Influencing Factors of Cutting Force for Apple Tree Branch Pruning

Abstract

Apple, which occupies the first position in the world with regard to its yield, is an important economic crop in China. Pruning of apple trees is still dominated by manual pruning, resulting in high labor costs and low efficiency. Additionally, there are some limitations with pruning machines. Thus, research regarding the mechanical properties of apple branches is the basis for the designing proper pruning machine. This paper aims to study the effect of the feed rate, cutting line speed, branch diameter, and moisture content on the cutting force. Results revealed that cutting force depended on the feed rate, cutting line speed, and branch diameter. Furthermore, both the cutting line speed and the branch diameter had a significant effect on the cutting force (p < 0.01), while the feed rate had a small effect on the cutting force (p > 0.05). However, the moisture content had no effect on the cutting force, with a difference of cutting force between samples with moisture content of 15% and 50% less than 5%. Based on the experiments performed, an equation relating the feed rate, the cutting line speed, the branch diameter was derived to calculate the cutting force. By verification test, it established that regression equation was valid with error less than 4%. This study explored the mechanical properties of apple branch, and obtained the optimal cutting parameters, which can provide a reference for the design of the pruning machine.

1. Introduction

Apple, as an important economic crop, is planted over 1938.57 thousand hectares in China. All apple trees require pruning in winter, which is a critical management to promote apple yield by adjusting nutrition distribution [1]. Pruning can reduce competition for assimilates thus providing maximum benefit in terms of assimilating distribution; and it is an environmentally friendly method of reducing crop load [2]. Pruning can be carried out manually or mechanically using pruning tool [3]. Despite the increasing application of multi-function machines in planting and horticulture, pruning of apple trees still needs to be performed correctly by professionals. This is mostly due to different growing conditions of apple trees, making mechanical pruning impossible using standardized methods as used in horticulture and other crops.

Recently machine manufacturers have been offering various equipment for pruning, automating this labor-intensive procedure [4]. However, indiscriminate mechanical pruning will lead to low yields, making it unsuitable to employ automatic pruning machine [5]. At present, pneumatic pruning machine still has an important role in apple tree pruning. Considering that potential labor savings may be offset by the disadvantages of poor wear resistance and short battery life, pneumatic pruning machine need to be optimized. Thus, for the optimization of apple pruning machine, it is essential to control the cutting process correctly and understand the interaction between tools and wood.

Measuring the cutting force is an important parameter for optimizing the machine. Factors influencing the process of pruning can be divided into two groups, the characteristics of different materials, such as moisture content, density, and the cutting parameters, such as cutting speed, feed rate [6,7,8,9,10]. The effect of diameter was well evaluated by several studies, which indicated that a linear relationship existed between diameter and cutting force [11,12]. As for the effect of moisture content, it is generally considered as the main factor of cutting force. However, the reports of moisture content were different. Krenke et al. reported that the cutting force of spruce with 6% moisture content was significantly lower than that with 18% moisture content [11]. Lucic et al. reported that the cutting force of green wood was significantly lower than that of dry wood [13].

Cutting force behavior is also affected by cutting speed and feed rate. Krilek et al. mentioned that the cutting force increased with the increase of feed rate [14]. Schmidt et al. indicated that the increase of cutting force can be explained by the reduction of feed force. The feed force decreased with the increase of feed rate except for the tool angle at 46 degrees to 80 degrees [15]. Vahid et al. reported that the cutting power and waviness increased with the increase of feed rate. This may be due to an increase in depth of cut resulting from an increase in feed rate [16]. Moradpour et al. stated that the cutting force decreased when the cutting speed increased [9]. Abdallah et al. showed that the cutting force decreases with the increase of cutting speed [17]. Ghahraei et al. showed that the rotary cutting speed had a significant effect on the cutting torque, and the cutting torque was reduced by 26.3% when the cutting speed was increased from 308 rpm to 788 rpm [18]. Johnson et al. proposed that the cutting energy of corn stalk increased at higher cutting speed, but more energy was absorbed by shock, vibration, and deflection making energy waste. Excessive increase of cutting speed had little effect on cutting efficiency [19].

Considering opposite results of cutting speed in previous research, it is mostly due to the different stems and cutting parameter combination. The optimization of cutting parameters for wood materials is relatively sufficient, but little attention is paid to the optimization of pruning parameters for fruit trees. Few studies summarized the specific cutting force law for pruning. Therefore, this study is conducted to determine the effect of physical properties (diameter, moisture content) and cutting factors (cutting speed, feed rate) of apple tree branches on cutting force, offering reliable estimates. This study also can make groundwork for the design of pruning machine of apple trees and other similar fruit tree.

