Investigation on the electro-hydro-mechanical coupling characteristics of the HMCVT transmission system

Authors

Yuan Yao, Hong-Liang Dai

Abstract

To address transmission efficiency and stability issues in hydro-mechanical continuously variable transmissions (HMCVT) arising from the coupling of mechanical, hydraulic, and electrical domains, this study proposes a dynamic modeling and optimization strategy based on the Port-Hamiltonian formalism. A multidomain energy transfer model has been constructed to characterize the nonlinear coupling among the mechanical, hydraulic, and electrical subsystems. Numerical simulations and experimental analyses are conducted to evaluate the system’s dynamic response. The calibrated model further shows that, under the neutral swash-plate condition in the medium-speed range, the achieved peak efficiency reaches 89.52% at 1700 r/min and 853.17 N∙m. This high-efficiency condition is associated with a larger proportion of power being transmitted through the mechanical branch. Across several control strategies, the Port-Hamiltonian (PH) HMCVT model shows adaptability and supports physically interpretable analysis of power flow, efficiency variation, and transient response within the tested bench operating range.

Keywords

efficiency optimization, electro-hydro-mechanical coupling, hmcvt, parameter analysis, parameter identification, port-hamiltonian

Citation

• Journal: Results in Engineering
• Year: 2026
• Volume: 32
• Issue:
• Pages: 112214
• Publisher: Elsevier BV
• DOI: 10.1016/j.rineng.2026.112214

BibTeX

@article{Yao_2026,
  title={{Investigation on the electro-hydro-mechanical coupling characteristics of the HMCVT transmission system}},
  volume={32},
  ISSN={2590-1230},
  DOI={10.1016/j.rineng.2026.112214},
  journal={Results in Engineering},
  publisher={Elsevier BV},
  author={Yao, Yuan and Dai, Hong-Liang},
  year={2026},
  pages={112214}
}

