176 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No.

Experimental research on affecting factors of the cutting quality of

sugarcane harvesters under complicated excitations

Hanning Mo1,2,3, Shaochun Ma1,3, Chen Qiu1,2,3*, Zhimin Huang1*, Shangping Li4
(1. Guangxi Key Laboratory of the Advanced Microwave Manufacturing Technology, Guangxi Academy of Sciences, Nanning 530007, China;
2. School of Mechanical and Resource Engineering, Wuzhou University, Wuzhou 543000, Guangxi, China;
3. State Key Laboratory of Intelligent Agricultural Power Equipment, College of Engineering, China Agricultural University,
Beijing 100083, China;
4. College of Electronic Information, Guangxi Minzu University, Nanning 530006, China)

Abstract: The sugarcane field excitation, cutting forces and the engine excitation constitute complicated excitations acting on
sugarcane harvesters. In this study, the sugarcane cutting mechanism under complicated excitations was analyzed. The
dynamics and the mathematical models of sugarcane harvesters were established and simulated. Based on theoretical analysis,
sugarcane cutting experiments were done on a self-built sugarcane harvester test platform (SHTP), designed as single-factor
and the orthogonal experiments. Effects of the sugarcane field excitation characterized by the sugarcane field excitation device
(SFED) output frequency, the engine excitation characterized by the actuating engine output frequency, the cutter rotating
speed, the sugarcane harvester travelling speed simulated through the sugarcane transporting speed of the SHTP and the cutter
inclination angle on the cutting quality of sugarcane harvesters were studied. Effects of the axial cutter vibration on three-
directional cutting forces and the sugarcane cutting quality (SCQ) as well as effects of three-directional cutting forces on the
SCQ were further studied. It is shown that the sugarcane field excitation, the axial cutter vibration amplitude and frequency as
well as the three-directional cutting forces have significantly negative monotonic correlated effects on the SCQ while the cutter
rotating speed, the sugarcane harvester travelling speed and the cutter inclination angle have significantly positive monotonic
correlated effects on the SCQ. Significance levels of effects on three-directional cutting forces and the SCQ form high to low
are as follow, the axial cutter vibration, the sugarcane field excitation, the cutter rotating speed, the engine excitation, the cutter
inclination angle, the sugarcane harvester travelling speed. The theoretical analysis results were verified through experiment
and an optimal combination was obtained with the cutter rotating speed of 700 r/min, sugarcane harvester travelling speed of
0.6 m/s and cutter inclination angle of 8º. This study can provide a reference for setting cutting parameters of sugarcane
harvesters with a good SCQ.
Keywords: sugarcane harvester, cutting quality, complicated excitations, experimental research, theoretical analysis
DOI: 10.25165/j.ijabe.20241705.7947

Citation: Mo H N, Ma S C, Qiu C, Huang Z M, Li S P. Experimental research on affecting factors of the cutting quality of
sugarcane harvesters under complicated excitations. Int J Agric & Biol Eng, 2024; 17(5): 176–192.

with an automatic in-soil-cutting-depth-controlling system

1 Introduction dependent on sugarcane field roughness. Johnson et al.[6,7] studied
Valued achievements on improving the cutting quality of effects of the cutting speed and the cutting-edge angle on the cutting
sugarcane harvesters have been obtained. Thanomputra et al.[1] energy of sugarcane harvesters. Kroes et al.[8] established a
improved the cutting efficiency of sugarcane harvesters through kinematic double-cutter model to study the cutter trajectory and
abrasive-sand-added high-pressure water cutting. Mello et al.[2,3] calculate the maximum ratio between the sugarcane harvester
used different cutters to do sugarcane cutting experiments and found travelling speed and the cutter rotating speed for the purpose to
the one with the best cutting quality. Silva et al.[4] evaluated the improve the sugarcane cutting quality (SCQ) theoretically. Liu et
sugarcane ratoon damage degree caused by the cutting height al.[9] obtained the shear modulus and the tensile strength of
through statistical experiment data. Ripoli et al.[5] designed a cutter sugarcanes through tension and compression experiments.
Taghijarah et al.[10] obtained the bending strength of sugarcanes
Received date: 2023-01-13 Accepted date: 2024-02-21 through measuring cutting forces. Lai et al.[11,12] found the sugarcane
Biographies: Hanning Mo, Post-Doctoral Research Fellow, Associate Professor, field excitation has a bad effect on the cutting system of sugarcane
research interest: agricultural mechanization, Email: 1433025842@qq.com; harvesters, causing the axial cutter vibration, which leads to a poor
Shaochun Ma, Post-doctoral supervisor, Professor, research interest: agricultural SCQ. Wang et al.[13] established a cutter vibration model to study the
mechanization, Email: cecau1905@163.com; Shangping Li, Doctoral
Supervisor, Professor, research interest: agricultural mechanization, Email:
effect of the bearing clearance on the cutting system vibration.
ceigun1952@163.com. Huang et al.[14] simulated the sugarcane cutting process through
*Corresponding author: Chen Qiu, Post-Doctoral Research Fellow, Associate infinite element analysis to study relationships among cutting
Professor, research interest: agricultural mechanization. School of Mechanical forces, the cutter inclination angle and the sugarcane cutting speed.
and Resource Engineering, Wuzhou University, Wuzhou 543000, China. Tel: +86- Liu et al.[15] studied relationships among the sliding cutting angle,
15878052157. Email: 303494977@qq.com; Zhimin Huang, Post-doctoral
the cutter inclination angle, the sugarcane cutting speed and cutting
supervisor, Professor, research interest: agricultural mechanization and
biophysics. Guangxi Key Laboratory of the Advanced Microwave Manufacturing forces. Xu et al.[16] established a cutting system model to obtain
Technology, Guangxi Academy of Sciences, Nanning 530007, China. Tel: +86- curves of cutting force changing with time and cloud pictures of the
18697952998. Email: clifegxu1978@163.com. cutting system vibration displacement in the sugarcane cutting
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 177

process. Yang et al.[17,18] studied effects of the cutter rotating speed In this study, a self-built sugarcane harvester test platform
and the sugarcane harvester travelling speed on the cutting quality (SHTP) with complicated excitations simulated through two
of sugarcane harvesters. sugarcane field excitation devices (SFED) and an actuating engine
Research above was about mechanics characteristics of was developed to study effects of these influence factors on the
sugarcanes, effects of the sugarcane cutting form, design parameters axial cutter vibration, three-directional cutting forces and the cutting
of the cutters, the cutting system vibration, the sugarcane harvester quality of sugarcane harvesters. That is, experiments in sugarcane
travelling speed and the cutter rotating speed on the cutting quality fields can be simulated in labs, which is never achieved in previous
of sugarcane harvesters and cutting forces. It is shown that the study. This study provided a reference for setting such cutting
sugarcane field excitation has a bad effect on the cutting quality of parameters as the cutter rotating speed, the cutter inclination angle
sugarcane harvesters in that it causes vibrations of sugarcane and the travelling speed of sugarcane harvesters with a good SCQ.
harvesters leading to vibrations of the cutters.
As is mentioned above, the axial cutter vibration has a bad 2 Sugarcane cutting mechanism under complicated
effect on the cutting quality of sugarcane harvesters. The sugarcane excitations
field excitation, cutting forces and the engine excitation constitute
complicated excitations acting on sugarcane harvesters. However, Simplified as a planar problem, the force diagram of a
none of the research above was focused on effects of the sugarcane sugarcane cut by a blade is shown in Figure 1[19,20]. The x axis points
field excitation, the engine excitation, the cutter rotating speed, the to the direction of the sugarcane harvester travelling speed. The z
cutter inclination angle, the sugarcane harvester travelling speed on axis along the cutter axes points to the upward vertical direction.
the cutting quality of sugarcane harvesters, the axial cutter vibration Forces and motions along the y axis are not considered, so gravities
and cutting forces comprehensively under actual complicated and the supporting force generated by the ground acting on the
excitations in sugarcane fields. sugarcane are not considered[19,20].

An upward axial blade vibration A downward axial blade vibration

vz vx
A crack region A crack region
A sugarcane A sugarcane
vx vz
A blade Fz1 or f1 Fz2 or f2
N1 φ F1 A blade N2 φ F2
F01 F02
θ θ
O Fx1 O Fx2
S Mz1 S Mz2
An axial crack FA1 An axial crack FA2
z D z D

x x
y y
a. Effect of the upward axial blade vibration on the sugarcane b. Effect of the downward axial blade vibration on the sugarcane
Figure 1 Force diagram of a sugarcane

