#
Dual-Motor Planetary Transmission to Improve Efficiency in Electric Vehicles^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Powertrain Modeling

_{S}, ω

_{R}, ω

_{o}are the velocities, respectively, of the sun, the ring, and the carrier of the planetary gear, ρ = r

_{R}/r

_{S}the ratio between the primitive radius of ring and sun, and i = ω

_{R}/ω

_{S}. Given ρ that defines the planetary gear geometry, the speed of the carrier ω

_{o}results as the weighted sum of the velocities of the sun and the ring, ω

_{S}and ω

_{R}; according to Equation (3) that is the only kinematic constraint of the system. Therefore, once the carrier velocity ω

_{o}is set by the required vehicle velocity, there is one remaining degree of freedom, i, that defines the relationship between the sun and the ring speed according to Equations (1) and (2), and that is the variable used in the parametric optimization process described later.

_{S}and T

_{R}refer, respectively, to the sun and ring torque, T

_{o}is the torque request, and η

_{pd}is the efficiency of the planetary gear. Equation (4) holds true for steady-state conditions. However, it can be considered a good approximation during transients as well if the motor inertia is small enough.

_{meR/S}is the mechanical power delivered by the ring/sun motor, and P

_{elR/S}and ${\eta}_{R/S}$ the corresponding electrical power and single motor efficiency, respectively. Note that in this analysis the loss in the power converters is not explicitly considered.

## 3. Electric Motor and Load Modeling

_{o}and T

_{o}, can be obtained under the assumption of planar driving as:

_{v}the rolling resistance, whereas ${\rho}_{a},{C}_{x},S$ define the aerodynamic resistance. The values of the vehicle parameters used in this research are collected in Table 1. The maximum vehicle speed is assumed as 115 km/h.

## 4. Controller and Design Optimization

- Optimization of the ratio i that maximizes the efficiency η
_{tot}for each operating pair (ω_{o}, T_{o}), given [ρ ω_{R,max}ω_{S,max}]. - Optimization of the parameter set [ρ, ω
_{R,max}, ω_{S,max}] to obtain the highest average efficiency over an urban cycle, η_{cyc}.

#### 4.1. Dual-Motor System Control

_{t}(around 0.6–0.8), whereas single-point crossover with a probability of p

_{cross}(around 0.8–0.9) is adopted. Once two new individuals are formed, mutation is enforced with probability of p

_{mut}(about 0.06–0.1) with either creep mutation (probability of 0.5 and creep rate of 10% of the full range) or full-range mutation (probability of 0.5). In addition, to avoid the best speed ratio found so far being lost in the pursuit of the next generation, this speed ratio is passed to the next generation according to the concept of elitism.

_{tot}(bottom plot), is compared against that of the single-motor, η

_{0}(upper plot). As expected, the largest discrepancy can be observed for low speed and high torque. The highest difference of about 0.24 (0.27 for regeneration) is found for a torque and a speed ranging, respectively, between 55% and 96% of the maximum torque and between 5% and 22% of the maximum speed.

#### 4.2. Powertrain Design

_{R,max}, ω

_{S,max}] can then be selected as the one that maximizes the average efficiency, η

_{cyc}, over the entire Artemis DC. η

_{cyc}is introduced as the ratio between the overall mechanical energy delivered during the urban cycle and the corresponding electric energy drawn by the motors:

_{maxR}) has been progressively incremented in the window [ω

_{o}/2, ω

_{o}·(ρ + 1)/ρ]. The upper limit corresponds to the maximum speed of the ring motor when the power of the sun motor is null. It is worth noting that, when the maximum velocity of the ring is set, in turn, the highest speed of the sun (ω

_{maxS}) is also determined since the power of the sun and the ring motors must be equal to the user-required power.

_{maxR}when the single planet gear set is adopted (Figure 9a), a larger impact is observed for the double-planet gear. Table 2 collects the optimized values of ω

_{maxR}, ω

_{maxS}, T

_{maxR}, T

_{maxS}and ρ, for both planetary gear types, showing that the dual-motor powertrain generally outperforms the single-motor counterpart, η

_{o,avg}, with an improvement in the overall efficiency estimated by Equation (11), η

_{cyc}

_{,opt}, of about 8.8% (8.9% during regeneration) for the single-planet and of about 8.7% (8.6% during regeneration) for the double-planet in the power delivery stage.

#### 4.3. Optimization Results

_{o}< 0.15 ω

_{o}

_{,max}), whereas the ring motor is blocked. In this working condition, the planetary gear works as a fixed-ratio reducer. At high vehicle velocity (i.e., ω

_{o}> 0.7 ω

_{o}

_{,max}), power is supplied simultaneously by both motors, as expected due to the design constraint that imposes that the maximum power demand must be balanced by the sum of the power delivered by the two motors. A similar behavior can be observed as well for the regeneration stage.

