# Performance Analysis and Improvement of Flat Torque Converters Using DOE Method

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## Abstract

Automotive torque converters have recently been designed with an increasingly narrower profile for the purpose of achieving a smaller axial size and reducing weight. Design of experiment (DOE) and computational fluid dynamics (CFD) techniques are applied to improve the performance of a flat torque converter. Four torque converters with different flatness ratios (0.204, 0.186, 0.172, and 0.158) are designed and simulated first to investigate the effects of flatness ratio on their overall performance, including efficiency, torque ratio, and impeller torque factor. The simulation results show that the overall performance tends to deteriorate as the flatness ratio decreases. Then a parametric study covering six geometric parameters, namely, inlet and outlet angles of impeller, turbine, and stator is carried out. The results demonstrate that the inlet and outlet angles play an important role in determining the performance characteristics of a torque converter. Furthermore, the relative importance of the six design parameters is investigated using DOE method for each response (stall torque ratio and peak efficiency). The turbine outlet angle is found to exert the greatest influence on both responses. After DOE analysis, an optimized design for the flat torque converter geometry is obtained. Compared to the conventional product, the width of the optimized flat torque converter torus is reduced by about 20% while the values of stall torque ratio and peak efficiency are only decreased by 0.4% and 1.7%, respectively. The proposed new optimization strategy based on DOE method together with desirability function approach can be used for performance enhancement in the design process of flat torque converters.

## Keywords

Torque converter Flatness ratio Computational fluid dynamics (CFD) Parametric study Design of experiment (DOE)## 1 Introduction

Torque converters are an important part of automatic transmissions in automobiles and other vehicles. It provides automatic torque amplification according to the different rotational speed between the input and output speeds without any active control, inherently suppressing engine torque fluctuations. Because it significantly affects the fuel economy, launch feeling and drivability, interests in the development of a high efficiency and performance have been increased recently.

In recent years, with the development of computer technology, computational fluid dynamics (CFD) has been widely used in hydraulic machine design and optimization. Zhao et al. [1] optimized a double-channel pump’s impeller by combined using of CFD, multi-objective genetic algorithm (MOGA) and artificial neural networks (ANN). Li et al. [2] carried out an entropy production analysis to investigate the hump characteristics of a pump turbine based on CFD simulations. Shojaeefard et al. [3], Tan et al. [4] studied effects of some geometric parameters on fluid dynamic characteristics of a centrifugal pump by CFD. Many researchers have also studied the flows in torque converters by using CFD codes employing various methods [5, 6]. Since a number of variables are involved in the design of a torque converter, it is very difficult to achieve an optimal design. In order to improve the converter performance, it is required to obtain detailed understanding and relationship between the governing parameter and its effect on the performance, including efficiency, torque ratio and impeller torque factor. Kubo et al. [7] described the relationship between the design parameters used to define the geometry of an automotive torque converter and the resultant efficiency in relation to the internal flow characteristics. Shin et al. [8, 9] investigated the effect of reactor blade geometry with varying thickness ratios, scroll angles and slot angles on the performance of a torque converter. Song et al. [10] presented an integrated design process TDOS (Torque converter Design Optimization System) including torque converter geometry designer, 3D CFD analysis module, and design optimizer. The system was used to investigate the effect of design parameters on the performance.