According to Figure 1a and Figure 1b, when an upward axial or Equation (3a). When the downward axial cutter vibration appears,
a downward axial vibration of the cutters appears, the blade will the friction force f2 is calculated through Equation (3b).
generate an upward pressure Fz1 or a downward pressure Fz2 acting  ( )
 N1
on the sugarcane and the upper or the lower surface of the cutter  f1 = Fz1 + µ (a)
cos θ1
will also generate a friction force, f1 or f2 acting on the upper or the ( ) (3)

 f2 = Fz2 + N2 µ
lower surface of the sugarcane. Fz1 and Fz2 are vertical to the wedge (b)
cos θ2
surface of the blade. Fz1 , Fz2 , f1 and f2 are along the same action line
at the contact point O. The sugarcane harvester travelling speed is Equation (1) and Equation (3) are combined to obtain Equation
vx. Therefore, the cutter will generate a pressure Fx along the x axis (4) used to calculate the resultant force, F1 or F2 are generated by
acting on the sugarcane at the point O. When stresses generated by the cutter along the tangential line of its circular motion.
Fx exceeded the lateral bending strength of the sugarcane, axial
cracks of the sugarcane will appear and the sugarcane ratoon may F⃗ = F⃗0 + f⃗ − F⃗ A (4)
be broken. Fz1 and Fz2 can be decomposed into the horizontal dx
2

cutting force F0, and the vertical compression N. The relationship FA = m (5)
dt2
between these two component forces is shown in Equation (1).
where, FA is the inertia force keeping the rest state of the sugarcane
F0
N= (1) when the axial cutter vibration shock acts on it, N; m is the
tan φ
equivalent mass of the sugarcane, kg.
F0 is calculated through the Experience Equation (2)[15]. Axial cutter vibration frequency components are complicated,
D which can be regarded as a combination of several simple axial
F0 = θ + S vx − ξφ + C (2)
2 harmonic vibrations shown in Equation (6a). According to force
where, vx is the sugarcane harvester travelling speed, m/s; D is the analysis of Figure 1, when the upward axial cutter vibration
diameter of the sugarcane, m; S is the cut-in depth, m; θ is the cutter appears, Fz1 will generate a bending moment Mz1 acting at the point
inclination angle, rad; φ is the cutting-edge angle, rad; ξ and C are O. According to the second Newton Law, Fz1 and Fz2 are calculated
constant dependent on mechanics characteristics of the sugarcane. through Equation (6b). When the downward axial cutter vibration
According to the classical friction law, when the upward axial appears, Fz2 will generate a bending moment Fz2 acting at the point
cutter vibration appears, the friction force f1 is calculated through O. Mz1 and Mz2 are calculated through Equation (6c).
 178 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5


 ∑N
relationship between Mz and the axial cutter vibration amplitude Ai

 = Ai sin (ωi t + φi )


z (a) and frequency ωi, the cut-in depth S while there is a negative

 i=1
correlated relationship between Mz and the cutter inclination angle
d2 z (6)

 Fz = m 2 (b) θ. Therefore, the greater the axial cutter vibration amplitude and

 dt


frequency as well as the cut-in depth are, the greater Fz and Mz will
M = F S (c) be, then the much more easily axial cracks of the sugarcane will
2 cos θ
z z
appear, the poorer the SCQ will be, matching the conclusion of the
where, Ai is the axial cutter vibration amplitude of the sine series, previous research[11,12] that the axial cutter vibration has a bad effects
m; ωi is the axial cutter vibration angular frequency, rad/s; φi is the on the cutting quality of sugarcane harvesters, which was further
initial phase, rad. verified through experiments in this study. The greater the cutter
The tensile strength along the axial direction of the sugarcane is inclination angle is, the smaller Fz and Mz will be, then the less
much greater than that along the lateral direction. If a sugarcane is easily axial cracks of the sugarcane will appear, the better the SCQ
not cut off at once along the lateral direction, cracks will be will be, also verified through experiments in this study.
extended along the axial direction. Therefore, if a sugarcane is cut
for several times, when the upward axial cutter vibration appears, 3 Dynamics and mathematical models of sugarcane
under the combined action of Mz1 and the moment generated by Fx, harvesters
Mx is calculated through Equation (7), the axial tearing cracks of the The dynamics model of a sugarcane harvester is simplified as a
sugarcane will be easy to appear. When the downward axial cutter multi-freedom-degree spring-damping-mass system shown in
vibration appears, the sugarcane ratoon will be broken if Fz2 is Figure 2[19]. Four wheels, two cutters, the body frame, the logistics
greater than the compressive strength of the sugarcane. frame and the engine of the sugarcane harvester are simplified as
S mass blocks. Connections of four wheels and the body frame as
Mx = F x (7)
2 sin θ well as the sugarcane field, the cutting system and the body frame,
According to Equation (6), there is a positive correlated the engine and the body frame are simplified as spring dampers.

z
Fe′
l3
z7

m4

Iz3, θ3 Fe m 2′

z6
K9 B9 K5 B5
2a m 1′ 2a′

z2′ ye z 4′
z5′
Iy1+ Iy2, θ2
l4
v z5′ Iy3, θ2
y

K3 B3 K 4′ B4′ z 3′ K10 B10

z 1′ z2 Fw4 z4
Fw2
m2 m 2″
K4′ B4′ β K4″, B4″
Icutter, θcutter, n z5
k1 B1 K B8 K6 B6 K B11
Fw1 z1
8
β Fz″ F m 3′ Fw3
11

r
z z3
Fx″
r′ m 1″
m1 K4″, B4″
Ix3,θ1′ z5 Fx Fy
B2 Fy″
k2 m 3′ K7 B7

l4′ 2β
Ix1+ Ix2,θ1
x l1 l2

Note: m1, m2, m′′1 , m′′2 , m′′3 , m′1 , m′2 , m′4 are masses of two front wheels, two rear wheels, one cutter, the body frame, the logistics frame and the engine, kg; Icutter, Ix3, Iy3,
Iz3, Ix1, Iy1, Ix2, Iy2 are rotational inertias of a cutter around x, y and z axes, the body frame and the logistics frame around x and y axes, kg·m2; K1, B1, K3, B3 are stiffness and
damping coefficients between two front wheels and the body frame, N/m, N/(m/s); K2, B2, K8, B8 are stiffness and damping coefficients between two front wheels and the
sugarcane field, N/m, N/(m/s); K6, B6, K10, B10 are stiffness and damping coefficients between two rear wheels and the body frame, N/m, N/(m/s); K7, B7, K11, B11 are
stiffness and damping coefficients between two rear wheels and the sugarcane field, N/m, N/(m/s); K4′ , B′4 are the stiffness and the damping coefficients between the
cutting system and the body frame, N/m, N/(m/s); K4′′ , B′′4 are the stiffness and the damping coefficients between two cutter axes and the cutter frame, N/m, N/(m/s); K9,
B9, K5, B5 are stiffness and damping coefficients of the front and the rear anti-vibration pads of the engine, N/m, N/(m/s).
Figure 2 Dynamics model of a sugarcane harvester
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 179

The mass center of the body frame is set as the coordinate origin. where, z1, z2, z3, z4, z5, z6, and z7 are vertical displacements of four
The z axis points to the upward vertical direction. The x axis along wheels, a cutter, the body frame and the engine, m; θcutter, θ1′ , θ2′ , and
radiuses of two cutters points to the left of the sugarcane harvester. θ3 are cutter rotating angles around its axis, the x, the y, and the z
The y axis along the sugarcane harvester travelling speed points to axes, rad. θ1 and θ2 are body frame rotating angles around the x and
the back of the sugarcane harvester. the y axes, rad; They are calculated through given values of
Fw1, Fw2, Fw3, and Fw4 are sugarcane field excitations acting on parameters above.
the four wheels, calculated through Equation (8)[21,22]. According to the D’Alembert principle, the mathematical
Fwi (t) = Ki ξ (t) + Bi ξ̇ (t) , i = 2, 8, 7, 11 (8) model of Figure 2 is written as Equation (14) in a matrix form[21-24].
where, ξ(t) is the piecewise fitting equation of sugarcane field M Z̈ + BŻ + KZ = F (14)
roughness every 20 s, m, shown in Equation (9)[21,22].
∑
8
∑
8 where, M, Z, B, K, and F are the generalized mass matrix, the
ξ (t) = ai sin(ωi t + φi ) = ai sin(2π fi t + φi ) (9) generalized displacement column vector, the generalized damping
i=1 i=1 coefficient matrix, the generalized stiffness coefficient matrix and
where, ai is the amplitude, m; ωi is the angular frequency, rad/s; fi is the generalized external force column vector. M, B, and K are
the frequency, Hz; φi is the initial phase, rad. 13×13 square matrixes while Z and F are 13-dimentional column
Fe and Fe′ are periodical forces acting on the body frame by the vectors. B and K depend on the force condition of Figure 2. All
engine and the engine by its internal structures, calculated through masses and rotational inertias are on the positive diagonal of M in
Equation (10). the order of the left and the right front wheels, the left and the right
Fe (t) = 55.17 sin (2π × 40.021t) rear wheels, the cutter, the body frame and the engine. The
(10) equivalent mass and rotational inertias of the body frame are
Fe′ (t) = 2493 cos (2 × 2π × 29.18t)
m′1 + m′2 , Ix1+Ix2, and Iy1+Iy2. Z and F are shown in Equation (15) and
where, Fx, Fy, and Fz are cutting forces along the x, the y, and the z Equation (16).
axes, N, calculated through Equation (11).
( ) Z = [z1 z2 z3 z4 z5 z6 z7 θcutter θ3 θ1′ θ2′ θ1 θ2 ]T (15)
F x (t) = 517.2 sin 2π × 19.067t
( )  
Fy (t) = 414.2 sin 2π × 19.067t (11) K2 ξ + B2 ξ̇
( )
Fz (t) = 373.2 sin 2π × 19.067t  K8 ξ + B8 ξ̇ 
 
 K7 ξ + B7 ξ̇ 
′′ ′′ ′′
where, F , F , and F are the radial, the tangential and the axial  
x y z
 K11 ξ + B11 ξ̇ 
cutting forces, N, calculated through Equation (12).  
( )  Fz′′ cos β + Fy′′ sin β − F x′′ sin β 
F x′′ (t) = 517.167 sin 2π × 19.067t  
 Fe 
( )  
Fy′′ (t) = 462.108 sin 2π × 19.067t (12) F=
 Fe′ 

( )  
F (t) = 383.903 sin 2π × 19.067t
′′
 −Fy′′ R 
z
 F x l4 cos β
′′ ′ 
 
where, a, a′, and R are halves of the front wheel distance, the rear  F ′′ l′ sin β + F ′′ r′ cos β − F ′′ l′ sin β − F ′′ l′ cos β − F ′′ r′ sin β 
 x 4 
 
y y 4 z 4 z
wheel distance and the centre distance of two cutters, a=0.68 m, a′= −F x′′ r′ cos β
 