2. Materials and Methods

2.1. Test Materials

Defect-free samples were taken from 9-year-old Red Fuji trees in an orchard in the north of Hebei Province and shown in Figure 1. The moisture content was between 15% and 55%, the diameter of the branch was between 10 mm and 30 mm, and the density of the branch was 0.55 g·cm⁻³.

The moisture content of the branches samples was measured according to the following drying procedure. A certain weight of branches was put into the rapid moisture meter at a temperature of 105 °C for 24 h; then, samples were weighed every 1 h by an electronic balance until the mass did not reduce. The moisture content was calculated by dividing the mass loss by the original total mass. According to EN 14774-2: 2009, the Equation (1) for calculating the moisture content is as follows:

$$W=\frac{\left(m_2-m_3\right)+m_4}{\left(m_2-m_1\right)+m_4}\times 100\%$$

(1)

where: W—the moisture content of branches (%); m₁—the mass of the empty drying container (g); m₂—the mass of the drying container and wet branches (g); m₃—the mass of the drying container and branches after drying (g); m₄—the mass of the moisture associated with packing (g).

The moisture content of newly cut branches is about 50~70%, and that of naturally dried branches is 10~15%. There is a slight difference in the cutting force between fresh apple branches and dried branches when we conducted the pre-experiment, however it is not presented in the manuscript. Two typical moisture contents, 15% and 50%, were selected to investigate the effect of moisture content on cutting force.

2.2. Test Equipment

The experimental setup is composed of sawing device, feeding device, and data acquisition device, as shown in Figure 2.

The 400-mm diameter, 3.4-mm thickness saw blade with 100 saw teeth is fixed on the frame, powered by AC motor. By the means of the variable-frequency drive, saw blade can modulate the rotational speed from 1 to 2880 r/min corresponding to cutting line speed from 0 to 60 m/s. The maglev feeding mechanism allows to regulate feed rate from 0 to 1 m/s. Therefore, when the feed mechanism moves, the branch sample, which is fixed on the maglev feed mechanism by a U clamp, is cut by the saw blade. The cutting force monitoring is conducted by the torque sensor and the pressure sensor. The torque sensor, which is fixed between saw blade and frame, detects the torque in the cutting process. Then, torque is processed by Excel, converting into the tangential force. The pressure sensor, which is mounted on the feed unit, detects the radial force. In order to reduce the influence of maglev feeding mechanism on sensors, data acquisition is performed using the NEC OMNIACEII RA1100 oscilloscope with a frequency of 400 kHz and 3-level low-pass filter. The technical parameters of sawing test benches are shown in

Table 1. Main technical parameters of test equipment.

Parameters	Values
Three-phase AC motor Rated rotating speed (r/min)	2880
Torque sensor range (N·m)	0~50
Torque sensor measurement accuracy (%)	≤0.5
Tension-compression sensor range (kg)	0~10
Tension-compression sensor measurement accuracy (%)	≤0.03
Acquisition frequency of oscilloscope (Hz)	1000

.

2.3. Cutting Force Experiments

A single factor experiment was conducted to study the effect of cutting line speed and feed rate and branch diameter on the cutting force. The parameters, five cutting line speeds (20, 30, 40, 50, and 55 m/s), nine feed rates (0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1 m/s), and five branch diameters (12, 15, 18, 20, and 25 mm) were chosen for the experiments. On the basis of single-factor test results, according to Box–Behnken principle, three levels of cutting line speeds (30, 40, and 50 m/s), three levels of feed rate (0.3, 0.6, and 0.9 m/s), and three levels of branch diameters (15, 20, and 25 mm) were chosen for the full factorial experiment. The combination of feed rate, cutting line speed, and branch diameters yielded different values of cutting force (

Table 2. Design and results of full factorial test.

Branch Diameter (mm)	Cutting Line Speed (m/s)	Feed Rate (m/s)	Cutting Force (N)
−1	0	1	18.01
0	0	0	8.16
0	1	−1	6.16
−1	−1	0	11.5
0	1	1	9.07
1	1	0	6.47
0	−1	1	10.09
0	0	0	7.64
−1	1	0	10.52
0	0	0	8.48
0	−1	−1	4.58
1	−1	0	6.45
0	−0	0	8.37
1	0	1	7.63
−1	0	−1	9.01
1	0	−1	5.32

). Each experiment in the same condition was repeated three times. The results were processed in Design Expert.

