Reducing Operation Emissions and Improving Work Efficiency Using a Pure Electric Wheel Drive Tractor

Chang-Kai Wen; Wen Ren; Qing-Zhen Zhu; Chun-Jiang Zhao; Zhen-Hao Luo; Sheng-Li Zhang; Bin Xie; Zhi-Jun Meng

doi:10.1016/j.eng.2024.01.026

Engineering ›› 2024, Vol. 37 ›› Issue (6) :230 -245. DOI: 10.1016/j.eng.2024.01.026

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Reducing Operation Emissions and Improving Work Efficiency Using a Pure Electric Wheel Drive Tractor

Chang-Kai Wen ^a^,^b^,^#
, Wen Ren ^c^,^#
, Qing-Zhen Zhu ^d^,^#
, Chun-Jiang Zhao ^a^,^b
, Zhen-Hao Luo ^e
, Sheng-Li Zhang ^c^,^*
, Bin Xie ^e^,^*
, Zhi-Jun Meng ^a^,^b^,^*

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Abstract

In response to the problems of excessive greenhouse-gas and particulate emissions and the low traction efficiency of conventional diesel tractors in the field, a purely electric wheel-side drive tractor was studied, including an electric motor drive system, a battery ballast system, and an electro-hydraulic suspension system. This paper develops a dynamics model of an electric tractor-ploughing unit under complex soil conditions, leading to the proposal of an active control method for drive wheel torque and a joint control method for the traction force of the suspension system and the front- and rear-axle loads of a tractor. Finally, the tractor is prototyped and assembled, and ploughing tests are carried out. The ploughing results show that the active torque-distribution control method proposed in this study reduces the tractor slip by 14.83% and increases the traction efficiency by 10.28% compared with the average torque-distribution mode. Compared with the conventional traction control mode, the joint control method for traction and ballast proposed in this paper results in a 3.7% increase in traction efficiency, a 15.05% decrease in slip, and a 4.9% reduction in total drive motor energy consumption. This study will help to improve the operation quality and traction efficiency of electric tractors in complex soil conditions.

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Keywords

Electric tractor / Ploughing unit / Torque distribution / Active ballast / Traction performance

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Chang-Kai Wen, Wen Ren, Qing-Zhen Zhu, Chun-Jiang Zhao, Zhen-Hao Luo, Sheng-Li Zhang, Bin Xie, Zhi-Jun Meng. Reducing Operation Emissions and Improving Work Efficiency Using a Pure Electric Wheel Drive Tractor. Engineering, 2024, 37 (6) : 230-245 DOI:10.1016/j.eng.2024.01.026

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1. Introduction

Rapid global development cannot be achieved without the consumption of petroleum fuels, but the extensive consumption of such fuels and the resulting air pollution and greenhouse effect are becoming increasingly severe [1], [2], [3]. Therefore, there is an urgent need to reduce petroleum fuel consumption and emissions of particulate matter (PM) and greenhouse gases, with agriculture being a critical area in this regard [4], [5], [6]. Agricultural production involves several key steps, including ploughing, planting, management, and harvesting; at the current stage of development, agricultural machinery powered by diesel engines is commonly used in each step [7], [8]. However, the emissions from such off-road machinery are severe. In 2020, China’s non-road mobile sources emitted 425 000 tonnes of hydrocarbons (HCs), 4 782 000 tonnes of nitrogen oxides (NOs), and 237 000 tonnes of PM. Of these, pollutant emissions from agricultural machinery accounted for 48.0%, 34.9%, and 38.8% of the total emissions, respectively [9]. Therefore, in order to achieve green agriculture, many scholars have researched the application of electric drive technology to tractors, and electric tractors have become a typical representative of green agricultural power machinery. However, electric tractors’ poor adaptability and low operational efficiency in agricultural environments are issues that need to be studied [10].

When traditional diesel tractors work on stubble and wet, muddy ground, there are many problems, such as an open field environment, varying soil conditions, complex workloads, and strict agronomic requirements [11], [12]. In such cases, the diesel tractor is subjected to significant differences in ground contact between the two sides of the wheels, poor front- and rear-axle load distribution, and suspension control that does not take agronomic quality into consideration, as shown in Fig. 1. This situation can lead to longitudinal wheel slip, a backward shift of the unit’s center of gravity, and a lack of traction power, accelerating damage to the soil structure, increasing tire misalignment, and significantly reducing traction efficiency [13]. The result is a diesel tractor that not only causes significant emissions pollution but also has no advantage in traction performance [14].

Realizing optimal wheel torque distribution is an excellent solution to address this problem. Here, research on the optimization of wheel torque distribution for electric wheel-drive vehicles in the field of automobiles can provide a basis for reference. Scholars in this field have relied on the advantages of the configuration of four-wheel independent drive, constructed a dynamics model of the electric vehicle, and studied the four-wheel torque allocation strategy based on multiple objectives such as energy conservation, stability, and dynamics. Such efforts have incorporated fuzzy control theory, sliding film algorithms, predictive control theory, multi-objective optimization algorithms, and even deep learning theory [15], [16], [17], [18], [19]. These studies provided innovative ideas to guide the research reported in this paper.

Unlike traditional fuel tractors, electric tractors have no exhaust emissions, rapid drive system response, flexible power output, or other advantages. Nevertheless, electric tractors are intended to be used in the field instead of traditional fuel tractors and can be used in greenhouse planting, indoor farming, mountainous operations, and other special operating scenarios. These scenarios require electric tractors to be able to adapt to complex drive and operating environments, putting higher requirements on the design of electric tractors and their control systems [20], [21]. In addition, considering the limitations of the range and recharging speed of an electric tractor, it is challenging to use electric tractors to carry out the highly time-sensitive activities involved in agricultural production; therefore, improving the operating efficiency of electric tractors and giving full play to their traction capacity have become urgent breakthrough issues.

Thus, for the common tractor ploughing operation described above, a new electric tractor chassis system should meet the following requirements:

(1) Given the complex soil environments and load fluctuations in typical operating situations, the electric tractor chassis system needs to achieve adaptive drive control of both drive wheels under different soil adhesion conditions [22]. Conventional diesel tractors use a mechanical transmission system to transfer the engine energy to the drive wheels. Moreover, the torque of the two drive wheels is distributed by a mechanical differential. This situation is prone to excessive drive wheel slip when there are differences in ground contact between the two wheels [23].

(2) When the front and rear axle load distribution of the tractor operating unit is not appropriate, the electric tractor chassis system needs to accurately calculate the current front- and rear-axle load requirements of the tractor and automatically adjust them [24]. Conventional tractors use counterweights to change the tractor’s front- and rear-axle load distribution, usually by manually adding or removing counterweights at the front and rear wheels or the front of the tractor [25]. The use of counterweights does not allow for continuous changes in tractor axle load, as the weight of individual counterweights is fixed [26].

(3) Traditional tractor traction control cannot appropriately balance the unit’s tillage quality with efficient traction. Due to the different agronomic requirements of different operations, a tractor’s ploughing operation is influenced by the soil environment, load fluctuations, and operating speed, and the tractor is prone to excessive tire skidding [27]. Most current studies control the tractor traction or skidding rate by adjusting the tillage depth; however, not much attention is paid to changes in tillage depth during the whole operation process, which results in large tillage-depth fluctuations that do not meet agronomic ploughing requirements [28].

In summary, existing fuel-fired tractors suffer from reduced traction efficiency, low fuel efficiency, and high greenhouse gas emissions when ploughing on complex field surfaces. These issues are manifested as follows: high wheel slip due to the inability to achieve differential torque distribution between the left and right drive wheels, unreasonable front- and rear-axle load distribution due to the inability to continuously and intelligently regulate the fixed counterweight, and low tillage quality due to the inability of the electro-hydraulic suspension system to balance the agronomic requirements of the operation with the traction performance of the unit. Therefore, this research takes the tractor unit system as the object and aims to improve the operation productivity and economy, in addition to studying the wire control scheme and control method of a pure electric tractor chassis system with a wheel-side drive. The main contributions of this work are as follows:

(1) A new overall configuration for an electric tractor, composed of a wheel-side motor independent drive system, a battery ballast system, and a direct-drive electro-hydraulic suspension system, is proposed to provide an intelligent carrier for the key system and the whole machine in order to realize high-efficiency control.

