Open AccessArticle

An Investigation of Energy Consumption Characteristics of the Pump-Control System for Electric Excavator Arms

School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China

School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Author to whom correspondence should be addressed.

Appl. Sci. 2024, 14(23), 10791; https://doi.org/10.3390/app142310791

Submission received: 19 October 2024 / Revised: 10 November 2024 / Accepted: 15 November 2024 / Published: 21 November 2024

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Figure 1
Principle of the variable-speed motor drive–variable-displacement hydraulic pump-control hydraulic cylinder. 1. Motor; 2. Hydraulic pump; 3. Accumulator; 4. Relief valve; 5. Hydraulic oil tank; 6. Hydraulic control check valve; 7. Single-rod hydraulic cylinder. "> Figure 2
Control principle of variable speed and constant displacement. "> Figure 3
Compound-control principle. "> Figure 4
Energy consumption experiment for a variable-displacement hydraulic pump driven by a variable-speed motor. 1. Variable hydraulic pump; 2. Three-phase asynchronous motor; 3. Hydraulic tank; 4. Electric proportional relief valve; 5. Control cabinet; 6. All kinds of sensors. "> Figure 5
Actual picture of the control part of the experimental platform. 1. Computer; 2. System control display interface; 3. Three-phase power meter; 4. PLC controller; 5. Inverter. "> Figure 6
Experimental schematic diagram. 1. Three-phase power supply; 2. Three-phase power meter; 3. Inverter; 4. Motor; 5. Variable pump; 6. Displacement controller; 7. Speed controller; 8. Pressure controller; 9. Electric proportional relief valve; 10. Torque sensor; 11. Speed sensor; 12. Pressure sensor; 13. Flow sensor. "> Figure 7
(a) Efficiency curves for P = 8 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement. "> Figure 8
(a) Efficiency curves for P = 10 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement. "> Figure 9
(a) Efficiency curves for P = 12 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement. "> Figure 10
(a) Efficiency curves for P = 14 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement. "> Figure 11
(a) Efficiency curves for P = 16 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement. "> Figure 12
Optimal speed rule for different load powers. "> Figure 13
Combined pump-control system of excavator motor arm. "> Figure 14
Simulation model of the hydraulic system of boom compound pump-control cylinder. 1—Hydraulic oil model; 2—Joint simulation interface; 3—Speed conversion; 4—Variable-displacement hydraulic pump; 5—Accumulator; 6-1, 6-2 Hydraulic control check valve; 7-1,2 Relief valve; 8—Boom cylinder; 9—Speed sensor ; 10—Force sensor; 11—displacement sensor; 12—Load. "> Figure 15
Control model of the composite pump-control system. "> Figure 16
Comparison of the boom displacement of the three control modes. "> Figure 17
Comparison of the energy consumption of the three control modes. ">

Versions Notes

Abstract

The conventional hydraulic system of excavators suffers from significant valve throttling losses and inadequate matching between the hydraulic power source and the load, which substantially impact the system’s overall energy consumption and severely impede the trend toward electrification and energy efficiency in construction machinery. To address this issue, a pump-controlled hydraulic cylinder system has been implemented to replace the original valve-controlled hydraulic system that utilizes a single pump with multiple actuators. The influence of energy conversion efficiency and the speed between the motor and the hydraulic pump under varying load-power conditions has been determined through experimental investigations. Based on these findings, a compound-control strategy is proposed that adjusts the displacement of the hydraulic pump to achieve precise control over the position of the hydraulic cylinder and facilitates both the speed and displacement coordination while ensuring optimal motor speed matching with the load power. This strategy is implemented in the boom pump’s hydraulic cylinder control system. The research findings indicate that this combined-control approach enhances efficiency by approximately 18.9% compared with traditional variable-speed pump-controlled hydraulic cylinder systems. Furthermore, energy consumption is reduced by about 39% compared with the conventional valve-controlled hydraulic system.

Keywords:

pump-controlled hydraulic cylinder; speed–displacement control strategy; power matching; efficiency

1. Introduction

The energy crisis has become a vital issue restricting the further development of human technology, and the saving of energy and green development have become new and essential concepts. The development of electrification in construction machinery has become a significant trend [1]. The traditional single pump corresponds to the hydraulic system of a multi-actuator excavator. Due to the load difference, the hydraulic system experiences profound throttle loss and overflow loss at the valve port. In hydraulic excavator arms, a variable-speed motor is employed to drive a pump-controlled hydraulic cylinder system, effectively mitigating throttle losses at the valve ports and significantly enhancing the system’s overall energy efficiency [2]. The development of electrification makes feasible the distributed hydraulic system. From the structure of the excavator, the traveling motor is decoupled from the boom, bucket rod, bucket, and rotary mechanism so that each actuator can be controlled according to the volume–speed regulation mode, eliminating the throttling loss caused by the load difference of multiple actuators, and the closed hydraulic system effectively reduces the corresponding pipeline and fuel tank volume [3].

Given problems such as the low energy utilization rate and poor endurance caused by profound energy consumption loss and load-power mismatching in the hydraulic system of the existing electric-driven excavator, the pump-controlled hydraulic cylinder system scheme is adopted for the excavator motor arm, which can eliminate the throttle loss at the valve port from the system configuration and control the motor speed and hydraulic pump displacement. The real-time matching between the output power of the hydraulic drive unit and the demand power of the load can effectively reduce the power loss in the energy conversion process of the motor to the hydraulic pump [4].

