This article focuses on the design and optimization of non – circular gear – driven drag – type carrot harvesting devices. It analyzes the problems of traditional harvesting devices, proposes the design concept of non – circular gear – driven devices, and conducts in – depth research on device design, simulation, experimental verification, and performance improvement. Through a series of studies, it aims to provide a reference for improving the performance of carrot harvesting machines and promoting the development of the carrot harvesting industry.
1. Introduction
Carrots are rich in nutrients and are widely planted around the world. China ranks among the top in the world in terms of carrot planting area and total output. The root – stem separation process in carrot harvesting is of great significance as it directly affects the harvesting efficiency and the quality of harvested carrots. Efficient and low – damage root – stem separation can increase production and income, making it a crucial link in the carrot harvesting process.
Traditional drag – type carrot harvesting devices, although having some advantages such as simple structure and high reliability, face significant problems. The constant – speed driving method often leads to poor root – stem separation effects. For example, the interaction between the drag rod and the carrot during the harvesting process easily causes scratches on the carrot, and there are cases where the root – stem separation is incomplete. These issues result in a high damage rate of carrots and a low harvesting success rate, which restricts the large – scale and efficient production of carrots.
In recent years, with the development of agricultural mechanization, there is an increasing demand for high – performance carrot harvesting equipment. Many researchers have carried out studies on improving the performance of carrot harvesting devices. Some focused on the mechanical properties of carrots, while others explored the optimization of the structure of harvesting devices. However, most of the research on the motion characteristics of drag rods remains at the theoretical analysis stage, and there is a lack of in – depth practical application research. Therefore, it is necessary to conduct more comprehensive and in – depth research on the design and optimization of carrot harvesting devices to meet the actual production needs.
2. Working Principle of Drag – type Carrot Harvesting Devices
The overall working process of the drag – type carrot harvesting device mainly includes three stages: carrot extraction, transportation, and root – stem separation. As shown in Figure 1, the device is mainly composed of a conveying device and a drag – type carrot root – stem separation device.
| Component | Function |
|---|---|
| Conveying device | Clamps the carrot tops and moves them upward along the conveyor belt direction |
| Drag – type carrot root – stem separation device | Pulls the carrots downward through the drag rods to achieve root – stem separation |
During operation, the digging component first loosens the carrots buried deep in the soil. Then, the conveyor belt clamps the carrot tops and moves upward. When the carrots reach a specific position, the two groups of drag rods in the drag device pull the carrots downward. Through the combined action of the drag rods and the conveyor belt, the root – stem separation of the carrots is realized.
The root – stem separation device is a key component of the drag – type carrot harvesting device, mainly consisting of a drive gearbox, a driving disc, drag rods, a driven disc, and a support plate, as shown in Figure 2.
| Component | Function |
|---|---|
| Drive gearbox | Transmits power to drive the rotation of the driving disc |
| Driving disc | Drives the drag rods to do circular translational motion in the plane of the driving disc |
| Drag rods | Pull the carrots to achieve root – stem separation when in contact with the carrots |
| Driven disc | Driven by the drag rods to rotate, and cooperates with the driving disc to ensure the movement of the drag rods |
| Support plate | Supports and fixes other components |
During operation, the power device drives the driving disc to rotate through the drive gearbox. The drag rods inserted into the hinge holes of the driving disc do circular translational motion in the plane of the driving disc. The other ends of the drag rods, under the constraint of the structure, push the driven disc to rotate, and drive the drag rods to continue circular translational motion. The overlapping area of the left and right drag rods during the movement is the working area of the carrot drag rods. When the conveyor belt clamps the carrot tops and enters this working area, the drag rods contact the carrot roots and generate a force along the z – axis direction. With the cooperation of the conveyor belt, the action of pulling the carrots is completed, achieving root – stem separation.
In traditional devices, the root – stem separation device is usually driven by cylindrical gears at a constant speed. When the driving disc with a rotation speed of ω drives the drag rod to do circular translational motion in the plane of the driving disc, the longitudinal translation speed v of the drag rod can be calculated by the formula \(v = ωR\sin(ωt)\) (where R is the radius of the circular translational motion of the drag rod, and t is the rotation time of the driving disc). According to the angle relationship between the drag rod and the driving disc, the speed \(v_z\) of the drag rod along the z – axis direction can be obtained as \(v_z=v\cos(0.5\pi – \alpha)\) (where \(\alpha\) is the angle between the driving disc and the drag rod). So, \(v_z = ωR\sin\alpha\cdot\sin(ωt)\).