#### 4.4. Performance over Different Driving Cycles

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

r_{R} | ring gear radius |

r_{S} | sun gear radius |

r_{P} | carrier radius |

ω_{R} | ring motor angular velocity |

ω_{S} | sun motor angular velocity |

ω_{o} | angular speed required by the user (speed of the carrier) |

i | ratio between the angular velocity of the ring and the sun (ω_{R}/ω_{S}) |

T_{R} | ring motor torque |

T_{S} | sun motor torque |

T_{o} | torque required by the user (torque on the carrier) |

ρ | planetary gear ratio |

ω_{maxS} | sun motor maximum angular velocity |

T_{maxS} | sun motor maximum torque |

P_{maxS} | sun motor maximum power |

ω_{maxR} | ring motor maximum angular velocity |

T_{maxR} | ring motor maximum torque |

P_{maxR} | ring motor maximum power |

T_{omax} | maximum torque of the carrier |

ω_{omax} | carrier maximum angular speed |

η_{S} | sun motor efficiency (power delivery) |

η_{R} | ring motor efficiency (power delivery) |

η_{pd} | planetary gear mechanical efficiency |

η_{tot} | efficiency of the dual-motor transmission for a given working point (power delivery) |

η_{tot, opt} | optimized efficiency of the dual-motor transmission for a given working point (power delivery) |

η_{0} | efficiency of the single-motor transmission for a given working point (power delivery) |

η_{cyc} | average efficiency of the optimized dual-motor transmission over a driving cycle (power delivery) |

η_{cyc, max} | average efficiency of the optimized dual-motor transmission over a driving cycle, given the best values of ρ, ω_{maxS}, ω_{maxR} |

η_{S, reg} | sun motor efficiency (power regeneration) |

η_{R, reg} | ring motor efficiency (power regeneration) |

η_{0,reg} | efficiency of the single-motor transmission for a given working point (power regeneration) |

η_{cyc, reg} | average efficiency of the optimized dual-motor transmission over a driving cycle (power regeneration) |

η_{cyc, max, reg} | average efficiency of the optimized dual-motor transmission over a driving cycle (power regeneration), given the best values of ρ, ω_{max}_{S}, ω_{max}_{R} |

