# Research on HMCVT Parameter Design Optimization Based on the Service Characteristics of Agricultural Machinery in the Whole Life Cycle

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## Abstract

**:**

## 1. Introduction

## 2. The Transmission Principle and Characteristic Description of HMCVT for Agricultural Tractor

#### 2.1. The Transmission Principle

_{1}~i

_{12}) and 5 wet clutches (C

_{0}, C

_{1}, C

_{2}, C

_{3}and C

_{4}). The HMCVT can realize one purely hydraulic system working stage (H

_{0}) and four hydro-mechanical power dividing working stages (stage HM

_{1}, stage HM

_{2}, stage HM

_{3}and stage HM

_{4}) by means of the operations of different wet clutches. The HMCVT makes the tractor move backward and forward by shifting gear pair i

_{1}and gear pairs i

_{2}and i

_{3}. Because the purely hydraulic system working stage depends on the variable-pump-constant-motor system alone for power output, and the working stage only serves when the tractor starts up, the optimization design research in the paper doesn’t say much about the optimization design process of this stage.

#### 2.2. The Speed Regulation Characteristics of the Total System

_{2}and stage HM

_{4}stages are the output of mechanical and hydraulic power after the confluence of the planetary row with characteristic parameter k

_{1}, and stage HM

_{1}and stage HM

_{3}stages are the output of mechanical and hydraulic power after the confluence of the planetary row with characteristic parameter is k

_{2}. The theoretical calculation models of the HMCVT each working stage transmission ratio are as follows:

_{1}, stage HM

_{2}, stage HM

_{3}and stage HM

_{4}

_{,}respectively, and $\epsilon $ is the displacement ratio (the value ranges from −1 to 1).

#### 2.3. The Efficiency Characteristics of the Hydraulic System

## 3. Establishment of HMCVT Total Efficiency Characteristic Model

#### 3.1. Stage HM_{1} and Stage HM_{3}

_{2}’s gear ring, closed component b is planetary row P

_{2}’s sun gear, and component c is planetary row P

_{2}’s planet carrier. Chain a-I is the transmission chain connecting planetary row P

_{2}’s gear ring and input shaft I, passing through two pairs of gear pairs. Chain b-I is the transmission chain connecting planetary row P

_{2}’s sun gear and input shaft I, passing through three pairs of gear pairs and one variable-pump-constant-motor system.

_{1}and stage HM

_{3}of 5-stage HMCVT when the displacement ratio $\epsilon \ge 0$; ${\eta}_{ig}$ is the gear engaging transmission efficiency between the output end of the planetary gear train and the output end of HMCVT; ${\eta}_{aI}={\eta}_{{i}_{2}}{\eta}_{{i}_{3}}$; ${\eta}_{bI}={\eta}_{P}{\eta}_{M}{\eta}_{{i}_{4}}{\eta}_{{i}_{5}}$; ${\psi}^{x}$ is the loss coefficient of engagement pair. The research in the paper sets the engaging transmission efficiency of a pair of gears to be 0.98.

_{1}and stage HM

_{3}of 5-stage HMCVT when displacement ratio $\epsilon <0$; ${\eta}_{aI}={\eta}_{{i}_{2}}{\eta}_{{i}_{3}}$; ${\eta}_{bI}={\eta}_{P}{\eta}_{M}{\eta}_{{i}_{4}}{\eta}_{{i}_{5}}$.

#### 3.2. Stage HM_{2} and Stage HM_{4}

_{1}’s sun gear, closed component b is planetary row P

_{1}’s planet carrier and component c is planetary row P

_{1}’s gear ring. Chain a-I is the transmission chain connecting planetary row P

_{1}’s sun gear and input shaft I, passing through three pairs of gear pairs and one variable-pump-constant-motor system. Chain b-I is the transmission chain connecting planetary row P

_{1}’s planet carrier and input shaft I, passing through two gear pairs.

