# More efficiency in fuel consumption using gearbox optimization based on Taguchi method

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## Abstract

Automotive emission is becoming a critical threat to today’s human health. Many researchers are studying engine designs leading to less fuel consumption. Gearbox selection plays a key role in an engine design. In this study, Taguchi quality engineering method is employed, and optimum gear ratios in a five speed gear box is obtained. A table of various gear ratios is suggested by design of experiment techniques. Fuel consumption is calculated through simulating the corresponding combustion dynamics model. Using a 95 % confidence level, optimal parameter combinations are determined using the Taguchi method. The level of importance of the parameters on the fuel efficiency is resolved using the analysis of signal-to-noise ratio as well as analysis of variance.

## Keywords

Fuel consumption Driving cycle Design of experiment optimization Taguchi ANOVA## Introduction

Efficiency of fuel consumption depends on several design factors. To optimize the fuel consumption and minimize the exhaust products, the parameters which can be effective in this matter must be found and discussed. Grugett et al. (1981) worked on the effect of under-inflated tire pressure in fuel consumption. Moreover, they admitted that the decreasing of 5 psi could increase fuel consumption to 3 % for a proper tire. Taguchi et al. (1995) examined the vehicle operating patterns to study fuel consumption behavior. Bradley and Delaval (2013) had shown that tire-rolling resistance as an effective parameter can be influential in fuel consumption. In addition, diagnosis and prediction for fuel consumption is common in the DOE literature. Kilagiz et al. (2005) used fuzzy logic to minimize the emission products. Wu and Liu (2012) presented a model based on artificial network to forecast the fuel consumption in an engine. Due to different motion and road types, there are some standard driving cycles. An example of this case is on study of Ergeneman et al. (1997) when they progressed a driving cycle to predict the emission products. Many scientists have worked on for the megacities to derive a driving cycle generally. Tzeng and Chen (1998) developed a driving cycle for Taipei. Furthermore, Tong et al. (2011) built a driving cycle for Hongkong city. Optimizing the fuel consumption is not straightforward. Common optimization algorithms such as genetic algorithm, pattern search, etc., cannot be efficient because the current engine model is not an absolutely clear mathematics model. It means that it is necessary to use a practical approach for this especial problem. Fuzzy logics, neural networks, artificial neural fuzzy, reinforcement learning and designing of experiments look like new methods to solve this optimization problem. Among these methods, designing of experiments based on Taguchi can be efficient for its minimum solution. This method is so famous in the industry (Taguchi and Yokoyama 1994; Taguchi et al. 1989; Taguchi 1986).

According to fuel consumption minimizing, Win et al. (2005) considered six main parameters in engine with two levels. They investigated the change of parameters using signal-to-noise ratio as a powerful statistical criterion. Although the designing of experiments decrease the number of experiments intensely, all proposed experiments are not possible. That is why a powerful simulator is needed to calculate the fuel consumption. This computer toolbox is able to define a specified vehicle to assess fuel consumption, exhaust products and useful performance characteristics (Wang et al. 2012; (ADVISOR) AVS 2002; Markel et al. 2002; Omidvar et al. 2012).

One of the major factors in Powertrain systems which are able to influence on fuel consumption is the gearbox. In this paper, an investigation on gear ratio effects and optimizing is presented so that a minimizing of fuel consumption can be achieved. The rest of the paper is organized as follows. Driving cycles and proposed car specification, respectively, are discussed in sections “Driving cycles” and “Car specification”. The design of experiments and simulation of each one in ADVISOR is presented in section “Designing experiments based on Taguchi method” and finally, conclusion is shown in section “Conclusion”.

## Driving cycle

Driving cycles’ characteristics (Barlow et al. 2009)

Driving cycle | Average speed (trip) (Km/h) | Average positive acceleration (m/s |
---|---|---|

HWFET (highway fuel economy test) | 77.7 | 0.157 |

FTP-72 (federal test procedure) | 31.6 | 0.429 |

LA92 (California dynamometer driving schedule) | 39.6 | 0.502 |

NYCC (New York city cycle) | 11.5 | 0.466 |

US06 supplemental FTP | 77.9 | 0.541 |

## Car specifications

Car specifications for a conventional automobile ((ADVISOR) AVS (2002)