0.605 m, R=0.27 m; l1 and l2 are distances between the mass centre  Fl 
e 3
of the body frame and the front axle, the mass centre of the body Fe ye
frame and the rear axle, l1=1.8 m, l2=1.2 m; l4 and l4′ are distances (16)
between the mass centre of the cutter frame and the z axis when the
cutter inclination angle is 0º, the mass center of a cutter and the z Relationship curves of z1, z2, z3, z4, z5, z6, z7, θ1, and θ2 changing
axis in the sugarcane cutting process, l4=0.9 m, l4′ =0.83 m; β and v with time drawn through MATLAB according to Equation (14) are
are the cutter inclination angle and the sugarcane harvester shown in Figures 3a-3i.
travelling speed, β=8º, v=0.6 m/s; l3 and ye are distances between As shown in Figures 3 that z1-z7, θ1 and θ2 change with time in
the mass centre of the body frame and the action line of Fe along the periodical damping variation laws with gradually decreasing
x axis and the y axis, l3=0.1 m, ye=0.303 m; r and r′ are the length of amplitudes in that Fw, Fe, and Fe′ are periodical excitations. θcutter,
a cutter axis and the distance between the mass centre of a cutter θ1′ , θ2′ , and θ3 become greater and greater along with time in that
and the y axis in the sugarcane cutting process, r=0.5 m, r′= two cutters keep rotating around their axes, the x, the y, and the z
0.495 m. axes in the sugarcane cutting process, so their relationship curves
z′1 , z′2 , z′3 , z′4 are vertical displacements of connection points of changing with time are simple monotonically-increasing lines
four wheels and the body frame; z′5 is the vertical displacement of neglected here. Therefore, the dynamics and the mathematical
connection points of the cutting system and the body frame. They models of sugarcane harvesters are reasonable. Besides, according
are calculated through Equation (13)[21,22]. to Equation (14), there are 13 dependent variables in the
a mathematical model of sugarcane harvesters, so the dynamics
z′1 = z6 − θ2 + r′ θ2 − l4′ θ1
2 model of sugarcane harvesters is a multi-input and multi-output
a second-order underdamped linear time-invariant discrete dynamics
z2 = z6 + θ2 + r′ θ2 − l4′ θ1
′
2 systems with 13 degrees of freedom.
a′ (13)
z3 = z6 − θ2 − r′ θ2 + l4′ θ1
′ Relationship curves of z5 changing with ai, fi, n, v and β drawn
2 through MATLAB according to Equation (14) are shown in
′
a
z′4 = z6 + θ2 − r′ θ2 + l4′ θ1 Figures 4a-4e.
2
As is shown in Figure 4, the greater ai and fi are, the greater z5
z′5 = z6 + r′ θ2 − l4′ θ1
is, showing the more obvious the sugarcane field excitation is, that
 180 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5

1.0 1.0 1.0

0.8 0.8
0.6 0.6
0.4 0.5 0.4
0.2
Z1/mm

Z2/mm

Z3/mm
0.2
0
0
−0.2
−0.4 0 −0.2
−0.6 −0.4
−0.8 −0.6
−1.0 −0.5 −0.8
0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160
t/s t/s t/s
a. z1 b. z2 c. z3

1.0 1.0 1.0

0.8 0.8
0.5 0.6
0.6
0.4 0 0.4
0.2
Z4/mm

Z5/mm

Z6/mm
0.2
−0.5 0
0 −0.2
−0.2 −1.0 −0.4
−0.4 −0.6
−1.5
−0.6 −0.8
−0.8 −2.0 −1.0
0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160
t/s t/s t/s
d. z4 e. z5 f. z6

1.0 2.0 2.5

1.5 2.0
0.5 1.5
1.0
1.0
0 0.5 0.5
Z7/mm

θ1/rad

θ2/rad
0 0
−0.5 −0.5 −0.5
−1.0
−1.0
−1.0 −1.5
−1.5 −2.0
−1.5 −2.0 −2.5
0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160
t/s t/s t/s
g. z7 h. θ5 i. θ6

Figure 3 Relationship curves between different dependent variables and time

10 10 0.4835
0.4830
8 8 0.4825
6 6 0.4820
0.4815
Z5/mm

Z5/mm
Z5/mm

4 4 0.4810
0.4805
2 2 0.4800
0 0 0.4795
0.4790
−2 −2 0.4785
0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 350 400
ai/m fi/m n/(r·m−1)
a. z5 m ai b. z5 m fi v. z5 m n

0.34725 0.45
0.34720 0.40
0.34715
0.34710 0.35
Z5/mm

Z5/mm

0.34705 0.30
0.34700 0.25
0.34695
0.34690 0.20
0.34685 0.15
−1.0 −0.6 −0.2 0.2 0.6 1.0 0 5 10 15 20 25 30
v/(m·s−1) β/(°)
d. z5 m v e. z5 m β

Figure 4 Relationship curves between z5 and different parameters

is, the hillier a sugarcane field is, the more severe the axial cutter Additionally, according to Figures 4c-4e, the greater n, v and β
vibration will be, then the poorer the SCQ will be according to are, the smaller z5 is, showing the greater the cutter rotating speed,
sugarcane cutting mechanism analysis, matching the conclusion of the sugarcane harvester travelling speed and the cutter inclination
research above[11,12] that the sugarcane field excitation and the axial angle are, the weaker the axial cutter vibration will be, then the
cutter vibration have bad effects on the cutting quality of sugarcane better the SCQ will be according to the sugarcane cutting
harvesters, further verified through experiments. mechanism, further verified through experiments.
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 181

instrument, a digital angle-measuring instrument, a laser speed-

4 Materials and methods measuring instrument, an LK-G150 laser displacement sensor, a
4.1 Experiment materials high-speed camera and a hydraulic system. Digital frequency
Fresh No.42 Guitang sugarcanes were used to do sugarcane convertors were used to control output frequencies and amplitudes
cutting experiments. Sugarcanes are laterally isotropic[25]. That is, of two SFEDs and the actuating engine. The main experiment
there are no differences in mechanics characteristics along their equipment is shown in Figure 7.
lateral direction. Significant differences exist in mechanics
6 7
characteristics along their fiber direction and the vertical direction.
Elasticity moduli along and vertical to the fiber direction of No.42
Guitang sugarcanes are 813.0 MPa and 152.5 MPa. Their Poisson 5
1 4
ratios are 0.530, 0.105, and 0.265. Their shear moduli of the
isotropic and the anisotropic planes are 17.75 MPa and 1.14 MPa. 2
3
Bodies of these sugarcanes were straight and their leaves as well as 9
burrs were wiped off. Their average diameter was (28±3) mm. 10
4.2 Experiment equipment 8
The manufactured SHTP and its structural diagram are shown
1. Sugarcane 2. Sugarcane-holding device 3. Sugarcane-transporting
in Figure 5. It is mainly made up of the sugarcane transporting vehicle 4. STP 5. SFED 6. Body frame 7. Actuating engine 8. Cutting
pathway (STP), the sugarcane-holding device, the sugarcane- system 9. Logistics frame 10. Vibration absorber
transporting vehicle, two SFEDs, two vibration absorbers, the a. Structural diagram of SHTP
actuating engine, the cutting system, the body frame and the
4 5
logistics frame. On the SHTP, the sugarcane field excitation is 1 6 7
simulated through two SFEDs and the engine excitation is simulated
through the actuating engine. The manufactured SFED and its three- 8
dimensional model are shown in Figure 6[21,22,26]. It was developed 2
based on characteristics of sugarcane field roughness signals
collected in a flat and a hilly sugarcane fields[21,22,26]. 3
Sugarcanes were inserted into nine sleeves of the sugarcane-
holding device. The distance between every group of three 9
sugarcanes is 300 mm. Two cutters with four blades were used. The
cutting-edge angle is 30º. The x axis points to the direction of the
sugarcane transporting speed of the sugarcane-transporting vehicle.
The sugarcane harvester travelling speed is simulated through the
sugarcane transporting speed. The z axis points to the upward 1. Sugarcane-transporting vehicle 2. Sugarcane-holding device 3. STP
vertical direction. The y axis is vertical to the plane formed by the x 4. Actuating engine 5. Cutter frame 6. Vibration absorber 7. Body frame
and the z axes. 8. SFED 9. Cutter
The experiment equipment is as follow: two digital frequency b. Prototype of SHTP

convertors, a piezoelectric three-directional force-measuring Figure 5 Structural diagram and prototype of SHTP

5 1 5 1
2
6 6 2
3
4 7 3
7

8
9 8
4
9

1, 2. External and the internal sleeves of the upper spring 3. Eccentric 1, 2. External and the internal sleeves of the upper spring 3. Eccentric
mass blocks 4. Axis coupler 5, 6, 9. Upper, middle and lower support mass blocks 4. Axis coupler 5, 6, 9. Upper, middle and lower support
platforms 7, 8. External and the internal sleeves of a lower spring platforms 7, 8. External and the internal sleeves of a lower spring
a. Three-dimensional model of SFED b. Prototype of SFED
Figure 6 Three-dimensional model and prototype of SFED

Three-directional cutting forces were measured through the forces were obtained through the common milling force-measuring
force-measuring system. According to the high-speed system in every group of experiments. In every column vector, the
photographing result in the sugarcane cutting process, there are number of absolute values much greater than others is equal to the
wave crests, showing in the sugarcane cutting process of sugarcane number of wave crests got by high-speed photographing. The
harvesters, a sugarcane is cut off in more than one time of cutting. average value of these greater absolute values was calculated as the
Three column vectors corresponding to three-directional cutting value of the cutting force along this direction.
 182 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5

a. The laser of the LK-G150 laser displacement sensor falling on the b. The digital angle-measuring instrument put on the cutter to
cutter along the z axis to measure the axial cutter vibration amplitude measure the cutter inclination angle

c. Piezoelectric three-directional force d. Three channels of the piezoelectric three e. Piezoelectric three-directional force
measuring instrument -directional forcemeasuring instrument measuring instrument installed under
corresponding to the x, the y and the z axes the sugarcane-holding device
Figure 7 Main experiment equipment