The working condition of the boom changes frequently, and the mismatch between the output power and the load power of the hydraulic drive unit results in profound energy consumption loss. The analysis of dynamic energy consumption during the switching of the variable-speed pump-control system under working conditions is of great significance for improving the global power matching of the system and reducing energy consumption [5]. There have been many studies on the use of pump-control systems to drive excavator working devices; for example, Hou Simin analyzed the position and velocity characteristics of the pump-controlled differential cylinder system by using double pumps to control the hydraulic cylinder system to drive the 37t excavator arm. The results showed that compared with the single-pump-controlled differential cylinder, the position and velocity response characteristics of the modified double-pump-controlled differential cylinder were improved, the system ran more smoothly, and the accumulator had a significant energy storage effect. The output energy consumption was reduced by 40% and 44% under no-load and on-load conditions. However, the influence of load change on the system energy consumption was not considered [6]. Zhang Shuzhong et al. transformed the pump-controlled cylinder system for the excavator’s working device and established simulation models for the traditional valve-control system and the pump-controlled cylinder system, respectively, for the working device. Through analysis and comparison, the energy consumption of the excavator using the servo motor pump-control cylinder under a typical cycle condition was about 65% less than that of the traditional valve-control system. However, the motor speed was not controlled for load changes to match the load with the power source [7]. Ren Wei designed a pump-controlled integrated hydraulic cylinder system for the excavator motor arm. The unique cavity hydraulic cylinder eliminated unbalanced flow and recovered and utilized the boom potential energy, and the system ran smoothly. The energy-saving effect was remarkable [8]. Cheng Donghong used an asymmetric pump to control a single-lever hydraulic cylinder to achieve flow matching and applied it to the excavator’s arm, achieving an excellent energy-saving effect [9].

The pump-controlled hydraulic cylinder system can effectively improve the energy utilization efficiency of the whole excavator. Still, the energy conversion efficiency of the motor to the hydraulic pump is different under different load powers, and there are problems such as high-speed motor operation and significant power loss under low-load conditions. According to the influence law of different load powers on the energy conversion efficiency of the motor–hydraulic pump, the corresponding control strategy is proposed, which can effectively improve the energy utilization efficiency of the whole excavator. Huang Haihong proved through experimental research that by controlling and adjusting the motor acceleration, the average energy consumption of the hydraulic system could be increased by 8% in a given working cycle, thus effectively improving the system efficiency [10].

To explore the energy consumption of the hydraulic system with variable speed and displacement compound volume–speed regulation, Tian Qingqing designed and completed a monitoring platform design of a composite-control hydraulic system, which can realize dynamic parameter monitoring of the hydraulic system [11]. Aiming at the hydraulic system drive unit of molding equipment, Liu Xiaopeng proposed a power-matching scheme under global working conditions for a variable-speed motor to drive a constant-power pump and effectively improved the operating efficiency of the hydraulic system through the control method of maximum efficient–optimal speed [12] Li Qiankun analyzed the energy consumption of the motor driven by the electric excavator and proposed a speed-control method based on the optimal efficiency of the motor so that the motor could meet the driving requirements and be in a high-efficiency working area during the operation of the electric excavator, thus reducing energy loss during the operation of the system. Based on an analysis of the energy consumption of the motor and hydraulic pump for an electric excavator, Shi Lingbo proposed a power-matching method for the motor and hydraulic pump under different working conditions [13]. Zhang De proposed a combined speed- and displacement-control strategy based on the optimal speed and displacement, aimed at addressing the power-matching problem between the motor and hydraulic pump in the working process of the pump-control motor–hydraulic system [14]. Liu Siqi modeled and analyzed the energy consumption of three-phase asynchronous motors and proposed an online search method for optimal flux linkage to optimize motor efficiency [15].

As for research on the compound-control strategy of speed and displacement, Wang Chengbin proposed a compound-control method of displacement and rotational speed for pump-controlled differential hydraulic cylinders. Through simulation and experimental research, it was found that under the control of inner-loop displacement and outer-loop rotational speed, the dynamic response of a pump-controlled differential cylinder system was faster than that under constant rotational speed, the time was shortened by 13.4%, and the system energy consumption could be reduced by about 3 kW under low rotational speed and a large displacement. However, the speed of the motor was not actively controlled according to the system’s energy consumption characteristics, which further improved the system’s efficiency [16]. Wang Haiyan established a closed pump-controlled hydraulic cylinder system with variable speed and displacement and superimposed the control speed and displacement to improve the response speed of the system effectively. The simulation analysis of the overall system scheme was carried out using the open-loop control method, closed-loop control method, and load characteristics, respectively, and the results showed that the closed-loop speed-control scheme could maintain a stable state. It is mainly unaffected by load but does not consider the system’s energy consumption [17]. Zhao Tianhong adopted the distribution decoupling control strategy based on hydraulic pump efficiency for the variable-speed and variable-displacement pump-controlled hydraulic cylinder system to solve the nonlinear problem of control-variable multiplication [18]. Zhao Jinbao proposed a control strategy based on working condition decoupling and a fuzzy gain-scheduling control algorithm for electro-hydrostatic servo actuators under the combined control of speed and displacement. Simulation and actual experiments proved that the proposed composite-control strategy can effectively improve the dynamic performance of the electro-hydrostatic actuator system [19]. The compensation loop of the passive valve using a hydraulic control check valve for flow compensation is simple and suitable for working conditions with small load-direction changes. A circuit using multiple pumps to compensate for the unbalanced flow rate also has high stability, but an increase in the number of pumps leads to increased installed power [20].

With the development of control technology, research on pump-controlled hydraulic cylinder systems has become more in-depth, especially research on the control strategy of pump-controlled hydraulic cylinders, which improves the control accuracy and response performance of the pump-controlled hydraulic cylinder and the more widely used PID control. PID control is widely used because of its strong adaptability and flexibility and easy implementation in practical applications [21]. Minav designed a fuzzy PID controller for a direct-drive pump-controlled hydraulic cylinder system to give the system better dynamic characteristics [22]. Perron applied the sliding-mode controller to the pump-controlled hydraulic cylinder system, significantly improving the system’s robustness [23]. Lee Lian-Wang designed an adaptive fuzzy controller for the position-control system of a variable-speed pump-controlled hydraulic cylinder and proved that the system has good position-control function through experimental research [24]. Wang Longke from the United States adopted the singularity perturbation theory to eliminate fluctuations in the working commutation speed of the pump-controlled cylinder [25]. Kyoung Kwan Ahn of Ulsan University in South Korea adopted an adaptive backthrusting control algorithm for the pump-control system, which significantly improved the robustness and anti-interference of the system [26]. In addition to the theoretical research on pump-controlled hydraulic cylinder technology, foreign experts have already achieved more achievements in applying pump-controlled hydraulic cylinder technology in aerospace, robot control, and other fields. American engineers applied variable-speed and constant-displacement pump-controlled hydraulic cylinders to fighter aircraft, achieving good operational test results [27]. Bobrow and Desai applied pump-controlled hydraulic cylinders to robot platforms, reducing the platform impact and improving the control performance [28,29]. Foreign experts have already achieved more in applying pump-controlled hydraulic cylinder technology in aerospace, robot control, and other fields.To sum up, foreign research on pump-controlled single-exit rod hydraulic cylinder systems mainly focuses on the asymmetric flow balance of the system and the control strategy of the pump-controlled hydraulic cylinder system as well as the application and promotion of pump-controlled hydraulic cylinder technology, and specific achievements have been achieved in the theoretical research and practical application of pump-controlled hydraulic cylinder systems.

