2.3.1. Analysis of Driving Stability
The roll angle [
30] refers to the angle between the support plane of the orchard operation-aid platform chassis and the horizontal plane. The maximum stable roll angle is the angle at which the orchard operation-aid platform is about to roll over but has not yet done so; it is a crucial indicator of the safe operation of the orchard operation-aid platform. Given the high center of gravity of the orchard operation-aid platform and its frequent operation in hilly terrains, it is necessary to determine its maximum stable roll angle to define safe operating limits and reduce the risk of rollover during travel. Considering the operational scenarios of the orchard operation-aid platform, there are three primary attitudes: longitudinal downhill, longitudinal uphill, and lateral slope driving. The force analysis for these three attitudes is shown in
Figure 5 (with the illustrated slope angle
θ = 15°), and the maximum stable roll angle of these primary attitudes must be greater than 15° to ensure the safety of operators. The forces acting on the orchard operation-aid platform mainly include its own weight
m0g, driving resistance
Ftotal, and the resultant normal force
FNc exerted by the ground on the entire track support area. To simplify the analysis, the following assumptions are made:
(1) When the orchard operation-aid platform is moving at a low constant speed on a slope, external factors can be neglected, and it can be assumed to be stationary on the slope.
(2) O1, O2 and O3 represent the front, rear, and left support points of the track-ground contact area, respectively. Depending on the driving attitude, the rollover axis k passes vertically through the support point. The length of the track-ground contact area in the X-axis direction is xc = 1100 mm, and in the Z-axis direction is zc = 1100 mm.
(3) Since the operator and the manned workbench are basically kept at a relative standstill, the two are considered as one unit for calculating the center of mass, center of gravity, etc. As a rule of thumb, the operator is weighed to be 75 kg, while the manned workbench’s gravity is weighed to be about 33 kg.
(4) Based on the mass and material parameters of each component of the orchard operation-aid platform, and using SolidWorks 2020 to define the properties of each part, the center of gravity Om0 of the orchard operation-aid platform in the base coordinate system O0X0Y0Z0 is determined to be (104, −3, 1031). Therefore, the distances between Om0 and the support points O1, O2 and O3 along the X, Y, and Z axis are rounded to xm01 = 446 mm, xm02 = 654 mm, xm03 = 553 mm, ym01 = ym02 = 0, ym03 = 553 mm, zm01 = zm02 = zm03 = 1031 mm.
After simplification, the maximum stable roll angles for the three attitudes of longitudinal downhill, longitudinal uphill, and lateral slope driving of the orchard operation-aid platform are calculated separately.
In
Figure 5a, the orchard operation-aid platform has only one potential rollover scenario when moving downhill longitudinally: rollover clockwise about point
O1. As the slope angle
θ changes, the masses on both sides of the rollover axis
k change, and the moments generated by these masses change accordingly.
For ease of calculation, further simplifications are made for the longitudinal downhill attitude of the orchard operation-aid platform: the extension mechanism, worker, and manned workbench are all located on the same side of the rollover axis k, and their positions are relatively fixed. They can be considered as a whole with a mass mm1 = 366 kg and center of gravity Om1 at (751, −1, 2027) in the base coordinate system O0X0Y0Z0. The distances from Om1 to support point O1 along the X and Z axis are xm11 = 201 mm and zm11 = 2027 mm, respectively. The remaining part of the orchard operation-aid platform is considered as another whole with mass m′m1 = 1216 kg and center of gravity O′m1 at (−91, 3, 730), with distances to O1 of x′m11 = 641 mm and z′m11 = 730 mm along the X and Z axes, respectively.
Establishing the moment balance formula at point
O1:
In the formula, MO1 is the moment acting at point O1; when MO1 <0, the orchard operation-aid platform will roll over. xi11 is the distance along the X-axis between the resultant normal force FNc and point O1, which varies with the position of the center of gravity; when rollover or about to roll over, xi11 = 0.
From Formula (6), the maximum stable roll angle of the orchard operation-aid platform during longitudinal downhill is calculated to be approximately 23.4°, exceeding the design requirement of 15°.
In
Figure 5b, the orchard operation-aid platform has only one potential rollover scenario when moving uphill longitudinally: rollover counterclockwise about point
O2.
For ease of calculation, further simplifications are made for the longitudinal uphill attitude: the hydraulic station and the center of gravity of the orchard operation-aid platform are located on opposite sides of the rollover axis, so the hydraulic station is considered an independent unit with mass mm2 = 196 kg and center of gravity Om2 at (−614, −3, 784) in the base coordinate system. The distances from Om2 to support point O2 are xm22 = 64 mm and zm22 = 784 mm along the X and Z axes, respectively. The remaining part of the orchard operation-aid platform is considered as another whole with mass m′m2 = 1385 kg and center of gravity O′m2 at (206, 1066, 3), with distances to O2 of x′m22 = 756 mm and z′m22 = 1066 mm.
Establishing the moment balance formula at point
O2:
In the formula, MO2 is the moment acting at point O2; when MO2 < 0, the orchard operation-aid platform will roll over. xi22 is the distance along the X-axis between the resultant normal force FNc and point O2, which varies with the position of the center of gravity; when rollover or about to roll over, xi22 = 0.
From Formula (7), the maximum stable roll angle of the orchard operation-aid platform during longitudinal uphill s calculated to be approximately 32.4° exceeding the design requirement of 15°.
In
Figure 5c, the orchard operation-aid platform has only one potential rollover scenario when driving laterally on a slope: rollover counterclockwise about point
O3.
Establishing the moment balance formula at point
O3:
In the Formula, MO3 is the moment acting at point O3; when MO3 < 0, the orchard operation-aid platform will roll over. yi03 is the distance along the Y-axis between the resultant normal force FNc and point O3, which varies with the position of the center of gravity; when there is no rollover, yi03 = 0.95 m, and when rollover or about to roll over, yi03 = 0.
From Formula (8), the maximum stable roll angle of the orchard operation-aid platform during lateral slope driving is calculated to be approximately 28.2°, exceeding the design requirement of 15°.
In summary, the maximum stable roll angles of the orchard operation-aid platform during longitudinal downhill, longitudinal uphill, and lateral slope driving are 23.4°, 32.4°, and 28.2°, respectively, all exceeding the design requirement of 15°. Therefore, the orchard operation-aid platform meets the stability requirements for driving on slopes.