4.3 Sugarcane cutting quality evaluating indexes 4.4 Experiment design

Sugarcane cutting quality evaluating indexes were the number 4.4.1 Single-factor experiment design
of sugarcanes whose ratoon were broken, the axial crack number, Single-factor experiments were done under simulated
the axial crack depth and the axial crack length[19,20,27,28]. The complicated excitations, that is, the combined action of two SFEDs,
sugarcane cutting quality evaluating value (SCQEV) was calculated the actuating engine and cutting forces. Experimental factors were
with these four indexes through the improved entropy the SFED output frequency, the cutter rotating speed, the cutter
method[19,20,27,28] shown in Equation (17). inclination angle and the sugarcane transporting speed.
 ¿∑ m
Experimental indexes were the axial cutter vibration amplitude,

 xi j − x j min three-directional cutting forces and the SCQEV. These experiments

 x ′
= , p = x ′
xi′ j
 x j max − x j min
ij i j ij


were aimed at studying effects of the axial cutter vibration


i=1


 ∑ m amplitude and frequency, the cutter rotating speed, the cutter

 k = 1/ ln m, e j = −k

 pi j ln pi j inclination angle and the sugarcane harvester travelling speed on
 i=1 three-directional cutting forces and the SCQ.
¿∑ (17)


4 In order to avoid the resonance of the SHTP, constant levels of

 g = 1 − e , w = g gj


j j j j the SFED output frequency and the actuating engine output




j=1
frequency were set as 4 Hz and 30 Hz[25]. According to previous

 ∑ 4
∑
m
¿

 research results, constant levels of the cutter rotating speed, the

 Q i = x ′
i j w j , Q = Q i m sugarcane transporting speed and the cutter inclination angle were
j=1 i=1
set as 650 r/min, 0.6 m/s and 15º[29]. Levels of these experimental
where, xi′ j , xij are the membership degree and the value of j-th index factors are listed in Table 1.
in i-th repeated experiment under the same condition, j=1, 2, 3, 4,
Table 1 Levels of experimental factors
respectively, the number of sugarcanes whose ratoons were broken,
Experimental factor Constant level Range Step length
the axial crack number, the axial crack depth and the axial crack
Cutter rotating speed/r·min–1 650 450-750 50
length, i=1, 2, 3, …, m, Every group of experiments in this study
Cutter inclination angle/(°) 15 0-20 2
were done for five times, so m=5; xjmax and xjmin are the maximum
Sugarcane transporting speed/m·s–1 0.6 0.1-0.8 0.1
and the minimum values of j-th index; pij is the proportion of j-th
SFED output frequency/Hz 4 1-9 1
index in i-th experiment; ej, gj, and wj are the entropy value, the Actuating engine output frequency/Hz 30
difference coefficient and the weight of j-th index; Qi is the SCQEV
of i-th experiment; Q is the average value of Qi, as the SCQEV of 4.4.2 Orthogonal experiment design
this experiment condition. The greater the SCQEV is, the poorer the Experimental factors of this orthogonal experiment were output
SCQ is. frequencies of the SSFE and the actuating engine, the cutter rotating
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 183

speed, the sugarcane transporting speed, the cutter inclination angle. vibration amplitude and three-directional cutting forces with the
Their levels are listed in Table 2. Experimental indexes were the SFED output frequency were studied.
axial cutter vibration displacement, three-directional cutting forces A three-directional cutting force signal under a 4 Hz output
and the SCQEV. This orthogonal experiment was aimed at studying frequency of the SFED and a 700 r/min cutter rotating speed is
significance levels of effects of the sugarcane field excitation, the shown in Figure 8. The total number of blades is 8 and the blades
engine excitation, the cutter rotating speed, the sugarcane harvester distribute uniformly around the cutters, so the shortest cutting time
travelling speed and the cutter inclination angle on the axial cutter interval of the cutters is 0.0106 s. There are two wave crests in
vibration, three-directional cutting forces and the SCQ. Effects of Figure 8, that is, the sugarcane was cut by the cutters twice and the
the axial cutter vibration on three-directional cutting forces and the sugarcane was cut off after two times of cutting according to what
was captured by the high-speed camera in Figure 9, so in the
SCQ as well as effects of three-directional cutting forces on the
sugarcane cutting process of sugarcane harvesters, a sugarcane is
SCQ were further studied. The L25(56) orthogonal table was chosen.
cut off by more than one time of cutting. Moreover, in Figure 9,
The experiment arrangement is listed in Table 3.
these two cut-in points were different, that is, there was a height
Table 2 Levels of the five experimental factors difference between them, so when the sugarcane was cut for the
Level second time, the cutters pressed the sugarcane and the axial cutter
Experiment factor vibration might make the sugarcane ratoon broken. Therefore, the
1 2 3 4 5
SFED output frequency A/Hz 8 11 17 20 25 axial cutter vibration amplitude and frequency directly affect the
Actuating engine output frequency B/Hz 19 22 26 28 30
SCQ. Three-directional cutting forces were measured through a
common milling force-measuring system.
Cutter rotating speed C/r·min–1 450 500 650 700 750
Sugarcane transporting speed D/m·s–1 0.4 0.5 0.6 0.7 0.8 x-direction y-direction z-direction

Three-directional cutting forces/N

600
Cutter inclination angle E/(°) 4 8 16 18 20
400
Table 3 Experiment arrangement of the orthogonal 200
experiment cutting sugarcanes under simulated 0
complicated excitations −200
Experimental factor −400
Group
A B C D E Blank column −600
1 1 1 1 1 1 1
−800 3.0
2 1 2 2 2 2 2 0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.0
3 1 3 3 3 3 3 Time/s
4 1 4 4 4 4 4 Figure 8 Three-directional cutting force signal
5 1 5 5 5 5 5
6 2 1 2 3 4 5 The second cut-in poing
7 2 2 3 4 5 1
8 2 3 4 5 1 2
9 2 4 5 1 2 3
10 2 5 1 2 3 4
11 3 1 3 5 2 4
12 3 2 4 1 3 5
13 3 3 5 2 4 1
14 3 4 1 3 5 2 The first cut-in point
15 3 5 2 4 1 3
16 4 1 4 2 5 3
17 4 2 5 3 1 4
Figure 9 High-speed photograph in the sugarcane cutting process
18 4 3 1 4 2 5
19 4 4 2 5 3 1 The average value of results of five times of experiments under
20 4 5 3 1 4 2 the same condition was chosen as the final result of this group of
21 5 1 5 4 3 2 experiments.
22 5 2 1 5 4 3 Relationship curves of the axial cutter vibration amplitude and
23 5 3 2 1 5 4 three-directional cutting forces changing with the SFED output
24 5 4 3 2 1 5 frequency are shown in Figure 10.
25 5 5 4 3 2 1 According to Figure 10a, the greater the SFED output
frequency was, the greater the axial cutter vibration amplitude was.
5 Results According to Figure 10b, determination coefficients of these fitting
5.1 Single-factor experiment result analysis curves and their fitting equations are greater than 0.95, so they have
5.1.1 Effects of the sugarcane field excitation on the axial cutter high accuracies. There are obviously positive monotonic correlated
vibration and cutting forces relationships between three-directional cutting forces and the SFED
The sugarcane field excitation has a bad effect on the cutting output frequency. That is, the greater the SFED output frequency
quality of sugarcane harvesters in that it causes vibrations of was, the greater three-directional cutting forces were. Monotonic
sugarcane harvesters, leading to vibrations of the cutters and the correlation and single-factor variance analysis results with the
axial cutter vibration has a bad effect on the cutting quality of SFED output frequency as the independent variable got though
sugarcane harvesters[11,12]. Therefore, change laws of the axial cutter SPSS are listed in Tables 4 and 5.
 184 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5

The x-directional cutting force

The y-directional cutting force
The axial cutter vibration

Three-directional cutting
4.5 700 The z-directional cutting force
amplitude/mm 4.0 600
3.5
3.0 500

forces/N
2.5 400
2.0 300
1.5 Fx=280.64e0.0553x R2=0.98
200 Fy=393.39e0.0501x R2=0.95
1.0
0.5 100 Fz=307.51e0.0547x R2=0.98
0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
The SFED output frequency/Hz The SFED output frequency/Hz
a. Axial cutter vibration amplitude and SFED output frequency b. Three-directional cutting forces and SFED output frequency
Figure 10 Relationship curves of the axial cutter vibration amplitude and three-directional cutting forces changing with the SFED
output frequency

Table 4 Monotonic correlation analysis results of the axial Moreover, monotonic correlation coefficients are greater than 0, so
cutter vibration amplitude and three-directional cutting forces there are significantly positive monotonic correlated relationships
changing with the SFED output frequency between the axial cutter vibration amplitude and the SFED output
Experimental index Monotonic correlation coefficient p-value frequency, three-directional cutting forces and the SFED output
Axial cuter vibration amplitude 0.957 0.000 frequency, matching what are found through Figure 10. Therefore,
x-directional cutting force 0.065 0.040 the more obvious the sugarcane field excitation is, that is, the hillier
y-directional cutting force 0.043 0.045 a sugarcane field is, the more severe the axial cutter vibration and
z-directional cutting force 0.190 0.039 the greater three-directional cutting forces will be. The more severe
the axial cutter vibration is, the greater the axial cutter vibration
It is listed in Table 4 that p values are smaller than 0.05, so amplitude and frequency will be, so the more obvious the sugarcane
there are significant monotonic correlated relationships between the field excitation is, that is, the hillier a sugarcane field is, the greater
axial cutter vibration amplitude and the SFED output frequency, the axial cutter vibration amplitude and frequency will be, matching
three-directional cutting forces and the SFED output frequency. what are found through Figures 4a and 4b.