A comprehensive control strategy that integrates speed and displacement is proposed to optimize motor velocity, achieve load-power matching, and adjust the hydraulic pump displacement for closed-loop control of the hydraulic cylinder’s position. The boom’s pump-controlled hydraulic cylinder system employs a control approach that combines displacement adjustment with motor speed regulation to ensure effective load-power matching. An experimental platform has been established for analyzing energy consumption in a variable-displacement hydraulic pump driven by a variable-speed motor. The experimental results indicate that optimizing speed under varying load conditions maximizes the energy conversion efficiency of the motor–hydraulic pump system while ensuring smooth boom operation. This method demonstrates significantly enhanced energy-saving effects compared with traditional valve-control systems and those utilizing only variable-speed pumps.

2. Working Principle of the Variable-Speed Motor—Variable-Displacement Hydraulic Pump-Controlled Hydraulic Cylinder

As illustrated in Figure 1, the variable-speed motor drives a variable-displacement hydraulic pump to regulate the hydraulic cylinder system. Serving as the power source for this system, motor 1 converts electrical energy into mechanical energy and transmits it to the hydraulic pump via a coupling mechanism. The hydraulic pump transforms this mechanical energy into hydraulic energy, delivering high-pressure oil to the system. Variable-displacement hydraulic pump 2 employs an electric proportional variable piston design. The system modulates working flow by adjusting the motor speed and hydraulic pump displacement. Accumulator 3 utilizes an air-bag accumulator that is sensitive, compact, and lightweight, and that operates at low pre-charge pressure; it supplements leakage from the hydraulic pump and cylinder while balancing asymmetric flow rates within the system. Relief valve 4-1 limits the maximum pressure within the accumulator; additionally, pre-filled high-pressure oil in this accumulator compensates for unbalanced flow resulting from area discrepancies between the two chambers of the hydraulic cylinder when reversing open check valves 6-1 and 6-2. Relief valves 4-2 and 4-3 act as safety valves designed to restrict maximum pressure across both chambers of the hydraulic cylinder.

The control principle of the hydraulic cylinder system is driven by a variable-speed motor and a fixed-displacement pump, as illustrated in Figure 2. The position of the hydraulic cylinder is regulated in a closed-loop manner solely through adjustments to the motor speed. However, certain operational conditions present challenges, such as inadequate matching between system power and load requirements and low energy utilization efficiency.

Figure 3 illustrates the integrated-control principle of speed and displacement. The primary controller regulates the position of the hydraulic cylinder within a closed-loop system by modulating the displacement of the hydraulic pump. The system continuously monitors external load forces and the operational speed of the hydraulic cylinder via force sensors and speed sensors, computes the real-time load power exerted on the hydraulic cylinder, and adjusts the motor speed accordingly to enhance the system–load power compatibility while minimizing energy consumption for both the motor and the pump.

3. Materials and Methods

3.1. Mathematical Model of the System

(1): Three-phase asynchronous motor mathematical model

u_{s α} = R_{s} i_{s α} + p ψ_{s α}

(1)

u_{s β} = R_{s} i_{s β} + p ψ_{s β}

(2)

Equations (1) and (2) are the voltage equations of the motor.

T_{e} = p_{m} L_{m} (i_{s q} i_{s d} - i_{s d})

(3)

Formula (3) is the torque equation of the motor.

T_{e} - T_{L} = \frac{J}{p_{m}} \frac{d ω_{r}}{d t}

(4)

where

R_{s}

is the stator resistance,

p_{m}

is the number of poles of the motor,

u_{s α}

and

u_{s β}

are the stator voltages in the coordinate system,

α

and

β

are the stator flux in a coordinate system,

i_{s d}

and

i_{rd}

are the stator and rotor current, respectively, in a rotating coordinate system,

J

is the moment of inertia on the motor spindle,

T_{L}

is the load torque, and

T_{e}

is the electromagnetic torque.

(2): Variable pump-flow equation

q_{p} = V_{p m a x} . i . n - C_{i p} (P_{L} - P_{i}) - C_{O P} P_{L}

(5)

where

V_{p m a x}

is the maximum displacement of the hydraulic pump,

i

is the ratio of the actual displacement to the maximum displacement,

n

is the speed of the hydraulic pump,

C_{i p}

is the leakage coefficient of the hydraulic pump,

C_{o p}

is the external leakage coefficient of the hydraulic pump,

p_{L}

is the load pressure, and

P_{i}

is the inlet pressure of the hydraulic pump.

(3): Continuity equation of hydraulic cylinder flow

The hydraulic cylinder rodless cavity flow continuity equation is as follows:

Q_{1} = A_{1} v_{1} + \frac{V_{1}}{β} \frac{d p_{1}}{d t} - C_{y} Δ p

(6)

where

Q_{1}

is the rodless cavity flow rate,

ν_{1}

is the rodless cavity volume of the hydraulic cylinder, β is the bulk elastic modulus of the hydraulic oil,

p_{1}

is the rodless chamber pressure of the hydraulic cylinder,

C_{y}

is the leakage coefficient of the hydraulic cylinder, and Δp is the pressure difference between the two chambers of the hydraulic cylinder.

