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Article

The Effects of Adding TiO2 and CuO Nanoparticles to Fuel on Engine and Hand–Arm Driver Vibrations

by
Ali Adelkhani
1,
Peyman Nooripour
1 and
Ehsan Daneshkhah
2,*
1
Department of Mechanical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah 67189-97551, Iran
2
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
*
Author to whom correspondence should be addressed.
Machines 2024, 12(10), 724; https://doi.org/10.3390/machines12100724
Submission received: 28 August 2024 / Revised: 28 September 2024 / Accepted: 8 October 2024 / Published: 13 October 2024
(This article belongs to the Special Issue Vibration-Based Machines Wear Monitoring and Prediction)
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Review Reports Versions Notes

Abstract

:
Occupant comfort is a key consideration in automobile dynamics, with vibrations potentially causing long-term physical discomfort, especially for drivers. This study investigates the impact of adding TiO2 and CuO nanoparticles to fuel on engine-induced vibrations. Experiments were conducted at various nanoparticle concentrations (0, 50, 100, and 150 ppm) and engine speeds (1000, 2000, and 3000 rpm). Key performance metrics, including kinematic viscosity, density, heating value, thermal conductivity, and brake power (BP), were analyzed. The results indicated that increasing nanoparticle concentration led to a rise in BP. The highest reduction in root mean square (RMS) vibration accelerations occurred at 3000 rpm and 150 ppm, with vibration reductions of 30.33% for CuO and 28.61% for TiO2. Additionally, 8–10% of engine vibrations were transmitted to the steering wheel. The use of 150 ppm CuO nanoparticles resulted in reduced vibration transmission to the steering wheel at all tested speeds. These findings suggest that nanoparticle-enhanced fuels can significantly reduce engine vibrations, potentially improving driver comfort and reducing wear on vehicle components.