3. Results

3.1. Single Factor Experiment

3.1.1. Cutting Line Speed

Figure 3 showed a relationship between the cutting line speed and the cutting force. Results showed that peak cutting force presents a parabola trend, when the cutting line speed increased. The trend of radial force coincided well with those of peak cutting force. The tangential force was inversely proportional to the cutting line speed. These results can probably be explained by the decreased feed per tooth due to the increase of the cutting line speed. Decreasing the feed per tooth was associated with a lower material removal rate (MRR) of sample resulting in lower cutting force [20,21]. Thus, enhancing cutting line speed from 20 to 50 m/s significantly decreased the cutting force [9,17]. However, when the cutting line speed exceeded 50 m/s, the cutting force increased with the increase of the cutting line speed. The increasing cutting force could also be explained by severe vibration and shock between circular saws and workpiece due to the excessively high rotation speeds (the cutting line speed) resulting in sawing deviation and wear of a circular saw. On the other hand, increasing the cutting line speed from 20 to 50 m/s was also associated with a better surface quality [16]. Good surface quality refers to the cut surface is smooth with no split and no charring, which was consistent with the reduction of cutting force, whereas excessively high cutting line speed (over 50 m/s) had a negative impact on surface quality. The result also established that the critical cutting line speed observed is 50 m/s.

3.1.2. Feed Rate

The cutting force and the radial force were directly proportional to the feed rate (Figure 4a,b). The tangential force had a cubic function to feed rate (Figure 4c), but the fitting coefficient was poor (R² = 0.476). Although the effect of feed rate on the tangential force was not well pronounced at a feed rate of 0.2–0.8 m/s, the tangential force was reduced significantly, when the feed rate exceeded a certain limit (0.8 m/s). It can be seen that increasing the feed rate from 0.2 to 1.0 m/s corresponded to an increase of 228% in cutting force and 254% in the radial force respectively. The increase of cutting force and radial force can be attributed to great radial impact between circular saws and workpiece caused by the increased feed rate. Results also indicated that saw blade vibrates violently, with the increase of feed rate, due to great radial impact leading to poor surface quality. Moreover, excessive impact will also accelerate the wear of the saw blade and shorten its life. However, the results contradicted that put forth by Barcik et al., Moradpour et al., Li et al. [9,13,22]. The contradictory results may be attributed to the different measuring methods and the different ratios of cutting line speed to feed rate.

3.1.3. Branch Diameter

It can be seen that there is a significant relationship between the branch diameter and the cutting force, the radial force, and the tangential force (Figure 5). As the branch diameter increased, the cutting force and radial force increased significantly. The increase of the tangential force was linear with branch diameter. The results were consistent with previous research [23]. The effect of branch diameter on cutting force increasing was contributed to the friction between circular saws and workpiece. The increase of branch diameter was associated with the increased plant fiber [24], leading to higher cutting force. Another positive effect of the branch diameter on the cutting force increasing can be attributed to the number of teeth involved in cutting. Under the same condition of feed per tooth, the increase of the cutting force came through the increased teeth numbers involved in cutting, which are owing to the increased cross-sectional area [25,26].

3.1.4. Moisture Content

It is observed in Figure 6 that the effect of moisture content on cutting force was not well pronounced. According to the results, the difference of cutting force between branches with 50% moisture content and branches with 15% moisture content was less than 5%. The result was inconsistent with previous research [11,27]. It can be explained by different cutting methods and different plant species. Comparing to pendulum type cutting and shear, sawing was less affected by the biological characteristics of plants. In addition, branches with higher moisture content were more likely to have poor surface quality.

3.2. Statistical Model

A full factorial test produced 16 different treatments (Table 2). The regression equations, which are composed of cutting line speed, feed rate, and branch diameter, can be obtained by processing the data with Design Expert 10 software. These correlations are illustrated in the following equations:

F = 10.17 − 2.56 D + 0.82 V_c + 35.61 V_f + 0.005 V_c D − 1.12V_f D − 0.22V_cV_f
+ 0.061 D − 0.0099 V_c2 + 2.98 V_f2

(2)

where F is the specific cutting force (N); D is the branch diameter (mm); V_c is cutting line speed (m/s); V_f is feed rate (m/s). Further analysis indicated that the correlation between cutting force and cutting line speed (p < 0.01) and branch diameter (p < 0.01) was statistically significant (

Table 3. Variance analysis of regression equation.

	Sum of Squares	Freedom	Mean Square	F Value	Significant Level (p)
Model	142.61	9	15.85	22.82	0.0002
Vc	67.11	1	67.11	96.66	<0.0001
Vf	0.02	1	0.02	0.029	0.87
D	48.66	1	48.66	70.09	<0.0001
VcVf	0.25	1	0.25	0.36	0.5674
VcD	11.19	1	11.19	16.12	0.0051
VfD	1.69	1	1.69	2.43	0.1627
Vc2	9.83	1	9.83	14.16	0.007
Vf2	4.12	1	4.12	5.94	0.045
D2	0.3	1	0.3	0.44	0.53
Residual	4.86	1	0.69
Lack of Fit	4.42	7	1.47	13.42	0.0149
Total	147.47	16

). An obvious reduction of the cutting force was observed when the cutting line speed increased from 30 m/s to 50 m/s (Table 2). Although the feed rate produced larger cutting force (Figure 4), according to the results in Table 3, little dependence on the feed rate was observed for cutting force (p < 0.87). The effect of feed rate on cutting force was consistent with previous research, which is put forward by Krilek et al. [14].

