3.1. Knife Movement Trajectory Analysis
According to the working principle of the laver harvester, the movement trajectory of the knife top presents a trochoid curve combined by circular movement and horizontal movement [
30]. The kinematic model of the knife top can be expressed as follows:
where
V0 represents the traveling speed of the loading device (m/s),
ω represents the angular speed of the cutter shaft (rad/s),
t represents time (s),
R represents the turning radius of the knife (mm).
The position of the knife top at any time can be expressed by Formulae (1) and (2). There are different shapes and characteristics of the movement trajectory with the changes in the traveling speed (V0), turning radius of the knife (R), and angular speed (ω).
As shown in
Figure 3, the speed of the knife top in the horizontal and vertical directions is the derivative of displacement (
X) and (
Y) to time (
t):
As shown in
Figure 4, due to the fact that the cutter can only contact laver in the solid line part during harvesting, only the movement trajectory of this part would be analyzed. The axle center of the cutter is point P
5, and the intersection point O of the net curtain and the Y axis is the origin. When the anterior knife top I contacts the laver at point P
1, the laver on the net curtain would be cut. Then, the knife top continues to move to the right side until the posterior knife top leaves the lowest pendulous point of the laver at point P
2. The range from point P
1 to point P
2 indicates the area for cutting laver. Point P
1 is the highest cutting point, and the rotation speed overlaps with the traveling speed, which induces the maximum cutting force on the laver. The distance from the net curtain to the cutting baseline represents the target stubble length (
H2), and the laver length is
H1. The movement trajectory of the posterior knife top II is the same as that of the anterior knife top I. Point P
4 represents the position entering the cutting area, the missing cutting length of laver is
H3, and the shaded area (P
1 P
3 P
4) represents the missing cutting area.
To avoid missing cutting, reducing the missing cutting length (
H3) can effectively reduce the missing cutting area (P
1 P
3 P
4),
H3 is related to the movement trajectory of the knife top and the cutting pitch. The cutting pitch (the distance from point P
1 to point P
3 in
Figure 3) is the traveling distance of the harvester during the time interval for the cutting of laver by two adjacent cutters. If the time interval for the cutting of laver by two adjacent cutters is set as:
the cutting pitch can be expressed as:
if the ratio of the rotation speed of the cutter to the traveling speed
λ is set as:
the approximate calculation can be completed as per the following formula:
when the value of angle a is not large, it can be considered that sin
a=
a.
hence, the missing cut length can be simplified as:
where
V0 represents the traveling speed of the loading device (m/s),
R represents the turning radius of the knife (mm).
Therefore, the traveling speed, the rotation speed of the cutter, and the turning radius of the knife directly affect the missing cutting length. When the turning radius is constant, the reducing speed ratio λ, the missing cutting length (H3) will decrease, and the missing cutting area.
3.2. Force Analysis in the Cutting Process
When the knife top cuts into the laver, the force is shown in
Figure 5.
Laver is selected as the research object, the X axis represents the traveling direction, the Y axis represents the pendulous direction of laver,
FX represents the horizontal component of the cutting force (
F), and
FY represents the vertical component of the cutting force (
F), as expressed in Formulae (12) and (13).
where
F represents the cutting force of the cutter on laver (N),
T represents the horizontal thrust of the knife on laver (the force on laver when the device moves forward) (N),
Tr represents the self-elasticity of laver (N),
G represents the weight of laver below the action point (N),
θ represents the cutting rotation angle (°),
θr represents the deflection angle of laver (°).
The horizontal component (FX) is perpendicular to laver. One end of the laver is fixed, and the other end is unconstrained. If the weight of the laver is very small relative to the horizontal component, the laver may jump forward unsteadily, which may cause cutting failure. The weight (G) of the harvested laver will change with the movement of the action point of the knife. The closer to the root, the greater the weight (G) will be. Therefore, in order to cut off laver successfully, it is necessary to consider the weight of the laver below the action point.
The direction of the vertical component (
FY) of laver is the same as that of the pendulous tension of laver. Some parts of the laver may be stretched and broken due to its soft texture, and hence there is a tensile force. The cutting stress and tensile stress on laver can be expressed as Formulae (14) and (15):
where
As represents the cross-sectional area of laver.
When
, laver would be cut off; when
, laver would be ruptured under a tensile force. If
θr,
F, and
As in Formulae (14) and (15) are constant,
and
would be proportional to the cutting rotation angle (
θ), and laver may be cut off or ruptured under a tensile force with the changes in the cutting rotation angle. When the cutting rotation angle is zero, namely when the cutting edge acts vertically on laver,
would reach the maximum, and laver can be harvested only by the cutting stress. If the cutting rotation angle increases,
would decrease; otherwise,
would increase. However, when the cutting rotation angle is close to 90°, the cutter would not affect the harvesting of laver, it is impossible to complete the harvesting of laver. For rotary cutting, Li and Yada gave similar laws and conclusions [
10,
31]. In summary, when the cutting rotation angle decreases, the proportion of laver under a cutting force would increase; when the cutting rotation angle increases, the proportion of laver under a tensile force would increase.
The cutting rotation angle (θ) is determined by the knife position, knife structure parameters including extension length (B) and inclination angle (A), and operating parameters including rotation speed (D) and traveling speed (C). Under the same knife position and operating parameters, the cutting rotation angle (θ) is determined by cutter structure parameters. When the extension length (B) increases and the inclination angle (A) decreases, θ increases; otherwise, θ decreases. The single grid of the laver net curtain is 80 mm, and the length of the laver stubble is 50–70 mm. In comprehensive consideration of the structure size of the knife should not be too large and the stubble space requirement, the knife extension length is 35~45 mm. In order to make the top of knife better contact with the laver, the inclination angle is 100~120°. Based on the knife movement trajectory analysis results and the speed of the existing fishing boats, the traveling speed is determined to be 0.51~1.03 m/s, and the rotation speed is 700~1100 r/min.