1. Introduction

Occupant comfort is a significant focus in modern automobile dynamics. Vibrations and vehicle dynamics are prominent topics in the automotive industry [1], and numerous studies have investigated the causes of engine vibrations and methods to reduce them. However, many areas of vibration modeling and isolation remain unexplored [2,3]. Combustion dynamics, influenced by fuel type and combustion chamber design, play a crucial role in generating vibrations. Reducing engine vibrations, particularly in internal combustion engines, has been a long-standing research focus [4]. Nanotechnology, with its ability to enhance surface-to-volume ratios and promote intermolecular interactions, offers a promising avenue for modifying material properties [5,6]. Silver nanoparticles, for example, have seen widespread use due to their unique physical and chemical properties across various industries, including medicine, agriculture, packaging, cosmetics, and the military [7].
Several studies have explored the incorporation of nanoparticles into fuels to enhance their quality. Research by Ganesh et al. [8] and Ghanbari et al. [9] examined the impact of ceramic oxide nanoparticles on biodegradable fuels and the effects of adding silver nanoparticles and carbon nanotubes to biodiesel on diesel engine performance and emissions, respectively. Additionally, Fangsuwannarak et al. [10] focused on the effects of adding TiO2 nanoparticles to palm oil biomass. Recent studies, such as those by Sarma et al. [11] and Kurre et al. [12], investigated the impact of TiO2 nanoparticles on biodiesel derived from mahua oil and diesel engine performance, respectively. Kalaimurugan et al. [13] and Elkelawy et al. [14] also examined the effects of copper oxide (CuO) nanoparticles on diesel and biodiesel fuels, aiming to enhance engine performance and reduce emissions.
Beyond performance, several studies have investigated how increasing engine speed affects vibrations transmitted to the driver’s hands. Notable contributions in this field include work by Ochiai and Nakano [15], Yildirim et al. [16], TaghiZadeh et al. [17], Ali et al. [18], and Aziz et al. [19]. Studies by Yaşar et al. [20] demonstrated the effectiveness of CuO nanoparticles in enhancing diesel engine performance. This was supported by Lenin et al. [21], who focused on improving diesel engine efficiency. Bhagwat et al. [22] and Solero [23] explored the effects of graphene and aluminum oxide nanoparticles, respectively, on engine vibrations and combustion dynamics.
Research consistently shows that the incorporation of nanoparticles into internal combustion engines improves performance while reducing vibrations. Notable studies by Yaşar et al. [20] examined the effects of adding TiO2, CuO, and CeO2 nanoparticles on diesel engine vibrations. Ağbulut et al. [24] investigated the addition of TiO2 and Al2O3 nanoparticles to biodiesel and their impact on engine performance and vibration levels. Similarly, Khan et al. [25] explored the effects of cerium oxide nanoparticles on biodiesel engines, focusing on vibration and emission indices. Collectively, these studies demonstrate that various metal oxide nanoparticles can enhance engine performance while reducing vibration levels.
Advances in materials science have shown that nanoscale particles possess superior physical–thermal properties compared to their micron-sized counterparts. These properties include greater stability, larger contact surfaces for faster oxidation, a higher heat of ignition, lower melting points, and higher rates of heat and mass transfer [26]. In the context of engines, the addition of hydrogen to natural gas increases combustion rates, enhances thermal and combustion efficiency, and reduces emissions while improving fuel economy [27].
Nanoparticles play a crucial role in increasing combustion stability and diesel engine performance by improving thermophysical properties. Metallic and non-metallic nanoparticles increase surface area, improve heat and mass transfer, and enhance ignition points in diesel and biodiesel fuels [28]. These nanoparticles can reduce engine vibrations by improving combustion uniformity and heat transfer. Due to their large surface areas, nanoparticles accelerate chemical reactions between fuel and air, leading to more complete combustion and reducing vibrations caused by incomplete or inconsistent combustion. Nanoparticles with suitable thermal properties also enhance heat transfer within the combustion chamber, promoting a more uniform temperature distribution and reducing local hot spots, which contribute to overall engine optimization [29,30].
Most studies have focused on the impact of adding nanoparticles to fuel on engine performance and emissions [31,32,33,34,35,36,37]. However, this study takes a different approach by investigating the effects of adding nanoparticles on engine vibrations. Based on the authors’ knowledge and the existing literature, no previous research has specifically explored the influence of adding TiO2 and CuO nanoparticles on the vibrations of the M11 engine.

2. Materials and Methods

2.1. The Test Engine

In this study, the effects of adding nanoparticles to the fuel on the vibrations and performance parameters of a Pride engine (KIA engine) were investigated. This vehicle is equipped with a 4-cylinder, 8-valve engine that can produce up to 63 horsepower at 5200 rpm, with a fuel consumption of seven liters per 100 km. Figure 1 displays the engine and the measurement systems used to evaluate performance parameters and vibrations.
An eddy current dynamometer was employed to measure the engine’s torque and output power. The dynamometer (model WE400, manufactured by Pars Andish Engineering Co., Tehran, Iran) measures torque by applying a magnetic field.

2.2. Nanoparticles

In this study, TiO2 nanoparticles in the anatase form (Sigma), known for having properties such as UV absorption, a high refractive index, photochemical activity, a relatively low synthesis cost, and compatibility in organic environments for photocatalysis, were used. Additionally, CuO nanoparticles, characterized as p-type semiconductor materials that are insoluble in water but soluble in alcohol or ammonia, were also utilized as fuel additives. This study investigated the effects of these two nanoparticles on engine vibrations. Three different concentrations were used for each type: 50, 100, and 150 ppm. To create a nano-fuel with a concentration of 50 ppm, 50 mg of nanoparticles was added to one liter of fuel.