The influence of the interaction of various factors on the cutting force was shown in Figure 7. By analyzing contours and response surfaces, the results showed that the interaction between any two factors affects the cutting force. The optimal combination of sawing was: cutting line speed 40 m/s, feed rate 0.6 m/s.

3.3. Verification Test

Another three groups of cutting parameters were chosen to test the accuracy of the prediction model. Each group of tests was repeated three times. The selected parameters and test results are shown in

Table 4. Results of verifying tests.

Branch Diameter (mm)	Cutting Line Speed (m/s)	Feed Rate (m/s)	Prediction of Cutting Force (N)	Measured Cutting Force (N)	Error (%)
15	30	0.6	11.93	11.5	3.7
15	40	0.3	8.75	9.01	2.9
20	40	0.6	8.2	8.48	3.4

. The results revealed that the error between the predicted cutting force and the measured cutting force was less than 4%, and the model was reliable.

4. Discussion

It can be found that the cutting force in this paper was well below that in previous studies which reported higher cutting force for stems such as litchi tree, longan tree, pear tree [21,26,28,29]. This was primarily due to the different cutting parameters, in particular the cutting line speed in previous studies was much lower than 40 m/s. Many existing studies were performed under ideal condition employing universal mechanical testing machine with quite a low cutting speed [17]. Previous research indicated that cutting speed and feed rate had significant influence on cutting force [30]. However present research showed that the effect of feed rate on cutting force was not significant. This phenomenon may attribute to the increasing vibration caused by feed rate induced by variability. Cutting line speed and feed rate affected cutting force by changing the feed per tooth. Feed per tooth was inversely proportional to cutting line speed and directly proportional to feed rate. Present results were consistent with the theoretical analysis. Therefore, the cutting force decreased significantly with the increase of cutting line speed and increases with the increase of feed rate.

The present results also showed that cutting force significantly increased with branch diameter. This was mostly due to lignin content, larger branch diameter relating to high lignin content led to higher cutting force. Lignin increases the hardness of the branch and fiber increases the toughness of the branch, hence both increase the cutting force. Previous studies indicated that the moisture content had a great influence on the tensile strength of branch fiber resulting in higher cutting force [21]. However, the present results showed that the moisture content had little effect on the cutting force, and the difference of cutting force was less than 5% and the moisture content was 15% and 50%. It can be explained by different cutting modes. The cutting mode of circular saw blade is unlimited by the biological characteristics of crops, so that the effect of moisture content on the cutting force is not significant. Although apple branches show different material properties under different moisture content, when the moisture content is less than 51%, the apple branch presents plastic material properties. When the moisture content is more than 51%, the apple branch shows brittle material properties. The cutting force increases first, and then decreases with the increase of moisture content [12]. The moisture content of apple branches used in this study is only 15% and 50%, so the decrease of cutting force is not observed when the moisture content is higher than 51%.

5. Conclusions

In this study, the effects of the cutting line speed, feed rate, and branch diameter (p < 0.01) on the cutting force were evaluated. It was revealed that the cutting line speed and the branch diameter have a significant effect on the cutting force. However, the feed rate played a relatively minor role in cutting (p < 0.87). To be more specific, the cutting line speed produced a reduction in the cutting force, when the cutting line speed was within 20–50 m/s. While high cutting line speed yielded an increase in cutting force and a decline in cutting quality. The larger cutting force was required by the increase of feed rate or the branch diameter. Additionally, the difference of cutting force between branches with 15% and 50% moisture content is less than 5%, which indicated that the effect of moisture content on cutting force can be ignored. Thus, three factors including cutting line speed, feed rate, and branch diameter were introduced in the regression equation, which described the rule of cutting force. The optimum combination of the cutting parameters is the speed of cutting line that is 40 m/s, and the feed rate is 0.6 m/s. There is good agreement between the predicted and measured cutting forces. This study provides reliable perspectives to estimated cutting force for developing cutting machines.

Furthermore, the more precise influence of the moisture content on cutting force can be further investigated. Due to the limitations of experimental conditions, the experimental state cannot completely simulate the natural state of cutting branches, and the experimental results may not be completely consistent with the actual results. Only three samples were used in each experiment, and the number of samples could be larger to ensure the reliable test results.