Most passenger cars with small and medium size engines have adopted a front-wheel-drive layout in recent years. Torque converters accordingly have been designed with an increasingly narrower profile for the purpose of achieving a smaller axial size and reducing weight. A number of researchers have studied the flat torque converter employing both analytical and experimental methods. Ejiri et al. [11] manufactured and tested four torque converters with different flatness ratios. The experimental results show that the overall performance deteriorates when the flatness ratio is reduced to less than about 0.2. Kim et al. [12] investigated effects of the stator with two different shapes suitable for an axially squashed torus on hydraulic performance variation. Ochi et al. [13], Kietlinski et al. [14], and Usui et al. [15] developed new super-flat torque converters to provide free space for new equipments without much depreciation of efficiency. Abe et al. [16] employed newly developed stator blades to develop the fluid flow channels for a thin type torque converter with a flattening ratio of 50%, while maintaining torque converter performance. Yan et al. [17] proposed a flexible flat torque converter and estimated the influence of the flatness ratio on performance. Liu et al. [18] investigated the internal flow characteristics of the flat torque converter based on elliptical design path. However, there are no reports regarding combination effect of the blade geometry including inlet and outlet angles of impeller, turbine, and stator on the flat torque converter performance characteristics.

DOE method is widely used to find the importance level of the design parameters with respect to the optimization target and obtain the best combination of design variables. Park et al. [19] studied a methane-fueled gas engine generator with addition of hydrogen using DOE method. Hatami et al. [20] applied central composite design based on DOE to obtain an optimal design of the vane geometry for a variable geometry turbine. Taghavifar et al. [21] applied DOE evaluation to introduce the optimum injection strategy-chamber geometry of diesel engine. However, there have been relatively few applications of DOE method to flat torque converters optimization.

In this paper, the main objective is to improve the overall performance of a flat torque converter by using DOE method and CFD calculations. Firstly, performance characteristics of four torque converters with different flatness ratios are investigated. Then, the sensitivity analysis is used to analyze the influence of inlet and outlet angles of impeller, turbine, and stator on the performance of a flat torque converter. Finally, the optimization analysis is performed by using DOE post-processing analysis together with desirability function approach.

## 2 Flat Torque Converter Design

### 2.1 Torus Design

Parameters of torus with different flatness ratios

Parameters | Type 1 | Type 2 | Type 3 | Type 4 |
---|---|---|---|---|

Nominal diameter | 250 | 250 | 250 | 250 |

Width of torus | 51 | 46.40 | 42.95 | 39.53 |

Flatness ratio \(e_{0}\) | 0.204 | 0.186 | 0.172 | 0.158 |

Redefined flatness ratio \(e\) | 1.0 | 0.9 | 0.8 | 0.7 |

### 2.2 Blade Design

Inlet and outlet angles of three elements

Parameters | Impeller | Turbine | Stator |
---|---|---|---|

Inlet angle \(\beta_{1}\) (°) | 131 | 34 | 97.5 |

Outlet angle \(\beta_{2}\) (°) | 50 | 144 | 21 |

## 3 Flat Torque Converter Design

### 3.1 Computational Method

*k*-

*ε*model was also used for the turbulence. Steady state simulations were performed for a range of speed ratios from 0.0 to 0.9 while maintaining an impeller speed of 2000 r/min.

### 3.2 Results and Discussion

## 4 Optimal Design of a Flat Torque Converter

The trend in future automatic-transmission designs is to achieve comparable performance to traditional designs but with reduced mass and in less space. The challenge in torque converter design is to develop a reduced-width torus without sacrificing performance. In this paper, CFD is used to analyze numerous iterations of torque converters to optimize the torus for the allowed space. The type 4 torque converter with flatness ratio 0.158 (\(e = 0.7\)) was chosen as the study object.

### 4.1 Sensitivity Analysis of Inlet and Outlet Angles

Since the blade transmits all of the torque of a torque converter, its design is of utmost importance. In fact, each of the blades would receive working fluid without shock, deflect the flow smoothly throughout the length of blade passage, and discharge the fluid at the optimum angle at all conditions of speed ratio and torque distribution. Unfortunately, it is very difficult to meet optimal requirements. In the present study, a sensitivity analysis was used to investigate the effect of the blade geometric parameters on the torque converter performance characteristics. The main parameters investigated in this paper were inlet and outlet angles of the impeller, turbine, and stator. To improve the design efficiency, a software was developed for generating the blades with various inlet and outlet angles [22]. The blades of type 1 torque converter with inlet and outlet angles shown in Table 2 were chosen as the reference blades in order to compare the performances of the others. Finally, blades of the impeller, turbine, and stator with various inlet and outlet angles (5°, 10°, or 15° below and above the reference value of the parameter) were generated.