(2) To overcome the problems of longitudinal wheel slip, rearward shift of the center of gravity of the unit, and insufficient traction power of the whole tractor during field operation, a nine-degrees-of-freedom (9-DOFs) electric tractor dynamics model is constructed; moreover, an active control method for the driving wheel torque and a joint control method for the traction force and the front- and rear-axle loads are researched.

(3) Based on the innovative configuration proposed in this paper, a prototype of a wheel-side-driven pure electric tractor is developed, and ploughing field tests of the subsystem configuration and control methods are carried out.

2. Chassis system configuration

To achieve the desired field-operation characteristics of the tractor ploughing unit, an overall configuration scheme for an electric tractor’s wire-control chassis is proposed, including a motor drive system, battery ballast system, and electro-hydraulic suspension system, as shown in Fig. 2. The specific structure of the designed battery ballast system is shown in Fig. 3.

The advantages of this electric tractor chassis system include: ① a flexible and efficient electric drive system configuration with good overload and dynamic performance, which can actively realize differential torque distribution of the drive wheels; ② a high-quality power battery pack that directly replaces the original counterweight and is supplemented by a real-time movable mechanism, making it possible to optimize the unit counterweight and achieve rational distribution of the axle load; and ③ a direct-drive electro-hydraulic suspension control system based on an electro-hydraulic combination, providing a variety of operational control methods for the tractor.

2.1. Motor drive system structure

According to the electric tractor chassis system solution proposed in this study, rear-wheel drive is used, and the drive form drive motor plus a wheel-side reducer. During the operation of the electric tractor, it is necessary to meet specific traction requirements; at the same time, the energy economy of the tractor should be ensured. Based on the traction performance indicators of a 14.7-kW conventional tractor, combined with the requirements in the Chinese standard “GBT18385-2005 Electric vehicle power performance test methods” for the tractor’s climbing and acceleration, design indicators are proposed for the electric tractor power system [29]. As for power indicators, the rated tractive effort, traction speed, maximum speed, and maximum climbing angle are 4000 N, 5 km∙h⁻¹, 4.17 m·s⁻¹, and 17°, respectively. As for economic indicators, the continuous operating time and maximum continuous distance traveled are 2 h and 15 km, respectively. Using a parameter-matching design method, the parameters of the electric tractor power system were designed to match the power system design index.

First, a twin-share plough was selected as the farm equipment for the electric tractor ploughing operation, and the rated tractive force of the electric tractor was calculated to be 4000 N. Subsequently, the rated power of the motor was calculated to be 12.8 kW, according to the power demand of the drive system at the rated tractive force and the maximum operating speed. A genetic algorithm was then used to optimize the design of the electric tractor drive system and transmission system. In this regard, a parameter-matching model of the power system with the objective of power system minimization—that is, an optimized design model for the motor parameters and transmission ratio, as shown in Eq. (1)—was established.

(1)

\{\begin{matrix} \min F (x) = [f_{1} (x), f_{2} (x), f_{3} (x), f_{4} (x)] \\ s .t . F_{e} \geq 4000 \\ v_{\max} \geq 15 \\ θ \geq 17 ° \\ n_{\max} \leq 3 n_{e} \\ T_{\max} \leq 2 T_{e} \\ x \in [n_{e}, n_{\max}, T_{\max}, i_{g}] \end{matrix}

Therefore, the objective optimization function can be expressed as follows:

(2)

\{\begin{matrix} F (x) = \sum_{i = 1}^{4} l_{i} f_{i} (x) = \sum_{i = 1}^{4} l_{i} {[\frac{x (i) - x_{\min} (i)}{x_{\max} (i) - x_{\min} (i)}]}^{2} \\ l_{1} + l_{2} + l_{3} + l_{4} = 1 \end{matrix}

The system parameters closely related to the traction performance of the electric tractor are selected as the optimization variables; these include the rated speed of the motor, the maximum speed, the maximum torque, and the transmission ratio of the gearbox. The boundary conditions of the optimization parameters are shown in Table 1.

Considering the calculation results of the system parameters, the rated traction force, maximum driving speed, maximum climbing degree, continuous operating time, and driving range of the electric tractor were recalculated; the results are shown in Table 2. Considering the powertrain design indicators, the powertrain parameter-matching results fully meet the electric tractor’s power and economy indicators. On this basis, the actual performance of the electric tractor and the design index of the variation between the design index is not more than 10%, which meets the design objective of minimizing the power system.

2.2. Battery ballast system structure

Unlike fuel tractors, electric tractors use a battery as the sole source of power. The battery mass often accounts for 30%-50% of the tractor’s structural mass. The total weight of the battery pack for the electric tractor designed in this paper is 520 kg, which accounts for approximately 40% of the overall weight of the machine. In order to reasonably distribute the axle load on the front and rear axles, the battery is divided into two parts, both 260 kg, which are placed at the front and rear ends of the chassis system. In addition, to achieve accurate axle load distribution between the front and rear axles of the tractor, a battery ballast system is designed in this paper. Its arrangement is shown in Fig. 2.

The front battery can be moved backward and forward on the frame by means of a V-shape pulley, whose power is supplied by an electric actuator. The front battery is moved backward and forward to achieve continuous change in the static load distribution coefficient of the tractor’s rear axle with a constant total mass. It is possible to achieve a precise distribution of the static load on the drive wheels solely through the continuous movement of the front battery, provided that the counterweights are appropriately matched.

An electric tractor design platform was used to design a 500-mm longitudinal travel space for the front power battery. As shown in Table 3, the static load distribution coefficient of the drive wheels varies with the position of the front battery pack and the rear-axle counterweight. By increasing the rear-axle counterweight and changing the front power pack position, the static load distribution coefficient can be continuously varied from 0.5921 to 0.7225.

2.3. Electro-hydraulic suspension system structure

In this research, we design a direct-drive electro-hydraulic suspension mechanism for a small-horsepower electric tractor, as shown in Fig. 4. We use a fixed lifting arm that is fixedly connected to the frame. A retractable hydraulic cylinder replaces the lifting rod, and the lifting mechanism is partly made of hydraulic cylinders instead of traditional lifting rods.

According to the standard calculation method for wheel traction power, the electric tractor traction power is determined to be 9.75 kW. Combined with the design requirements for the electric tractor’s three-point hitch mechanism, according to the relevant standards for three-point hitch mechanisms, we choose reasonable rod parameters, as shown in Table 4.

The principle of the hydraulic system used in the electro-hydraulic suspension system is shown in Fig. 5. The hydraulic system uses a one-way constant displacement pump with a reversing valve solution. The hydraulic lifting cylinder is fitted with a liquid-controlled check valve. An H-shaped valve body is used in the middle of the three-position four-way reversing valve. A synchronized motor is added to the oil circuit to ensure the synchronized extension and shortening of the two hydraulic cylinders. In addition, location sensors are used to monitor changes in the hydraulic rod extension in real time.

Based on the above hydraulic system scheme, the working pressure of the system and the size of the hydraulic lifting cylinder are calculated and determined, respectively. Then the components such as the constant displacement pump, speed control motor, liquid-controlled check valve and synchronous motor are selected.

3. Model and methods

3.1. Dynamics model for electric tractor ploughing units

When an electric tractor is ploughing in a field, significant differences in the contact between the tire and ground and uneven soil properties can cause problems such as longitudinal wheel slip, rearward shift of the unit’s center of gravity, and lack of traction power for the whole machine. Therefore, we developed a 9-DOFs dynamics model for an electric tractor ploughing unit with efficient traction control, emphasizing ploughing resistance, tillage depth, longitudinal acceleration, lateral acceleration, vertical acceleration, pitch angle, and lateral tilt angle, as shown in Fig. 6.