_{2}and stage HM

_{4}of 5-stage HMCVT when displacement ratio $\epsilon \ge 0$; ${\eta}_{aI}={\eta}_{P}{\eta}_{M}{\eta}_{{i}_{4}}{\eta}_{{i}_{5}}$; ${\eta}_{bI}={\eta}_{{i}_{2}}{\eta}_{{i}_{3}}$.

_{2}and stage HM

_{4}of 5-stage HMCVT when displacement ratio $\epsilon <0$; ${\eta}_{aI}={\eta}_{P}{\eta}_{M}{\eta}_{{i}_{4}}{\eta}_{{i}_{5}}$; ${\eta}_{bI}={\eta}_{{i}_{2}}{\eta}_{{i}_{3}}$.

## 4. The New HMCVT Optimization Design Method

_{4}). Next, suppose the minimum steady speed in stage HM

_{1}required by a tractor in field operations is 2 km/h (stage H

_{0}, i.e., the hydraulic transmission system, offers the speed for the tractor to start up and the speed less than 2 km/h). Additionally, to meet the tractor’s field driving requirement to large torque, the engine’s working speed is about 1500 r/min. Therefore, we can calculate and obtain that ${i}_{{\mathrm{HM}}_{1}\_\mathrm{max}}$, the maximum transmission ratio of stage HM

_{1}of HMCVT, is 9.09.

^{th}HM stage; ${L}_{k\_1}$ is the proportion of transmission ratio of the k

^{th}HM stage in interval $[{i}_{\_\mathrm{min}1},{i}_{\_\mathrm{max}1}]$; ${L}_{k\_2}$ is the proportion of transmission ratio of the k

^{th}HM stage in interval $[{i}_{\_\mathrm{min}2},{i}_{\_\mathrm{max}2}]$;${L}_{k\_3}$ is the proportion of transmission ratio of the k

^{th}HM stage in other transmission ratio intervals; ${L}_{k\_0}$ is the rest of transmission ratio range of all HM stages in the intervals except $[{i}_{\_\mathrm{min}1},{i}_{\_\mathrm{max}1}]$ and $[{i}_{\_\mathrm{min}2},{i}_{\_\mathrm{max}2}]$.

_{1}, so the optimization design in the paper doesn’t take the parameter into account.); ${a}_{1}$ and ${a}_{2}$ are the weight coefficients of the objective function; ${f}_{1}(X)$ is the objective function realizing the continuity of transmission ratio and the variation range of transmission ratio matching the required vehicle speed of the tractor, as shown in Equation (16); ${f}_{2}(X)$ is the objective function realizing the service efficiency maximization of the tractor in the whole life cycle, as shown in Equation (17).

_{4}set in the optimization design of HMCVT. According to the design requirement, ${i}_{d}$ should take a value of 0.87. However, to ensure that HMCVT’s speed regulating characteristics meet the maximum vehicle speed requirement after optimization design, and also for the expectation of getting a vehicle speed as high as possible, the optimization design stage in the paper takes the value of ${i}_{d}$ less than 0.87.

^{th}HM stage with displacement ratio of $\epsilon $ (Section 2 and Section 3 give the efficiency models of HM stages of the HMCVT); Constant 2 presents the variable length of displacement ratio of each HM stage.

## 5. Results and Discussion

_{1}is 2 km/h). Specifically, the transmission ratio varies from 5.44 to 9.15 (stage HM

_{1}), 2.86 to 5.47 (stage HM

_{2}), 2.83 to 1.68 (stage HM

_{3}), and 1.65 to 0.86 (stage HM

_{4}) for each HMCVT working stage. The transmission ratio of HMCVT presents a nonlinear change characteristic, which corresponds to Equations (1)–(4), and the degree of nonlinearity decreases with the increase of the HM stage.

_{1}and stage HM

_{3}, the mean transmission efficiency is improved by 4.08% to the most and 1.72% on average. For stage HM

_{2}and stage HM

_{4}, the mean transmission efficiency is improved by 1.64% to the most and 0.71% on average. As for the improvement result considering HMCVT service efficiency in the whole life cycle of the tractor (i.e., objective function ${f}_{2}(X)$), the value after optimization is improved by 19.93% compared with the value before optimization.

