# Fuel Consumption Comparison between Hydraulic Mechanical Continuously Variable Transmission and Stepped Automatic Transmission Based on the Economic Control Strategy

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. A Novel 5-Stage HMCVT

#### 2.1. The Working Principle of HMCVT

_{p}input to the variable pump. When HMCVT works, the displacement can be adjusted by controlling the swash plate inclination of the variable pump, and the speed of the fixed motor can be changed to realize stepless speed regulation.

_{1}and P

_{2}. The power output by the hydraulic transmission system is input to the sun gear of P

_{1}and P

_{2}through i

_{m}, and the remaining power output by the engine is input to the planet gear of P

_{1}and the gear ring of P

_{2}through i

_{1}or i

_{R}(the clutch C

_{V}engages in the forward stage, and the clutch CR engages in the backward stage) to achieve convergence. Engage or disengage clutches C

_{1}, C

_{2}, C

_{3}and C

_{4}so that power is output through i

_{3}or i

_{4}, i

_{5}or i

_{6}to form different stages. There are five working stages in the forward stage (named H

_{0}, HM

_{1}, HM

_{2}, HM

_{3}, and HM

_{4}). When the clutch C

_{V}is disengaged and the brake B

_{1}is engaged, the power of the engine is only input into the hydraulic transmission system, which is a pure hydraulic working stage, so that the vehicle can start smoothly. When the clutch C

_{V}is engaged, it is the hydraulic-mechanical coupling working stage. The backward stage has the same five stages as the forward stage.

#### 2.2. Transmission Ratio Variation Characteristics of HMCVT

_{1}and k

_{2}are the transmission characteristic constants of planetary gears P

_{1}and P

_{2}.

_{2}engages, the power is output from the planet gear of the planetary gear P

_{2}, and the transmission ratio decreases. When the ε changes from +1 to −1, the clutch C

_{1}engages and the power is output from the ring of planetary gear P

_{1}, but the transmission ratio still decreases. The transmission ratio range of adjacent stages overlaps, so that the overall transmission ratio can change continuously.

#### 2.3. HMCVT Efficiency Characteristics

_{cvt}is the efficiency characteristic model of HMCVT, x

_{1}is the influencing factor, a

_{1}, a

_{2}, b

_{1}, b

_{2}are all coefficients (see Table 2).

## 3. Formulation of Transmission Ratio Control Strategy

#### 3.1. Engine Model

_{e}is the brake-specific fuel consumption of the engine, α is the throttle opening, T is the engine torque, and n is the engine speed.

#### 3.2. Transmission System Model

_{gk}represents the transmission ratio of gear k, and q is the common ratio.

_{amax}as 120 km/h and wheel radius r

_{d}as 0.34 m. According to the minimum transmission ratio of the transmission in the paper, 0.72, the transmission ratio of the final drive can be calculated by the equation (Reference for the calculation formula of the physical quantity related to the vehicle when the vehicle is running [35]):

_{min}is the minimum transmission ratio of the transmission, n

_{max}is the maximum engine speed, and 0.377 is used for unit conversion.

_{0}is 3.264.

#### 3.3. Economical Optimal Transmission Ratio Control Strategy of SAT

_{ek}is the equation of the brake-specific fuel consumption in k gear and the speed obtained is the shifting speed with the lowest brake-specific fuel consumption under the throttle opening.

#### 3.4. Economic Optimal Transmission Ratio Control Strategy of HMCVT

_{P}of the pickup truck is calculated as follows:

_{T}is the total transmission efficiency of the transmission system except the HMCVT, and η

_{cvt}is the transmission efficiency of the five-stage HMCVT studied in this paper (see Section 2.3).

## 4. Establishment of a Simulation Test Platform

#### 4.1. Transmission Ratio Control Model of SAT

#### 4.2. Transmission Ratio Control Model of HMCVT

_{0}. According to Equation (1), theoretically the transmission ratio in the stage of H

_{0}can reach infinity. In this model, the range of H

_{0}is 7.55–20. If the vehicle speed is lower than the minimum speed, the vehicle is judged to be in the starting stage, and the transmission ratio is controlled according to the map of the H

_{0}stage. If the speed is greater than the minimum speed, the map of the HM

_{1}- HM

_{4}stage is used to control the transmission ratio (see Figure 6). The transmission efficiency corresponding to the transmission ratio is shown in Section 2.

