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

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.

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

To have an obvious study on estimating fuel consumption it is needed to test every vehicle based on an international standard. These tests have the standard in every country. The protocol is named driving cycle. Driving cycle is a series of data, which shows the speed of vehicle versus time. They are different all over the world. Some of them such as European models are smooth. In Fig. 1, European driving cycles are shown.

Fig. 1

European driving cycle (Barlow et al. 2009)

In Fig. 2, FTP75 (federal test procedure), one of the most famous driving cycles is demonstrated. In Table 1, some characteristics for some driving cycles are presented.

Fig. 2

FTP driving cycle (Barlow et al. 2009)

Table 1 Driving cycles’ characteristics (Barlow et al. 2009)

Car specifications

Upon obtaining a gearbox model that relates gear ratio input with capacitance output, we can proceed to optimize the fuel consumption. Fuel consumption in automobile can be defined regarding to a certain driving cycle. Furthermore, to develop a reliable study, two internal combustion engines with 50 and 150 horsepower are assumed respectively (Figs. 3, 4)

Fig. 3

Conventional automobile ((ADVISOR) AVS (2002); Markel et al. 2002)

Fig. 4

Fuel efficiency map ((ADVISOR) AVS (2002)

Other specification for this automobile is listed in Table 2.

Table 2 Car specifications for a conventional automobile ((ADVISOR) AVS (2002)

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.

In the present study, six parameters are used as control factors. All parameters designed to have five levels are presented in Table 3. To use a proper range for each level, a hundred populations of gearboxes are considered.

Table 3 Input factors and their levels used in the experiments

Optimization results based on Taguchi method

Utilizing the Taguchi Method, the 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.

Table 4 Taguchi orthogonal table

Optimization and analysis of experimental results

In Taguchi method, a loss function is used to put the cost of deviation from target into perspective. The loss function is further transformed into a signal-to-noise (S/N) ratio. It provides a measure of the impact of noise factors on performance. The larger the S/N, the more robust the product has against noise. Several S/N ratios depend on the experimental objective. For example one may choose, lower is better (LB), nominal is better (NB) or larger is better (LB). In this paper, the lower fuel consumption is the indication of better performance. Therefore, to obtain optimum performance characteristics, “LB” for the fuel consumption is selected. Using LB, the definition of the loss function (L) for fuel consumption output, Y _i , of n repeated experiments using different levels of noise factors is shown in Eq. 1.

$$L_{\text{LB}}=\frac{1}{n}\sum _{i=1}^n{y}_i^2$$

(1)

The S/N ratio η_ij can be expressed as

$${\mathit{\eta }}_{ij}=-10log(L_{ij})$$

(2)

where i and j indices represent ith performance characteristic and jth experiment, respectively.

The optimal level of the parameters and better performance is indicated by greater values of η. The S/N ratio for each experiment of L₂₅ (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.

Table 5 Signal-to-noise values for fuel consumption for power 50 hp

Table 6 Signal-to-noise values for fuel consumption for power 150 hp

Figures 5 and 6 show the effect of parameters on the fuel consumption for 50 and 150 horsepower engines, respectively. For getting this conclusion, the relative importance of the input parameters with respect to the fuel consumption is going to bet using the analysis of variance (ANOVA). By using this method, the optimum combinations of the input parameters are more accurately determined. It also provides the percent contribution of the input parameters on the sensitivity. The results of ANOVA analysis, at 95 % confidence level, are presented for the fuel consumption in Tables 7 and 8. Data were submitted to analyses of variance using the general linear model. The main effect terms are denoted by the number of gears in table (1st gear, 2nd gear, 3rd gear, 4th gear, 5th gear and differential gear assumes as a covariate). In ANOVA, 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).

Fig. 5

The effect of parameters on fuel consumption in 50 hp engine

Fig. 6

The effect of parameters on fuel consumption in 150 hp engine

Table 7 Analysis of variance for fuel consumption of 50 hp engine

Table 8 Analysis of variance for fuel consumption of 150 hp engine

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.

This pattern has changed for 150 hp engine in three first gear ratios. Table 9 describes the general linear model coefficients for two engines. The ranking of the parameters can be evaluated by their P values in the each row.

Table 9 General linear model coefficients with their P values

Prediction

The last step on the Taguchi experimental design is the optimum prediction. A new experiment is performed using the optimum conditions provided by the earlier Taguchi analysis. The response under these conditions is also predicted. Using the optimal levels of the parameters, the predicted S/N ratio $\widehat{\mathit{\eta }}$ can be defined as the following formula:

$$\widehat{\mathit{\eta }}={\mathit{\eta }}_m+\sum _{i=1}^p\left({\overline{\mathit{\eta }}}_i-{\mathit{\eta }}_m\right)$$

(3)

where ${\overline{\mathit{\eta }}}_{\text{i}}$ is the mean of S/N ratio at the optimum control factor settings; 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.

Table 10 Results of the confirmation experiment for fuel consumption

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.