2.3. Preparation of Nano-Fuel and Its Stabilization

Once the appropriate proportions of fuel and nanoparticles were prepared, they were mixed using an ultrasonic mixer to stabilize the solution and prevent nanoparticle deposition. Figure 2 illustrates the steps for nano-fuel production. Due to the strong Van der Waals forces between nanoparticles, they tend to agglomerate, necessitating stabilization. Instability in nano-fuels can result in clumps of nanoparticles, leading to variations in physical and chemical properties, making it difficult to generalize the findings [37].
Instability in the fuel can cause the nanoparticles to agglomerate and deposit, potentially resulting in clogs and blockages in fuel ducts and injectors. Therefore, stabilization is essential. Ultrasonic cleaning is one of the most commonly used methods for stabilizing nanoparticle suspensions in a base fluid. In this method, the specimens are placed in special containers and immersed in a German-made six-liter ultrasonic bath (S60H model) manufactured by Elma Corporation for one day to achieve complete stabilization. This method is particularly effective for low-viscosity and high-volume nanofluids.
The instruments used for fuel analysis were as follows: Tanaka AKV-202 Auto Kinematic Viscosity tester (Tanaka Scientific Limited, Tokyo, Japan) for determining viscosity, Kyoto Electronics DA-130 (Kyoto Electronics Manufacturing Co., Ltd., Kyoto, Japan) for density measurement, IKA Werke C 2000 b. (Artisan Technology Group, Champaign, IL, USA) calorimeter with an accuracy of 0.001 K for heating value determination, and KD2 Pro thermal properties analyzer (Wafer Sensor, Inc., Montreal, QC, Canada) for measuring thermal conductivity. Table 1 presents the fuel properties for the different gasoline blends.
Brake power (BP), the power available at the engine crankshaft for useful work, is influenced by torque and angular speed. BP is measured using a dynamometer and a crank angle sensor (B.P = 2πNT/60). An AC dynamometer was used for loading in this experimental setup. The detailed experimental setup is shown in the schematic diagram in Figure 3.

2.4. Different Engine RPMs

Since engine vibrations are influenced by engine speed, this study investigated the effects of adding nanoparticles to fuel at 1000, 2000, and 3000 rpm. To maintain a constant engine speed during the experiment, a weight was placed on the gas pedal.

2.5. Data Acquisition System

In this study, data collection was done offline. A database was established using Spectropro4 Software and transferred to the data acquisition system, serving as an interface between the computer and data collection. Vibration data were recorded using a VMI-102 piezoelectric accelerometer sensor (sensitivity: 100 mv/g, frequency response: +/−3 db, 0.7–15,000 Hz), which was part of the data acquisition system. The data collection device, Easy Viber, was manufactured by the Swedish company VMI.

2.6. Data Gathering

Two types of nanoparticles, TiO2 and CuO, were tested at three concentrations (50, 100, and 150 ppm) and three engine speeds (1000, 2000, and 3000 rpm). Each test was repeated five times.

2.7. Data Analysis

The outputs from the sensor array consist of raw signals that require processing. The relevant attributes must be extracted from these signals for further analysis. These features are essential for creating patterns that allow for differentiation between various types of vibration intensities using a detection system [38]. The root mean square (RMS) of the values in independent domains is calculated as follows:
R M S = 1 T ∫ 0 T s ( t ) 2 d t
In this study, the root mean square (RMS) of vibration acceleration was compared across different nanoparticle concentrations. After analyzing the effects of these concentrations on the reduction in engine-produced vibrations, the optimal nanoparticle concentration was identified and reported.