Table 5 Single-factor variance analysis results with the SFED output frequency as the independent variable
Experimental index Axial cutter vibration amplitude x-directional cutting force
Source Quadratic sum Freedom degree Mean square value F value p value Quadratic sum Freedom degree Mean square value F value p value
Inter-group 458.398 17 26.965 302.562 0.000 2 865 071.943 17 168 533.644 3.27 0.001
Intra-group 3.208 36 0.089 1 855 500.245 36 51 541.673
Total value 461.606 53 4 720 572.188 53
Experimental index y-directional cutting force z-directional cutting force
Source Quadratic sum Freedom degree Mean square value F value p value Quadratic sum Freedom degree Mean square value F value p value
Inter-group 7 628 341.311 17 448 725.959 3.247 0.001 4 769 919.277 17 280 583.487 9.029 0.000
Intra-group 4 974 733.432 36 138 187.040 1 118 757.555 36 31 076.599
Total value 12 603 074.743 53 5 888 676.831 53

Besides, as shown in Table 5 that p values are smaller than forces will be.
0.05, so the SFED output frequency has significant effects on the 5.1.2 Effects of the cutter rotating speed on the axial cutter
axial cutter vibration amplitude and three-directional cutting forces. vibration and three-directional cutting forces
Therefore, the sugarcane field excitation has significantly positive Relationship curves of the axial cutter vibration amplitude and
monotonic correlated effects on the axial cutter vibration and three- three-directional cutting forces changing with the cutter rotating
directional cutting forces. speed are shown in Figure 11.
On the other hand, according to Figure 10a, when the SFED According to Figure 11a, the axial cutter vibration amplitude
output frequency was 6 Hz, the axial cutter vibration amplitude increased along with the cutter rotating speed increasing at the
increased to 4.03 mm, the maximum value. According to LMS beginning. When the cutter rotating speed was 550 r/min, the axial
modal test results of the SHTP got previously by our research cutter vibration amplitude reached the maximum value, 0.36 mm.
group[21,22], there is an inherent frequency of the SHTP near 6 Hz. In Then the axial cutter vibration amplitude decreased along with the
order to avoid the resonance of the SHTP, the SFED output cutter rotating speed increasing and it kept being 0.24 mm.
frequency should be far away from 6 Hz. According to Figure 10b, Therefore, there should be a resonance point of the SHTP near
the resonance of the SHTP made three-directional cutting forces 9.2 Hz, the output frequency of 550 r/min, matching results of the
increase significantly. Therefore, the greater the SFED output LMS modal test of the SHTP got previously by our research group
frequency and the axial cutter vibration amplitude are, making the that there is an inherent frequency of the SHTP near 10 Hz[21,22].
compressive frequency and the pressure of the cutters acting on the According to Figure 11b, along with the cutter rotating speed
sugarcane greater, then causing three-directional cutting forces to increasing, three-directional cutting forces increased firstly and then
increase. That is, the more obvious the sugarcane field excitation decreased. When the cutter rotating speed was 550 r/min, three-
and the more severe the axial cutter vibration are, that is, the hillier directional cutting forces increased significantly. Change laws of
a sugarcane field is and the greater the axial cutter vibration three-directional cutting forces with the cutter rotating speed are
amplitude and frequency are, the greater three-directional cutting similar to that of the axial cutter vibration amplitude.
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 185

The x-directional cutting force

Three-directional cutting forces/N

The y-directional cutting force
The z-directional cutting force
The axial cutter vibration
0.40 700
0.35 600
amplitude/mm

0.30 500
400
0.25
300
0.20 200
0.15 100
0.1 0
400 450 500 550 600 650 700 750 800 400 450 500 550 600 650 700 750 800
The cutter rotating speed/(r·min−1) The cutter rotating speed/(r·min−1)
a. Axial cutter vibration amplitude and the cutter rotating speed b. Three-directional cutting forces and the cutter rotating speed
Figure 11 Relationship curves of the axial cutter vibration amplitude and three-directional cutting forces changing with the cutter
rotating speed

Monotonic correlation and single-factor variance analysis forces will be, so the greater the cutter rotating speed is, the greater
results with the cutter rotating speed as the independent variable got the axial cutter vibration amplitude and frequency will be, matching
though SPSS are listed in Tables 6 and 7. what is found through Figure 4c.
As is listed in Table 6, p values are smaller than 0.05, so there
are significant monotonic correlated relationships between the axial Table 6 Monotonic correlation analysis results of the axial
cutter vibration amplitude and the cutter rotating speed, three- cutter vibration amplitude and three-directional cutting forces
directional cutting forces and the cutter rotating speed. Moreover, changing with the cutter rotating speed.
monotonic correlation coefficients are smaller than 0, so there are Experimental index Monotonic correlation coefficient p-value
significantly negative monotonic correlated relationships between Axial cuter vibration amplitude –0.025 0.044
the axial cutter vibration amplitude and the cutter rotating speed,
x-directional cutting force –0.043 0.040
three-directional cutting forces and the cutter rotating speed.
y-directional cutting force –0.023 0.045
Therefore, the greater the cutter rotating speed is, the more severe
z-directional cutting force –0.120 0.044
the axial cutter vibration and the greater three-directional cutting

Table 7 Single-factor variance analysis results with the cutter rotating speed as the independent variable
Experimental index The axial cutter vibration amplitude x-directional cutting force
Source Quadratic sum Freedom degree Mean square value F value p value Quadratic sum Freedom degree Mean square value F value p value
Inter-group 39.466 11 3.588 108.757 0.000 244 532.067 11 22 230.188 4.574 0.001
Intra-group 0.792 24 0.033 116 652.457 24 4860.519
Total value 40.258 35 361 184.524 35
Experimental index y-directional cutting force z-directional cutting force
Source Quadratic sum Freedom degree Mean square value F value p value Quadratic sum Freedom degree Mean square value F value p value
Inter-group 934 882.281 11 84 989.298 4.342 0.001 628 898.261 11 57 172.569 10.044 0.000
Intra-group 469 822.212 24 19 575.926 136 610.341 24 5692.098
Total value 1 404 704.493 35 765 508.602 35

Moreover, it is shown in Table 7 that p values are smaller than fitting equations are greater than 0.96, so they have high accuracies.
0.05, so the cutter rotating speed has significantly negative There are obviously positive monotonic correlated relationships
monotonic correlated effects on the axial cutter vibration and three- between three-directional cutting forces and the sugarcane
directional cutting forces. transporting speed, three-directional cutting forces, and the cutter
5.1.3 Effects of the sugarcane harvester travelling speed and the inclination angle. That is, the greater the sugarcane transporting
cutter inclination angle on three-directional cutting forces speed and the cutter inclination angle were, the greater three-
Relationship curves of three-directional cutting forces changing directional cutting forces were. Monotonic correlation and single-
with the sugarcane transporting speed and the cutter inclination factor variance analysis results with the sugarcane transporting
angle are shown in Figures 12 and 13. speed and the cutter inclination angle as independent variables got
Determination coefficients of these fitting curves and their though SPSS are listed in Tables 8-11.
Three-directional cutting forces/N
Three-directional cutting forces/N

The x-directional cutting force The x-directional cutting force

The y-directional cutting force The y-directional cutting force
700 The z-directional cutting force 700 The z-directional cutting force
600 600
500 500
400 400
300 Fx=251.94e0.8458x R2=0.99 300 Fx=271.34e0.0324x R2=0.96
200 Fy=299.45e0.8474x R2=0.99 200 Fy=358.55e0.0259x R2=0.99
100 Fz=280.26e0.5536x R2=0.97 100 Fz=319.88e0.0196x R2=0.97
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 2 4 6 8 10 12 14 16 18 20 22
The sugarcane transporting speed/(m·s−1) The cutter inclination angle/(°)
Figure 12 Relationship curves between three-directional cutting Figure 13 Relationship curves between three-directional cutting
forces and the sugarcane transporting speed forces and the cutter inclination angle
 186 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5

Table 8 Monotonic correlation analysis results of three- Table 9 Monotonic correlation analysis results of three-
directional cutting forces and the sugarcane transporting speed directional cutting forces and the cutter inclination angle
Experimental index Monotonic correlation coefficient p value Experimental index Monotonic correlation coefficient p value
The x-directional cutting force 0.688 0.000 x-directional cutting force 0.154 0.042
The y-directional cutting force 0.665 0.000 y-directional cutting force 0.144 0.044
The z-directional cutting force 0.867 0.000 z-directional cutting force 0.194 0.049

Table 10 Single-factor variance analysis results with the sugarcane transporting speed as the independent variable
Experimental
x-directional cutting force y-directional cutting force z-directional cutting force
index
Quadratic Freedom Mean square F p Quadratic Freedom Mean square F p Quadratic Freedom Mean square F p
Source
sum degree value value value sum degree value value value sum degree value value value
Inter-group 144 558.591 7 20 651.227 3.060 0.030 552 587.222 7 78 941.032 3.636 0.015 370 760.430 7 52 965.776 12.010 0.000
Intra-group 107 987.836 16 6749.240 347 384.372 16 21 711.523 70 564.646 16 4410.290
Total value 252 546.428 23 899 971.594 23 441 325.076 23

Table 11 Single-factor variance analysis results with the cutter inclination angle as the independent variable
Experimental
x-directional cutting force y-directional cutting force z-directional cutting force
index
Quadratic Freedom Mean square F p Quadratic Freedom Mean square F p Quadratic Freedom Mean square F p
Source
sum degree value value value sum degree value value value sum degree value value value
Inter-group 106 469.987 10 10 646.999 1.955 0.041 406 990.367 10 40 699.037 2.323 0.048 273 071.685 10 27 307.169 7.673 0.000
Intra-group 119 810.773 22 5445.944 385 417.389 22 17 518.972 78 290.343 22 3558.652
Total value 226 280.760 32 792 407.756 32 351 362.028 32