_{1}and stage HM

_{3}) and Figure 6 (corresponding to stage HM

_{2}and stage HM

_{4}) show the gross transmission efficiencies of the system of HMCVT in different working conditions (for example, in the case that engine speed is 750~2300 r/min, motor output end load is 34.71~138.84 Nm, and the displacement ratio is in −1~1)

_{1}and stage HM

_{3}, the mean transmission efficiency is reduced by 24.30% to the most and 13.05% on average. For stage HM

_{2}and stage HM

_{4}, the mean transmission efficiency is reduced by 5.35% to the most and 2.21% on average. Considering the whole life cycle of the tractor, the design result of HMCVT service efficiency decreases by 20.42%.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Xie, B.; Wu, Z.B.; Mao, E.R. Development and prospect of key technologies on agricultural tractor. Trans. Chin. Soc. Agric. Mach.
**2018**, 49, 1–17. [Google Scholar] - Liu, Z.J.; Zhang, G.Q.; Chu, G.P.; Niu, H.L.; Zhang, Y.Z.; Yang, F.Z. Design matching and dynamic performance test for an HST-based drive system of a hillside crawler tractor. Agriculture
**2021**, 11, 466. [Google Scholar] [CrossRef] - Qian, Y.; Cheng, Z.; Lu, Z.X. Study on stepwise optimization of shift quality of heavy-duty tractor HMCVT based on five factors. J. Nanjing Agric. Univ.
**2020**, 43, 564–573. [Google Scholar] - Fang, S.S.; Lu, Z.X.; Wang, Z.C.; Diao, X.Y.; Lu, Y.; Gong, J.H.; Zhu, C.Y. Design and prototype performance experiments of steering-by-wire hydraulic pressure system of tractor. Trans. Chin. Soc. Agric. Eng.
**2017**, 33, 86–93. [Google Scholar] - Sun, J.B.; Chu, G.P.; Pan, G.T.; Meng, C.; Liu, Z.J.; Yang, F.Z. Design and performance test of remote control omnidirectional leveling hillside crawler tractor. Trans. Chin. Soc. Agric. Mach.
**2021**, 52, 358–369. [Google Scholar] - Liu, M.N.; Zhou, Z.L.; Xu, L.Y.; Zhao, J.H.; Yan, X.H. Multi-objective optimization and design of tractor trailer systems. Trans. Chin. Soc. Agric. Eng.
**2017**, 33, 62–68. [Google Scholar] - Xia, Y.; Sun, D.Y. Characteristic analysis on a new hydro-mechanical continuously variable transmission system. Mech. Mach. Theory
**2018**, 126, 457–467. [Google Scholar] [CrossRef] - Cheng, Z.; Zheng, S.Q.; Qian, Y.; Lu, Z.X.; Zhang, H.J. Based on improved SA and GA a new method for optimizing transmission parameters of automotive HMCVT. J. Mech. Strength
**2020**, 42, 61–66. [Google Scholar] - Rossetti, A.; Macor, A. Multi-objective optimization of hydro-mechanical power split transmissions. Mech. Mach. Theory
**2013**, 62, 112–128. [Google Scholar] [CrossRef] - Zhang, G.Q.; Zhang, H.T.; Ge, Y.Y.; Qiu, W.; Xiao, M.H.; Xu, X.M.; Zhou, M.H. Mechanical efficiency of HMCVT under steady-state conditions. Shock Vib.
**2021**, 2021, 4275922. [Google Scholar] [CrossRef] - Cheng, Z.; Lu, Z.X. System response modeling of HMCVT for tractors and the comparative research on system identification methods. Comput. Electron. Agric.
**2022**, 202, 107386. [Google Scholar] [CrossRef] - Chen, Y.; Qian, Y.; Lu, Z.X.; Zhou, S.; Xiao, M.H.; Bartos, P.; Xiong, Y.P.; Jin, G.H.; Zhang, W. Dynamic characteristic analysis and clutch engagement test of HMCVT in the high-power tractor. Complexity
**2021**, 2021, 8891127. [Google Scholar] [CrossRef] - Yu, J.; Chen, H.; Liu, J.H. Speed ratio follow-up control of HMCVT based on variable universe fuzzy PID. China Mech. Eng.
**2019**, 30, 1226–1232. [Google Scholar] - Zhang, M.Z.; Wang, Q.S.; Bai, D.Y.; Yin, Y.X.; Hao, X.Y. Speed changing law of hydro-mechanical CVT based on maximum efficiency of tractors. Trans. Chin. Soc. Agric. Eng.
**2016**, 32, 74–78. [Google Scholar] - Ince, E.; Guler, M.A. Design and analysis of a novel power-split infinitely variable power transmission system. J. Mech. Des.
