Keywords

1 Introduction

As one of the most functional construction machineries, excavators are widely applied in fields like architectural engineering, transportation construction and so on. Excavators can achieve different complex actions by regulating the speed of actuators such as boom and arm cylinders. The positive flow control system is one of the commonest excavator systems, whose main function is to supply the demanded flow rate by controlling the displacement of the main pump. The speed of actuators is determined by the inlet flow rate. On the one hand, it is influenced by the flow rate of the main pump, namely the positive flow control. On the other hand, it is related to the fluid distribution of the multiway valve, namely the throttling characteristics. A conventional sequential design is usually structure designs of components followed by adjustments of controller programs. However, the global optimal solution, even the feasible solution can hardly be reached if the relationship among subsystems is cut off by decomposing the coupling hardware and controller program artificially. It is necessary to carry out an integrated design of excavator positive flow control systems with the increasing demand for the comprehensive performance.

The multidisciplinary design optimization (MDO) is a methodology to design complicated engineering systems and subsystems by fully exploring and utilizing the cooperative interaction mechanism in systems, which is widely applied in fields like aerospace and so on [1,2,3]. Qian [4] carried out the MDO of the composite cooling structure for a nickel-based alloy turbine blade. Nscimento [5] proposed the hybrid optimization algorithm for preliminary design of multistage launch vehicles through the application of MDO.

In the field of construction machineries, Sun [6] optimized the bucket shape line of an excavator. The bucket weight and excavation resistance were decreased. Ranjan et al. [7, 8] utilized hydro-pneumatic accumulators to store the substantial potential energy during downward movement of the boom and arm. The linear position control of them was accomplished by proportional-integral-derivative control. The mentioned researches only considered the individual design of excavator’s hardware or controller. The coupling relationship between them was neglected, which made it difficult to reach the global optimal solution. Yuan [9] optimized the structural and control parameters of a bucket wheel reclaimer at the same time, reducing the energy consumption and achieving smaller vibration amplitude than the conventional sequential solution.

Hydraulic components are one of the most significant components that determine the operation performance of excavators. There have been few researches on their integrated design with the controller. This paper takes an excavator with the positive flow control system as an example, carrying out the MDO of its hydraulic component and controller.

2 Materials and Methods

2.1 Model of the Positive Flow Control System

The system schematic of a positive flow excavator is shown in Fig. 1. The driver controls the stroke of the multiway valve spool through the joystick. The controller adjusts the displacement of the main pump according to the pilot pressure of the joystick, making the main pump supply required flow rate. The multiway valve distributes the fluid from the main pump into the actuator or back to the tank. The inlet flow rate of the multiway valve can be changed through adjusting the displacement of the main pump, thus influencing the speed of the actuator. Meanwhile, the fluid distribution varies with the stroke of the multiway valve spool, so that the speed of actuators is changed.

Fig. 1
A schematic of an excavator runs as follows. Tank, main pump, multiway valve, actuator. A controller is fitted to the main pump. A joystick is fitted to the controller and multiway vale. The multiway vale is connected to the tank.

System schematic of an excavator

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Normal operations of excavators require accurate speed regulating. As mentioned above, the speed of actuators is closely related to both the multiway valve and the positive flow control. A model of the positive flow control system was developed through a commercial software AMESim to describe the relationship among the actuator, the multiway valve and the positive flow control. The model is showed in Fig. 2.

Fig. 2
A schematic of the positive flow control system. The components are labeled from 1 to 5. A swing motor on the top is labeled 1 followed by a multiway valve, positive flow controller, main pump, and joystick.

System model of the positive flow control system (1—swing motor; 2—multiway valve; 3—positive flow controller; 4—main pump; 5—joystick)

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This model described the swing circuit of the excavator as an example. Field and bench tests had been carried out to calibrate the model, as described in Chen et al. [10, 11]. The stable flow rate of the swing motor qm was obtained under different valve spool stroke x by setting different pilot pressure in the joystick of the swing circuit system model. The results are demonstrated in Fig. 3.

Fig. 3
A line graph of q m versus x. The estimated values are as follows. (0, 0), (2, 0), (4, 40), (6, 70), (8, 135), (10, 185).

Stable flow rate of swing motor (1—dead zone; 2—speed regulating zone)

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According to Fig. 3, when the valve spool stroke stays within the dead zone, the swing motor remains still. If the dead zone is too large, the micro movement performance will be influenced, which goes against the delicate operations. Within the speed regulating zone, the flow rate increases nonlinearly with the spool stroke. There will be differences between the required and actual speed due to the nonlinear characteristics. Drivers have to adjust the joystick repeatedly to achieve the required speed, which will lead to tiredness.

2.2 Flow-Number Model

The fluid through the multiway valve adheres to the throttling equation, as shown in Eq. (1).

$$q = C_{{\text{d}}} A\sqrt {2\Delta p/\rho }$$
(1)

where q is the flow rate, Cd is the flow coefficient, A is the orifice area, Δp is the pressure drop and ρ is the density of the fluid.