Parameter | Nominal value |
---|---|

Maximum power: low performance | 50 hp |

Maximum power: high performance | 150 hp |

Mass: low performance | 848 kg |

Mass: high performance | 1,187 kg |

Gearbox | Manual |

Nominal gear ratios | |

Gear 1*Gear_diff | 13.45 |

Gear 2*Gear_diff | 7.57 |

Gear 3*Gear_diff | 5.01 |

Gear 4*Gear_diff | 3.77 |

Gear 5*Gear_diff | 2.83 |

## Designing experiments based on Taguchi method

Taguchi method is a powerful tool characterization, design and performance optimization. The Taguchi experimental design method offers a wide range of its applications, simple concept and the use of the method as well as variation reduction. Additionally, Taguchi method reduces the cost of experiments by reducing the number of necessary experiments. The Taguchi process combines mathematical and statistical techniques that are used in experimental studies. By using this method, optimal conditions with minimum experiments can be determined. The method treats variation as a factor of signal-to-noise (S/N) ratio. Then, experimental conditions having maximum S/N ratio are viewed as optimal conditions. To investigate the effects of parameters on fuel consumption and to identify the performance characteristics under the efficient consumption, Taguchi quality engineering method (TQEM) is used. By using this method, optimal parameters resulting in maximum sensitivity are identified. Taguchi method divides input parameters into two branches: control factors and noise factors. The control factors are used to find the optimal sensitivity in the design process. Noise factors, according to Taguchi method, are those that influence the response of a process, but cannot be economically controlled. The Taguchi method allows inclusion of the noise factors in the experimental array.

This technique has seven steps: determination of function that needs to be optimized, determination of controllable factors and their levels, selection of a suitable orthogonal array, performing the experiments and measuring outputs, calculation of S/N ratio and selecting the parameters corresponding to optimal conditions, analyzing the data and prediction of output in optimum case and the last step which is conducting the confirmation experiment.

Input factors and their levels used in the experiments

Parameter | Symbol | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 |
---|---|---|---|---|---|---|

Gear 1 | A | 3.19 | 3.45 | 3.71 | 3.97 | 4.23 |

Gear 2 | B | 1.83 | 2.00 | 2.17 | 2.34 | 2.52 |

Gear 3 | C | 1.25 | 1.35 | 1.46 | 1.56 | 1.67 |

Gear 4 | D | 0.89 | 0.97 | 1.06 | 1.15 | 1.24 |

Gear 5 | E | 0.69 | 0.76 | 0.84 | 0.92 | 1 |

Gear diff | F | 3.23 | 3.55 | 3.88 | 4.20 | 4.53 |

### Optimization results based on Taguchi method

*L*

_{ 25 }orthogonal arrays table with 25 rows is constructed for the controllable factors (Table 4). Each row corresponds to the number of experiments that needs to be performed. As stated before, the level settings for the input factors are chosen to represent typical fuel consumption.

Taguchi orthogonal table

No. | Parameters | Results | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Gear1 | Gear2 | Gear3 | Gear4 | Gear5 | Gear differential | Power 50 (hp) | Power 150 (hp) | |||