2.8. Checking the Vibrations Transferred to the Steering Wheel

Mechanical vibrations can cause the driver’s muscles and tendons to vibrate, potentially interfering with their ability to work. The primary transmission of vibration energy occurs in the upper and lower limbs, which is why the local effects of vibration are referred to as hand–arm syndrome [39]. One area where the hands and arms are particularly exposed to vibration is the steering wheel. Since the hands remain in constant contact with the steering wheel, especially over long distances, this can lead to early fatigue and harm to the driver’s body. Reducing vehicle vibrations not only improves the driver’s health but also minimizes potential damage to the vehicle. The transfer capability is calculated using Equation 2. The term ‘transfer’ refers to the portion of vibration generated by the machine that is transmitted to the vehicle’s operator [40].
T r = Z o u t Z i n
where Tr is the transmittance, Zout represents the output vibration rate (m/s2), and Zin corresponds to the input vibration rate (m/s2). In this study, Zout is the vibration value recorded at the steering wheel, while Zin represents the vibration rate recorded in the engine. This section examines how the reduction in engine-produced vibrations, achieved through the addition of nanoparticles, affects the vibrations experienced at the steering wheel.

3. Results and Discussion

3.1. Fuel Properties

The density, viscosity, heating value, and thermal conductivity of the test fuels were measured. No significant changes in properties were observed with the addition of nanoparticles to gasoline. However, there was a slight increase in all of the properties, and the effect of CuO nanoparticles on property enhancement was more pronounced than that of TiO2 nanoparticles. This difference can be attributed to the higher density and thermal conductivity of copper oxide nanoparticles compared to titanium oxide nanoparticles, which have a greater impact on the density and thermal conductivity of the fuel mixture.

3.2. Brake Power

As shown in Figure 4, the brake power increases with the addition of different nanoparticles to the fuel. It can be seen that an increase in the concentration of TiO2 and CuO nanoparticles results in a higher power output. The maximum growth rates of 11.71% and 10.59% were achieved for blends containing 150 ppm CuO and 150 ppm TiO2 fuels at 2000 rpm, respectively. The presence of metal particles in the combustion chamber improves the mixing of fuel and air. Additionally, due to the catalytic properties of Cu and Ti, a higher rate of energy release is observed. This generates more energy in the cylinder and enhances the heat transfer coefficient when nanoparticles are introduced into the fuel.
The addition of TiO2 and CuO nanoparticles significantly affects the combustion process and engine performance from a thermodynamic perspective. By improving fuel–air mixing and increasing the contact surface area in the combustion chamber, the nanoparticles accelerate chemical reactions and improve combustion. These improvements lead to an increase in the energy released during each combustion cycle. From a thermodynamic viewpoint, these enhancements improve the efficiency of the combustion cycle and reduce thermal energy loss. By improving the heat transfer coefficient, the nanoparticles facilitate a more effective transfer of thermal energy to the cylinder walls, which in turn increases the efficiency of converting chemical energy into mechanical energy. This improvement directly leads to an increase in engine brake power and overall output power.

3.3. Vibration Signals

The comparison of vibration signals showed that adding CuO and TiO2 nanoparticles to gasoline at different engine speeds resulted in a slight reduction in the range of engine vibrations. However, it is difficult to draw definitive conclusions regarding the optimal concentrations based solely on visual signal analysis.
In all of the fuel combinations, an increase in engine speed corresponded to a rise in vibration levels. This suggests that as the engine speed increases, the piston’s power output per unit of time also increases, leading to greater vibrations within the engine. This finding aligns with previous studies by Ochiai and Nakano [15], Yildirim et al. [16], and TaghiZadeh et al. [17].
The root mean square (RMS) of engine vibration acceleration for 0 ppm nanoparticles was measured as 0.63, 0.16, and 0.23 m/s2 at 1000, 2000, and 3000 rpm, respectively. The RMS increased proportionally to the engine speed. However, the addition of CuO and TiO2 nanoparticles resulted in a reduction in the RMS. As the engine speed increased, the effects of the nanoparticles on reducing engine vibrations became more pronounced.

3.4. RMS Analysis

Table 2 reports the results of the variance analysis on the impact of adding CuO and TiO2 nanoparticles to gasoline on the RMS of engine vibration acceleration. The results indicate that the effects of different concentrations of CuO and TiO2 nanoparticles in gasoline on the RMS were statistically significant at a 1% probability level.
The findings show that across all test conditions, increasing the concentration of nanoparticles led to a reduction in the RMS of engine vibration acceleration. As illustrated in Figure 5, the comparison of the average RMS of engine vibration acceleration indicates that adding CuO and TiO2 nanoparticles reduced engine vibrations.