The hydraulic cylinder rod cavity flow continuity equation is as follows:

Q_{2} = A_{2} v + \frac{V_{2}}{β} \frac{d p_{2}}{d t} + C_{y} Δ p - C_{y} p_{1}

(7)

In the formula,

Q_{2}

is the flow rate of the hydraulic cylinder with a rod cavity,

ν_{2}

is the volume of the rod cavity in the hydraulic cylinder,

p_{2}

is the pressure of the hydraulic cylinder with the rod cavity, and Δp is the pressure difference between the two chambers of the hydraulic cylinder.

(4): Hydraulic cylinder force balance equation

F = p_{1} A_{1} - p_{2} A_{2} + B \frac{d_{x}}{d_{t}} + F_{f} + m \frac{d^{2} x}{d t^{2}}

(8)

where F is the load force on the boom hydraulic cylinder,

p_{1}

and

p_{2}

are the pressure of the rodded cavity and the rodless cavity of the hydraulic cylinder, respectively.

A_{1}

and

A_{2}

are the areas of the rodded and rodless cavities of the boom, respectively. B is the viscous damping of the hydraulic cylinder piston and load,

F_{f}

is the friction force, and m is the mass of the moving parts.

(5): Accumulator equation

The thermodynamic equation of ideal gas in an accumulator is as follows:

P_{1} {V_{1}}^{n} = P_{2} {V_{2}}^{n}

(9)

P₁ is the pressure in the initial working state of the accumulator, V₁ is the working volume in the initial state, P₂ is the pressure in the working state of the accumulator, and V₂ is the working volume in the working state. By integrating the mathematical model of the pump-controlled hydraulic cylinder system with the load-condition requirements of the excavator arm, a comprehensive calculation and selection of the system components was conducted. The findings are presented in Table 1 and Table 2.

3.2. Variable-Speed Motor Drive–Variable-Displacement Hydraulic Pump Energy Consumption Model

(1): Motor energy consumption model

In analyzing a three-phase asynchronous motor, the leakage inductance between the rotor and stator sides is neglected, while the mutual inductance between these two components is considered. A motor loss model is developed within a two-phase rotating coordinate system. The primary contributors to motor losses include copper losses and iron losses. Additionally, this comprehensive assessment considers stray and frictional losses during load variations to be relatively minor, and these are thus disregarded. Consequently, the overall motor loss can be expressed as

P_{l o s s} = P_{C u r} + P_{F e} + P_{C u s} = a T_{e} ω_{m} + (b_{1} + b_{2} {ω_{m}}^{2}) {ψ_{r d}}^{2} + c \frac{{T_{e}}^{2}}{{ψ_{r d}}^{2}}

(10)

of which

a = \frac{2 (R_{r} + R_{m})}{{R_{m}}^{2}} (R_{s} + \frac{R_{r} R_{m}}{R_{r} + R_{m}})

(11)

b_{1} = \frac{R_{s}}{{L_{m}}^{2}}, b_{2} = {P_{m}}^{2} (\frac{R_{s}}{{R_{m}}^{2}} + \frac{1}{R_{m}})

(12)

c = (R_{s} + \frac{R_{m} R_{r}}{R_{m} + R_{r}}) \frac{(R_{m} + R_{r})^{2}}{{p_{m}}^{2} {R_{m}}^{2}}

(13)

where T_e is the rated torque of the motor, ω_m is the angular speed of the motor, ψ_rd is the d axis to the P particle flux-linkage component, ω_r is the rotor angular frequency, P_m is the polar logarithm, R_s is the stator resistance, R_m is the equivalent resistance of stator iron loss, and L_m is the viscous damping of the stator rotor mutual inductance load.

(2): Variable-displacement hydraulic pump energy consumption model

The energy consumption of a variable piston pump is mainly the mechanical friction loss caused by the mutual movement of each friction pair and the volume loss caused by oil leakage and oil compressibility in the hydraulic pump, where the volume efficiency and mechanical efficiency are, respectively,

η_{v} = 1 - C_{s} \frac{60 Δ p}{μ n} . \frac{1}{β}

(14)

η_{m} = [1 + C_{v} (\frac{μ n}{60 Δ p β}) + \frac{C_{f}}{β} + \frac{2 π T_{s}}{Δ p q_{t} β}]^{- 1}

(15)

where T_s is the input torque of the plunger pump, T is the actual torque of the pump, ΔT is the torque loss of the piston pump due to mechanical friction, C_f is the oil friction coefficient under the laminar-flow state in the hydraulic pump, and C_v is the mechanical friction coefficient between the friction pairs in the pump.

(3): Variable-speed motor—variable-displacement hydraulic pump energy conversion efficiency model

Based on the above analysis of the energy consumption of the motor and the hydraulic pumps, the energy conversion efficiency model of the motor–hydraulic pumps is established.

The efficiency of converting electrical energy to mechanical energy is given by

η_{m} = \frac{p_{o u t}}{p_{o u t} + p_{l o s s}} = \frac{A n^{2}}{B n^{4} + C n^{2} + D}

(16)

of which

\{\begin{matrix} A = p_{o u t} \\ B = \frac{b_{2} π^{2} ψ_{r d}^{2}}{900} \\ C = (b_{1} ψ_{r d}^{2} + c P_{o u t}) \\ D = P_{o u t} + a \frac{3600 P_{o u t}^{2}}{4 π^{2} ψ_{r d}^{2}} \end{matrix}

The conversion efficiency of mechanical energy to hydraulic energy of a piston hydraulic pump is given by

η_{p} = η_{M} . η_{V} = \frac{E}{F n^{2} + G n + H}

(17)

\{\begin{matrix} E = 60 (μ n V_{m} - 60 C_{s} Δ P V_{m}^{m a x} \\ F = μ^{2} C_{v} V_{m}^{m a x} \\ G = (60 Δ P C_{f} V_{m}^{m a x_{s}} \\ H = 60 μ Δ P n V_{m} \end{matrix}

The energy conversion efficiency of the motor–hydraulic pump is

η = η_{m} . η_{p}

(18)

Equation (18) shows that the energy conversion efficiency of the motor–hydraulic pump exhibits a multiplicative relationship with speed n. By regulating the operating speed of the hydraulic pump, which is driven by the motor under varying load conditions, both the motor and the hydraulic pump can operate within their high-efficiency zones across different load scenarios by optimizing the efficiency of the pump-controlled hydraulic cylinder system.