Based on the results in Figures 8, 9, 10, it is concluded that the inlet and outlet angles of the impeller, turbine and stator play an important role in determining the performance characteristics of a torque converter including stall torque ratio and peak efficiency. The sensitivity analysis provides useful information of the influence of design parameters individually on the flat torque converter, but not provides information on their combinations effect. Later, a DOE technique would be used to gauge the combination effect of these six dominant parameters.

### 4.2 DOE Method

*L*

_{25}[5

^{6}]) configurations with different combinations were generated for DOE. The original values of the six parameters are listed in Table 2 and the step values were chosen to be 3° for each factor. The final configurations for DOE can be constructed as shown in Table 3.

Configurations and simulation results in DOE

Case number | Factors | Responses | ||||||
---|---|---|---|---|---|---|---|---|

Turbine inlet angle \(\beta_{\text{T1}}\) (°) | Turbine outlet angle \(\beta_{\text{T2}}\) (°) | Impeller inlet angle \(\beta_{\text{I1}}\) (°) | Impeller outlet angle \(\beta_{\text{I2}}\) (°) | Stator inlet angle \(\beta_{\text{S1}}\) (°) | Stator outlet angle \(\beta_{\text{S2}}\) (°) | Stall torque ratio \(Tr_{0}\) | Peak efficiency \(\eta^{*}\) (%) | |