3.5. Reducing the RMS of Engine Vibration Acceleration

Figure 6 illustrates the impact of adding copper and titanium nanoparticles to the fuel on the RMS rate of engine vibration acceleration. The smallest percentage reduction in engine vibration was observed at a concentration of 50 ppm and an engine speed of 1000 rpm for both types of nanoparticles. At this lower engine speed and nanoparticle concentration, the impact on improving gasoline combustion during the combustion process was minimal. As a result, no significant reduction in vibrations was observed at lower speeds and concentrations.
However, the results show that as the engine speed increased from 1000 rpm to 2000 and 3000 rpm, the time required for complete fuel combustion inside the cylinder decreased. Consequently, the presence of 50 ppm of nanoparticles became more effective at higher speeds, improving the combustion process and reducing engine vibrations.
Additionally, this study demonstrated that at all three nanoparticle concentrations in gasoline at 1000 rpm, the effects on reducing the RMS of engine vibration acceleration were less pronounced compared to higher engine speeds. The most significant reduction in the RMS of engine vibration acceleration was observed at 3000 rpm with a concentration of 150 ppm, resulting in reductions of 30.33% for CuO and 28.16% for TiO2.
The reduction in engine vibration levels can be attributed to the improved combustion characteristics of nanoparticles, mainly due to their higher surface area-to-volume ratio, which enhances fuel–air mixing in the combustion chamber. This improvement is a result of enhanced atomization and the rapid evaporation of the nanoparticles, leading to more efficient fuel–air mixing, allowing a larger fuel surface area to react with oxygen molecules, and facilitating a more complete combustion process.
The results in this section demonstrate that the addition of nanoparticles to the fuel significantly improves combustion quality and reduces engine vibrations, particularly at higher speeds. A study by Yaşar et al. [20] indicated that CuO nanoparticles were the most effective metal nanoparticles for enhancing diesel engine performance. Similarly, Lenin et al. [21] examined the effects of adding magnesium oxide and CuO nanoparticles to fuel, finding that CuO nanoparticles were more efficient and provided better performance, aligning with the results of this study.
It can be concluded that compared to TiO2 nanoparticles, CuO nanoparticles in the combustion chamber reduce ignition delay by increasing heat transfer to the fuel and accelerating the combustion process. Additionally, they facilitate greater fuel infiltration into the compressed air flow, leading to a more complete combustion process and reduced vibration levels.
Overall, the results suggest that due to the unique physical and chemical properties of nanoparticles, their addition can significantly alter the characteristics of liquid fuels. These particles enhance fuel combustion properties by acting as nanocatalysts. Some studies indicate that nanoparticles function as high-energy particles when oxidized in fuel, accelerating the combustion process and ensuring the complete injection of gasoline into the combustion chamber, as documented in numerous studies [41,42,43].