Download the bib file

References

• Yu Q, He X, Chen Y, Jiang Z, Tan Y, Liu L, Xie B, Wen C (2025) Multi-objective optimization for energy-efficient management of electric Tractors via hybrid energy storage systems and scenario recognition. Applied Energy 391:125898. https://doi.org/10.1016/j.apenergy.2025.125898 – 10.1016/j.apenergy.2025.125898
• Zhang J, Hou J, Liu M, Xu L, Wu Y (2026) Energy-Efficient path tracking control for autonomous tractors equipped with Hydro-Mechanical continuously variable transmission based on coordinated control methods. Computers and Electronics in Agriculture 252:112115. https://doi.org/10.1016/j.compag.2026.112115 – 10.1016/j.compag.2026.112115
• Chang, Shifting strategy for power shift tractors based on digital twin-driven reinforcement learning[J]. Computers and Electronics in Agriculture (2025)
• Gade CR, W․ RS, V․ S (2025) Towards sustainable farming: A state of art review on electrification of a farm tractor. Results in Engineering 25:104403. https://doi.org/10.1016/j.rineng.2025.104403 – 10.1016/j.rineng.2025.104403
• Zhang, Research on shift quality considering nonlinear characteristics[J]. Results in Engineering (2025)
• Li, Towed DC Electrical System for Zero-Emission Agricultural Machinery and Its Boundary Conditions[J]. Results in Engineering (2025)
• Xue L, Jiang H, Zhao Y, Wang J, Wang G, Xiao M (2022) Fault diagnosis of wet clutch control system of tractor hydrostatic power split continuously variable transmission. Computers and Electronics in Agriculture 194:106778. https://doi.org/10.1016/j.compag.2022.106778 – 10.1016/j.compag.2022.106778
• Li A, Qin D, Guo Z, Xia Y, Lv C (2023) Wet clutch pressure hysteresis compensation control under variable oil temperatures for electro-hydraulic actuators. Control Engineering Practice 141:105723. https://doi.org/10.1016/j.conengprac.2023.105723 – 10.1016/j.conengprac.2023.105723
• Liu M, Li W, Xu L, Li Y, Zhao T, Hou S (2024) Coordinated dual-rolling control of shifting in HMCVT based on KF-MPC algorithm with anti-disturbance capabilities. Computers and Electronics in Agriculture 227:109561. https://doi.org/10.1016/j.compag.2024.109561 – 10.1016/j.compag.2024.109561
• Radrizzani S, Panzani G, Savaresi SM (2024) Simultaneous Energy Management and Speed Control in a Hybrid Tractor With Experimental Validation. IEEE Trans Contr Syst Technol 32(4):1285–1297. https://doi.org/10.1109/tcst.2024.3362934 – 10.1109/tcst.2024.3362934
• Lu L, Zhang Z, Zhang G, Han B, Yang H, Zhu Z, Song Z, Zhai Z, Wang J, Zhang C (2025) Application of a deep learning model with physical model constraints and attention mechanism for state prediction in high-power power-shift tractors. Computers and Electronics in Agriculture 238:110883. https://doi.org/10.1016/j.compag.2025.110883 – 10.1016/j.compag.2025.110883
• Zhang Y, Wang D, Du Y, Wen C, Wang L, Wu Z (2026) Sensorless wet clutch pressure control method for high-power tractors using physical and digital twins. Biosystems Engineering 261:104322. https://doi.org/10.1016/j.biosystemseng.2025.104322 – 10.1016/j.biosystemseng.2025.104322
• Liu F, Wu W, Hu J, Yuan S (2019) Design of multi-range hydro-mechanical transmission using modular method. Mechanical Systems and Signal Processing 126:1–20. https://doi.org/10.1016/j.ymssp.2019.01.061 – 10.1016/j.ymssp.2019.01.061
• Xia Y, Sun D, Qin D, Zhou X (2020) Optimisation of the power-cycle hydro-mechanical parameters in a continuously variable transmission designed for agricultural tractors. Biosystems Engineering 193:12–24. https://doi.org/10.1016/j.biosystemseng.2019.11.009 – 10.1016/j.biosystemseng.2019.11.009
• Wang G, Song Y, Wang J, Xiao M, Cao Y, Chen W, Wang J (2020) Shift quality of tractors fitted with hydrostatic power split CVT during starting. Biosystems Engineering 196:183–201. https://doi.org/10.1016/j.biosystemseng.2020.06.001 – 10.1016/j.biosystemseng.2020.06.001
• Cheng Z, Lu Z (2022) System response modeling of HMCVT for tractors and the comparative research on system identification methods. Computers and Electronics in Agriculture 202:107386. https://doi.org/10.1016/j.compag.2022.107386 – 10.1016/j.compag.2022.107386
• Xiao M, Zhao Y, Li X, Hussain G, Wang S, Zhu Y (2022) Dynamic simulation of the tractor HMCVT under typical working conditions based on AMESim. International Journal of Agricultural and Biological Engineering 15(2):102–110. https://doi.org/10.25165/j.ijabe.20221502.6815 – 10.25165/j.ijabe.20221502.6815
• Ye S, Zheng C, Bao Y, Miao K, Liu H, Zhao S (2025) Dynamic characteristics analyses of coupled-multibody axial piston pump model. International Journal of Mechanical Sciences 299:110379. https://doi.org/10.1016/j.ijmecsci.2025.110379 – 10.1016/j.ijmecsci.2025.110379
• Zhou H, Lu Z, Cheng Z (2026) Optimization of Transmission Parameters for a Tractor Equipped with HMCVT Based on Power Flow Analysis to Improve Efficiency. Applied Sciences 16(3):1641. https://doi.org/10.3390/app16031641 – 10.3390/app16031641