1 | 28 | 138 | 125 | 44 | 91.5 | 15 | 1.7996 | 80.96 |

2 | 28 | 141 | 128 | 47 | 94.5 | 18 | 1.8055 | 81.65 |

3 | 28 | 144 | 131 | 50 | 97.5 | 21 | 1.8359 | 82.98 |

4 | 28 | 147 | 134 | 53 | 100.5 | 24 | 1.8055 | 81.23 |

5 | 28 | 150 | 137 | 56 | 103.5 | 27 | 1.7852 | 80.36 |

6 | 31 | 138 | 128 | 50 | 100.5 | 27 | 1.7621 | 78.34 |

7 | 31 | 141 | 131 | 53 | 103.5 | 15 | 1.7961 | 79.17 |

8 | 31 | 144 | 134 | 56 | 91.5 | 18 | 1.8014 | 80.29 |

9 | 31 | 147 | 137 | 44 | 94.5 | 21 | 1.8147 | 80.37 |

10 | 31 | 150 | 125 | 47 | 97.5 | 24 | 1.8199 | 80.11 |

11 | 34 | 138 | 131 | 56 | 94.5 | 24 | 1.7699 | 77.19 |

12 | 34 | 141 | 134 | 44 | 97.5 | 27 | 1.7996 | 79.82 |

13 | 34 | 144 | 137 | 47 | 100.5 | 15 | 1.8269 | 82.36 |

14 | 34 | 147 | 125 | 50 | 103.5 | 18 | 1.8455 | 82.76 |

15 | 34 | 150 | 128 | 53 | 91.5 | 21 | 1.8347 | 83.21 |

16 | 37 | 138 | 134 | 47 | 103.5 | 21 | 1.7806 | 79.24 |

17 | 37 | 141 | 137 | 50 | 91.5 | 24 | 1.7982 | 81.25 |

18 | 37 | 144 | 125 | 53 | 94.5 | 27 | 1.7717 | 79.53 |

19 | 37 | 147 | 128 | 56 | 97.5 | 15 | 1.8426 | 83.24 |

20 | 37 | 150 | 131 | 44 | 100.5 | 18 | 1.8364 | 81.71 |

21 | 40 | 138 | 137 | 53 | 97.5 | 18 | 1.7998 | 80.21 |

22 | 40 | 141 | 125 | 56 | 100.5 | 21 | 1.7516 | 77.59 |

23 | 40 | 144 | 128 | 44 | 103.5 | 24 | 1.7817 | 79.24 |

24 | 40 | 147 | 131 | 47 | 91.5 | 27 | 1.7995 | 78.47 |

25 | 40 | 150 | 134 | 50 | 94.5 | 15 | 1.8106 | 81.56 |

### 4.3 Numerical Simulation

The 25 cases with different blade dimensions were simulated using the above-mentioned method. Stall torque ratio and peak efficiency were selected as the dynamic characteristic and economic characteristic, respectively, to evaluate the performance characteristics of the flat torque converter. The simulation results are also presented in Table 3. It can be seen that among the cases, numbers 14 and 19 have the two best results of stall torque ratio, and number 19 and 15 have the two best results of peak efficiency. It is clear that the maximum stall torque ratio and the maximum peak efficiency can not be obtained at the same time. So, an optimization study is needed to improve the overall performance of the flat torque converter.

### 4.4 DOE Post-processing and Optimization

Overall DOE analysis data

Indicator | Influence level | Turbine inlet angle \(\beta_{\text{T1}}\) | Turbine outlet angle \(\beta_{\text{T2}}\) | Impeller inlet angle \(\beta_{\text{I1}}\) | Impeller outlet angle \(\beta_{\text{I2}}\) | Stator inlet angle \(\beta_{\text{S1}}\) | Stator outlet angle \(\beta_{\text{S2}}\) |
---|---|---|---|---|---|---|---|

Stall torque ratio \(Tr_{0}\) | | 1.80634 | 1.78240 | 1.79766 | 1.80640 | 1.80668 | 1.81516 |

| 1.79884 | 1.79020 | 1.80532 | 1.80648 | 1.79448 | 1.81772 | |

| 1.81532 | 1.80352 | 1.80756 | 1.81046 | 1.81956 | 1.80350 | |

| 1.80590 | 1.82156 | 1.79954 | 1.80156 | 1.79650 | 1.79504 | |

| 1.78864 | 1.81736 | 1.80496 | 1.79014 | 1.79782 | 1.78362 | |

\({\text{R}}\) | 0.02668 | 0.03916 | 0.00990 | 0.02032 | 0.02508 | 0.03410 | |

\({\text{C}}\) | 17% | 25% | 7% | 13% | 16% | 22% | |

Peak efficiency \(\eta^{*}\) (%) | | 81.436 | 79.188 | 80.190 | 80.420 | 80.836 | 81.458 |