Fuel consumption | SNR | Fuel consumption | SNR | |||||||

1 | 1 | 1 | 1 | 1 | 1 | 1 | 5.7 | −15.1175 | 9.8 | −19.8245 |

2 | 1 | 2 | 2 | 2 | 2 | 2 | 5.7 | −15.1175 | 9.9 | −19.9127 |

3 | 1 | 3 | 3 | 3 | 3 | 3 | 5.9 | −15.417 | 10.5 | −20.4238 |

4 | 1 | 4 | 4 | 4 | 4 | 4 | 6.1 | −15.7066 | 10.8 | −20.6685 |

5 | 1 | 5 | 5 | 5 | 5 | 5 | 6.3 | −15.9868 | 11.2 | −20.9844 |

6 | 2 | 1 | 2 | 3 | 4 | 5 | 6.2 | −15.8478 | 11 | −20.8279 |

7 | 2 | 2 | 3 | 4 | 5 | 1 | 5.9 | −15.417 | 10.4 | −20.3407 |

8 | 2 | 3 | 4 | 5 | 1 | 2 | 5.7 | −15.1175 | 9.9 | −19.9127 |

9 | 2 | 4 | 5 | 1 | 2 | 3 | 5.8 | −15.2686 | 10.1 | −20.0864 |

10 | 2 | 5 | 1 | 2 | 3 | 4 | 6 | −15.563 | 10.7 | −20.5877 |

11 | 3 | 1 | 3 | 5 | 2 | 4 | 5.9 | −15.417 | 10.3 | −20.2567 |

12 | 3 | 2 | 4 | 1 | 3 | 5 | 6.1 | −15.7066 | 10.8 | −20.6685 |

13 | 3 | 3 | 5 | 2 | 4 | 1 | 5.8 | −15.2686 | 10.2 | −20.1720 |

14 | 3 | 4 | 1 | 3 | 5 | 2 | 6 | −15.563 | 10.7 | −20.5877 |

15 | 3 | 5 | 2 | 4 | 1 | 3 | 5.8 | −15.2686 | 9.9 | −19.9127 |

16 | 4 | 1 | 4 | 2 | 5 | 3 | 6.1 | −15.7066 | 10.8 | −20.6685 |

17 | 4 | 2 | 5 | 3 | 1 | 4 | 5.8 | −15.2686 | 10 | −20.0000 |

18 | 4 | 3 | 1 | 4 | 2 | 5 | 6 | −15.563 | 10.5 | −20.4238 |

19 | 4 | 4 | 2 | 5 | 3 | 1 | 5.8 | −15.2686 | 9.9 | −19.9127 |

20 | 4 | 5 | 3 | 1 | 4 | 2 | 5.9 | −15.417 | 10.4 | −20.3407 |

21 | 5 | 1 | 5 | 4 | 3 | 2 | 5.8 | −15.2686 | 10.1 | −20.0864 |

22 | 5 | 2 | 1 | 5 | 4 | 3 | 6 | −15.563 | 10.7 | −20.5877 |

23 | 5 | 3 | 2 | 1 | 5 | 4 | 6.2 | −15.8478 | 11 | −20.8279 |

24 | 5 | 4 | 3 | 2 | 1 | 5 | 5.9 | −15.417 | 10.2 | −20.1720 |

25 | 5 | 5 | 4 | 3 | 2 | 1 | 5.8 | −15.2686 | 9.8 | −19.8245 |

### Optimization and analysis of experimental results

*L*) for fuel consumption output,

*Y*

_{ i }, of

*n*repeated experiments using different levels of noise factors is shown in Eq. 1.

*η*

_{ij}can be expressed as

where *i* and *j* indices represent *i*th performance characteristic and *j*th experiment, respectively.

*η*. The S/N ratio for each experiment of

*L*

_{25}(Table 4) is calculated and shown in Tables 5 and 6 for 50 and 150 hp, respectively. As shown in Table 5, the efficient performance for the fuel consumption is obtained at the third level of gear 1 (4.23), second level of gear 2 (2), the fifth level of gear 3 (1.67) second level of gear 4 (0.97), the first level of gear 5 (0.65) and finally, the first level of differential gear (3.23). This behavior is similar to the engine with 150 hp. But as, Table 6 shows, the first gear is ranked as the fourth effective gear ratio.

Signal-to-noise values for fuel consumption for power 50 hp

Parameters | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Delta | Rank |
---|---|---|---|---|---|---|---|

Gear 1 | −15.47 | −15.44 | −15.44 | −15.44 | −15.47 | 0.03 | 6 |

Gear 2 | −15.47 | −15.41 | −15.44 | −15.44 | −15.50 | 0.09 | 4 |

Gear 3 | −15.47 | −15.47 | −15.42 | −15.50 | −15.41 | 0.09 | 3 |

Gear 4 | −15.47 | −15.41 | −15.47 | −15.44 | −15.47 | 0.06 | 5 |

Gear 5 | −15.24 | −15.33 | −15.44 | −15.56 | −15.70 | 0.47 | 1 |

Gear diff | −15.27 | −15.30 | −15.44 | −15.56 | −15.70 | 0.44 | 2 |

Signal-to-noise values for fuel consumption for power 150 hp

Parameters | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Delta | Rank |
---|---|---|---|---|---|---|---|

Gear 1 | −20.36 | −20.35 | −20.32 | −20.27 | −20.30 | 0.09 | 4 |

Gear 2 | −20.33 | −20.30 | −20.35 | −20.29 | −20.33 | 0.07 | 5 |

Gear 3 | −20.40 | −20.28 | −20.31 | −20.35 | −20.27 | 0.14 | 3 |

Gear 4 | −20.35 | −20.30 | −20.33 | −20.29 | −20.33 | 0.06 | 6 |

Gear 5 | −19.96 | −20.10 | −20.34 | −20.52 | −20.68 | 0.72 | 1 |

Gear diff | −20.01 | −20.17 | −20.34 | −20.47 | −20.62 | 0.6 | 2 |

*F*test, by means of

*F*value, can be used to test if the estimates are significantly different using a desirable confidence level. The degree of significance of the computed

*F*value can be determined by looking up

*F*tables. The greater

*F*value shows that the variation of the parameter has a larger impact on the fuel consumption (Taguchi 1986; Taguchi et al. 1989; Taguchi Gi and Yokoyama 1994).