• Iqbal S, Al-Bender F, Ompusunggu AP, Pluymers B, Desmet W (2015) Modeling and analysis of wet friction clutch engagement dynamics. Mechanical Systems and Signal Processing 60–61:420–436. https://doi.org/10.1016/j.ymssp.2014.12.024 – 10.1016/j.ymssp.2014.12.024
• Bao, Investigation of engagement characteristics of a multi-disc wet friction clutch[J]. Tribology International (2021)
• Park J, Choi S, Oh J, Eo J (2022) Adaptive slip engagement control of a wet clutch in vehicle powertrain based on transmitted torque estimation. Mechanical Systems and Signal Processing 171:108861. https://doi.org/10.1016/j.ymssp.2022.108861 – 10.1016/j.ymssp.2022.108861
• Li A, Qin D (2022) Adaptive model predictive control of dual clutch transmission shift based on dynamic friction coefficient estimation. Mechanism and Machine Theory 173:104804. https://doi.org/10.1016/j.mechmachtheory.2022.104804 – 10.1016/j.mechmachtheory.2022.104804
• Ren Y, Xi J, Chen H, Yu H, Meng F, Zhou W (2023) Study on dynamic characteristics variation mechanism of wet-clutches during the filling phase considering temperature and rotational speed of the oil. Control Engineering Practice 135:105514. https://doi.org/10.1016/j.conengprac.2023.105514 – 10.1016/j.conengprac.2023.105514
• Rogkas N, Vasilopoulos L, Spitas V (2023) A hybrid transient/quasi-static model for wet clutch engagement. International Journal of Mechanical Sciences 256:108507. https://doi.org/10.1016/j.ijmecsci.2023.108507 – 10.1016/j.ijmecsci.2023.108507
• Jin J, Li X, Yang S, Yi H, Sun H, Hao W (2025) Calculation and analysis of wet clutch sliding torque based on fluid-solid coupling dynamic behavior. Tribology International 202:110363. https://doi.org/10.1016/j.triboint.2024.110363 – 10.1016/j.triboint.2024.110363
• Li A, Guo Z, Duan S, Qin D (2025) Temperature dependent pressure model of wet clutch electro-hydraulic actuator. Measurement 256:118378. https://doi.org/10.1016/j.measurement.2025.118378 – 10.1016/j.measurement.2025.118378
• Helian B, Mustalahti P, Mattila J, Chen Z, Yao B (2022) Adaptive robust pressure control of variable displacement axial piston pumps with a modified reduced-order dynamic model. Mechatronics 87:102879. https://doi.org/10.1016/j.mechatronics.2022.102879 – 10.1016/j.mechatronics.2022.102879
• Yu B, Li H, Ma G, Liu X, Chen C, Zheng B, Ba K, Kong X (2024) Design and matching control strategy of electro-hydraulic load-sensitive hydraulic power unit for legged robots. Energy 313:133730. https://doi.org/10.1016/j.energy.2024.133730 – 10.1016/j.energy.2024.133730
• Zhao L, Wu T (2025) Design and robust control of a dual-loop valve-controlled cylinder system. Results in Engineering 27:106515. https://doi.org/10.1016/j.rineng.2025.106515 – 10.1016/j.rineng.2025.106515
• Qiao K, Wei D, Han L, Li Y, Peng C, Yang W (2026) An advanced flexible dynamic model and experimental verification for armature assembly in servo valve. Results in Engineering 29:108866. https://doi.org/10.1016/j.rineng.2025.108866 – 10.1016/j.rineng.2025.108866
• Kalman RE (1963) Mathematical Description of Linear Dynamical Systems. Journal of the Society for Industrial and Applied Mathematics Series A Control 1(2):152–192. https://doi.org/10.1137/0301010 – 10.1137/0301010
• HO ΒL, KALMAN RE (1966) Editorial: Effective construction of linear state-variable models from input/output functions. at - Automatisierungstechnik 14(1–12):545–548. https://doi.org/10.1524/auto.1966.14.112.545 – 10.1524/auto.1966.14.112.545
• Rosenberg RC (1971) State-Space Formulation for Bond Graph Models of Multiport Systems. Journal of Dynamic Systems, Measurement, and Control 93(1):35–40. https://doi.org/10.1115/1.3426458 – 10.1115/1.3426458
• Rosenberg RC, Karnopp DC (1972) A Definition of the Bond Graph Language. Journal of Dynamic Systems, Measurement, and Control 94(3):179–182. https://doi.org/10.1115/1.3426586 – 10.1115/1.3426586
• Willems JC (1972) Dissipative dynamical systems part I: General theory. Arch Rational Mech Anal 45(5):321–351. https://doi.org/10.1007/bf00276493 – 10.1007/bf00276493
• Maschke BM, van der Schaft AJ (1992) Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes 25(13):359–365. https://doi.org/10.1016/s1474-6670(17)52308-3 – 10.1016/s1474-6670(17)52308-3
• Butcher JC (2000) Numerical methods for ordinary differential equations in the 20th century. Journal of Computational and Applied Mathematics 125(1–2):1–29. https://doi.org/10.1016/s0377-0427(00)00455-6 – 10.1016/s0377-0427(00)00455-6
• Wang W (2022) Stage-based interpolation Runge–Kutta methods for nonlinear Volterra functional differential equations. Calcolo 59(3). https://doi.org/10.1007/s10092-022-00474-5 – 10.1007/s10092-022-00474-5
• Akrivis G, Makridakis CG (2022) A posteriori error estimates for Radau IIA methods via maximal parabolic regularity. Numer Math 150(3):691–717. https://doi.org/10.1007/s00211-022-01271-6 – 10.1007/s00211-022-01271-6