It is listed in Tables 8 and 9 that p values are smaller than 0.05, The optimal sugarcane transporting speed is 0.6 m/s with the best
so there are significant monotonic correlated relationships between SCQ, that is, the optimal sugarcane harvester travelling speed is
three-directional cutting forces and the sugarcane transporting 0.6 m/s. According to Figure 17, the SCQ will be poorer when the
speed, three-directional cutting forces and the cutter inclination cutter inclination angle increases. The optimal cutter inclination
angle. Moreover, monotonic correlation coefficients are greater than angle is 8º with the best SCQ.
0, so there are significantly positive monotonic correlated
The curve The fitting curve
relationships between three-directional cutting forces and the 0.55
sugarcane transporting speed, three-directional cutting forces and 0.50
The SCQEV

0.45
the cutter inclination angle, matching what are found through 0.40
Figure 12 and Figure 13. Therefore, the greater the sugarcane 0.35
harvester travelling speed and the cutter inclination angle are, the 0.30 y=−0.0042x2+0.0604x+0.264
greater three-directional cutting forces will be. 0.25 R2=0.826
0.20
Meanwhile, according to Tables 10 and 11, p values are smaller 0 1 2 3 4 5 6 7 8 9 10
than 0.05, so the sugarcane transporting speed and the cutter The SFED output frequency/Hz
inclination angle have significant effects on three-directional cutting Figure 14 Relationship between SCQEV and SFED
forces. Therefore, the sugarcane harvester travelling speed and the output frequency
cutter inclination angle have significantly positive monotonic
correlated effects on three-directional cutting forces. 0.65 The curve The fitting curve
5.1.4 Effects of field excitation, cutter rotating speed, harvester 0.60
The SCQEV

travelling speed and cutter inclination angle on the SCQ 0.55

0.50
Relationship curves of the SCQEV changing with the SFED
0.45
output frequency, the cutter rotating speed, the sugarcane 0.40 y=−2E−0.6x2+0.0027x−0.1564
transporting speed and the cutter inclination angle are shown in 0.35 R2=0.6683
Figures 14-17. 0.30
400 450 500 550 600 650 700 750 800
Determination coefficients of these fitting curves and their The cutter rotating speed/(r·min−1)
fitting equations are greater than 0.65, so they have high accuracies.
Figure 15 Relationship between SCQEV and cutter rotating speed
According to Figure 14, when the SFED output frequency
increased, the SCQEV increased with a poorer SCQ. When the The curve The fitting curve
0.70
SFED output frequency was 6 Hz, the SCQEV reached the 0.65
maximum value, 0.53 with the poorest SCQ. According to Figure 15, 0.60
The SCQEV

0.55
the SCQ can be improved when the cutter rotating speed increases. 0.50
The optimal cutter rotating speed is 700 r/min. When the cutter 0.45
rotating speed was 550 r/min with the output frequency of 9.2 Hz, 0.40 y=1.1429x2−1.1881x+0.7732
0.35 R2=0.9064
the SCQ was the poorest in that the resonance of the SHTP 0.30
appeared, causing the greatest axial cutter vibration amplitude 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
according to Figure 10a. According to Figure 16, along with the The sugarcane transporting speed/(m·s−1)

sugarcane transporting speed increasing, the SCQEV decreased Figure 16 Relationship between SCQEV and sugarcane
firstly with a better SCQ and then it increased with a poorer SCQ. transporting speed
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 187

0.65 The curve The fitting curve SCQ will be, matching what are found through Figures 4a and 4b.
0.60 Monotonic correlation coefficients between the SCQEV and the
The SCQEV

0.55
cutter rotating speed, the SCQEV and the sugarcane transporting
0.50
0.45 speed, the SCQEV and the cutter inclination angle are smaller than
0.40 y=6E−0.5x2−0.0112x+0.578 0, so there are significantly negative monotonic correlated
0.35 R2=0.5775 relationships between the SCQEV and the cutter rotating speed, the
0.30 SCQEV and the sugarcane transporting speed, the SCQEV and the
0 2 4 6 8 10 12 14 16 18 20 22
The cutter inclination angle/(°) cutter inclination angle, matching what are found through
Figures 15-17. Therefore, the greater the cutter rotating speed, the
Figure 17 Relationship between SCQEV and cutter
sugarcane harvester travelling speed and the cutter inclination angle
inclination angle
are, the better the SCQ will be, matching the sugarcane cutting
Based on analysis above, optimal level combination of the mechanism and what are found through Figures 4c-4e.
cutter rotating speed, the sugarcane harvester travelling speed and Furthermore, it is listed in Table 13 that p values are smaller
the cutter inclination angle is 700 r/min, 0.6 m/s and 8º for than 0.05, so the SFED output frequency, the cutter rotating speed,
sugarcane harvesters with a good SCQ. the sugarcane transporting speed and the cutter inclination angle
Monotonic correlation and single-factor variance analysis have significant effects on the SCQEV. Therefore, the sugarcane
results with the SFED output frequency, the cutter rotating speed, field excitation has a significantly positive monotonic correlated
the sugarcane transporting speed and the cutter inclination angle as effects on the SCQ while the cutter rotating speed, the sugarcane
independent variables and the SCQEV as the dependent variable got harvester travelling speed and the cutter inclination angle have
though SPSS are listed in Tables 12 and 13. significantly negative monotonic correlated effects on the SCQ.
5.2 Orthogonal experiment result analysis
Table 12 Monotonic correlation analysis results of the SCQEV Main effect analysis results obtained through multi-factor
changing with SFED output frequency, cutter rotating speed, variance analysis of SPSS are listed in Tables 14-16.
sugarcane transporting speed and the cutter inclination angle
Experimental factor Monotonic correlation coefficient p-value
Table 14 Main effect analysis result of the axial cutter
SFED output frequency 0.106 0.046
vibration displacement in the sugarcane cutting process as the
Cutter rotating speed –0.012 0.045
dependent variable
Dependent variable: axial cutter vibration displacement in the
Sugarcane transporting speed –0.664 0.000
sugarcane cutting process G
Cutter inclination angle –0.167 0.044 Source Mean Partial
III-type Freedom F- p-
square eta
quadratic sum degree value value
value square
Table 13 Single-factor variance analysis results with SFED The corrected
260.423a 20 13.021 141.663 0.000 0.981
output frequency, cutter rotating speed, sugarcane transporting model
speed and cutter inclination angle as independent variables and The intercept 2754.351 1 2754.351 29 965.851 0.000 0.998
SCQEV as the dependent variable The SFED
output 247.260 4 61.815 672.513 0.000 0.980
Mean frequency A
Experimental Quadratic Freedom F- p-
Source square
factor sum degree value value The actuating
value
engine output 2.577 4 0.644 7.009 0.000 0.342
Inter-group 41.001 17 2.412 1.207 0.048 frequency B
SFED output
Intra-group 71.942 36 1.998 The cutter
frequency
Total value 112.943 53 rotating 7.742 4 1.936 21.058 0.000 0.609
speed C
Inter-group 0.276 11 0.025 0.159 0.049 The sugarcane
Cutter rotating
Intra-group 3.801 24 0.158 transporting 1.262 4 0.316 3.433 0.014 0.203
speed
Total value 4.077 35 speed D
The cutter
Inter-group 0.161 7 0.023 1.424 0.043 inclination 1.582 4 0.395 4.303 0.004 0.242
Sugarcane
Intra-group 0.259 16 0.016 angle E
transporting speed
Total value 0.420 23 Error 4.963 54 0.092
Inter-group 0.119 10 0.012 1.096 0.046 Total value 3019.738 75
Cutter inclination Corrected total
Intra-group 0.238 22 0.011 265.387 74
angle value
Total value 0.357 32
a. R2=0.981 (Corrected R2=0.974)

According to Table 12, p values are smaller than 0.05, so there As listed in Tables 14-16, when the axial cutter vibration
are significant monotonic correlated relationships between the displacement in the sugarcane cutting process is the dependent
SCQEV and the SFED output frequency, the SCQEV and the cutter variable, the p value of the sugarcane transporting speed is smaller
rotating speed, the SCQEV and the sugarcane transporting speed, than 0.05 while those of the other four experimental factors are
the SCQEV and the cutter inclination angle. Moreover, the smaller than 0.01, so the sugarcane harvester travelling speed has a
monotonic correlation coefficient between the SCQEV and the significant effect on the axial cutter vibration in the sugarcane
SFED output frequency is greater than 0, so there is a significantly cutting process while the cutter inclination angle, the sugarcane
positive monotonic correlated relationship between the SCQEV and field excitation, the cutter rotating speed and the engine excitation
the SFED output frequency, matching what is found through have highly significant effects on the axial cutter vibration in the
Figure 14. Therefore, the more obvious the sugarcane field sugarcane cutting process. Moreover, partial eta square values of
excitation is, that is, the hillier a sugarcane field is, the poorer the these five experimental factors are greater than 0.14, so effect sizes
 188 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5

of the sugarcane field excitation, the engine excitation, the cutter cutter inclination angle on the axial cutter vibration in the sugarcane
rotating speed, the sugarcane harvester travelling speed and the cutting process are large.