First, the longitudinal, lateral, and vertical accelerations of the electric tractor, as implemented in the body coordinate system, are as follows:

(3)

(\begin{matrix} a_{x}^{T} \\ a_{y}^{T} \\ a_{z}^{T} \end{matrix}) = \frac{1}{Δ t} ((\begin{matrix} u_{T} + Δ u_{T} \\ v_{T} + Δ v_{T} \\ w_{T} + Δ w_{T} \end{matrix}) \cdot R_{φ} \cdot R_{θ} \cdot R_{γ} - (\begin{matrix} u_{T} \\ v_{T} \\ w_{T} \end{matrix}))

where R_φ, R_θ, and R_γ can be expressed as follows:

(4)

R_{φ} = (\begin{matrix} 1 & 0 & 0 \\ 0 & \cos Δ φ & - \sin Δ φ \\ 0 & \sin Δ φ & \cos Δ φ \end{matrix})

(5)

R_{θ} = (\begin{matrix} \cos Δ θ & 0 & \sin Δ θ \\ 0 & 1 & 0 \\ - \sin Δ θ & 0 & \cos Δ φ \end{matrix})

(6)

R_{γ} = (\begin{matrix} \cos Δ γ & - \sin Δ γ & 0 \\ \sin Δ γ & \cos Δ γ & 0 \\ 0 & 0 & 1 \end{matrix})

Based on the dynamics model, the speed of the mass center in the tractor body coordinate system is converted to a geodetic coordinate system, and the position of the mass center is calculated:

(7)

\{\begin{matrix} u = [u_{T} \cos θ + (v_{T} \sin φ + w_{T} \cos φ) \sin θ] \cos γ - (v_{T} \cos φ - w_{T} \sin φ) \sin γ \\ v = (v_{T} \cos φ - w_{T} \sin φ) \cos γ + [u_{T} \cos θ + (v_{T} \sin φ + w_{T} \cos φ) \sin θ] \sin γ \\ w = (v_{T} \sin φ + w_{T} \cos φ) \cos θ - u_{T} \sin θ \end{matrix}

The connection of the tractor to the ploughing implement is considered to be rigid, and only longitudinal movements are considered. The plough is separated to analyze its force equilibrium and determine the forces on the plough according to ΣF_x = 0, ΣF_y = 0, and ΣF_z = 0.

(8)

\{\begin{matrix} P_{x}^{'} = m_{p} a_{x}^{W} + Q_{x} + R_{x} + F_{x} \\ P_{y}^{'} = R_{y} - F_{y} - m_{p} a_{y}^{W} \\ P_{z}^{'} = m_{p} g + m_{p} a_{z}^{W} + R_{z} - Q_{z} \end{matrix}

(9)

Q_{z} = \frac{1}{x_{PvD} + x_{DU}} [\begin{matrix} m_{p} g (x_{PvD} + x_{DW}) + R_{z} (x_{PvD} + x_{DU} + h_{P} + S_{R x}) \dots \\ + m_{p} a_{x}^{W} (z_{PvD} + z_{DW}) - R_{x} (z_{PvD} + z_{DU} + h_{P} - S_{R z}) \end{matrix}]

The tractor is then separated and the differential equations of motion for the ploughing unit in the longitudinal, transverse, and vertical directions are calculated.

(10)

(F_{q3} + F_{q4}) + (Y_{1} + Y_{2}) \sin δ + m_{T} g \sin θ - (F_{f 1} + F_{f 2}) \cos δ - (F_{f 3} + F_{f 4}) - P_{x} = m_{T} a_{x}^{T}

(11)

(F_{f1} + F_{f2}) \sin δ - (Y_{1} + Y_{2}) \cos δ - (Y_{3} + Y_{4}) - m_{T} g \cos θ \sin φ + P_{y} = m_{T} a_{y}^{T}

(12)

(Z_{1} + Z_{2} + Z_{3} + Z_{4}) - m_{T} g \cos θ \cos φ - P_{z} = m_{T} a_{z}^{T}

The roll, pitch, and yaw movements of the tractor body in the longitudinal, transverse, and vertical directions can be represented as follows:

(13)

(Z_{3} - Z_{4}) \cdot BH / 2 - (Y_{3} + Y_{4}) \cdot (R_{r} + h_{c}) + (m_{r} g \cdot \sin φ - m_{r} a_{y}) h_{r} \dots - P_{y} (h_{r} - z_{PvO}) = (J_{x r} + m_{r} h_{r}^{2}) \ddot{φ}

(14)

\begin{matrix} (Z_{3} + Z_{4}) \cdot x_{Or} - (Z_{1} + Z_{2}) \cdot x_{Of} + [(Y_{1} + Y_{2}) \sin δ + (F_{f1} + F_{f 2}) \cos δ] \cdot (R_{r} + h_{c}) - P_{x} (h_{r} - z_{PvO}) \dots \\ + P_{z} x_{PvO} - (F_{q3} + F_{q4} - F_{f3} - F_{f 4}) \cdot (R_{r} + h_{c}) + (m_{r} g \sin θ - m_{r} a_{x}) h_{r} = (J_{y} + m_{r} h_{r}^{2}) \ddot{θ} \end{matrix}

(15)

\begin{matrix} P_{y} x_{PmO} - (F_{f1} + F_{f 2}) \sin δ \cdot x_{Of} + (F_{f 1} \cdot - F_{f 2}) \cos δ \cdot BJ / 2 - (Y_{1} + Y_{2}) \cos δ \cdot x_{Of} \dots \\ + (Y_{2} - Y_{1}) \sin δ \cdot BJ / 2 + (Y_{3} + Y_{4}) \cdot x_{Or} + (F_{q4} - F_{q3} + F_{f3} - F_{f4}) \cdot BH / 2 = J_{z} \ddot{γ} \end{matrix}

The roll motion of the front axle can be expressed as follows:

(16)

(Z_{1} - Z_{2}) \cdot BJ / 2 - (Y_{1} + Y_{2}) \cos δ \cdot (R_{f} + h_{r}) - (m_{f} g \cdot \sin φ_{f} - m_{f} a_{y}) h_{f} - (F_{f 1} + F_{f 2}) \sin δ \cdot (R_{f} + h_{f}) = (J_{x f} + m_{f} h_{f}^{2}) {\ddot{φ}}_{f}

The drive wheel rotation can be expressed as follows:

(17)

T_{3} - F_{q3} r_{d3} - M_{f3} = J_{w} {\dot{w}}_{3}

(18)

T_{4} - F_{q4} r_{d 4} - M_{f 4} = J_{w} {\dot{w}}_{4}

Unlike a car, there is no suspension device between the tractor chassis and the wheels, so the tire is reduced to a simple radial element mainly consisting of a linear spring and damping. The radial stiffness and damping coefficients are used to describe the dynamic characteristics of the tire so that the tire vertical force can be expressed as follows:

(19)

Z_{i} = k_{i} (q_{i} - z_{i} - z_{0 i}) + c_{i} ({\dot{q}}_{i} - {\dot{z}}_{i} - {\dot{z}}_{0 i})

The change in displacement of the mass center is calculated based on the differential equations of the tractor motion z. We consider the pitch and tilt motion of the tractor and calculate the change in the vertical displacement of the four-wheel centers.

(20)

\{\begin{matrix} z_{1} = z - θ x_{Of} + φ_{f} \cdot BJ / 2 \\ z_{2} = z - θ x_{Of} - φ_{f} \cdot BJ / 2 \\ z_{3} = z + θ x_{Or} + φ \cdot BH / 2 \\ z_{4} = z + θ x_{Or} - φ \cdot BH / 2 \end{matrix}

This research uses the Brixius semi-empirical equation to analyze the tire-soil interaction mechanism. This model can effectively take into account the effects of wheel slip, wheel droop load, and soil parameters on tire driving force and rolling resistance [30]. The formula for calculating the driving force and rolling resistance of a tractor drive wheel is shown below.

(21)

F_{q} = [0.88 (1 - e^{- 0.1 B_{n}}) (1 - e^{- 7.5 SR}) + 0.04] \cdot Z

(22)

F_{f} = (\frac{1}{B_{n}} + 0.04 + \frac{0.5 SR}{\sqrt{B_{n}}}) \cdot Z

The formula for calculating the mobility number is:

(23)

B_{n} = \frac{CI b d}{Z} [\frac{1 + 5 (δ / h)}{1 + 3 (b / d)}]

In addition, the soil is subjected to shear deformation by the wheel action, and the wheel is subjected to lateral forces Y. Moreover, this force Y is influenced by the slip angle α and the vertical load of the wheel [31], [32].