3. Motion Characteristics Analysis of Drag Rods
The speed change of the drag rod in the traditional drag – type carrot root – stem separation device in the z – axis direction (the direction of action on the carrot) is a key factor affecting the root – stem separation effect. When \(R = 50\) mm and \(\alpha=30^{\circ}\), the speed curve of the drag rod in the direction of action is a sine curve, as shown in Figure 3.
| Phase | Speed Change | Acceleration Change |
|---|---|---|
| During the entire working period | From \(0.35\) m/s to the highest speed of \(0.5\) m/s | Gradually decreases |
In actual work, when the rotation angle of the driving disc is between \(50^{\circ}\) and \(95^{\circ}\), the two opposite drag rods overlap or even cross each other. This stage is the working period of the drag rod interacting with the carrot. From the speed curve, it can be seen that the speed of the drag rod is in a variable – acceleration state throughout the working period, and the speed increase is \(0.15\) m/s. This kind of speed change may cause the drag rod to have a relatively long – term and non – stable interaction with the carrot, which is not conducive to efficient root – stem separation and may easily cause damage to the carrot.
Based on previous research results, it has been found that the impact of the structural parameters of the carrot harvester on the root – stem separation effect has received much attention, while the impact of the motion characteristics of the drag rod has been ignored. Through mechanical property tests on carrot tops, it has been shown that when the drag rod acts on the carrot at a high speed instantaneously, the root – stem separation effect is better.
The improved drag rod speed curve is proposed, as shown in Figure 4. Its characteristics are as follows: the overall shape is similar to a sine curve. In the first stage, the speed of the drag rod rapidly and uniformly accelerates to the highest point; in the second stage, it enters the working state and maintains a stable high – speed state with a speed increase of 0 m/s. During the working stage, the drag rod can act on the carrot at a high speed instantaneously and continuously output force, which meets the condition of the drag rod acting on the carrot at a high speed instantaneously and is conducive to improving the root – stem separation effect. However, this conclusion has only been analyzed on a mechanical tester and has not been deeply studied and verified on a carrot root – stem separation device.
4. Design and Simulation of the New Root – Stem Separation Device
To improve the performance of the drag – type carrot harvesting device, a non – circular gear – driven drag – type carrot root – stem separation device is proposed based on the improved drag rod speed curve. The non – circular gear pair has a flexible and variable transmission ratio, which can meet the diverse motion characteristic requirements of the drag – type carrot root – stem separation device. The non – circular gearbox with the non – circular gear pair as the core is a key component to achieve the improved motion characteristics of the drag rod.
As shown in Figure 5, the non – circular gearbox includes a non – circular gear pair, a reduction gear pair, and an equal – speed gear pair. The power transmission route is as follows: the power from the driving shaft is transmitted to the reduction gear pair through the non – circular gear pair and the transmission shaft, and then through the equal – speed gear pair, it is transmitted to the drag rod driving disc through output shaft I and output shaft II.
| Component | Function |
|---|---|
| Non – circular gear pair | Adjusts the transmission ratio according to the required motion characteristics of the drag rod |
| Reduction gear pair | Reduces the speed and increases the torque |
| Equal – speed gear pair | Ensures the synchronous movement of the drag rods |
The design of the non – circular gear pair adopts a reverse – design method based on the motion characteristics of the drag rod. First, a mathematical relationship is established between the improved drag rod speed curve and the rotation angle of the driving non – circular gear, as well as the rotation angle of the driven non – circular gear, to calculate the transmission ratio of the non – circular gear.
The mathematical relationship between the output speed of the drag rod and the rotation angle of the driving non – circular gear is \(V_z = f(\varphi_1)\) (\(\varphi_1\) is the rotation angle of the driving non – circular gear, \(V_z\) is the improved drag rod speed). The mathematical relationship between the output speed of the drag rod and the rotation angle of the driven non – circular gear is \(V_z=\varphi_2’R\sin\varphi_2\) (\(\varphi_2\) is the rotation angle of the driven non – circular gear). From these two formulas and the transmission characteristics of the non – circular gear pair, the relationship between the transmission ratio i of the non – circular gear and the rotation angle of the driving non – circular gear can be determined as \(i = g(\varphi_1)\).
Given the center distance of the gear pair and the calculated transmission ratio of the non – circular gear, the pitch curve of the non – circular gear can be calculated. The instantaneous transmission ratio of the non – circular gear pair is calculated by the formula \(i=\frac{\omega_1}{\omega_2}=\frac{r_2}{r_1}=\frac{a – r_1}{r_1}\) (a is the center distance of the non – circular gear pair, \(\omega_1\) and \(\omega_2\) are the instantaneous angular velocities of the driving and driven non – circular gears respectively, \(r_1\) and \(r_2\) are the distances from the instantaneous center P to the centers of the driving and driven non – circular gears respectively).