4. Motor–Hydraulic Pump Energy Consumption Analysis Experiment

To enhance the overall energy efficiency of the excavator system, a compound-control strategy integrating speed and displacement was proposed based on the typical operating conditions of the excavator manipulator. Due to the challenges in measuring relevant structural parameters of the motor and hydraulic pump during actual calculations, it is not feasible to determine specific optimal combinations of speed and displacement across various load conditions for different types of motors and hydraulic pumps. Consequently, it is essential to experimentally analyze the energy consumption characteristics of specific motor types driving hydraulic pumps by establishing optimal speed guidelines for varying loads. This will provide data support aimed at further reducing energy consumption. An experimental platform was established to assess the energy consumption for a hydraulic pump driven by a variable-speed motor, focusing on evaluating the energy conversion efficiency from the motor to the hydraulic pump under diverse load-power scenarios.

4.1. Experimental Platform Construction

The experimental platform, shown in Figure 4, was built according to the experimental scheme for the energy consumption analysis of a variable-displacement hydraulic pump driven by a variable-speed motor. Each component was installed.

The experimental system, as shown in Figure 4, is built and divided into electrical control and hydraulic system parts. The hydraulic system includes a variable-speed motor, variable-displacement hydraulic pump, relief valve, and hydraulic oil tank. The electrical control consists of a three-phase power supply, frequency converter, and various sensors and controllers. The motor is connected with the variable axial piston pump through a coupling, and the speed and torque sensor is installed on the drive shaft to detect and collect the motor speed and torque signal on the drive shaft. The pressure sensor is installed at the outlet of the hydraulic pump to monitor the working pressure of the hydraulic pump. The flow sensor is installed at the oil-return port of the relief valve to monitor the system’s working-flow data and to ensure that the hydraulic pump is at the preset load power. The motor’s operating speed can be configured and fine-tuned, with the motor speed-control signal transmitted to the inverter. The motor speed is modulated by varying the power input frequency, while the displacement of the variable hydraulic pump can also be adjusted accordingly. This experiment aims to calculate the energy conversion efficiency from the motor to the hydraulic pump at different speeds and displacements under a specified load power for the hydraulic pump.

In the experiment, one variable hydraulic pump adopts an electric proportional variable piston pump, two three-phase asynchronous motors drive the motor, and the temperature sensor and cooling device are set on hydraulic tank 3. When the oil temperature exceeds 50 °C, the oil cooling device is turned on to eliminate the influence of the oil temperature change on the hydraulic pump’s operating efficiency during the experiment.

The experiment uses electric proportional relief valve 4 to load the hydraulic pump’s outlet pressure. Control cabinet 5 includes the frequency converter and various sensor wirings, and multi-sensor 6 includes a temperature sensor, speed sensor, torque sensor, pressure sensor, and flow sensor at the pump’s outlet.

As illustrated in the experimental console depicted in Figure 5, the input current of the electric proportional relief valve can be regulated by manipulating the pressure adjustment knob. This allows the loading pressure at the hydraulic pump outlet to be modified, enabling the pump to operate under varying load conditions. The motor’s running speed can also be configured and adjusted; a control signal for the motor speed is transmitted to the inverter, allowing for modulation of the motor speed through adjustments in the power input frequency. Additionally, the displacement of the variable hydraulic pump can be fine-tuned. The experiment facilitates the calculation of energy conversion efficiency between the motor and hydraulic pump across different speeds and displacements while maintaining a constant load power on the pump.

Computer 1 is used to collect and process the relevant data from the three-phase power meter to detect and calculate the input power of the motor. The control platform is used to adjust and control the working pressure of the relief valve at the outlet of the hydraulic pump, the speed of the motor, and the displacement of the hydraulic pump, and to process and calculate the data collected by the pressure sensor, the flow sensor and the speed and torque sensor. The main parameters of the components used in the experiment platform are shown in Table 1.

4.2. Experimental Analysis

4.2.1. Experimental Scheme

Experimental purpose

Under varying load-power conditions, there exists an optimal motor speed that maximizes the energy conversion efficiency of the motor–hydraulic pump system. By setting different load-power levels (given a specific working pressure and system flow rate), we can adjust various combinations of motor speed and hydraulic pump displacement to analyze the energy conversion efficiency and motor speed performance of the motor–hydraulic pump across these load-power scenarios. The analysis aims to identify the optimal motor speed that achieves peak efficiency for each distinct load-power condition.

2.: Experimental principle

As illustrated in the experimental schematic diagram presented in Figure 6, variable-speed motor 4 drives variable-displacement hydraulic pump 5, while load management is facilitated through electric proportional relief valve 9. To accommodate varying flow requirements, the set pressure of the electric proportional relief valve is meticulously controlled and adjusted to optimize the performance of the hydraulic pump under diverse load conditions.

Under varying load conditions, the motor speed is regulated by frequency converter 3, while the displacement controller is fine-tuned by variable-displacement controller 5. The outlet flow signal from the hydraulic pump is monitored via flow sensor 13 to ensure that it meets the target value. Additionally, the pressure signal at the outlet of the hydraulic pump is captured through pressure sensor 12 to confirm that its operational load remains within specified parameters. Torque and speed signals from both the motor and hydraulic pump’s rotating shafts are gathered using torque speed sensors 10 and 11 to guarantee operation at designated speeds.

The input power signal of the motor is acquired through power meter 2, and the operational efficiency of the motor is assessed by integrating its input power with the output speed and torque. The input power for the hydraulic pump is determined by correlating it with the output speed and torque signals from the motor. Furthermore, the operational efficiency of the hydraulic pump is evaluated by analyzing its outlet pressure in conjunction with its output flow.