(24)

Y = A \cdot (1 - e^{- B α}) \cdot Z

The slip angle of the tires during tractor-ploughing operations in the field is calculated as follows:

(25)

\{\begin{matrix} α_{1} = \arctan (\frac{v_{1} + x_{Of} {\dot{γ}}_{1}}{u_{1} - BJ / 2 \cdot {\dot{γ}}_{1}}) - δ_{1} \\ α_{2} = \arctan (\frac{v_{1} + x_{Of} {\dot{γ}}_{1}}{u_{1} + BJ / 2 \cdot {\dot{γ}}_{1}}) - δ_{2} \\ α_{3} = \arctan (\frac{v_{1} - x_{Or} {\dot{γ}}_{1}}{u_{1} - BH / 2 \cdot {\dot{γ}}_{1}}) \\ α_{4} = \arctan (\frac{v_{1} - x_{Or} γ_{1}}{u_{1} + BH / 2 \cdot {\dot{γ}}_{1}}) \end{matrix}

3.2. Electric tractor subsystem control method

Effective use of the electric tractor’s subsystems can improve traction efficiency and reduce the energy consumption of the electric tractor. Based on the independent drive of the wheel-side motor, adopting a suitable torque control method for the drive wheel can effectively solve the issues due to the significant difference between the left and right tires coming into contact with the ground, which result in lower traction efficiency and increased energy consumption. Based on the direct-drive electro-hydraulic suspension system and the battery ballast system, a reasonable joint control method can effectively make it possible to balance the unit tillage quality with efficient traction—a problem that cannot be solved by traditional tractor traction control.

3.2.1. Active control method for drive-wheel torque

Tractor ploughing units often operate in fields where the two wheels are positioned on soil with entirely different soil characteristics. In such a situation, the vertical load on the two wheels will change, resulting in a difference in the slip of the two wheels, which requires different driving forces to be achieved on the two wheels. This situation cannot be adequately addressed by a conventional diesel tractor and can lead to a rapid reduction in traction efficiency, a sudden increase in fuel consumption, and a surge in particulate and gas emissions. Therefore, to address the problem of reduced traction efficiency and increased energy consumption due to a significant difference in the contact between the left and right tires and the ground during tractor operation in the field, we propose an active control method for the tractor’s drive-wheel torque based on optimal slip. This method consists of two main parts: a solution for the optimal slip of the drive wheel and active torque control. Details are provided below.

3.2.2. Optimal slip solution method for drive wheels

When the tractor operates at constant speed, the total tractive force provided by the tractor is equal to the longitudinal force exerted on the tractor by the plough implement. The wheel traction force distribution ratio β is determined as follows:

(26)

β = \frac{F_{t3}}{F_{t3} + F_{t4}} = \frac{F_{t3}}{P_{x}}

Eq. (27) is further used to calculate the value of the wheel slip:

(27)

F_{t i} = F_{q i} - F_{f i} = [0.88 (1 - e^{- 0.1 B_{n i}}) (1 - e^{- 7.5 {SR}_{i}}) - \frac{1}{B_{n i}} + 0.04 + \frac{0.5 {SR}_{i}}{\sqrt{B_{n i}}}] Z_{i}

The wheel slip, tractor slip, and traction energy efficiency are calculated in order to evaluate the slip state of the driving wheels and the traction energy consumption of the tractor when ploughing. The slip of the driving wheel is calculated as follows:

(28)

{SR}_{i} = \frac{w_{i} \times r_{d i} - u_{w i}}{w_{i} \times r_{d i}}

For a tractor with rear-wheel independent drive, the slip efficiency of the tractor is calculated as follows:

(29)

SE = 1 - \frac{{SR}_{3} \times F_{q 3} \times u_{3} + {SR}_{4} \times F_{q 4} \times u_{4}}{F_{q 3} \times u_{3} + F_{q 4} \times u_{4}}

The traction efficiency of an electric tractor when ploughing is defined as the ratio of the ploughing power to the motor output power, which can be expressed as follows:

(30)

TE = \frac{P_{plo}}{P_{m 3} + P_{m 4}} = \frac{1}{\frac{1}{9.55} (n_{m 3} \times T_{m 3} + n_{m 4} \times T_{m 4})}

We add tractor slip and traction efficiency to the objective optimization function for determining the optimal wheel slip.

(31)

f (β) = λ \cdot SE (β) + (1 - λ) \cdot TE (β), λ \in (0, 1)

When the value of Eq. (31) is maximized, the slip rotation of the two drive wheels is optimal, and the distribution of traction between the left and right wheels is also optimal.

3.2.3. Active control method for drive wheel torque based on sliding theory

The drive system solution proposed in this paper enables the left and right wheels to be driven independently. The torque control of the two drive motors can be achieved separately and is eventually iteratively adjusted to achieve the optimum slip rotation calculated in the previous section. This part of the calculation assumes that the speed and rolling radius of the left and right drive wheels are the same.

Therefore, the optimal slip ratio ρ of the two driving wheels when the tractor is operating in the field can be expressed as follows:

(32)

ρ = \frac{{SR}_{3opt}}{{SR}_{4opt}} = \frac{(ω_{3} r_{d 3} - u_{3}) / ω_{3} r_{d 3}}{(ω_{4} r_{d 4} - u_{4}) / ω_{4} r_{d 4}} = \frac{1 - u / ω_{3} r_{d}}{1 - u / ω_{4} r_{d}}

The sliding mode switching function designed for this study is shown below.

(33)

s = 1 - u / ω_{3} r_{d} - ρ (1 - u / ω_{4} r_{d})

Further solving the equation yields the following:

(34)

\frac{u}{ω_{3}^{2} r_{d}} {\dot{ω}}_{3} - ρ \frac{u}{ω_{4}^{2} r_{d}} {\dot{ω}}_{4} = - ξ \cdot sgn (s) - k s

It should be noted that we use sliding mode control based on the exponential convergence law—that is, $ \dot{s}=-\xi \cdot \operatorname{sgn}(s)$, ξ > 0, k > 0. The Lyapunov function is defined as $ V=\frac{1}{2} s^{2}$. The final first-order derivative of it yields $ \dot{V}=\dot{s} s=-\xi \cdot \operatorname{sgn}(s) s-k s^{2}$. Finally, the differential equations of motion for the tractor transverse pendulum and front axle sway are calculated to give the drive motor torque:

(35)

\{\begin{matrix} T_{m 3} = \frac{ω_{3}^{2} ω_{4}^{2} r_{d}}{(ω_{3}^{2} + ρ ω_{4}^{2}) i_{g} η_{t}} [\frac{u}{ω_{3}^{2}} (F_{q 3} + F_{f 3}) + \frac{ρ u}{ω_{4}^{2}} (T_{m} \frac{i_{g} η_{t}}{r_{d}} - (F_{q 4} + F_{f 4})) - J_{w} ξ g sgn (s) - J_{w} k s] \\ T_{m 4} = T_{req} - T_{m 3} \end{matrix}

3.2.4. A joint control method for traction force and front- and rear-axle loads

Traditional tractor traction control cannot balance the unit tillage quality with efficient traction. Therefore, we propose a joint control method for the traction force and the rear- and front-axle loads during electric tractor ploughing operation based on joint adjustment of the tillage depth and battery position. Details are provided below.