In the polar coordinate system, the pitch curve equation of the non – circular gear is \(\left\{\begin{array}{l}r_1(\varphi_1)=\frac{a}{1 + i}\\r_2(\varphi_2)=a – r_1(\varphi_1)=\frac{ai}{1 + i}\\\varphi_2=\int_{0}^{\varphi_1}\frac{1}{i}d\varphi_1\end{array}\right.\). The pitch curve of the non – circular gear not only determines the transmission law of the gear but also affects the generation of the tooth profile and the difficulty of its processing and manufacturing. Therefore, it is necessary to check the convexity and concavity of the pitch curve according to the radius of curvature of the pitch curve. The radius of curvature of the pitch curve is calculated by the formula \(\rho=\frac{[r^{2}+(\frac{dr}{d\varphi})^{2}]^{\frac{3}{2}}}{r^{2}+2(\frac{dr}{d\varphi})^{2}-r\frac{d^{2}r}{d\varphi^{2}}}\) (r is the radius of the gear pitch curve, \(\varphi\) is the angle of the pitch curve radius relative to the initial line).
By using MATLAB software, a design program for the non – circular gear pitch curve is written based on the non – circular gear pitch curve equation and the formula for calculating the radius of curvature of the pitch curve. The pitch curve of the non – circular gear is obtained, and then the tooth profile of the non – circular gear is calculated according to the mathematical relationship between the tooth profile of the non – circular gear and the pitch curve of the gear. The solution results of the non – circular gear pair are shown.
According to the structural parameters and working space requirements of the non – circular gear – driven drag – type carrot root – stem separation device, the UG three – dimensional design software is used to establish a three – dimensional model of the carrot root – stem separation mechanism, as shown in Figure 7.
| Step | Operation |
|---|---|
| 1 | Import the three – dimensional solid models of parts into the UG assembly module for assembly |
| 2 | Add corresponding constraints and drives in the UG motion simulation module for virtual simulation |
| 3 | Compare the simulation results with the theoretical results |
The simulation result of the drag rod speed curve is compared with the theoretically designed speed curve, as shown in Figure 8. The results show that the two curves are in good agreement, indicating that the design of the non – circular gear – driven drag – type carrot root – stem separation device is reasonable and correct, and can meet the expected motion characteristics.
5. Experiment and Results
A test bench for the non – circular gear – driven drag – type carrot harvesting device was developed. In the farmland experimental field in Paojiang, Shaoxing, Zhejiang, the “New Red Carrot” variety commonly planted in Zhejiang was cultivated. Mature carrots were selected as experimental samples.
The experimental reference object was the structural parameters in the literature. The success rate of carrot root – stem separation (the probability that the carrot root – stem is successfully separated during the experiment) and the damage rate (the probability that the carrot is damaged during the experiment) were used as the evaluation indexes of the carrot root – stem separation effect. A control experiment of carrot root – stem separation was carried out. To eliminate the interference of other parameters on the experimental results, except for the speed curve of the drag rod, the rest of the parameters were kept consistent with those in the reference literature. The maximum movement speed of the drag rod in the direction of action was when the angle between the drag rod and the conveyor belt was \(40^{\circ}\). The experiment was carried out in accordance with GB/T 8097 – 2008 “Test Methods for Combine Harvesters for Harvesting Machinery”. The calculation formulas for the success rate of carrot root – stem separation \(\eta_2\) and the damage rate \(\eta_1\) of carrots are \(\eta_1=\frac{n_1}{n}\times100\%\) and \(\eta_2=\frac{n_2}{n}\times100\%\) (\(n_1\) is the number of damaged carrots, \(n_2\) is the number of carrots with successfully separated roots and stems, n is the total number of carrots). The experimental process is shown .
Each group of experiments was repeated 10 times, with 10 carrots each time, and the data were averaged. The selected carrots were regular in shape, undamaged, and similar in size. The experimental results are shown in Table 1.
| Experimental Object | Success Rate (%) | Damage Rate (%) |
|---|---|---|
| Traditional Drag – type | 94 | 7.7 |
| New Drag – type | 97.1 | 4.9 |
The results show that compared with the traditional drag – type carrot root – stem separation device, the root – stem separation success rate of the non – circular gear – driven drag – type carrot harvesting device is increased by 3.1%, and the carrot damage rate is reduced by 2.8%. Through the analysis of the experimental process.