Table 15 Main effect analysis result of the axial cutter vibration displacement in the sugarcane cutting process as the co-variate and
three-directional cutting forces as dependent variables
Dependent variable: three-directional cutting forces
Source III-type quadratic sum Freedom degree Mean square value F-value p-value Partial eta square
x y z x y z x y z x y z x y z x y z
Corrected
1 848 069.754a 6 188 978.115a 4 138 789.808a 21 21 21 88 003.322 294 713.244 197 085.229 20.344 12.004 55.158 .000 .000 .000 .890 .826 .956
model
Intercept 85 460.645 237 130.145 53 768.583 1 1 1 85 460.645 237 130.145 53 768.583 19.756 9.659 15.048 .000 .003 .000 .272 .154 .221
A 83 861.492 232 124.313 52 785.409 4 4 4 20 965.373 58 031.078 13 196.352 4.847 2.364 3.693 .002 .045 .010 .268 .151 .218
B 30 388.189 77 931.778 19 250.230 4 4 4 7597.047 19 482.945 4812.557 1.756 0.794 1.347 .152 .535 .265 .117 .057 .092
C 51 190.817 149 376.589 32 068.590 4 4 4 12 797.704 37 344.147 8017.148 2.958 1.521 2.244 .028 .209 .077 .183 .103 .145
D 16 854.042 49 835.837 10 544.992 4 4 4 4213.510 12 458.959 2636.248 0.974 0.507 0.738 .430 .730 .570 .068 .037 .053
E 21 046.915 55 002.884 13 312.254 4 4 4 5261.729 13 750.721 3328.063 1.216 0.560 0.931 .315 .693 .453 .084 .041 .066
G 219 503.045 20 673.922 2389.249 1 1 1 219 503.045 20 673.922 2389.249 50.743 2.842 4.669 .000 .043 .007 .489 .160 .312
Error 229 266.206 1 301 200.634 189 374.076 53 53 53 4325.777 24 550.955 3573.096
Total
19 249 394.378 73 010 425.262 48 135 884.017 75 75 75
value
Corrected
2 077 335.960 7 490 178.749 4 328 163.884 74 74 74
total value
2
a. R 0.890 0.826 0.956

Table 16 Main effect analysis result of the axial cutter inclination angle are greater than 0.05 while those of the SFED
vibration displacement in the sugarcane cutting process as the output frequency and the axial cutter vibration displacement are
co-variate and the SCQEV as the dependent variable smaller than 0.05, so except the cutter rotating speed, the engine
Dependent variable: SCQEV excitation, the sugarcane harvester travelling speed and the cutter
Source Mean inclination, the sugarcane field excitation and the axial cutter
III-type Freedom F- p- Partial eta
square vibration have significant effects on the y-directional cutting force.
quadratic sum degree value value square
value
Moreover, partial eta square values of the SFED output frequency
The corrected
2.150a 21 0.102 0.663 0.849 0.208 and the axial cutter vibration displacement are greater than 0.14, so
model
The intercept 0.637 1 0.637 4.125 0.047 0.072 effect sizes of the sugarcane field excitation and the axial cutter
A 0.628 4 0.157 1.016 0.048 0.144 vibration on the y-directional cutting force are large.
B 0.238 4 0.060 0.385 0.818 0.028 When the z-directional cutting force is the dependent variable,
C 0.370 4 0.092 0.599 0.665 0.043 p values of the cutter rotating speed, the actuating engine output
D 0.121 4 0.030 0.195 0.940 0.015 frequency, the sugarcane transporting speed and the cutter inclination
E 0.163 4 0.041 0.264 0.900 0.020 angle are greater than 0.05 while that of the SFED output frequency
G 0.378 1 0.378 2.449 0.004 0.171 is smaller than 0.05 and that of the axial cutter vibration displacement
Error 8.186 53 0.154 are smaller than 0.01, so except the cutter rotating speed, the engine
Total value 29.095 75 excitation, the sugarcane harvester travelling speed and the cutter
Corrected total
10.336 74 inclination angle, the sugarcane field excitation has a significant
value
effect on the z-directional cutting force and the axial cutter vibration
a. R2=0.208 (Corrected R2=0.106)
has a highly significant effect on the z-directional cutting force.
When the x-directional cutting force is the dependent variable, Moreover, partial eta square values of the SFED output frequency
p values of the actuating engine output frequency, the sugarcane and the axial cutter vibration displacement are greater than 0.14, so
transporting speed and the cutter inclination angle are greater than effect sizes of the sugarcane field excitation and the axial cutter
0.05 while those of the SFED output frequency, the axial cutter vibration on the z-directional cutting force are large.
vibration displacement are smaller than 0.01 and that of the cutter When the SCQEV is the dependent variable, the p value of the
rotating speed is smaller than 0.05, so except the engine excitation, SFED output frequency is smaller than 0.05 and that of the axial
the sugarcane harvester travelling speed and the cutter inclination cutter vibration displacement is smaller than 0.01 while those of the
angle, the sugarcane field excitation and the axial cutter vibration other four experimental factors are greater than 0.05, so except the
have highly significant effects on the x-directional cutting force engine excitation, the cutter rotating speed, the sugarcane harvester
while the cutter rotating speed have a significant effect on the x- moving speed and the cutter inclination angle, the sugarcane field
directional cutting force. Moreover, partial eta square values of the excitation has a significant effect on the SCQ and the axial cutter
SFED output frequency, the axial cutter vibration displacement and vibration has a highly significant effect on the SCQ. Moreover,
the cutter rotating speed are greater than 0.14, so effect sizes of the partial eta square values of the SFED output frequency and the axial
sugarcane field excitation, the axial cutter vibration and the cutter cutter vibration displacement are greater than 0.14, so effect sizes of
rotating speed on the x-directional cutting force are large. the sugarcane field excitation and the axial cutter vibration on the
When the y-directional cutting force is the dependent variable, SCQ are large.
p values of the cutter rotating speed, the actuating engine output In addition, significance levels of effects of the sugarcane field
frequency, the sugarcane transporting speed and the cutter excitation, the engine excitation, the cutter rotating speed, the
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 189

sugarcane harvester travelling speed and the cutter inclination angle directional cutting forces, the axial cutter vibration displacement
on the axial cutter vibration in the sugarcane cutting process from and the SCQEV, three-directional cutting forces and the SCQEV.
high to low are A>C>B>E>D. Significance levels of effects of these That is, the greater the axial cutter vibration displacement is, the
five experimental factors and the axial cutter vibration on three- greater three-directional cutting forces are. The greater the axial
directional cutting forces and the SCQ from high to low are G> cutter vibration displacement and three-directional cutting forces
A>C>B>E>D. are, the greater the SCQEV is, the poorer the SCQ will be. Their
Fitting equations of the axial cutter vibration displacement, monotonic correlation analysis results obtained through SPSS are
three-directional cutting forces and the SCQEV changing with these listed in Tables 17 and 18.
five experimental factors obtained through multi-factor linear
0.65 The curve The fitting curve
regression analysis of SPSS are shown in Equations (18)-(22), in
0.60
which experimental factors with p values greater than 0.05, that is,

The SCQEV
0.55
without significant effects, were removed. 0.50
0.45
y1 = 1.022 + 0.37A − 0.38B + 0.015C + 3.999D − 0.054E (18) 0.40 y=0.824x+0.001
0.35 R2=0.9971
y2 = 59.121 + 29.426A + 1.156C + 308.059G (19) 0.30
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0
y3 = 107.738 + 57.613A + 69.262G (20) The axial cutter vibration displacement/mm
Figure 19 Fitting curve of the SCQEV changing with the axial
y4 = 149.544 + 46.357A + 58.608G (21) cutter vibration displacement

y5 = 0.233 + 0.029A + 0.069G (22) The fitting equation of the SCQEV changing with the
x-directional cutting force: y=0.001Fx+0.002 R2=0.9961
where, y1-y5 are the axial cutter vibration displacement, the x- The fitting equation of the SCQEV changing with the
directional cutting force, the y-directional cutting force, the z- y-directional cutting force: y=0.0005Fx+0.0001 R2=0.9961
directional cutting force and the SCQEV; A-G are the SFED output The fitting equation of the SCQEV changing with the
z-directional cutting force: y=0.0007Fx+0.0005 R2=0.9976
frequency, the actuating engine output frequency, the cutter rotating
0.8
speed, the sugarcane transporting speed, the cutter inclination angle 0.7
The SCQEV

0.6
and the axial cutter vibration displacement in the sugarcane cutting 0.5
process. 0.4
0.3
Effects of the axial cutter vibration on three-directional cutting 0.2
0.1
forces and the SCQ as well as effects of three-directional cutting 0
forces on the SCQ were further studied. Fitting curves of three- 0 200 400 600 800 1000 1200 1400
Cutting force/N
directional cutting forces changing with the axial cutter vibration
displacement, the fitting curve of the SCQEV changing with the The fitting curve of the SCQEV changing with the x-directional
cutting force
axial cutter vibration displacement and fitting curves of the SCQEV
The fitting curve of the SCQEV changing with the y-directional
changing with three-directional cutting forces drawn through cutting force
Excel based on the orthogonal experiment result are shown in The fitting curve of the SCQEV changing with the z-directional
Figures 18-20. cutting force

The fitting equation of the x-directional cutting force

Figure 20 Fitting curves of the SCQEV changing with three-
Fx=79.073x−0.6894 R2=0.9999 directional cutting forces
The fitting equation of the y-directional cutting force
Fx=153.89x+2.0913 R2=0.9999 Table 17 Monotonic correlation analysis results of three-
The fitting equation of the z-directional cutting force directional cutting forces and the axial cutter
Fx=126.03x+0.5311 R2=0.9999
1400 vibration displacement
Cutting force/N

1200
1000 Cutting force
Coefficient
800 x y z
600
400 Monotonous correlation coefficient 0.999 0.999 0.998
200 p value 0.000 0.000 0.000
0
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0
The axial cutter vibration displacement/m
As shown in Table 17 that p values are all 0, so there are
significant monotonic correlated relationships between three-
The fitting curve of the x-directional cutting force changing
with the axuak cutter vibration displacement directional cutting forces and the axial cutter vibration
The fitting curve of the y-directional cutting force changing displacement. Moreover, monotonic correlation coefficients are all
with the axuak cutter vibration displacement greater than 0, so there are significant positive monotonic correlated
The fitting curve of the z-directional cutting force changing relationships between three-directional cutting forces and the axial
with the axuak cutter vibration displacement
cutter vibration displacement, that is, the greater the axial cutter
Figure 18 Fitting curves of three-directional cutting forces vibration displacement is, the greater three-directional cutting forces
changing with the axial cutter vibration displacement will be. Therefore, the more severe the axial cutter vibration in the
Determination coefficients of these fitting curves and fitting sugarcane cutting process is, the greater three-directional cutting
equations are all greater than 0.95, so they have high accuracies. forces will be. This verifies the discovery about the effect of the
There are obvious positive monotonic correlated relationships axial cutter vibration on three-directional cutting forces obtained in
between the axial cutter vibration displacement and three- single-factor experiments.
 190 October, 2024 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 17 No. 5