3.2.4.1. Effect of rear-axle loading on traction performance

First, the rear axle’s static load factor λ₀ is defined as the ratio of the static load on the rear axle to the total weight of the tractor:

(36)

λ_{0} = \frac{m_{T} g \cdot x_{Of} / L}{m_{T} g} = \frac{x_{Of}}{L}

Further calculations are performed to determine the front- and rear-axle dynamic loads as a function of the static load factor on the rear axle and tillage resistance:

(37)

W_{f} = m_{T} g \cos θ (1 - λ_{0}) + (m_{W} g + R_{V} - Q_{z}) (1 - λ_{0}) + [\begin{matrix} m_{T} g \sin θ (z_{Or} + R_{r}) - m_{W} g \cdot x_{W} - \dots \\ R_{V} (x_{P} + S_{RH}) + Q_{z} \cdot x_{U} + R_{H} (h_{P} - S_{RV}) \end{matrix}] / L

(38)

W_{r} = m_{T} g \cos θ \cdot λ_{0} + (m_{W} g + R_{V} - Q_{z}) λ_{0} + [\begin{matrix} - m_{T} g \sin θ (z_{Or} + R_{r}) + m_{W} g \cdot x_{W} + \dots \\ R_{V} (x_{P} + S_{RH}) - Q_{z} \cdot x_{U} - R_{x} (h_{P} - S_{RV}) \end{matrix}] / L

Therefore, the coefficient of the dynamic load on the front axle is calculated for tractor-ploughing operations:

(39)

CDLF = \frac{W_{f}}{(W_{f} + W_{r})} = \frac{m_{T} g \cos θ (1 - λ_{0}) + (m_{W} g + R_{V} - Q_{z}) (1 - λ_{0}) + [\begin{matrix} m_{T} g \sin θ (z_{Or} + R_{r}) - m_{W} g \cdot x_{W} - \dots \\ R_{V} (x_{P} + S_{RH}) + Q_{z} \cdot x_{U} + R_{H} (h_{P} - S_{RV}) \end{matrix}] / L}{m_{T} g \cos θ + m_{W} g + R_{V} - Q_{z}}

Next, the variation in the tractor traction performance with several parameters is calculated, as shown in Fig. 7.

3.2.4.2. Multi-objective particle swarm optimization-based method to determine the optimal location for the battery

In active ballast mode, determining the target position of the battery is key. Here, we focus on the three aspects of traction efficiency, wheel slip, and front-axle dynamic load factor to improve the tractor’s traction performance. Among other factors, extensive tests have shown that, to ensure the tractor’s safety during traction operations, the front-axle dynamic load distribution ratio should be at least 0.2 [33].

We describe the motion of the battery position back and forth to improve the traction performance of an electric tractor as a multi-objective function optimization problem; the specific multi-objective optimization model for the tractor’s traction performance is shown below:

(40)

\{\begin{matrix} P : max [g_{1} (X), g_{2} (X)] \\ s .t . \{\begin{matrix} lb \leq X \leq ub \\ j (X) \geq 0 \end{matrix} \end{matrix}

where each sub-objective function f_k (X), (k = 1, 2) in P is maximized as far as possible.

(41)

\{\begin{matrix} g_{1} (X) = η_{D} \cdot η_{M} \times \frac{F_{T}}{0.75 (1 - e^{- 0.3 C_{n} SR})} \times (1 - SR) \\ g_{2} (X) = 1 - SR \\ j (X) = \frac{W_{f}}{G + Δ BW} - 0.2 \end{matrix}

where f₁(x) and f₂(x) represent the relationship between traction efficiency, slip efficiency, and the rear axle static load factor; and j(X) represents the bounded relationship for the dynamic load factor of the tractor’s front axle.

3.2.4.3. A joint control method for traction force and front- and rear-axle loads

The battery ballast and electro-hydraulic suspension systems in the electric tractor chassis system designed in this study hold potential. However, the battery ballast system uses an electric actuator to change the battery’s position, which is limited by its great weight and cannot move at a high speed of 20 mm∙s⁻¹. In this case, if an electro-hydraulic suspension system is used, the tillage depth and battery position can be jointly adjusted. The electro-hydraulic suspension system can be directly adjusted to align with the tillage depth when the tractive effort varies considerably. When the tractive effort does not vary much, the battery position can be changed using the battery ballast system, which ultimately adjusts the optimum axle load in real time. This idea ensures both the tillage depth and the traction performance.

Therefore, we use the developed chassis system configuration and propose a joint control method for the traction and the rear- and front-axle loads during electric tractor ploughing operations based on joint adjustment of the tillage depth and battery position. The control principle is shown in Fig. 8. This control method requires real-time measurements of the traction resistance, the actual battery position, the target battery position, and the working depth.

The tractor only controls the tractive force when the tractive force varies beyond a set range. When the battery position deviation (BPD) is within the set range and the tractive force varies within the set range, the tractor only controls the active ballast. When the BPD is outside the set range and the tractive force varies within the set range, the tractor controls both the active ballast and the tractive force. The three main modes are as follows:

(1) In the draught force control mode, the traction resistance of the tractor is measured in real time by a traction force sensor, and the controller controls the extension of the hydraulic lifting cylinder to adjust the tillage depth and eventually change the traction resistance. When the draught force deviation (DFD) is greater than the draught force deviation threshold (DFDT) and the actual draught force (DF) is greater than the draught force reference (DFR), the controller controls the lifting of the implement through the hydraulic cylinder to reduce the tillage depth and traction resistance. When the DFD is greater than the DFDT and the actual DF is less than the DFR, the controller controls the lowering of the implement through a hydraulic cylinder to increase the tillage depth and traction resistance.

(2) In the active ballast control mode, the real-time battery position is measured indirectly via a potentiometer, and the controller calculates the BPD to adjust the battery position in real time. When the BPD is greater than the battery position deviation threshold (BPDT) and the battery target position (BTP) is greater than the battery actual position (BAP), the BTP is behind the BAP, and the controller moves backward using an electric actuator. When the BPD is greater than the BPDT and the BTP is less than the BAP, the BTP is in front of the BAP, and the controller moves forward using the motorized actuator.

(3) In the joint control mode, the controller realizes joint control of the traction and the front and rear loads. On the one hand, the controller analyzes the tractor’s traction resistance and threshold value and adjusts the tillage depth in real time; on the other hand, the controller adjusts the battery position to achieve optimal front and rear axle load distribution.

4. Experiments

4.1. Test prototypes

Based on the electric tractor chassis system solution, a 14.7-kW electric tractor prototype was developed, and a field test platform was built, as shown in Fig. 9. The test prototype’s length, width, and height dimensions were 2650, 1200, and 1280 mm, respectively. The main components and operating parameters of the test prototype are shown in Table 5.

An acquisition system to obtain information on the tractor’s field-operation conditions was built. The test system can acquire digital and analogue voltage/current quantities and controller area network (CAN) telegrams. The encoder collects the speed of the drive motor and transmits it via the CAN bus. In addition, a position sensor is mounted on the hydraulic lifting cylinder and can be converted to measure the tillage depth. A traction force sensor is mounted at the lower tie bar suspension point, allowing direct measurement of traction resistance. A potentiometer is built into the electric pushrod and measures the pushrod extension in real time, which is ultimately converted into the battery’s position on the slide. The actual speed is measured directly by a Doppler low-speed radar mounted on the frame.

Before carrying out the ploughing test, the soil’s cone index (CI; i.e., soil compactness) must be measured first. Soil compactness in the depth range of 0-25 cm was measured using the five-point sampling method; the results are shown in Table 6.

4.2. Field tests

Field tests were conducted to verify the effectiveness of the subsystems included in the electric tractor and the accuracy of the control methods of each subsystem.

4.2.1. Testing the active drive-wheel torque control

The aim of this ploughing test was to verify the accuracy and effectiveness of the active control method for the driving wheel torque of the electric tractor. The control group was an average control method for the distribution of the drive-wheel torque. The test program was as follows:

Mode D1: Active torque-distribution control mode. The motor control method of the electric tractor based on active torque distribution can distribute different torques to the left and right drive wheels according to the contact situation between the left and right wheels and the ground.

Mode D2: Average torque-distribution control mode. The torque is equally distributed between the left and right drive motors, simulating the characteristics of a conventional tractor whose torque cannot be controlled independently.

In addition, the electric tractor was mounted on a single-share plough at 5 km∙h⁻¹ (within 0.2 km∙h⁻¹), and the suspension operated in the traction control mode (target tractive force of 3500 N) to ensure consistent traction resistance in the ploughing operations. The soil compactness was measured using an SC-900 soil compactness meter. The final soil parameters for the left- and right-wheel contact were CI = 588 kPa for the unploughed field and CI = 1523 kPa for the furrow, respectively.

4.2.2. Testing the joint control of the traction and ballast

The aim of this ploughing test was to verify the accuracy and effectiveness of the joint control method for the traction force and the front- and rear-axle loads for the electric tractor, based on the combined adjustment of tillage depth and battery position. The control group was a ploughing test with only traction control of the suspension system. The test protocol was as follows:

Mode F1: Traction control mode. The electric tractor uses only the traction control method, there is no ballast control, and the test soil is stubble land. The tractive force range is [3200 N,3800 N], the tractive force deviation threshold is 50 N, and the tractive force reference value is 3500 N.