#### 4.3. Vehicle Parameters

#### 4.4. United Simulation Test

_{S}is used as an economic evaluation index, and its expression is as follows:

#### 4.5. Setting of Driving Cycle

## 5. Results and Discussion of Fuel Consumption Comparison

_{S}between SAT and HMCVT from the 50th second after the test started.

_{S}of HMCVT is lower than that of SAT. Combined with the data in Figure 11, in the EPA cycle, the speed was lower than 80 km/h before the 327th second, and the Q

_{S}of HMCVT was significantly lower. However, as the speed increased to more than 80 km/h, the Q

_{S}gap between the two transmissions was narrow. The Q

_{S}gap of NEDC is larger and more stable. In the six-mode cycle, HMCVT gradually showed advantages in the acceleration process before the 75th second.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Transmission ratio control strategy model of SAT. Transmission ratio control strategy model of SAT. Transmission ratio control strategy subsystems refer to Figure 7.

**Figure 11.**Simulation results of EPA suburban cycle for pickup. (

**a**) EPA cycle; (

**b**) NEDC; (

**c**) 6-mode cycle.

**Figure 12.**Simulation test results comparison of fuel consumption between HMCVT and 8-speed SAT. (

**a**) EPA cycle; (

**b**) 6-mode cycle; (

**c**) NEDC.

**Table 1.**Design values of transmission system parameters [32].

Parameter | i_{p}i_{m} | i_{1} | i_{R} | i_{3} | i_{4} | i_{5} | i_{6} | k_{1} | k_{2} |
---|---|---|---|---|---|---|---|---|---|

Value | 1.18 | 1.27 | 1.27 | 1.16 | 1.22 | 2.76 | 1.00 | 2.00 | 3.79 |

a_{1} | a_{2} | b_{1} | b_{2} | |
---|---|---|---|---|

HM_{1} | 0.9236 | 0.05808 | 0.9215 | −0.04164 |

HM_{2} | 0.9211 | 0.04814 | 0.9264 | −0.08895 |

HM_{3} | 0.9238 | 0.05846 | 0.9217 | −0.04208 |

HM_{4} | 0.9215 | 0.04862 | 0.9267 | −0.08928 |

SAT | i_{g}_{1} | i_{g}_{2} | i_{g}_{3} | i_{g}_{4} | i_{g}_{5} | i_{g}_{6} | i_{g}_{7} | i_{g}_{8} |
---|---|---|---|---|---|---|---|---|

8-speed | 7.55 | 5.40 | 3.86 | 2.76 | 1.97 | 1.41 | 1.01 | 0.72 |

Parameter or Indicator | Value |
---|---|

Sprung Mass/kg | 1306 |

Frontal Area/m^{2} | 3 |

Wheel Base/m | 2.78 |

Final Drive Ratio | 3.264 |

Total Driveline Efficiency excluding Transmission | 0.9 |

Wheel Radius/m | 0.34 |

Maximum Speed/(km/h) | 120 |

Averages of Fuel Consumption per Unit Journey of a Pickup Truck | |||
---|---|---|---|

EPA | NEDC | 6-Mode | |

HMCVT (g/km) | 46.29 | 170.52 | 80.17 |

8-Speed SAT (g/km) | 48.48 | 183.38 | 84.25 |

Averages of Fuel Saving | 4.52% | 7.01% | 4.84% |

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**MDPI and ACS Style**

Chen, Y.; Cheng, Z.; Qian, Y.
Fuel Consumption Comparison between Hydraulic Mechanical Continuously Variable Transmission and Stepped Automatic Transmission Based on the Economic Control Strategy. *Machines* **2022**, *10*, 699.
https://doi.org/10.3390/machines10080699

**AMA Style**

Chen Y, Cheng Z, Qian Y.
Fuel Consumption Comparison between Hydraulic Mechanical Continuously Variable Transmission and Stepped Automatic Transmission Based on the Economic Control Strategy. *Machines*. 2022; 10(8):699.
https://doi.org/10.3390/machines10080699

**Chicago/Turabian Style**

Chen, Yuting, Zhun Cheng, and Yu Qian.
2022. "Fuel Consumption Comparison between Hydraulic Mechanical Continuously Variable Transmission and Stepped Automatic Transmission Based on the Economic Control Strategy" *Machines* 10, no. 8: 699.
https://doi.org/10.3390/machines10080699