3.: Experimental element

The variable-speed motor employs a three-phase asynchronous design, with its rotational speed regulated by a frequency conversion drive system. The operational speed range of the motor is from 0 to 3000 r/min. The variable-displacement hydraulic pump utilizes a variable piston mechanism, controlled through electric proportional modulation, with a maximum displacement capacity of 100 mL/r. Additionally, the relief valve is rated for a pressure of 35 MPa.

4.2.2. Selection Basis for the Experimental Parameters

In conjunction with the load-condition requirements of the excavator boom under investigation, specific working conditions were established. The operating speed of the hydraulic cylinder for the boom was set at 1200 m/s, necessitating a hydraulic pump flow rate of 85 L/min and an operational pressure range between 8 to 14 MPa. To enhance experimental efficiency within the specified load-condition parameters, the hydraulic pump’s working flow was maintained at 85 L/min while varying the working pressure to values of 8, 10, 12, and 14 MPa respectively. Special load conditions were defined to analyze through experimentation the correlation between optimal speed and load power. As indicated by the theoretical analysis in Section 3.2, when both the displacement of the hydraulic pump is minimal and the motor speed is excessively low, there exists a reduction in operational efficiency for both the motor and the hydraulic pump systems. Therefore, since the experiments were aimed at improving overall efficiency, a setting range for speeds from 1200 to 1800 was adopted alongside a displacement range from 70.8 mL/R to 47.2 mL/R, thus establishing a displacement ratio range of approximately −0.5 to −0.85.

Based on the operational requirements of the boom, the motor speed range is established between 1200 and 1800 r/min, utilizing a speed regulation interval of 25 r/min to increase the motor speed while concurrently reducing the hydraulic pump displacement incrementally. The outlet flow of the hydraulic pump is maintained at a predetermined value of Q = 85 L/min. Pressure and flow data are monitored via the outlet pressure and flow sensors associated with the hydraulic pump. As illustrated in Figure 7a, under conditions where the hydraulic pump pressure p = 8 MPa and the working-flow demand Q = 85 L/min, it is observed that as motor speed increases under this load condition, the displacement decreases; consequently, the energy conversion efficiency between the motor and the hydraulic pump initially rises before subsequently declining. At a motor speed of n = 1325 r/min with a hydraulic pump displacement ratio i = 0.852, both components can operate within their high-efficiency zones, achieving an energy conversion efficiency of up to 61.05%. As illustrated in Figure 7b, the motor efficiency increases first and then decreases with the increase in speed, and the hydraulic pump efficiency gradually declines with the speed growth; that is, the efficiency space Δη = 19.8% can be improved within the whole speed range.

As illustrated in Figure 8a, under a hydraulic pump pressure of p = 10 MPa and a working-flow demand of Q = 85 L/min, it is observed that with increasing speed, the displacement decreases under this load condition. Furthermore, the energy conversion efficiency of the motor–hydraulic pump initially increases before subsequently decreasing. When the motor speed reaches n = 1375 r/min, and the hydraulic pump displacement ratio is i = 0.727, the motor and the hydraulic pump can operate within their high-efficiency zones, achieving an energy conversion efficiency of up to 68.12%. As illustrated in Figure 8b, the efficiency of the hydraulic pump increases first and then decreases; that is, the efficiency space Δη = 20.9% can be improved in the speed range.

As illustrated in Figure 9a, under a hydraulic pump pressure of p = 12 MPa and a working-flow demand of Q = 85 L/min, the displacement decreases as the speed increases under this load condition. Furthermore, the motor–hydraulic pump’s energy conversion efficiency initially rises before declining. When the motor speed is n = 1425 r/min, and the hydraulic pump displacement ratio is i = 0.701, the motor and the hydraulic pump can operate within an optimal efficiency range, achieving an energy conversion efficiency of up to 69.78%. As illustrated in Figure 9b, the efficiency of the hydraulic pump increases first and then decreases; that is, the efficiency space Δη = 22.7% can be improved in the speed range.

As illustrated in Figure 10a, under a hydraulic pump pressure of p = 14 MPa and a working-flow demand of Q = 85 L/min, it is observed that with increasing speed, the displacement decreases under this load condition. Furthermore, the energy conversion efficiency of the motor–hydraulic pump initially increases before subsequently decreasing. When the motor speed reaches n = 1475 r/min, and the hydraulic pump’s displacement ratio is i = 0.677, both the motor and hydraulic pump operate within an optimal efficiency range, achieving an energy conversion efficiency of up to 70.5%. As illustrated in Figure 10b, the efficiency of the hydraulic pump increases first and then decreases; that is, the efficiency space Δη = 24.7% can be improved in the speed range.

As illustrated in Figure 11a, under a hydraulic pump pressure of p = 16 MPa and a working-flow demand of Q = 85 L/min, it is observed that with increasing speed, the displacement decreases under this load condition. Furthermore, the energy conversion efficiency of the motor–hydraulic pump initially increases before subsequently decreasing. When the motor speed reaches n = 1525 r/min, and the hydraulic pump displacement ratio is i = 0.655, both the motor and the hydraulic pump operate within an optimal efficiency range, achieving an energy conversion efficiency of up to 73.8%. As illustrated in Figure 11b, the efficiency of the hydraulic pump increases first and then decreases; that is, the efficiency space Δη = 26.7% can be improved in the speed range.

4.3. Optimal Speed Rule of Different Load Powers

Through the analysis of the experimental data on the energy consumption adjustment of motor speed and hydraulic pump displacement under different load powers, it can be seen that when the load power of the hydraulic pump is constant, there is an optimal combination of speed and displacement that makes the energy conversion gauge efficiency of motor to hydraulic pump under the load power the highest. For the boom pump-control hydraulic cylinder system, when the power source uses a variable-speed motor to drive the variable-displacement hydraulic pump as the power source, the energy consumption characteristics of the system can be further optimized by adjusting the speed and displacement combination. The optimal speed and displacement rule under different load powers are analyzed and summarized, and the speed and displacement compound-control strategy is proposed to make the motor and hydraulic pump in the high energy efficiency zone under different load conditions; the specific parameters are shown in Table 2.