Mode F2: Joint control mode. The electric tractor uses the joint control method for the tractive force and the ballast. The test soil is stubble land. The tractive force deviation threshold is 50 N, the tractive force reference value is 3500 N, the tractive force range is [3200 N,3800 N], the BPD range is [-50 mm, 50 mm], and the BPDT is 5 mm.

The ploughing test was carried out using a single plough with an operating speed of 3.6 km∙h⁻¹ (within 0.2 km∙h⁻¹). The left wheel was in contact with the untilled surface (CI = 588 kPa) and the right wheel was in contact with the furrow (CI = 1523 kPa).

5. Results and discussion

5.1. Testing results for the active drive-wheel torque control

This section verifies the accuracy and effectiveness of the active control method for the electric tractor drive-wheel torque proposed in this paper in terms of key aspects such as motor output torque, drive-wheel slip, and tractor traction efficiency. The output torque data for the left and right drive motors during the test is shown in Fig. 10.

Fig. 10(a) shows that, in the active torque control mode, the average torque values of the left and right drive wheels are 13.68 and 18.95 N∙m, respectively, and the left motor torque is significantly lower than that of the right motor. This situation occurs because, during the tractor ploughing operation, the left wheel is on unploughed ground and the right wheel is on ploughed ground. The tractor is tilted to the right side, and the vertical load of the right wheel is greater than the vertical load of the left wheel. At this time, the driving torque of the right wheel should be greater than that of the left wheel. Fig. 10(b) shows that, in the average torque control mode, the average values of the left and right drive motors are 17.55 and 17.83 N∙m, respectively, and are basically the same. This phenomenon proves that our active torque control method can allocate different torques to the left and right drive motors, following the optimal wheel slip target.

The results of the drive-wheel slip and tractor slip during the test are shown in Fig. 11.

It is worth stating that the volatility of the wheel slip in the active torque distribution mode in Fig.11(c) is more significant than that in the average torque distribution mode. In the average torque distribution mode, the torques of the left and right motors are the same and remain stable, as shown in Fig. 10(b), making the wheel speeds of the left and right sides stable. In the active torque distribution mode, the torque of the right motor is more significant than that of the left motor, and the torques of the motors on both sides vary with changes in the traction resistance, vertical tire load, soil conditions, and other factors.

Based on the ploughing power of the electric tractor in the ploughing test and the drive system’s input power, the unit’s traction efficiency was calculated, as shown in Fig. 12.

Fig. 12(b) shows that the active torque control mode enables the electric tractor to produce 3.493 kW of ploughing power during the same test period, while the average torque control mode enables the electric tractor to produce 3.048 kW of ploughing power. Thus, the active torque control mode ensures the electric tractor can achieve excellent traction performance. Fig. 12(c) shows that the average values of the traction efficiency of the electric tractor in the active and average torque-distribution control modes are 51.17% and 46.40%, respectively, with a 10.28% increase in traction efficiency in the active torque distribution mode compared with the average torque-distribution control. In summary, the wheel slip and traction efficiency under the active torque-distribution control method are better than those under the average torque-distribution control mode.

5.2. Testing the joint control of traction and ballast

This section focuses on the key aspects of the coefficient of the dynamic load on the front axle, the draught force, the tillage depth, the drive-wheel slip, and the unit traction efficiency to verify the accuracy and effectiveness of the joint control method proposed in this paper for the electric tractor ploughing unit.

The battery actual position (BAP) and the coefficient of the dynamic load on the front axle during the test are shown in Fig. 13.

In the active ballast control mode, the rear axle’s static load factor is varied by adjusting the longitudinal battery position in order to optimize the traction performance of the tractor plough unit. As shown in Fig. 13(b), there is no adjustment of the front battery position in this mode, while the dynamic loads of the front and rear axle vary with the traction resistance. Throughout the test, the average values of the efficient of the dynamic load on the front axleare 0.2279 and 0.2500 for the active ballast and no-ballast control modes, respectively; as these are greater than 0.2 s, they meet the handling stability requirements of the electric tractor. The mean value of the coefficient of the dynamic load on the front axle is smaller in the active ballast control mode than in the no-ballast mode, which ensures the driving stability of the unit while shifting more of the front-axle load to the rear axle to improve the drive-wheel load and optimize the traction performance of the tractor.

In addition, Fig. 13(b) shows that there is a discrepancy between the actual position of the BBS and the target position at some moments. This is because an electric actuator in the BBS powers the battery pack movement. The speed limitation of the movement of the electric actuator prevents the battery pack from reaching the target position immediately, which leads to the phenomenon of a discrepancy between the actual position of the BBS and the target position of the BBS at the moments when the target position of the BBS changes abruptly. It is worth explaining that the battery pack position adjustment is performed only when the draught force exceeds the set range, as shown in Fig. 8. Therefore, the frequency of battery position regulation is low. This difference between the BBS target and actual positions is allowed to exist.

The draught force and tillage depth of the electric tractor during the test are shown in Fig. 14.

As shown in Fig. 14, the draught force increases as the tillage depth increases and decreases as the tillage depth decreases. The draught force in both modes fluctuates above and below the target set value of 3.500 kN, and the average draught forces in the traction control and joint control modes are 3.505 kN and 3.532 kN, respectively. Both control methods achieve the target draught force control.

An analysis of the tillage depth data shows that the average tillage depth in the traction control mode is 18.47 cm, with a tillage depth variation range of 11.6-25.3 cm, a tillage depth standard deviation of 1.67, and a variation coefficient of tillage depth stability of 9.04%. The average tillage depth in the joint control mode is 16.78 cm, with a tillage depth variation range of 12.3-21.8 cm, a tillage depth standard deviation of 1.11, and a variation coefficient of tillage depth stability of 6.61%. The standard deviation of tillage depth and the variation coefficient of tillage depth stability in the joint control mode are lower than those in the traction control mode. The variation coefficient of tillage depth stability in both modes is less than 10%, which meets the quality index of the ploughing operation. In summary, both control strategies achieve control of the target traction, while the tillage depth stability under the traction-ballast joint control method is better than that under the traction control method.

The electric tractor slip during the test is shown in Fig. 15. As shown in Fig. 15, the mean values of the tractor slip in the traction and joint control modes are 14.35% and 12.19%, respectively. Compared with the traction control mode, the slip of the tractor in the joint control mode decreased by 15.05%. Therefore, the effectiveness of our method for the joint control of traction and ballast in order to reduce the tractor slip is verified.

The traction efficiency of the tractor during the test is shown in Fig. 16.

Fig. 16 shows that the average tractor traction efficiencies in the traction control and the joint control modes are 46.72% and 48.45%, respectively. Compared with the traction control mode, the traction efficiency in the joint control mode increases by 3.7%. The total energy consumption of the drive motor in the joint control mode (561.4 W·h) is reduced by 4.9% compared with the total energy consumption in the traction control method (590.6 W·h) throughout the test. The tractor’s slip and traction efficiency in the joint control mode are better than those in the traction control mode. Thus, the joint control method for the traction and ballast proposed in this paper effectively reduces the tractor slip, improves tractor traction efficiency, and improves tillage depth uniformity.

6. Conclusions

To reduce greenhouse-gas and particulate emissions from the operation of agricultural machinery and to improve operational efficiency, a purely electric wheel-side drive tractor was developed. The electric tractor’s chassis system was designed to improve the unit’s traction and agronomic performance in terms of drive control, axle load distribution, and operation control. A method for optimizing the ploughing performance and the efficient traction control of the electric tractor based on three subsystems was proposed. A 14.7-kW electric tractor prototype was developed, and a field-testing platform for ploughing was built. Finally, ploughing tests were carried out. The main conclusions are as follows:

(1) This study proposed a wire-controlled chassis solution for electric tractors, including a motor drive system, battery ballast system, and electro-hydraulic suspension system. Final trial production and assembly of the electric tractor was carried out. A field-testing platform for the ploughing unit was built, and ploughing tests were carried out.