Analysis of variance for fuel consumption of 50 hp engine

Source | | Sum of square | Mean of square | | |
---|---|---|---|---|---|

1st Gear | 4 | 0.002400 | 0.000600 | 0.18 | 0.932 |

2nd Gear | 4 | 0.010400 | 0.002600 | 0.80 | 0.598 |

3rd Gear | 4 | 0.014400 | 0.003600 | 1.10 | 0.487 |

4th Gear | 4 | 0.006400 | 0.001600 | 0.49 | 0.749 |

5th Gear | 4 | 0.322400 | 0.080600 | 24.73 | 0.012 |

Differential gear | 1 | 0.304624 | 0.304624 | 93.48 | 0.002 |

Error | 3 | 0.009776 | 0.003259 | ||

Total | 24 |

Analysis of variance for fuel consumption of 150 hp engine

Source | | Sum of square | Mean of square | | |
---|---|---|---|---|---|

1st Gear | 4 | 0.04560 | 0.01140 | 24.01 | 0.013 |

2nd Gear | 4 | 0.02160 | 0.00540 | 11.37 | 0.037 |

3rd Gear | 4 | 0.08560 | 0.02140 | 45.07 | 0.005 |

4th Gear | 4 | 0.02160 | 0.00540 | 11.37 | 0.037 |

5th Gear | 4 | 2.47760 | 0.61940 | 1304.48 | 0.000 |

differential gear | 1 | 1.62018 | 1.62018 | 3412.16 | 0.000 |

Error | 3 | 0.00142 | 0.00047 | ||

Total | 24 |

Referring to Tables 7 and 8 for 50 and 150 hp engine, respectively, controllable factors can be ranked as gear 5, gear diff, gear 3, gear 2, gear 4, and gear 1 for 50 hp engine and gear 5, gear diff, gear 3, gear 1, gear 4, and gear 2 for 150 hp engine. The most significant factors affecting the fuel consumption are gear 5, the second ranking factor is differential gear and a third ranking factor is gear 3. According to the *F* value, the remaining factors, gear 1, 2 and 4 are not significant. They are sensitive a little for an engine with a low engine power.

*P*values in the each row.

General linear model coefficients with their *P* values

50 hp engine | 150 hp engine | |||
---|---|---|---|---|

Coefficient value |
| Coefficient value |
| |

Constant | 4.99665 | 0.000 | 8.23610 | 0.000 |

1st Gear coef. | 0.01200 | 0.636 | 0.056000 | 0.008 |

2nd Gear coef. | 0.01200 | 0.636 | 0.016000 | 0.164 |

3rd Gear coef. | 0.01200 | 0.636 | 0.096000 | 0.002 |

4th Gear coef. | 0.01200 | 0.636 | 0.036000 | 0.026 |

5th Gear coef. | −0.14800 | 0.007 | −0.424000 | 0.000 |

Differential gear coef. | 0.24016 | 0.002 | 0.553868 | 0.000 |

### Prediction

*η*

_{ m }is the total mean of S/N ratio, and

*p*represents the number of main parameters that significantly affect the performance. Table 10 shows the predicted value of the fuel consumption and signal-to-noise ratio using the optimal parameters and the experimental values simulated by ADVISOR.

Results of the confirmation experiment for fuel consumption

Level | Engine 50 horsepower | Engine 150 horsepower | ||||
---|---|---|---|---|---|---|

Starting parameters | Optimal parameters | Optimal parameters calculation with ADVISOR | Starting parameters | Optimal parameters | Optimal parameters calculation with ADVISOR | |