3.6. Vibrations at the Steering Wheel

In the previous section, the optimal type and concentration of nanoparticles were selected to reduce engine vibrations. This section focuses on the effects of vibration reduction on the vehicle’s steering wheel using CuO nanoparticles at a concentration of 150 ppm. Figure 7 displays the RMS rates of vibration acceleration in the engine and steering wheel at different speeds when using pure gasoline. The results show that approximately 8–10% of the engine vibrations were transmitted to the steering wheel, with the transmission rate being higher at 3000 rpm compared to lower speeds.
Figure 8 illustrates the percentage of vibrations transmitted from the engine to the steering wheel in different scenarios when using 0 ppm and 150 ppm of CuO nanoparticles. As depicted in Figure 8, when 0 ppm of CuO nanoparticles was used in the gasoline, the percentage of vibrations transmitted from the engine to the steering wheel increased with speed. The transmission rates were 10%, 11.19%, and 11.24% at 1000, 2000, and 3000 rpm, respectively.
Several researchers, including Ali et al. [18] and Aziz et al. [19], have reported that as engine speed increases, the percentage of vibration transferred to the steering wheel also increases, particularly at lower RPMs, which is consistent with the findings of this study. The results further reveal that when using 150 ppm of CuO nanoparticles, the rate of vibration transmission to the steering wheel was reduced to 9.77%, 8.58%, and 8.36% at 1000, 2000, and 3000 rpm, respectively.
As nanoparticles are introduced into the fuel and the engine speed increases, the percentage of transmitted vibrations decreases. This reduction is attributed to the engine’s smoother operation at higher RPMs. At lower speeds, a minimum level of vibration is always present in the engine. However, at higher speeds, due to the successive piston strokes and increased combustion, vibrations are reduced. The addition of nanoparticles enhances the combustion process, leading to smoother engine operation. Consequently, the effects of vibration reduction become more pronounced at higher speeds in both the engine and the steering wheel.

4. Conclusions

The present study aimed to investigate the effects of adding TiO2 and CuO nanoparticles to fuel on engine-induced vibrations. The following conclusions can be drawn from the research results:
  • The results indicate that the RMS increased with engine speed, but the addition of CuO and TiO2 nanoparticles to the fuel led to a reduction in the RMS. This effect became more noticeable as the engine speed increased.
  • The effects of different concentrations of CuO and TiO2 nanoparticles in gasoline on the RMS of engine vibration acceleration were statistically significant at a 1% probability level.
  • The lowest engine vibration rates were observed with a concentration of 50 ppm at a speed of 1000 rpm for both types of nanoparticles.
  • In general, the highest reduction in the RMS of engine vibration acceleration for both TiO2 and CuO nanoparticles was observed at a speed of 3000 rpm and a concentration of 150 ppm, with reductions of 30.33% for CuO and 28.61% for TiO2.
  • Approximately 8–10% of engine vibrations were transmitted to the steering wheel, with a higher transmission rate at 3000 rpm compared to lower speeds.
  • When using 0 ppm of CuO nanoparticles in gasoline, the percentage of vibrations transmitted to the steering wheel increased with speed, with transmission rates of 10.83%, 11.19%, and 11.24% at 1000, 2000, and 3000 rpm, respectively.
  • The rates of vibrations transmitted to the steering wheel were reduced to 9.77%, 8.58%, and 8.36% at 1000, 2000, and 3000 rpm, respectively, when 150 ppm of CuO nanoparticles were added.
  • The addition of nanoparticles to the fuel, combined with increased engine speed, resulted in reduced vibration transmission to the steering wheel, likely due to the engine’s smoother operation at higher RPMs.
For future research, special attention should be given to the long-term effects of nanoparticles on engine durability and wear. While TiO2 and CuO nanoparticles significantly improve combustion efficiency and brake power, their long-term impact on engine wear and lifespan needs to be investigated. Due to their small size and unique physical properties, nanoparticles may penetrate internal engine surfaces, potentially causing unwanted wear or increased erosion. Future studies should focus on evaluating engine durability when exposed to nanoparticles and investigating their long-term effects on engine component life.

Author Contributions

Conceptualization, A.A.; Data curation, A.A.; Formal analysis, P.N.; Investigation, A.A., P.N. and E.D.; Methodology, A.A., P.N. and E.D.; Supervision, A.A.; Validation, A.A. and P.N.; Visualization, P.N. and E.D.; Writing—original draft, A.A., P.N. and E.D. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

RMSRoot Mean Square
S(t)Time Signal
TrTransmittance
ZinInput vibration rate
ZoutOutput vibration rate