(2) In the ploughing tests, the active control method for torque distribution ensured a 14.83% reduction in tractor slip and a 10.28% increase in traction efficiency compared with the average control mode for torque distribution. The method proposed in this study effectively reduced the slip and improved the traction efficiency of the electric tractor.

(3) In the ploughing tests, the joint control method for the traction and ballast ensured a smaller standard deviation in the tillage depth and variation coefficient of tillage stability in comparison with the conventional traction control mode. The joint control mode increased the traction efficiency by 3.7%, reduced the slip by 15.05%, and reduced the total energy consumption of the drive motor by 4.9%. Therefore, the joint control method proposed in this paper effectively reduces the slip and increases the tractor traction efficiency while improving the ploughing stability.

The joint control method for the tractor unit proposed in this paper combines the control of the battery ballast system with that of the suspension system; however, it is still necessary to consider the effect of operating speed on tillage resistance. In addition, our optimization study on the traction performance of the unit did not consider change in the efficiency of the drive system. Therefore, in future research, it will be necessary to study not only a drive control method that can achieve optimal efficiency of the drive motor and tire traction efficiency but also the use of the drive system to regulate the operating speed to control the tillage resistance. Finally, the purely electric wheel-side drive tractor and the sub-system control method for traction performance optimization developed in this study will help to improve the operational quality and traction efficiency of electric tractors under complex soil conditions.

Acknowledgments

This work was supported by the National Key Research and Development Plan of China (2022YFD2001201), the Beijing Postdoctoral Research Foundation (2023-ZZ-112), the National Natural Science Foundation of China (52272444), and the Natural Science Foundation of Jiangsu Province (BK20230548).

Compliance with ethics guidelines

Chang- Kai Wen, Wen Ren, Qing-Zhen Zhu, Chun-Jiang Zhao, Zhen-Hao Luo, Sheng-Li Zhang, Bin Xie, and Zhi-Jun Meng declare that they have no conflict of interest or financial conflicts to disclose.

Nomenclature

a_x: Absolute acceleration component on the x-axis (m·s⁻²)

a_y: Absolute acceleration component on the y-axis (m·s⁻²)

a_z: Absolute acceleration component on the z-axis (m·s⁻²)

A: Empirical coefficient

b: Tire width (m)

B: Empirical coefficient

B_n: Mobility number

BH: Rear wheel tread (m)

BJ: Front wheel tread (m)

c_i: Tire vertical damping factor (kN·s·m⁻¹)

CDLF: Coefficient of the dynamic load on the front axle

CI: Cone index (kPa)

d: Overall tire diameter (m)

f₁(x): Minimization functions for the rated rotary speed

f₂(x): Minimization functions for the maximum speed

f₃(x): Minimization functions for the peak torque

f₄(x): Minimization functions for the transmission ratio

F(x): Optimization objective function

F_e: Rated tractive effort (N)

F_f: Wheel rolling resistance (N)

F_q: Wheel driving force (N)

F_q3: Driving force of the left-hand wheel (N)

F_q4: Driving force of the right-hand wheel (N)

F_t: Net wheel traction force (N)

F_t3: Traction force of the left-hand drive wheel (N)

F_t4: Traction force of the right-hand drive wheel (N)

F_x: Ploughing traction resistance (N)

F_z: Wheel load (N)

g: Gravitational acceleration (m·s⁻¹)

h_c: Distance from tractor gravity center to x-axis (m)

h_f: Distance from articulation point to gravity center of front axle (m)

h_r: Distance from center line of rear axle to x-axis (m)

i_g: Transmission ratio

J_w: Rotating inertia of driving wheel (kg·m²)

J_x_r: Rotating inertia of tractor body around mass centroid axis in roll direction (kg·m²)

J_y: Rotating inertia of tractor around mass centroid axis in pitch direction (kg·m²)

J_z: Rotating inertia of tractor around mass centroid axis in yaw direction (kg·m²)

k_c,k_φ: Pressure-sinkage parameters

k_i: Tire radial stiffness (kN·m⁻¹)

lbMinimum values of X

l_i: Weighting factor of each optimization objective

L: Wheelbase (m)

m_f: Front axle mass (kg)

m_r: Tractor mass except for front axle (kg)

m_T: Gross tractor mass (kg)

m_p: Plough mass (kg)

m_W: Implement mass (kg)

M_f: Rolling resistance moment (N·m)

n: Sinkage exponent

n_max: Maximum speed (r∙min⁻¹)

n_e: Rated speed (r∙min⁻¹)

n_m: Output speed of the drive motor (r∙min⁻¹)

p: Tire inflation pressure (MPa)

P: Maximization of the multi-objective function vector

P_plo: Ploughing power (kW)

P_m: Drive motor output power (kW)

P_x: Longitudinal force of the tractor on the implement (N)

P_y: Lateral force of the tractor on the implement (N)

P_z: Vertical force of the tractor on the implement (N)

q_i: Vertical displacement variation of the ground (m)

Q_z: Braced force of ground to the depth-limiting wheel (N)

r_d: Wheel dynamic rolling radius (m)

R_H: Horizontal plowing resistance (N)

R_r: Rear wheel rolling radius (m)

R_V: Vertical plowing resistance (N)

R_θ: Pitch transformation matrices

R_γ: Yaw transformation matrices

R_φ: Roll transformation matrices

s: Sliding mode switching function

s₀: Tire radial deformation (m)

SE: Slip efficiency

SR: Wheel slip

S_RH: Horizontal distance from the plow tip to the point of total plowing resistance (m)

S_R_x: Horizontal distance from the point of action of the resistance of the plow to the plow tip P (m)

S_RV: Vertical distance from the plow tip to the point of total plowing resistance (m)

t: Time (s)

T: Driving torque (N·m)

T_e: Rated torque (N·m)

T_m: Driving motor output torque (N·m)

T_max: Maximum torque (N·m)

TE: Traction efficiency

ub: Maximum values of X

u: Tractor longitudinal speed (m·s⁻¹)

u_T: Longitudinal speed of the tractor’s center of mass (m·s⁻¹)

u_w_i: Longitudinal speed of the driving wheel central (m·s⁻¹)

v: Tractor lateral speed (m·s⁻¹)

v_T: Lateral speed of the tractor’s center of mass (m·s⁻¹)

v_max: Maxmium speed (m·s⁻¹)

w: Tractor vertical speed (m·s⁻¹)

w_i: Drive wheel rotation angular speed (rad·s⁻¹)

w_T: Vertical speed of the tractor’s center of mass (m·s⁻¹)

W_f: Dynamic load on the front axle (N)

W_r: Dynamic load on the rear axle (N)

x: Number of optimization variable

x_b: Location of the front power battery (mm)

x_DU: Horizontal distance from the lower suspension point D to depth limit wheel center U (m)

x_DW: Horizontal distance from the lower suspension point D to the center of gravity W of the plow (m)

x_Of: Distance from the center of mass to the front axle (m)

x_Or: Distance from the center of mass to the rear axle (m)

x_p: Horizontal distance from tractor center of mass to plow tip (m)

x_PvD: Horizontal distance from the longitudinal center P of the suspension rod to the lower suspension point D (m)

x_PvO: Horizontal distance from point P to the center of mass of the tractor in the longitudinal view (m)

x_PmO: Horizontal distance from point P to the center of mass of the tractor in the vertical view (m)

x_U: Horizontal distance from the center of mass of the tractor to the center of the depth limiting wheel (m)

Y_i: Tire lateral force (N)

z₀_i: Soil sinkage under the vertical reaction force of the tire (m)

z_DU: Vertical distance from the lower suspension point D to limit wheel center U (m)

z_DW: Vertical distance from the lower suspension point D to the center of gravity W of the plow (m)

z_i: Vertical displacement of the wheel center (m)

z_Or: Vertical distance from the center of mass of the tractor to the center of the drive wheel (m)

z_PvD: Vertical distance from the longitudinal center P of the suspension rod to the lower suspension point D (m)

z_PvO: Vertical distance from point P to the center of mass of the tractor in the longitudinal view (m)

Z_i: Tire vertical force (N)

α: Tire side slip angle (rad)

β: Wheel traction force distribution ratio

γ: Tractor yaw angle (rad)

δ: Front wheel steering angle (rad)

Δt: Variation of time (s)

ΔBW: Weight of the tractor’s rear axle counterweight

η_D: Drive system efficiency

η_M: Mechanical efficiency of transmission system

η_t: Tractive efficiency

θ: Tractor pitch angle (rad)

k: Constant

λ: Weight coefficient

λ₀: Rear axle’s static load factor

ξ: Constant

ρ: Optimal slip ratio

φ: Tractor roll angle (rad)

φ_f: Front axle roll angle (rad)

∑F_x: Resultant longitudinal external tractor force (N)

∑F_y: Resultant lateral external tractor force (N)

∑F_z: Resultant vertical external tractor force (N)

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	M.J. Brear. Prospects of reciprocating engines and fuels. Engineering, 5 (3) (2019), pp. 395-396.

