1. Introduction
Agricultural residues are the most important resources for biomass and animal feeding. Size reduction is an important prerequisite to produce forage and biomass energy. Nevertheless, this procedure was also considered as one of the most energy-inefficient tasks [
1,
2]. The efficiency of the size reduction has typically been assessed through the amount of cutting force and energy required [
3,
4,
5]. It has been found that equipment using shear mode for size reduction may hold promise for improved energy efficiency [
6]. The energy required for cutting forage stems has been evaluated for a wide range of plant species, cutting velocities, moisture contents, and stem sizes [
7]. The results were classified into three categories [
8]: quasistatic shearing (cutting velocities less than 30 mm/s), cutting with a counter-edge (at velocities greater than 0.5 m/s), and impact cutting without a counter-edge (at speeds up to 60 m/s). It has been shown that minimal energy is required for quasistatic shearing and for cutting with a counter-edge. Prasad and Gupta [
9] found specific energies for corn stalks in the range of 19–24 mJ/mm
2 in quasistatic measurements. However, the energies required for impact cutting are generally 1 or 2 orders of magnitude greater than those recorded for quasistatic or counter-edge cutting [
8].
Quasistatic tests have been used in many studies of cutting force and cutting energy for various kinds of agricultural residues. For example, the change of shear force and energy of cotton stalk were evaluated by Pekitkan and Eliçin [
10]. Another quasistatic test using a universal machine was implemented to study the effects of diameter and age of grape canes on cutting force and energy [
11]. Using the same experimental apparatus, the effects of moisture content, internode region, and oblique angle on the mechanical properties of sainfoin stem were evaluated by Boydaş et al. [
12]. Other authors [
13] found that the shearing angle has a strong effect on the cutting force and specific energy. A smaller cutting angle was related to a larger cutting resistance.
Impact cutting tests have been investigated in many studies, where the effect of various factors on the force and energy were evaluated. For corn stalks, Prasad and Gupta [
9] showed that the optimum values of bevel angle, knife approach angle, and shear angle providing the minimum cutting force and energy consumption were 23°, 32°, and 55°, respectively. An investigation by Azadbakht and Zahedi [
4] showed that the effects of height, moisture content, and their interaction on cutting energy are significant. The energy consumption during impact cutting of canola stalk [
14] was considered as a function of moisture content and cutting height.
Generally, agricultural chopping systems are designed based on two main cutting principles: scissor shearing to provide shear stress, and rotary knives to generate both impact and shear stress on the stalks [
15]. For the first case, the plants to be cut are pressed against the fixed counter edge with the help of cutter. The knife speed is resolved into two components: chopping speed, which penetrates into the material, and the sliding cut speed [
16].
The analysis of the literature above indicates that cutting speed and blade geometry have strong effects on cutting force and cutting energy for agricultural residues. Most of the investigations had been done for impact cutting with a single knife. Several others have functioned with counter edge cutting but under quasistatic mode, where the cutting velocity is extremely low. There have been few studies on chopping processes with counter edges and under high-velocity conditions. Besides, it is worth noting that the power consumption may be large, even when the shearing force is small, if the corresponding cutting velocity is high. Consequently, it is expected to minimize both cutting force and power consumption simultaneously. A recent investigation with such purpose was conducted using factorial experimental designs [
17]. The main aims of this study are to provide another approach of solving such problem by using Taguchi–grey relational analysis technique. The Taguchi method with grey relational analysis (GRA) has been employed in several experimental investigations in agriculture and biotechnology [
18,
19,
20,
21]. However, there has not been found a similar study for optimization of chopping agricultural residues.
2. Materials and Methods
2.1. Experimental Setup
The setup was made based on the outline of a 93ZP-1000 straw chopper produced by the Liaoning Fengcheng Donfeng Machinery Factory (Liaoning, Dandong, China).
Figure 1 illustrates a 3D model of the chopping device.
In
Figure 1, a belt wheel (1) receives and transfers drive torque from a Direct-current (DC) motor to the cutting knifes (3) via the main spindle (2). Being made in the form of a circular sector, the cutter can be easily adjusted to obtain a required approach angle α by using the screw (4) and the clamp set (5). In the figure, the position of the stalk to be cut (6) is determined by two angles: the feed angle β and the tilt angle φ. In this study, the tilt angle φ remained at 90°.
The experimental setup was then implemented as illustrated in
Figure 2. In this figure, all parts are labelled similar to those in
Figure 1. As mentioned, the approach angle α is adjusted by the screw (4) and the clamp set (5) (
Figure 2a). In addition, a dynamic force sensor (9) is used to measure instant cutting force. In
Figure 2b, the way to adjust the feed angle β by the clamp set (10) is illustrated.
The force sensor model 9712A500 (Kistler, Winterthur, Switzerland), with sensitivity of 2.4729 mV/N, was placed under the counter shear bar to measure the cutting force. A DAQ model NI-USB-6008 (National Instruments, Austin, Texas, USA) and the Ni Signal Express software were employed to collect the cutting force data. The experimental rig was driven by a commercial 1.5 kW DC motor, working with a voltage supply ranging from 50 to 220 V. By adjusting the voltage provided by an Alternating-current (AC) variable transformer combined with a rectifier, the variable speed of the cutting spindle could be obtained. The maize stalks used for this experimental study were kept in an air-conditioned room for one week after harvest from the fields in the northern part of Vietnam. The wet basis moisture content of the samples was then measured by drying–weighting method. The wet basis moisture content was around 81%.
2.2. The Multiobjective Function
The average power consumption is the amount of energy consumed per unit time. Consequently, given a cutting force
Fc and the corresponding cutting velocity
V, the cutting power
Pc can be expressed as:
In chopping machines, where a number of knifes are equally arranged on a rotating disk, the cutting force signal appears as a train of periodic, near identical pulses, as shown in
Figure 3a. The peaks of the cutting force signal were collected for this experimental study.
With the chopping disk driven by an electrical motor, it can be assumed that the cutting velocity is approximately constant during each cutting process. Applying Equation (1), the instantaneous cutting power at a function of time can be obtained from the cutting force signal, as shown in
Figure 3b.
Denoting the period as
T, i.e., the time between two consecutive chopping processes, the energy consumed for cutting during such time can be expressed as:
The total consumed power then can be calculated by:
denoting the pulse time as τ so that:
The duty cycle of the pulse train then can be defined as:
In this study, the duration of each cutting pulse is approximately calculated as the time required for a point on the cutting edge to completely pass the stalk diameter. To simplify the calculation, the stalk diameters are assumed to be their average value and thus a constant, assigned as
daverage. In this study,
daverage was set to be 0.02 m. Consequently, the pulse time τ is defined as:
Finally, the power consumption at a certain cutting velocity
V can be calculated as:
To simplify the notation in the experimental analysis, the peak value of the cutting force in each chopping event will be considered as demonstrative of cutting force and thus will be noted as the cutting force
F in this study. Consequently, the multiobjective optimisation problem can be expressed as:
2.3. Design of Experiments and Multiobjective Optimization Process
In this study, the approach angle, the feed angle and the cutting velocity were selected to be three experimental variables. The design of experiments was built using three parameters at three levels each, leading to the L27(3
3) orthogonal array of tests. The investigated parameters and their levels considered in this study are shown in
Table 1.
As mentioned, the two objective responses, including peak values of cutting force and cutting power, were selected for the optimization process. Once the normalized signal-to-noise (S/N) ratio values of the responses were calculated, corresponding grey relational coefficients were carried out. The grey relational analysis was then implemented in order to find the trade-off optimum condition. Detailed steps of calculation techniques and results are presented in the next section.