The optimal speed rule under different load powers is obtained after analyzing the optimal speed under different load powers: the optimal speed under different load powers places the motor and hydraulic pump in the high-efficiency area.

As shown in Figure 12, with the increase in load power, the optimal speed can increase the energy conversion efficiency of the motor and the hydraulic pump, and with an increase in load power, the optimal speed increases in a linear proportional relationship.

5. Simulation Analysis

According to the operation principle of the boom pump-controlled hydraulic cylinder system and the requirements of the boom load condition, the simulation model of the composite pump-controlled hydraulic cylinder system was built and applied to the excavator working device to drive the hydraulic system, as shown in Figure 13.

In this paper, MATLAB2017a and AMESim21 were selected, and Visual Studio 2013 was used as the compilation language. Co-simulation also required the corresponding software installation sequence and software, which was completed according to this sequence: Visual Studio 2013, AMESim, MATLAB2017a.

According to the working principle of the boom compound pump-controlled hydraulic cylinder, the hydraulic system simulation model is built in AMESim, as shown in Figure 14. The data interaction with Simulink is carried out through the co-simulation interface to realize the co-simulation. The load-power signal of the boom hydraulic cylinder and the displacement signal of the hydraulic cylinder are the input signals of the co-simulation interface. The motor’s speed signal of the motor and the displacement control signal of the hydraulic pump are the output signals of the co-simulation interface. The main parameter settings of the system simulation model are shown in Table 3.

A composite-control strategy model was developed in Simulink. As illustrated in Figure 15, the S-Function module serves as the data interface for exchanging information with AMESim to facilitate the co-simulation. The input signals include the motor speed control and hydraulic pump displacement control signals, while the output signals consist of the hydraulic cylinder displacement and load-power signals. Using the operational principles of the boom compound pump-controlled hydraulic cylinder system, a simulation and an analysis of the speed and displacement compound-control strategy was conducted through AMESim–Simulink co-simulation. The response characteristics, energy-saving attributes, and applications under typical working conditions of the mining boom were examined in detail. For assessing system-response characteristics, sinusoidal displacement control signals at varying frequencies and step-displacement control signals at different magnitudes were input into the boom complex pump-controlled hydraulic cylinder system. The dynamic tracking performance of the system’s displacement control signal and its dynamic response performance to these displacement signals were evaluated. Additionally, various load forces on the hydraulic cylinder were established to implement motor speed-matching control strategies under differing load conditions.

These were applied to the driving system of the excavator working device, combined with the action requirements of the excavator, which completed the system simulation.

Figure 16 illustrates three control methods for simulating the boom’s typical mining operation period. It compares the boom valve-control system’s control performance and energy-saving characteristics with those of the variable-speed pump-control and compound pump-control systems.

The traditional valve-control boom hydraulic cylinder, the variable-speed pump-control boom hydraulic cylinder, and the compound pump-control hydraulic cylinder can all make the boom run smoothly and drive the working device to complete the digging action, which further proves the rationality of the parameter-matching design of the pump-control system. The displacement-control error of the hydraulic cylinder of the valve-controlled boom is the smallest, and the response speed is the fastest. As shown in Figure 15, the expected displacement of 0.801 m can be reached within 12.02 s. The response speed and error of the variable-speed pump-control arm are the second best; 12.07 s can achieve a displacement of 0.805 m compared with the response time and the displacement error of the valve-control system, which are increased by 0.05 s and 4 mm, respectively. Compared with the valve-control system, the response time is increased by 0.07 s and the displacement error is increased by 6 mm for the displacement of the composite pump-control arm, which reaches 0.795 m in 12.09 s.

As illustrated in Figure 17, in the driving system of the electric excavator’s working device, the composite pump-controlled hydraulic cylinder system’s energy consumption is reduced by about 18.9% compared with the variable-speed pump-controlled hydraulic cylinder system and by about 39% compared with the traditional valve-controlled hydraulic system.

6. Conclusions

Aiming at the operating conditions of the excavator boom, the mathematical model of the boom pump-control system is established, the energy loss model of the motor–hydraulic pump is established, the relationship between the energy conversion efficiency of the motor–hydraulic pump and the motor speed is theoretically derived and analyzed, and load-power matching is proposed by adjusting the motor speed. Adjusting the hydraulic pump displacement realizes the compound-control strategy of speed and displacement of hydraulic cylinder position closed-loop control.

An experimental platform for the energy consumption analysis of variable-displacement hydraulic pumps driven by variable-speed motors was set up. According to the operating conditions of the boom, an experimental study was conducted on the energy conversion efficiency of the motor–hydraulic pump and the rule of motor speed under different load power. It was concluded that under different load power, the combined-control strategy of speed and displacement could increase the energy conversion efficiency of the motor–hydraulic pump by more than 10%. With the increase of load power, the optimal speed of the motor to hydraulic pump energy conversion efficiency increases gradually.

According to the experimental results, given the boom’s operating conditions, the effect of rotational speed on the energy conversion efficiency of the motor–hydraulic pump was obtained. The pump-controlled hydraulic cylinder system with combined rotational speed and displacement control was applied to the excavator working device. The results showed that the energy consumption of the combined pump-controlled hydraulic cylinder system was reduced by about 18.9% compared with the pump-controlled hydraulic cylinder system with only variable rotational speed. The energy consumption is approximately 39% lower than in conventional valve-controlled hydraulic systems.

Author Contributions

In this paper, L.W. and A.H. proposed the control method of the compound control pump-controlled hydraulic cylinder system. Q.L. carried out the software simulation, A.H. conducted the verification, A.H. investigated the background significance, P.H. collected the resources, Q.L. managed the data, A.H. wrote and prepared the manuscript, and A.H. reviewed and edited it. L.W. supervised and managed the project. All authors have read and agreed to the published version of the manuscript.

