the values of the flash point on the fuel characterization (see Tab. I), it is  
observed that this value increases with increase of the biodiesel concentration in the blend. It  
causes that the combustion process takes place at higher temperatures and pressures, which  
reflects the reached vibration levels (see Fig. 3).  
Within the engine speed range from 3000 to 4000 rpm the fuel blend of 5% biodiesel and  
9
5% neat diesel creates a lower vibration level even compared with neat diesel, which can be  
attributed to the higher cetane value for this type of the fuel blend. It reduces the ignition delay  
producing a more efficient combustion at higher engine rotation speeds.  
A regular and uniform frequencies spectrum along the frequencies spectrum, demonstrate  
that there is a better energy conversion from the fuel into torque to the engine [6]. In the obtained  
results, it is observed at 4000 rpm with the blend consisting of 90% neat diesel and 10% recycled  
vegetable palm oil.  
It was observed as well, that at around 23 Hz there is an amplitude that varies with the  
fuel blend concentration, which effects at 3000 rpm and higher. It is attributed to a mechanical  
effect and engine condition, because the 23 Hz are below the minimum ignition frequency of  
3
3.3 Hz.  
Conclusion  
The engine vibrations are an indicator of mechanical failures, but they are also a factor  
that determines the performance and stability of the engine in function of the fuel properties.  
In the present research, an experimental methodology was shown to evaluate the engine  
vibrations with a non-intrusive procedure, in function of the cetane number and flash point of the  
fuel blend based on recycled vegetable palm oil.  
It is demonstrated that the characteristics that determine the engine stability, are  
associated to the properties of the fuel and engine operation condition.  
The results of the tests with each fuel blends and with neat diesel, demonstrate that the  
vibration level depends on the engine rotation speed and the concentration of biodiesel on the  
fuel blend.  
Bibliography  
Somashekar V., Dr. K. Satish, Jamuna AB., Ranjitha P. "Vibration Signature Analysis of IC  
Engine". International Journal of Innovative Research & Development. December, 2013.  
Vol 2, Issue 13. P.224–238.  
T. Ramachandran, K. P. Padmanaban. "Review of Internal Combustion Engine Vibrations and  
Mountings". International Journal of Engineering Sciences & Emerging Technologies.  
August, 2012. Vol 3, Issue 1. p.63–73.  
Satish V. Dawange, V. L. Kadlag. "A Review Paper on Vibration Analysis of DI Engine".  
Revista de la Universidad Internacional del Ecuador. URL: https://www.uide.edu.ec/  
18  
INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
International Journal of Science and Research. February, 2015. Vol 4, Issue 2. p.759–761.  
F. Östman, H.T. Toivonen. "Model-based torsional vibration control of internal combustion  
engines". IET Control Theory and Applications. June, 2008. Vol 2, No. 11. p.1024-  
1
032.DOI: 10.1049/iet-cta:20070479  
L. Barelli, G. Bidini, C. Buratti, R. Mariani. "Diagnosis of internal combustion engine through  
vibration and acoustic pressure non – intrusive measurements ". Applied Thermal  
Engineering, Elsevier.  
July, 2008. Vol 29, Issues 8-9. p.1707–1713. DOI:  
1
0.1016/j.applthermaleng.2008.07.025  
S. C. V. Ramana Murty Naidu, B. V. Appa Rao, Aditya Kolakoti. "Experimental Investigations on  
Combustion and Vibration Analysis of an Indirect Injection Diesel Engine Fuelled With  
Palm Methyl Ester (PME) and 1, 4-Dioxane as an Additive". International Journal of  
Informative & Futuristic Research. April, 2015. Vol 2, Issue 8.p.2770–2780.  
Camilo José Carrillo González, "Fundamentos del Análisis de Fourier". Departamento de  
Enxeñería Eléctrica. Escola Técnica Superior de Enxeñeiros Industriáis. Universidade de  
Vigo. 2003.  
Ben Ari J., de Botton G., Itzhaki R., et al. "Fault detection in internal combustion engines by the  
vibration analysis method". SAE Technical Paper 1999. DOI: 10.4271/1999-01-1223.  
Sina Abroumand Azar, Arash Hosseinian Ahangarnejad. "Simulating the Diesel Engine Vibration  
with Fuzzy Neural Network". Research Journal of Applied Sciences, Engineering and  
Technology. September, 2014. Vol 8, Issue 9. p.1045-1051.  
B. Heidary, S. R. Hassan-beygi, B. Ghobadian, A. Taghizadeh. "Vibration analysis of a small diesel  
engine using diesel-biodiesel fuel blends". Agric Eng Int: CIGR Journal. September, 2013.  
Vol. 15, No.3. p.117–126.  
K. Srinivasa Rao, Dr. A. Ramakrishna, P V Rao. "Performance Evaluation, Combustion, Emission  
and Vibration Characteristics of DI-CI engine using Chicken Fat Biodiesel". Proceedings  
of National Conference NCIET 2013, Gudlavalleru Engineering College. December, 2013.  
p.176–181.  
Dr. B. V. Appa Rao, Ch. Satyanarayana, P. V. Rao, Dr. S. Chandraparasad, et. al. "Investigations  
of Combustion Performance, Exhaust Emissions and Cylinder Vibration of DI Diesel  
Engine Using Neat Preheated Pongam Methyl Ester" 6th Asia-Pacific Conference on  
Combustion, Nagoya Congress Center, Nagoya, Japan. May, 2007.  
Y. Ashok Kumar Reddy, B. V. Appa Rao. "Combustion and Vibration Analysis of Idi- Diesel  
Engine Fuelled With Neat Preheated Jatropha Methyl Ester". Journal of Engineering  
Research and Applications. March, 2014. Vol 4, Issue 3. p.780–790.  
Sruthi Gopal, Sajitha C.M. "Production of Biodiesel from Vegetable Oil Using CAO Catalyst &  
Revista de la Universidad Internacional del Ecuador. URL: https://www.uide.edu.ec/  
19  
INNOVA Research Journal 2019, Vol 4, No. 1, pp. 9-20  
Analysis of its Performance in Four Stroke Diesel Engine". International Journal of  
Scientific and Research Publications. November, 2013. Vol 3, Issue 11. p.1–6.  
Grey C. Castellar Ortega, Edgardo R. Angulo Mercado, Beatriz M. Cardozo Arrieta.  
"Transesterificación de aceites vegetales empleando catalizadores heterogéneos". Prospect.  
2
014. Vol. 12, No. 2. p.90–104  
Hannu Tienhaara. "Guidelines to engine dynamics and vibration". Wärtsilä Corporation, 2004.  
Revista de la Universidad Internacional del Ecuador. URL: https://www.uide.edu.ec/  
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