## References

- Chu, W.; Zhu, Z.; Zhang, J.; Liu, X.; Stone, D.; Foster, M. Investigation on Operational Envelops and Efficiency Maps of Electrically Excited Machines for Electrical Vehicle Applications. IEEE Trans. Magn.
**2015**, 51, 1–10. [Google Scholar] [CrossRef] - Wang, H.; Song, X.; Saltsman, B.; Hu, H. Comparative Studies of Drivetrain Systems for Electric Vehicles; SAE Technical Paper 2013-01-2467; 2013. Available online: https://www.sae.org/publications/technical-papers/content/2013-01-2467/ (accessed on 11 March 2021).
- Derammelaere, S.; Dereyne, S.; Defreyne, P.; Algoet, E.; Verbelen, F.; Stockman, K. Energy efficiency measurement procedure for gearboxes in their entire operating range. In Proceedings of the IEEE Industry Application Society Annual Meeting, Vancouver, BC, Canada, 5–9 October 2014. [Google Scholar]
- Verstraten, T.; Furnémont, R.; López-García, P.; Rodriguez-Cianca, D.; Cao, H.; Vanderborght, B.; Lefeber, D. Modeling and design of an energy-efficient dual-motor actuation unit with a planetary differential and holding brakes. Mechatronics
**2018**, 49, 134–148. [Google Scholar] [CrossRef] - De Pinto, S.; Chatzikomis, C.; Sorniotti, A.; Mantriota, G. Comparison of Traction Controllers for Electric Vehicles with On-Board Drivetrains. IEEE Trans. Veh. Technol.
**2017**, 66, 6715–6727. [Google Scholar] [CrossRef] [Green Version] - Stockman, K.; Dereyne, S.; Defreyne, P.; Algoet, E.; Derammelaere, S. Efficiency Measurement Campaign on Gearboxes. In Proceedings of the Energy Efficiency in Motor Driven Systems, Henslink, Denmark, 15–17 September 2015. [Google Scholar]
- De Santiago, J.; Bernhoff, H.; Ekergård, B.; Eriksson, S.; Ferhatovic, S.; Waters, R.; Leijon, M. Electrical motor drivelines in commercial all-electric vehicles: A review. IEEE Trans. Veh. Technol.
**2012**, 61, 475–484. [Google Scholar] [CrossRef] [Green Version] - Chen, L.; Wang, J.; Lazari, P.; Chen, X. Optimizations of a permanent magnet machine targeting different driving cycles for electric vehicles. In Proceedings of the 2013 International Electric Machines & Drives Conference, Chicago, IL, USA, 12–15 May 2013; pp. 1–6. [Google Scholar]
- Lazari, P.; Wang, J.; Chen, L. A Computationally Efficient Design Technique for Electric-Vehicle Traction Machines. IEEE Trans. Ind. Appl.
**2014**, 50, 3203–3213. [Google Scholar] [CrossRef] - Carraro, E.; Morandin, M.; Bianchi, N. Traction PMASR Motor Optimization According to a Given Driving Cycle. IEEE Trans. Ind. Appl.
**2016**, 52, 209–216. [Google Scholar] [CrossRef] - Mao, Y.; Niu, S.; Yang, Y. Differential Evolution-Based Multiobjective Optimization of the Electrical Continuously Variable Transmission System. IEEE Trans. Ind. Electron.
**2018**, 65, 2080–2089. [Google Scholar] [CrossRef] - Mallik, S.; Mallik, K.; Barman, A.; Maiti, D.; Biswas, S.; Deb, N.; Basu, S. Efficiency and Cost Optimized Design of an Induction Motor Using Genetic Algorithm. IEEE Trans. Ind. Electron.
**2016**, 64, 9854–9863. [Google Scholar] [CrossRef] - Sarigiannidis, A.; Beniakar, M.; Kladas, A. Fast Adaptive Evolutionary PM Traction Motor Optimization Based on Electric Vehicle Drive Cycle. IEEE Trans. Veh. Technol.
**2017**, 66, 5762–5774. [Google Scholar] [CrossRef] - Ramelan, L.; Firmansyah, E.; Liu, T.; Tseng, S.; Hsu, J. An improved maximum efficiency control for dual-motor drive systems. In Proceedings of the 2014 6th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia, 7–8 October 2014. [Google Scholar]
- Ruan, J.; Walker, P.D.; Wu, J.; Zhang, N.; Zhang, B. Development of Continuously Variable Transmission and Multi-Speed Dual-Clutch Transmission for Pure Electric Vehicle. Adv. Mech. Eng.
**2018**, 10, 1–15. [Google Scholar] [CrossRef] - Mooney, L.; Herr, H. Continuously-variable series-elastic actuator. In Proceedings of the IEEE 13th International Conference on Rehabilitation Robotics (ICORR), Seattle, WA, USA, 24–26 June 2013; pp. 1–6. [Google Scholar]
- Bottiglione, F.; De Pinto, S.; Mantriota, G.; Sorniotti, A. Energy Consumption of a Battery Electric Vehicle with Infinitely Variable Transmission. Energies
**2014**, 7, 8317–8337. [Google Scholar] [CrossRef] [Green Version] - Mantriota, G. Power split transmissions for wind energy systems. Mech. Mach. Theory
**2017**, 117, 160–174. [Google Scholar] [CrossRef] - Ontañón-Ruiz, J.; Daniel, R.; McǍree, P. On the use of differential drives for overcoming transmission nonlinearities. J. Robot. Syst.
**1998**, 15, 641–660. [Google Scholar] [CrossRef] - Sun, L.; Feng, K.; Chapman, C.; Zhang, N. An Adaptive Power-Split Strategy for Battery–Supercapacitor Powertrain—Design, Simulation, and Experiment. IEEE Trans. Power Electron.
**2017**, 32, 9364–9375. [Google Scholar] [CrossRef] - Mantriota, G.; Reina, G. Efficient Power-Split Powertrain for Full Electric Vehicles. In Advances in Italian Mechanism Science; Mechanisms and Machine Science; Niola, V., Gasparetto, A., Eds.; Springer: Cham, Switzerland, 2021; Volume 91. [Google Scholar]
- Mi, C.; Masrur, M.A. Hybrid Electric Vehicles; Wiley & Sons Ltd.: New York, NY, USA, 2018. [Google Scholar]
- Verstraten, T.; Furnémont, R.; López-García, P.; Rodriguez-Cianca, D.; Vanderborght, B.; Lefeber, D. Kinematically redundant actuators, a solution for conflicting torque–speed requirements. Int. J. Robot. Res.
**2019**, 38, 612–629. [Google Scholar] [CrossRef] - Crispel, S.; López-García, P.; Verstraten, T.; Saerens, E.; Lefeber, D. Introduction of a redundant actuator using planetary gear trains for human centred robotics. MATEC Web Conf.
**2020**, 317, 01003. [Google Scholar] [CrossRef] - De Carlo, M.; Mantriota, G. Electric vehicles with two motors combined via planetary gear train. Mech. Mach. Theory
**2020**, 148, 103789. [Google Scholar] [CrossRef] - Mantriota, G.; Pennestrì, E. Theoretical and experimental efficiency analysis of multi-degrees-of-freedom epicyclic gear trains. Multibody Syst. Dyn.
**2003**, 9, 389–408. [Google Scholar] [CrossRef] - Li, K.; Cui, S.; Bouscayrol, A.; Hecquet, M. Analytical Derivation of Efficiency Map of an Induction Machine for Electric Vehicle Applications. In Proceedings of the IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, 27–30 August 2018. [Google Scholar]
- Nicola, R. The Different Driving Cycles. Available online: https://www.car-engineer.com/the-different-driving-cycles/ (accessed on 24 October 2020).