The product of Cd and A was defined as flow-number. The throttling characteristics of the multiway valve were described with the flow-number in the model of the positive flow control system. The flow-number model had been established in Checn et al. [12] to predict the flow-number of a single groove. The flow-number of the multiway valve could be obtained by a simple linear superposition of each groove’s flow-number. Therefore, the mapping relationship between the spool geometries and the flow-number was established.

3 Discussion

3.1 Objective Function

The comprehensive performance was evaluated from three aspects of micro movement, speed regulating and energy consumption.

The dead zone as well as the flow rate at the beginning should be as little as possible to improve the micro movement performance. The micro movement performance was evaluated by the distance from the origin when the swing motor just started. The micro movement performance function is shown in Eq. (2).

$$f_{1} = \left[ {\left( {q_{{{\text{m}}1}} /q_{{{\text{m}}\max }} } \right)^{2} + \left( {x_{1} /x_{\max } } \right)^{2} } \right]^{0.5}$$
(2)

where f1 is the micro movement performance function. qm1 and x1 are the swing motor’s flow rate and the spool stroke at the beginning. qmmax and xmax are the two at the maximum spool displacement. The difference of order of magnitudes and dimensions can be cleared through normalization.

The speed regulating performance was evaluated by the linearity of the flow rate, as shown in Eq. (3). The less the value of f2, the more linear the swing motor’s flow rate.

$$f_{2} = \max \left( {\left| {q_{{{\text{m}}i}} - y_{i} } \right|} \right)/q_{{{\text{m}}\max }}$$
(3)

where f2 is the speed regulating performance function. qmi is the swing motor’s flow rate at the ith spool stroke. yi is the linear fitting value of qmi. f2 represents the maximum difference between the flow rate curve and its fitting line within the speed regulating zone.

The energy consumption performance was evaluated by the power of the main pump, as demonstrated in Eq. (4).

$$f_{3} = \sum\limits_{i = 1}^{n} {p_{{{\text{pump}}}} (x_{i} ) \cdot q_{{{\text{pump}}}} (x_{i} )}$$
(4)

where f 3 is the energy consumption function. ppump and qpump are the pressure and flow rate of the main pump respectively. xi is the ith spool stroke.

The comprehensive performance of excavators was evaluated by the weighted mean of f1, f2 and f3, as shown in Eq. (5).

$$F = \alpha_{1} f_{1} + \alpha_{2} f{}_{2} + \alpha_{3} f_{3}$$
(5)

where F is the comprehensive performance function. α1, α2 and α3 are weight coefficients.

3.2 Sequential Design

In conventional sequential design, every subsystem is designed independently. The comprehensive performance was optimized with the positive flow control parameters, leaving the throttling characteristics unchanged. The sequential design procedure is illustrated in Fig. 4.

Fig. 4
A schematic of the design procedure. The optimizer points to the system model via parameters. A controller points to the valve and the valve points back to the controller under the system model. The system model points to the optimizer via F.

Sequential design procedure

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The optimizer only changed the parameters of the positive flow controller in the system model. Then the comprehensive performance function F was computed as the objective function. The optimal control parameters were obtained through the sequential design.

3.3 Multidisciplinary Design Optimization

The MDO of the positive flow control system was carried out with the control parameters, multiway valve’s throttling characteristics and the spool geometries as design variables simultaneously. The MDO procedure is demonstrated in Fig. 5.

Fig. 5
A flowchart for the M D O procedure. It flows through collaborative optimizer, optimizer 1, parameters, C d A, F, system model, controller, valve, structure, spool, flow number model, and optimizer 2.

MDO procedure

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The optimizer 1 optimized the comprehensive performance with both the control parameters and multiway valve’s flow-number changeable. The optimizer 2 designed the spool structures to meet the required throttling characteristics. The collaborative optimizer was responsible for minimizing the interdisciplinary discrepancies while satisfying specific local constraints.

4 Results

The optimized and original flow rate is shown in Fig. 6.

Fig. 6
A line and dot plot of q m versus x. The estimated values for the dots are as follows. (0, 0), (2, 0), (4, 45), (6, 100), (140), (8, 150), (200). It has two increasing lines for sequential and M D O.

Optimized and original flow rate

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Both the sequential design and MDO can improve the linearity within the speed regulating zone. However, the dead zone can only be minimized through the MDO strategy. The detailed performance functions are listed in Table 1.

Table 1 Detailed performance functions
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The speed regulating performance and energy consumption performance were improved by both the sequential design and MDO. The micro movement performance was mainly modified through the MDO. Decreasing the dead zone would cause more throttling loss by the sequential design because only the displacement of the main pump was adjusted. In contrast, the MDO took control parameters, multiway valve’s throttling characteristics and spool geometries as design variables at the same time. The micro movement performance could be optimized with the coordination of different subsystems, with little influence on the speed regulating or energy consumption performance.

5 Conclusions

Main conclusions are as follows.

  1. (1)

    The coupling relationship among different subsystems can be fully explored through the MDO method. The global optimal solution can be searched in a larger design space.

  2. (2)

    The comprehensive performance function of excavators’ swing circuit was proposed to guide the design of the positive flow control system. The quantification operation performance was evaluated from three aspects of micro movement, speed regulating and energy consumption.

  3. (3)

    The comprehensive performance function of the MDO was 17.1% better than that of the sequential design.