Prediction | Prediction | |||||

A1B1C1D1E1F1 | A5B2C2D4E1F1 | A1B1C1D1E1F1 | A4B4C5D4E1F1 | |||

Fuel consumption (L/100 km) | 5.7 | 5.64 | 5.7 | 9.8 | 9.48 | 9.8 |

S/N ratio for fuel consumption (dB) | −15.11 | −15.03 | −19.82 | −19.56 |

## Conclusion

About 100 common automobiles, classes A–E, currently on the road were considered. Ranges of gear ratios for the six gears were determined. For each of the six gears, its ratio range is divided into five levels. Taguchi experimental method is used, and an *L*_{ 25 } orthogonal arrays table is constructed. Combustion dynamics model for each of the combination for the gearbox was simulated using ADVISOR software and FTP driving cycle. Efficient performance for the fuel consumption is obtained for the various levels of each gear ratio. Analysis of variances reveals that the significant factor effecting the fuel consumption is gear 5, followed by the differential gear and gear 3. According to the *F* values, the remaining factors, gear 1, 2 and 4 are not significant. The conclusions drawn during the analysis is validated with confirmation experiment using two different automobiles with power, 50 and 150 hp. Results obtained in this study demonstrate that the Taguchi experimental techniques can effectively predict the optimum gear ratio arrangements and facilitate the engine design process leading to improved fuel consumption.

## References

- (ADVISOR) AVS (2002) National Renewable Energy LaboratoryGoogle Scholar
- Barlow T, Latham S, McCrae I, Boulter P (2009) A reference book of driving cycles for use in the measurement of road vehicle emissions, vol 1. Department for transport cleaner fuels and vehiclesGoogle Scholar
- Bradley CR, Delaval A (2013) On-road fuel consumption testing to determine the sensitivity coefficient relating changes in fuel consumption to changes in tire rolling resistance. Tire Sci Technol 41(1):2–20Google Scholar
- Ergeneman M, Sorusbay C, Goktan A (1997) Development of a driving cycle for the prediction of pollutant emissions and fuel consumption. Int J Veh Des 18(3/4):391–399Google Scholar
- Grugett BC, Reineman ME, Thompson GD (1981) Effects of tire inflation pressure on passenger-car fuel consumption. Paper presented at the Society of Automotive Engineers international engineering congress and exposition, 23 Feb 1981Google Scholar
- Kilagiz Y, Baran A, Yildiz Z, Çetin M (2005) A fuzzy diagnosis and advice system for optimization of emissions and fuel consumption. Expert Syst Appl 28(2):305–311. doi:10.1016/j.eswa.2004.10.016 CrossRefGoogle Scholar
- Markel T, Brooker A, Hendricks T, Johnson V, Kelly K, Kramer B, O’Keefe M, Sprik S, Wipke K (2002) ADVISOR: a systems analysis tool for advanced vehicle modeling. J Power Sources 110(2):255–266CrossRefGoogle Scholar
- Omidvar H, Azari KK, Taheri AM, Saghafi AA (2012) Impact and ballistic behavior optimization of Kevlar-Epoxy composites by Taguchi method. Arab J Sci Eng 38:1–7. doi: 10.1007/s13369-012-0381-4Google Scholar
- Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes. The Organization, TokyoGoogle Scholar
- Taguchi G, Yokoyama Y (1994) Taguchi methods: On-line production, vol 2. American Supplier InstituteGoogle Scholar
- Taguchi G, Elsayed EA, Hsiang TC (1989) Quality engineering in production systems. McGraw-Hill College, New YorkGoogle Scholar
- Taguchi T, Taniguchi M, Yamaguchi T, Koga M, Okamoto S (1995) Analysis of fuel consumption structure based on vehicle operating patterns. JSAE Rev 16(3):310. doi: 10.1016/0389-4304(95)95005-FGoogle Scholar
- Tong HY, Tung HD, Hung WT, Nguyen HV (2011) Development of driving cycles for motorcycles and light-duty vehicles in Vietnam. Atmos Environ 45(29):5191–5199. doi: 10.1016/j.atmosenv.2011.06.023CrossRefGoogle Scholar
- Tzeng G-H, Chen J–J (1998) Developing a Taipei motorcycle driving cycle for emissions and fuel economy. Transp Res Part D Transp Environ 3(1):19–27MathSciNetCrossRefGoogle Scholar
- Wang X, Qin DC, Zhu J (2012) Simulation research on dynamic performance of electric vehicle based on ADVISOR. Adv Mater Res 588:355–358Google Scholar
- Win Z, Gakkhar RP, Jain S, Bhattacharya M (2005) Investigation of diesel engine operating and injection system parameters for low noise, emissions, and fuel consumption using Taguchi methods. Proc Inst Mech Eng D J Automobile Eng 219(10):1237–1251CrossRefGoogle Scholar
- Wu J-D, Liu J-C (2012) A forecasting system for car fuel consumption using a radial basis function neural network. Expert Syst Appl 39(2):1883–1888. doi: 10.1016/j.eswa.2011.07.139CrossRefGoogle Scholar

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