Table 18 Monotonic correlation analysis results of the SCQEV appear. When a sugarcane is cut for the second time, the cutters will
and the axial cutter vibration displacement, the SCQEV and press the sugarcane and the axial cutter vibration will make the
three-directional cutting forces sugarcane ratoon broken. The breaking degree of the sugarcane is
Independent variable dependent on the axial cutter vibration amplitude and frequency, so
Coefficient Axial cutter
x-directional y-directional z-directional
the axial cutter vibration amplitude and frequency directly affect the
vibration SCQ, matching the sugarcane cutting mechanism.
cutting force cutting force cutting force
displacement
Monotonous There are positive monotonic correlated relationships between
correlation 0.993 0.992 0.992 0.995 three-directional cutting forces and the axial cutter vibration
coefficient amplitude and frequency. The greater the axial cutter vibration
p value 0.000 0.000 0.000 0.000
amplitude is, the greater the pressure, the friction force and the z-
directional cutting force generated by the cutters acting on the
What’s more, as listed in Table 18 that p values are all 0, so
sugarcane will be, which makes the x-directional and the y-
there are significant monotonic correlation relationships between
directional cutting forces also increase.
the SCQEV and the axial cutter vibration displacement, the SCQEV
Along with the cutter rotating speed increasing, three-
and three-directional cutting forces. Moreover, monotonic
directional cutting forces increased firstly and then decreased. This
correlation coefficients are all greater than 0, so there are significant
is mainly relative to cutter rotations around cutter axes and
positive monotonic correlated relationships between the SCQEV
sugarcane toughness. Effects of the axial cutter vibration amplitude
and the axial cutter vibration displacement, the SCQEV and three-
on three-directional cutting forces are significant. When the cutter
directional cutting forces, that is, the greater the axial cutter
rotating speed decreases, causing lack of cutting energies, the
vibration displacement and three-directional cutting forces are, the
cutters will push down and compress the sugarcane instead of
greater the SCQEV will be, the poorer the SCQ will be. Therefore,
cutting off the sugarcane at once. This will cause a cutting force
the more severe the axial cutter vibration in the sugarcane cutting
accumulation.
process is, the poorer the SCQ will be. This verifies the discovery
Three-directional cutting forces increase along with the cutter
about effects of the axial cutter vibration and three-directional
inclination angle increasing in that the contact area between the
cutting forces on the SCQ obtained in single-factor experiments.
cutters and the sugarcane is increased when the cutter inclination
On the other hand, there is an obviously positive monotonic
angle increases. When the sugarcane harvester moves forward, the
correlated relationship between SCQEV and the axial cutter
cutters will generate a pushing force acting on the sugarcane. The
vibration amplitude according to Figure 19. That is, the greater the
cutters are inclined, so this pushing force can be decomposed into
axial cutter vibration amplitude is, the greater the SCQEV is, the
three-directional component forces, that is, three-directional cutting
poorer the SCQ will be. It is also shown by their monotonic
forces. The greater the cutter inclination angle is, the greater these
correlation analysis result that there is a highly significant positive
three-directional component forces will be.
monotonic correlated relationships between the SCQEV and the Three-directional cutting forces increase along with the
axial cutter vibration amplitude, matching the conclusion of the sugarcane harvester travelling speed increasing. This is similar to
previous research[11,12] and the sugarcane cutting mechanism that the effects of the cutter inclination angle on three-directional cutting
axial cutter vibration has a bad effect on the cutting quality of forces, so Figures 12 and 13 are similar. When the cutter inclination
sugarcane harvesters. Therefore, the more severe the axial cutter angle is constant, the greater the sugarcane harvester travelling
vibration is, that is, the greater the axial cutter vibration amplitude speed is, the greater the pushing force generated by the cutters
and frequency are, the poorer the SCQ will be, so the more obvious acting on the sugarcane will be. Thus, three-directional cutting
the sugarcane field excitation is, that is, the hillier a sugarcane field forces will be greater. Based on analysis above, some SCQ-
is, the poorer the SCQ will be in that the more obvious the improving methods can be obtained as follow:
sugarcane field excitation is, the more severe the axial cutter When the axial cutter vibration amplitude and frequency
vibration will be, making the axial cutter vibration amplitude and increase, the sugarcane will suffer from the pressure Fz and the
frequency greater, further matching what are found through bending moment Mz. When the sugarcane is cut for the second time,
Figures 4a and 4b. The greater the cutter rotating speed, the the sugarcane will be easy to be compressed and torn. The
sugarcane harvester travelling speed and the cutter inclination angle sugarcane ratoon will be broken if the axial cutter vibration
are, the better the SCQ will be in that the greater the cutter rotating amplitude is extremely great, so the axial cutter vibration amplitude
speed, the sugarcane harvester travelling speed and the cutter should be reduced through vibration reducing methods of sugarcane
inclination angle are, the weaker the axial cutter vibration is, harvesters. Inherent frequencies of sugarcane harvesters should be
making the axial cutter vibration amplitude and frequency smaller, increased to avoid their resonance. Besides, it is good for improving
further matching what are found through Figures 4c-4e. the cutting quality of sugarcane harvesters to increase the cutter
rotating speed. Lack of cutting energies appear with a low cutter
6 Analysis and discussions
rotating speed, making the cutters generate shocks acting on the
According to the sugarcane cutting mechanism, the pressure Fz sugarcane, compress and shock it instead of cutting it off rapidly.
and the bending moment Mz generated by the cutter acting on the Then sugarcane toughness prevents cutting energies and the cutters
sugarcane increase along with the axial cutter vibration amplitude reaching the interior of the sugarcane rapidly, causing damages and
and frequency increasing. This will make axial cracks of the cracks of the sugarcane. Therefore, the cutter rotating speed ought
sugarcane appear and the ratoon broken. to be great enough to cut off the sugarcane rapidly in order to
There are height differences among different cut-in points. This effectively improve the cutting quality of sugarcane harvesters.
is bad for the cutting quality of sugarcane harvesters, making a Moreover, a great cutter inclination angle increases the contact area
sugarcane cut off by more than one time of cutting and Fz increase. between the cutters and the sugarcane, making the sugarcane ratoon
Then Mz generated by Fz will make axial cracks of the sugarcane not easy to be broken by the cutters. The axial tensile strength of the
 October, 2024 Mo H N, et al. Affecting factors of the cutting quality of sugarcane harvesters under complicated excitations Vol. 17 No. 5 191

cutters is much greater than the radial one, so a great cutter Research Ability Promotion Project of Guangxi Universities, China
inclination angle is able to help cut off the sugarcane. Additionally, (Grant No. 2024KY0697); Wuzhou University Research
under a low sugarcane harvester travelling speed, the sugarcane Foundation for Advanced Talents, China (Grant No.
may be cut off after several times of cutting, which leads to a poor WZUQDJJ17179); Major Special Project of Guangxi Sugarcane
SCQ while under a high sugarcane harvester travelling speed, the Science and Technology in the 14th Five-year Plan, China (Grant
cutters may generate a great pushing force acting on the sugarcane, No. 2022AA01010); the general program of the National Natural
which makes it easy to break the sugarcane ratoon. Therefore, it is Science Foundation Project, China (Grant No. 32071916); a
necessary to find suitable values of such cutting parameters as the horizontal technical service project of the Zhenkang Professor
cutter rotating speed, the cutter inclination angle and the sugarcane Workstation, Yunnan, China; the Double First-class Discipline
harvester travelling speed for sugarcane harvesters with a good Construction Project: Mechanized sugarcane harvesting equipment
SCQ. development of Zhenkang, Yunnan, China; the first university-
directly-under-Education-Ministry-served innovative rural
7 Conclusions revitalization test project: the China-Agricultural-University-served
1) The sugarcane field excitation, the sugarcane harvester innovative Bangdong Village revitalization test plan, mechanized-
travelling speed and the cutter inclination angle have significantly sugarcane-harvesting assistant rural revitalization in hilly areas,
positive monotonic correlated effects on the axial cutter vibration Zhenkang, Yunnan, China; the Portable Sugarcane Harvester
and three-directional cutting forces while the cutter rotating speed Research and Development, China (Grant No. NK2022160504); the
has a significantly negative monotonic correlated effect on the axial 2115 Talent Development Program of China Agricultural
cutter vibration and three-directional cutting forces. University; Guangxi Science and Technology Project, China (Grant
2) The sugarcane field excitation, the axial cutter vibration No. Guike AA22117007); Guangxi Science and Technology
amplitude and frequency have significantly negative monotonic Project, China (Grant No. Guike AA22117005); Guangxi Special
correlated effects on SCQ while the cutter rotating speed, the Project of Science Technology Bases and Talents, China (Grant No.
sugarcane harvester travelling speed and the cutter inclination angle Guike AD23026033); the Opening Project of Guangxi Key
have significantly positive monotonic correlated effects on the SCQ. Laboratory of Advanced Microwave Manufacturing Technology,
3) Optimal level combination of the cutter rotating speed, the China (Grant No. 2024GKLAMMTKFKT001).
sugarcane harvester travelling speed, and the cutter inclination angle
is 700 r/min, 0.6 m/s, and 8º for sugarcane harvesters with a good [References]
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