**2019**, 141, 054501. [Google Scholar] [CrossRef] - Cheng, Z.; Lu, Z.X. Regression-Based Correction and I-PSO-Based Optimization of HMCVT’s Speed Regulating Characteristics for Agricultural Machinery. Agriculture
**2022**, 12, 580. [Google Scholar] [CrossRef] - Cheng, Z.; Lu, Z.X.; Qian, J. A new non-geometric transmission parameter optimization design method for HMCVT based on improved GA and maximum transmission efficiency. Comput. Electron. Agric.
**2019**, 167, 105034. [Google Scholar] [CrossRef] - Zhu, Z.; Gao, X.; Zhu, Y. Reverse Design of a Hydro-mechanical Continuously Variable Transmission. Mech. Sci. Technol. Aerosp. Eng.
**2016**, 35, 545–550. [Google Scholar] - He, C.K.; Lang, P.F.; Kang, M.; Zhang, H.J. Transmission design and force analysis of HMCVT for high power tractor. J. Mech. Transm.
**2018**, 42, 54–59. [Google Scholar] - Zhang, P.C.; Ni, X.D.; Mei, W.J.; Peng, X.R. Design and characteristic analysis of hydro-mechanical continuous variable transmission of cotton picker. Mach. Des. Manuf.
**2017**, 10, 64–66. [Google Scholar] - Cheng, Z. Research on System Dynamics Analysis and Continuously Variable Speed of Tractor. Ph.D. Thesis, Nanjing Agricultural University, Nanjing, China, 2020. [Google Scholar]
- Li, J.L.; Liu, L.T.; Xiao, M.H.; Wang, T.T.; Wang, X.; Zhang, H.J. Research on dynamic characteristics of hydro-mechanical continuously variable transmission. J. Mech. Strength
**2017**, 39, 14–19. [Google Scholar] - Wang, C. Study of efficiency calculation of planetary gear trains based on meshing power method. Manuf. Technol. Mach. Tool
**2016**, 80–82. [Google Scholar] [CrossRef] - Zhang, M.Z. Control Strategy Development for Multi-Range Hydro-Mechanical Continuously Variable Transmission in Tractors. Ph.D. Thesis, Xi’an University of Technology, Xi’an, China, 2007. [Google Scholar]
- Li, D.X.; Xu, B.; Tian, J.; Ma, Z.S. Energy management strategy for fuel cell and battery hybrid vehicle based on fuzzy logic. Processes
**2020**, 8, 882. [Google Scholar] [CrossRef] - Li, T.H.; Xie, B.; Li, Z.; Li, J.K. Design and optimization of a dual-input coupling powertrain system: A case study for electric tractors. Appl. Sci.
**2020**, 10, 1608. [Google Scholar] [CrossRef] - Li, Y.J.; Ma, Z.S.; Zheng, M.; Li, D.X.; Lu, Z.H.; Xu, B. Performance analysis and optimization of a high-temperature PEMFC vehicle based on particle swarm optimization algorithm. Membranes
**2021**, 11, 691. [Google Scholar] [CrossRef] - Wang, G.M. Study on Characteristics, Control and Fault Diagnosis of Tractor Hydro-Mechanical CVT. Ph.D. Thesis, Nanjing Agricultural University, Nanjing, China, 2014. [Google Scholar]
- Xu, X.M.; Lin, P. Parameter identification of sound absorption model of porous materials based on modified particle swarm optimization algorithm. PLoS ONE
**2021**, 16, e0250950. [Google Scholar] [CrossRef] - Chang, C.C.; Zheng, Y.P.; Yu, Y. Estimation for battery state of charge based on temperature effect and fractional extended kalman filter. Energies
**2020**, 13, 5947. [Google Scholar] [CrossRef] - Wang, H.; Zheng, Y.P.; Yu, Y. Joint estimation of soc of lithium battery based on dual kalman filter. Processes
**2021**, 9, 1412. [Google Scholar] [CrossRef] - Lin, Y.; Xiao, M.H.; Liu, H.J.; Li, Z.L.; Zhou, S.; Xu, X.M.; Wang, D.C. Gear fault diagnosis based on CS-improved variational mode decomposition and probabilistic neural network. Measurement
**2022**, 192, 110913. [Google Scholar] [CrossRef] - Zhang, Y.Q.; Hu, Z.; Zhang, M.; Ba, W.T.; Wang, Y. Emergency Response Resource Allocation in Sparse Network Using Improved Particle Swarm Optimization. Int. J. Environ. Res. Public Health
**2022**, 19, 10295. [Google Scholar] [CrossRef] - Li, Y.J.; Li, D.X.; Ma, Z.S.; Zheng, M.; Lu, Z.H.; Song, H.L.; Guo, X.J.; Shao, W. Performance analysis and optimization of a novel vehicular power system based on HT-PEMFC integrated methanol steam reforming and ORC. Energy
**2022**, 257, 124729. [Google Scholar] [CrossRef]