**Figure 1.**Functional schemes of the standard single-motor, single-speed powertrain (

**a**) and the proposed dual-motor multispeed system (

**b**).

**Figure 4.**Efficiency map of a standard induction electric motor normalized with respect to maximum angular speed and torque.

**Figure 5.**Load profile prescribed by the Artemis urban cycle: (

**a**) speed demand; (

**b**) corresponding torque; and (

**c**) power demand.

**Figure 6.**Working points of the Artemis drive cycle (DC) overlaid over the efficiency map during: (

**a**) power supply; and (

**b**) power regeneration.

**Figure 7.**Comparison of the efficiency map provided by the single-motor (

**a**) and dual-motor (

**b**) powertrains (ρ = 3.5, ω

_{R,max}= 0.8 ω

_{omax}and ω

_{S,max}= 1.7 ω

_{omax}).

**Figure 8.**Relative percentage improvement in efficiency obtained by the dual-motor powertrain compared with the single-motor powertrain over the Artemis driving cycle (ρ = 3.5, ω

_{R,max}= 0.8 ω

_{o,max}, and ω

_{S,max}= 1.7 ω

_{omax}).

**Figure 9.**Average efficiency over the Artemis DC by varying ρ and ω

_{maxR}: (

**a**) single-planet gear; (

**b**) double-planet gear.

**Figure 10.**Distribution of the driving cycle time as a function of the efficiency for the single- and dual-motor power transmissions.

**Figure 11.**Optimal speed profiles that ensure efficiency maximization for the power supply stage over the Artemis DC: (

**a**) ring motor; and (

**b**) sun motor.

Parameter | Value |
---|---|

${\rho}_{a}$ | 1.2 kg/m^{3} |

${C}_{x}$ | 0.32 |

S | 2.2 m^{2} |

M | 1500 kg |

f_{v} | 0.01 |

R | 0.35 m |

Parameter | Optimal Value Single-Planet | Optimal Value Double-Planet |
---|---|---|

ρ | 3.5 | −4.5 |

η_{0, avg} | 0.79 (0.78 reg) | 0.8 (0.79 reg) |

η_{cyc}_{, opt} | 0.86 (0.85 reg) | 0.87 (0.85 reg) |

ω_{maxS} | 1.7 ω_{omax} | 0.4 ω_{omax} |

ω_{maxR} | 0.8 ω_{omax} | 1.6 ω_{omax} |

T_{maxS} | 0.2 T_{omax} | 0.5 T_{omax} |

P_{maxS} | 0.38 P_{omax} | 0.221 P _{omax} |

T_{maxR} | 0.8 T_{omax} | 0.5 T_{omax} |

P_{maxR} | 0.62 P_{omax} | 0.78 P_{omax} |

**Table 3.**Percentage efficiency gain obtained from the proposed dual-motor powertrain compared with standard single-motor transmission for various cycles.

Dual-Motor Architecture | Artemis Urban Δη% | ECE-15 Δη% | Artemis Rural Road Δη% | Artemis Motorway Δη% | ||||
---|---|---|---|---|---|---|---|---|

Drive | Regeneration | Drive | Regeneration | Drive | Regeneration | Drive | Regeneration | |

Single planet | 8.8 | 8.9 | 9.1 | 9.7 | 5.0 | 12.5 | 4.1 | 14.3 |

Double planet | 8.7 | 8.6 | 10.9 | 11.1 | 5.7 | 13.6 | 4.2 | 10.1 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mantriota, G.; Reina, G.
Dual-Motor Planetary Transmission to Improve Efficiency in Electric Vehicles. *Machines* **2021**, *9*, 58.
https://doi.org/10.3390/machines9030058

**AMA Style**

Mantriota G, Reina G.
Dual-Motor Planetary Transmission to Improve Efficiency in Electric Vehicles. *Machines*. 2021; 9(3):58.
https://doi.org/10.3390/machines9030058

**Chicago/Turabian Style**

Mantriota, Giacomo, and Giulio Reina.
2021. "Dual-Motor Planetary Transmission to Improve Efficiency in Electric Vehicles" *Machines* 9, no. 3: 58.
https://doi.org/10.3390/machines9030058