Funding

This study was supported by the Key Research and Development Program of China, with Grant Number 2022YFB3403003.

Data Availability Statement

Due to legal constraints, the data presented in this study were not furnished upon the request of the corresponding authors.

Conflicts of Interest

Funders have no role in the research design. Data analysis: neither in data collection, analysis, nor interpretation. None of the authors has a conflict of interest.

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Figure 1. Principle of the variable-speed motor drive–variable-displacement hydraulic pump-control hydraulic cylinder. 1. Motor; 2. Hydraulic pump; 3. Accumulator; 4. Relief valve; 5. Hydraulic oil tank; 6. Hydraulic control check valve; 7. Single-rod hydraulic cylinder.

Figure 2. Control principle of variable speed and constant displacement.

Figure 3. Compound-control principle.

Figure 4. Energy consumption experiment for a variable-displacement hydraulic pump driven by a variable-speed motor. 1. Variable hydraulic pump; 2. Three-phase asynchronous motor; 3. Hydraulic tank; 4. Electric proportional relief valve; 5. Control cabinet; 6. All kinds of sensors.

Figure 5. Actual picture of the control part of the experimental platform. 1. Computer; 2. System control display interface; 3. Three-phase power meter; 4. PLC controller; 5. Inverter.

Figure 6. Experimental schematic diagram. 1. Three-phase power supply; 2. Three-phase power meter; 3. Inverter; 4. Motor; 5. Variable pump; 6. Displacement controller; 7. Speed controller; 8. Pressure controller; 9. Electric proportional relief valve; 10. Torque sensor; 11. Speed sensor; 12. Pressure sensor; 13. Flow sensor.

Figure 7. (a) Efficiency curves for P = 8 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement.

Figure 8. (a) Efficiency curves for P = 10 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement.

Figure 9. (a) Efficiency curves for P = 12 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement.

Figure 10. (a) Efficiency curves for P = 14 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement.

Figure 11. (a) Efficiency curves for P = 16 MPa, Q = 85 L/min. (b) Efficiency changes under different combinations of speed and displacement.

Figure 12. Optimal speed rule for different load powers.

Figure 13. Combined pump-control system of excavator motor arm.

Figure 14. Simulation model of the hydraulic system of boom compound pump-control cylinder. 1—Hydraulic oil model; 2—Joint simulation interface; 3—Speed conversion; 4—Variable-displacement hydraulic pump; 5—Accumulator; 6-1, 6-2 Hydraulic control check valve; 7-1,2 Relief valve; 8—Boom cylinder; 9—Speed sensor ; 10—Force sensor; 11—displacement sensor; 12—Load.

Figure 15. Control model of the composite pump-control system.

Figure 16. Comparison of the boom displacement of the three control modes.

Figure 17. Comparison of the energy consumption of the three control modes.

Table 1. The main parameters of the experimental platform.

Name	Item	Quantity Value
three-phase power meter	voltage	10.0–500.0 V
	current	0.03–40 A
	voltage	10.0–500.0 V
three-phase induction motor	rated power	110 kW
three-phase induction motor	rated voltage	380 V
	input capacitance	160 kVA
frequency changer	speed stability accuracy	±0.5%
	torque control accuracy	±5%
	input capacitance	160 kVA
hydraulic pump	maximum displacement	85 mL/r
	speed range	500–3000 r/min
	maximum pressure	35 MPa
overflow valve	diameter	30 mm
overflow valve	maximum working pressure	31.5 MPa
	maximum flow rate	650 L/min
torque-speed sensor	power source	±24 V
	torque signal	5–15 khz

Table 2. Optimal speed rule for different load powers.

Load Power (kW)	Optimum Speed (r/min)	Efficiency (%)
11.56	1325	61.05
14.45	1375	68.12
17.34	1425	69.78
20.23	1475	70.51
23.12	1525	73.82

Table 3. Main parameters of the pump-control system.

Item	Numerical Value
variable pump maximum displacement (mL/r)	25
rated torque of the motor (Nm)	80
rated motor speed (r/min)	2000
rated power of the motor (kW)	15
hydraulic cylinder bore (mm)	40
hydraulic cylinder rod diameter (mm)	25
accumulator volume (L)	6
accumulator pre-charge pressure (bar)	15

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He, A.; Wei, L.; Lu, Q.; He, P. An Investigation of Energy Consumption Characteristics of the Pump-Control System for Electric Excavator Arms. Appl. Sci. 2024, 14, 10791. https://doi.org/10.3390/app142310791

AMA Style

He A, Wei L, Lu Q, He P. An Investigation of Energy Consumption Characteristics of the Pump-Control System for Electric Excavator Arms. Applied Sciences. 2024; 14(23):10791. https://doi.org/10.3390/app142310791

Chicago/Turabian Style

He, Aihuan, Liejiang Wei, Quanfeng Lu, and Pengfei He. 2024. "An Investigation of Energy Consumption Characteristics of the Pump-Control System for Electric Excavator Arms" Applied Sciences 14, no. 23: 10791. https://doi.org/10.3390/app142310791

APA Style

He, A., Wei, L., Lu, Q., & He, P. (2024). An Investigation of Energy Consumption Characteristics of the Pump-Control System for Electric Excavator Arms. Applied Sciences, 14(23), 10791. https://doi.org/10.3390/app142310791

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An Investigation of Energy Consumption Characteristics of the Pump-Control System for Electric Excavator Arms

Abstract

1. Introduction

2. Working Principle of the Variable-Speed Motor—Variable-Displacement Hydraulic Pump-Controlled Hydraulic Cylinder

3. Materials and Methods

3.1. Mathematical Model of the System

3.2. Variable-Speed Motor Drive–Variable-Displacement Hydraulic Pump Energy Consumption Model

4. Motor–Hydraulic Pump Energy Consumption Analysis Experiment

4.1. Experimental Platform Construction

4.2. Experimental Analysis

4.2.1. Experimental Scheme

4.2.2. Selection Basis for the Experimental Parameters

4.3. Optimal Speed Rule of Different Load Powers

5. Simulation Analysis

6. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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