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Figure 1. Overview of test bench setup and associated equipment.
Figure 1. Overview of test bench setup and associated equipment.
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Figure 2. The steps of nano-fuel production.
Figure 2. The steps of nano-fuel production.
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Figure 3. Schematic diagram of experimental setup.
Figure 3. Schematic diagram of experimental setup.
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Figure 4. The effect of adding nanoparticles on engine brake power.
Figure 4. The effect of adding nanoparticles on engine brake power.
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Figure 5. The comparison of the effects of adding CuO and TiO2 nanoparticles to gasoline on the RMS of engine vibration acceleration.
Figure 5. The comparison of the effects of adding CuO and TiO2 nanoparticles to gasoline on the RMS of engine vibration acceleration.
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Figure 6. The reduction in the RMS of engine vibration acceleration compared between using pure fuel and CuO and TiO2.
Figure 6. The reduction in the RMS of engine vibration acceleration compared between using pure fuel and CuO and TiO2.
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Figure 7. The rate of vibrations transmitted from the engine to the steering wheel at different speeds.
Figure 7. The rate of vibrations transmitted from the engine to the steering wheel at different speeds.
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Figure 8. The rate of vibrations transmitted to the steering wheel when using 0 and 150 ppm of CuO nanoparticles.
Figure 8. The rate of vibrations transmitted to the steering wheel when using 0 and 150 ppm of CuO nanoparticles.
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Table 1. Properties of test fuel.
Table 1. Properties of test fuel.
FuelDensity
(kg/m3) at 15 °C		Viscosity
(cSt)
at 40 °C		Heating Value (MJ/kg)Thermal Conductivity
(W/m K)
Gasoline719.80.54345.70.15
G+50ppm TiO2720.10.54545.90.16
G+50ppm CuO720.80.54646.10.19
G+100ppm TiO2720.70.54946.40.18
G+100ppm CuO722.60.55246.60.21
G+150ppm TiO2721.10.55646.70.20
G+150ppm CuO723.90.55546.80.25
Table 2. The analysis of variance of adding CuO and TiO2 nanoparticles to fuel on the RMS of engine vibration acceleration.
Table 2. The analysis of variance of adding CuO and TiO2 nanoparticles to fuel on the RMS of engine vibration acceleration.
S.VDfCuOTiO2
SSMSFP > FSSMSFP > F
1000 rpmNanoparticle concentration30.001990.0006615.280.001990.001990.0006615.285.88−9
Error160.00690.00004 0.00690.00690.00004
Total190.00268 0.002680.00268
2000 rpmNanoparticle concentration30.002870.000964.180.002870.002870.000964.182.3e−2
Error160.003660.00023 0.003660.003660.00023
Total 190.00654 0.006540.00654
3000 rpmNanoparticle concentration30.012940.00431100.250.012940.012940.00431100.25e−10
Error160.000690.00004 0.000690.000690.00004
Total190.01363 0.013630.01363
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Adelkhani, A.; Nooripour, P.; Daneshkhah, E. The Effects of Adding TiO2 and CuO Nanoparticles to Fuel on Engine and Hand–Arm Driver Vibrations. Machines 2024, 12, 724. https://doi.org/10.3390/machines12100724

AMA Style

Adelkhani A, Nooripour P, Daneshkhah E. The Effects of Adding TiO2 and CuO Nanoparticles to Fuel on Engine and Hand–Arm Driver Vibrations. Machines. 2024; 12(10):724. https://doi.org/10.3390/machines12100724

Chicago/Turabian Style

Adelkhani, Ali, Peyman Nooripour, and Ehsan Daneshkhah. 2024. "The Effects of Adding TiO2 and CuO Nanoparticles to Fuel on Engine and Hand–Arm Driver Vibrations" Machines 12, no. 10: 724. https://doi.org/10.3390/machines12100724

APA Style

Adelkhani, A., Nooripour, P., & Daneshkhah, E. (2024). The Effects of Adding TiO2 and CuO Nanoparticles to Fuel on Engine and Hand–Arm Driver Vibrations. Machines, 12(10), 724. https://doi.org/10.3390/machines12100724

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