[2]	P. Ni, X. Wang, H. Li. A review on regulations, current status, effects and reduction strategies of emissions for marine diesel engines. Fuel, 279 (2020), Article 118477.

[3]	S. Ushakov, H. Valland, V. Æsøy. Combustion and emissions characteristics of fish oil fuel in a heavy-duty diesel engine. Energy Convers Manage, 65 (2013), pp. 228-238.

[4]	K. Kendall, S. Ye, Z. Liu. The hydrogen fuel cell battery: replacing the combustion engine in heavy vehicles. Engineering, 21 (2023), pp. 39-41.

[5]	R. Dagiliūtė, R. Juknys. Eco-efficiency: trends, goals and their implementation in Lithuania. J Environ Eng Landsc Manage, 20 (4) (2012), pp. 265-272.

[6]	C. Wen, S. Zhang, B. Xie, Z. Song, T. Li, F. Jia, et al. Design and verification innovative approach of dual-motor power coupling drive systems for electric tractors. Energy, 247 (2022), Article 123538.

[7]	D. Llewellyn. Does global agriculture need another green revolution?. Engineering, 4 (4) (2018), pp. 449-451.

[8]	D. Ganesh, P.R. Ayyappan, R. Murugan. Experimental investigation of iso-butanol/diesel reactivity controlled compression ignition combustion in a non-road diesel engine. Appl Energy, 242 (2019), pp. 1307-1319.

[9]	X. Hou, X. Zhang, S. Huang, P. Xu, J. Shen. Measurement of engine performance and maps-based emission prediction of agricultural tractors under actual operating conditions. Measurement, 222 (2023), Article 113637.

[10]	S. Zhang, C. Wen, W. Ren, Z. Luo, B. Xie, Z. Zhu, et al. A joint control method considering travel speed and slip for reducing energy consumption of rear wheel independent drive electric tractor in ploughing. Energy, 263 (2023), Article 126008.

[11]	C. Wen, B. Xie, Z. Li, Y. Yin, X. Zhao, Z. Song. Power density based fatigue load spectrum editing for accelerated durability testing for tractor front axles. Biosyst Eng, 200 (2020), pp. 73-88.

[12]	C. Wen, B. Xie, Z. Song, Z. Yang, N. Dong, J. Han, et al. Methodology for designing tractor accelerated structure tests for an indoor drum-type test bench. Biosyst Eng, 205 (2021), pp. 1-26.

[13]	S. Zhang, W. Ren, B. Xie, Z. Luo, C. Wen, Z. Chen, et al. A combined control method of traction and ballast for an electric tractor in ploughing based on load transfer. Comput Electron Agric, 207 (2023), Article 107750.

[14]	F. Bauer, P. Porteš, A. Polcar, J. Čupera, M. Fajman. Differences in the wheel loads and contact pressure of the in-furrow and on-land rear tractor tyres with mounted and semi-mounted ploughs. Soil Tillage Res, 215 (2022), Article 105190.

[15]	J. Wang, S. Gao, K. Wang, Y. Wang, Q. Wang. Wheel torque distribution optimization of four-wheel independent-drive electric vehicle for energy efficient driving. Control Eng Pract, 110 (2021), Article 104779.

[16]	W. Li, H. Du, W. Li. Four- wheel electric braking system configuration with new braking torque distribution strategy for improving energy recovery efficiency. IEEE Trans Intell Transp Syst, 21 (1) (2019), pp. 87-103.

[17]	S. Mashrouteh, A. Khajepour, A. Kasaiezadeh, E. Esmailzadeh, S.K. Chen, B. Litkouhi. Multi-actuation controller for performance vehicles: optimal torque allocation and active aerodynamic. IEEE Trans Vehicular Technol, 71 (3) (2022), pp. 2721-2733.

[18]	S. Wu, Y. Li, Y. Guan, T. Liu, C. Che. Distribution method of automotive torque for hub motor considering energy consumption optimization. Int J Automot Technol, 24 (3) (2023), pp. 913-928.

[19]	T. Shen, G. Yin, Y. Ren, F. Wang, B. Feng, J. Liang. Stability and maneuverability guaranteed torque distribution strategy of DDEV in handling limit: a novel LSTM-LMI approach. IEEE/ASME Trans Mechatron, 27 (6) (2022), pp. 5647-5658.

[20]	R.R. Melo, F.L. Antunes, S. Daher, H.H. Vogt, D. Albiero, F.L. Tofoli. Conception of an electric propulsion system for a 9 kW electric tractor suitable for family farming. IET Electr Power Appl, 13 (12) (2019), pp. 1993-2004.

[21]	R.R. de Melo, F.L. Tofoli, S. Daher, F.L.M. Antunes. Wheel slip control applied to an electric tractor for improving tractive efficiency and reducing energy consumption. Sensors, 22 (12) (2022), p. 4527.

[22]	Janulevičius G. Pupinis J. Lukštas V. Damanauskas V. Kurkauskas. Dependencies of the lead of front driving wheels on different tire deformations for a MFWD tractor. Transport, 32 (1) (2017), pp. 23-31.

[23]	Moinfar G. Shahgholi Y.A. Gilandeh T.M. Gundoshmian. The effect of the tractor driving system on its performance and fuel consumption. Energy, 202 (2020), Article 117803.

[24]	Janulevičius V. Damanauskas. How to select air pressures in the tires of MFWD (mechanical front-wheel drive) tractor to minimize fuel consumption for the case of reasonable wheel slip. Energy, 90 (2015), pp. 691-700.

[25]	Janulevičius K. Giedra. Tractor ballasting in field work. Mechanics, 73 (5) (2008), pp. 27-34.

[26]	S. Kumar, M.T. Noori, K.P. Pandey. Performance characteristics of mode of ballast on energy efficiency indices of agricultural tyre in different terrain condition in controlled soil bin environment. Energy, 182 (2019), pp. 48-56.

[27]	F. Bauer, P. Porteš, D. Slimařík, J. Čupera, M. Fajman. Observation of load transfer from fully mounted plough to tractor wheels by analysis of three point hitch forces during ploughing. Soil Tillage Res, 172 (2017), pp. 69-78.

[28]	Lagnelöv G. Larsson D. Nilsson A. Larsolle P.A. Hansson. Performance comparison of charging systems for autonomous electric field tractors using dynamic simulation. Biosyst Eng, 194 (2020), pp. 121-137.

[29]	Standardization Administration of the People’s Republic of China, 2005. GB/T 18385-2005: Electric vehicle power performance test methods. Chinese standard. Beijing: Standards Press of China; 2005. Chinese.

[30]	Brixius WW. Traction prediction equations for bias ply tires. Urbana: American Society of Agricultural Engineers;1987.

[31]	S. Li, H. Chen, R. Li, Z. Liu, Z. Wang, Z. Xin. Predictive lateral control to stabilise highly automated vehicles at tire-road friction limits. Veh Syst Dyn, 58 (5) (2020), pp. 768-786.

[32]	Peiret E. Karpman L.L. Kovács J. Kövecses D. Holz M. Teichmann. Modelling of off-road wheeled vehicles for real-time dynamic simulation. J Terramechs, 97 (2021), pp. 45-58.

[33]	F. Habarta. Determination in relation to safety of operation of the minimal load on the front steering axle of a tractor with implements attached. J Agric Eng Res, 16 (2) (1971), pp. 126-140.

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