**Figure 5.**The transmission efficiency of stage HM

_{1}and stage HM

_{3}in the working conditions. (

**a**) displacement ratio is −1; (

**b**) displacement ratio is −0.5; (

**c**) displacement ratio is 0.5; (

**d**) displacement ratio is 1.

**Figure 6.**The transmission efficiency of stage HM

_{2}and stage HM

_{4}in the working conditions. (

**a**) displacement ratio is −1; (

**b**) displacement ratio is −0.5; (

**c**) displacement ratio is 0.5; (

**d**) displacement ratio is 1.

**Figure 7.**The optimization design results from the method from reference [16]. (

**a**) HMCVT transmission parameter optimization iteration evolution curve; (

**b**) HMCVT speed regulating and transmission characteristics after optimization; (

**c**) the transmission efficiency comparison results of each HM stage between two methods (Method 1: proposed in this paper, Method 2: proposed in the reference [16]).

parameters | i_{2} i_{3} | i_{4} | i_{5} | i_{6} | i_{7} |

original value | 1.438 | 0.678 | 1.960 | 0.982 | 3.520 |

optimal value | 1.702 | 1.315 | 1.450 | 0.970 | 3.215 |

i_{8} | i_{9} | i_{11} | i_{12} | k_{1} | k_{2} |

2.767 | 0.794 | 0.823 | 1.093 | 2.560 | 3.560 |

4.012 | 1.242 | 1.057 | 0.777 | 1.848 | 3.510 |

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**MDPI and ACS Style**

Cheng, Z.; Lu, Z.
Research on HMCVT Parameter Design Optimization Based on the Service Characteristics of Agricultural Machinery in the Whole Life Cycle. *Machines* **2023**, *11*, 596.
https://doi.org/10.3390/machines11060596

**AMA Style**

Cheng Z, Lu Z.
Research on HMCVT Parameter Design Optimization Based on the Service Characteristics of Agricultural Machinery in the Whole Life Cycle. *Machines*. 2023; 11(6):596.
https://doi.org/10.3390/machines11060596

**Chicago/Turabian Style**

Cheng, Zhun, and Zhixiong Lu.
2023. "Research on HMCVT Parameter Design Optimization Based on the Service Characteristics of Agricultural Machinery in the Whole Life Cycle" *Machines* 11, no. 6: 596.
https://doi.org/10.3390/machines11060596