| 79.656 | 79.896 | 81.136 | 80.366 | 80.060 | 81.324 | |

| 81.068 | 80.880 | 79.904 | 81.378 | 81.272 | 80.678 | |

| 80.994 | 81.214 | 80.028 | 80.670 | 80.246 | 79.804 | |

| 79.014 | 81.390 | 80.910 | 79.734 | 80.154 | 79.304 | |

\({\text{R}}\) | 2.022 | 2.202 | 1.232 | 1.644 | 1.212 | 2.154 | |

\({\text{C}}\) | 19% | 21% | 12% | 16% | 12% | 20% |

The range \({\text{R}}\) reflects the influence level of each geometrical parameter on the hydrodynamic characteristics of a torque converter. The contribution value \({\text{C}}\) was defined as the percentage of the \({\text{R}}\) value of a specific factor to the total \({\text{R}}\) values of all the factors. A factor with larger \({\text{R}}\) would have more influence on torque converter performance indicators, and was considered as an important factor during converter design. While factors with small range value \({\text{R}}\) would be considered as less important factors during design procedure. It could be found in Table 4 that, parameters turbine outlet angle \(\beta_{\text{T2}}\) and stator outlet angle \(\beta_{\text{S2}}\) are the two most important factors. To be more precise, the descending sort of range \({\text{R}}\) is \(\beta_{\text{T2}} > \beta_{\text{S2}} > \beta_{\text{T1}} > \beta_{\text{S1}} > \beta_{\text{I2}} > \beta_{\text{I1}}\) for stall torque ratio, and \(\beta_{\text{T2}} > \beta_{\text{S2}} > \beta_{\text{T1}} > \beta_{\text{I2}} > \beta_{\text{I1}} > \beta_{\text{S1}}\) for peak efficiency. Therefore, more focuses are needed on the optimization of turbine outlet angle and stator outlet angle in the design phase, in order to achieve better performance of the flat torque converter. It should be noted that the results may have some difference with the conclusions studied before. This is possible caused by the level selection of design parameters. In the present study, the desirability function was used to carry out the optimization [27]. The optimization results depend on the response weights of stall torque ratio and peak efficiency. In this study, optimization analysis was performed provided that the stall torque ratio and peak efficiency had the same response weight. The results show that case 19, that is, 37° for \(\beta_{\text{T1}}\), 147° for \(\beta_{\text{T2}}\), 128° for \(\beta_{\text{I1}}\), 56° for \(\beta_{\text{I2}}\), 97.5° for \(\beta_{\text{S1}}\), and 15° for \(\beta_{\text{S2}}\), have the best overall performance of the flat torque converter. Compared to the conventional product (\(e = 1.0\)), the flat torque converter with flatness ratio 0.158 (\(e = 0.7\)) is developed that reduce the width of the torus by about 20%. The axial length of the optimal flat torque converter and its weight have been substantially reduced while the values of stall torque ratio and peak efficiency are only decreased by 0.4% and 1.7%, respectively.

## 5 Conclusions

- 1.
DOE method based on CFD technique is applied to obtain an optimized design of a flat torque converter geometry. To this end, 25 cases with different inlet and outlet angles of impeller, turbine, and stator are designed, constructed and simulated. The main advantage of DOE is its ability to consider the combination effect of design parameters on performance, as it is not limited to traditional one-factor-at-a-time approach.

- 2.
The analysis of the DOE array identified the dominant geometrical influences on the performance of the flat torque converter. In general, the turbine outlet angle and stator outlet angle are the two strongest influences on the converter performance characteristics, including stall torque ratio and peak efficiency.

- 3.
Based on the calculation results in DOE, desirability function approach is employed to optimize the flat torque converter geometry. It should be noted that the maximum values of stall torque ratio and peak efficiency can not be obtained at the same time. Finally, the best design configuration is achieved at case 19, that is, 37° for turbine inlet angle, 147° for turbine outlet angle, 128° for impeller inlet angle, 56° for impeller outlet angle, 97.5° for stator inlet angle, and 15° for stator outlet angle. The optimization method first used in performance improvement of flat torque converters can provide fundamental guidelines for designers.

## Notes

### Authors’ Contributions

G-QW and JC were in charge of the whole trial; JC wrote the manuscript; JC and W-JZ assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.

### Authors’ Information

Guang-Qiang Wu, born in 1965, is currently a professor and a PhD candidate supervisor at *School of Automotive Studies, Tongji University, China* and *Institute of Industrial Science, the University of Tokyo, Japan*. He received his PhD degree from *Jilin University, China*, in 1994. His main research interests include advanced design theory and method of the automobile.

Jie Chen, born in 1988, is currently a PhD candidate at *School of Automotive Studies, Tongji University, China*. His main research interests include flow simulation, modification and optimal design theory for the torque converter.

Wen-Jie Zhu, born in 1989, is currently a master candidate at *School of Automotive Studies, Tongji University, China*. His research interests include flow simulation, modification and optimum design theory for the torque converter.

### Competing Interests

The authors declare that they have no competing interests.

### Funding

Supported by National Natural Science Foundation of China (Grant No. 51575393).

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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