# Stress and Fatigue Analysis of Picking Device Gears for a 2.6 kW Automatic Pepper Transplanter
## 2 Materials and Methods
### Determination of Suitable Face Width and Material
#### 2.2.2 Gear Contact Stress Analysis by FEA Simulation  
An FEA software package (midas NFX-2019, MIDAS Information Technology Co. Ltd., Seongnam, Korea) was used to estimate the contact stress and determine the maximum stress location in the picking device gears by FEA numerical simulation. The gear sets were assumed to make of SCM 420H carbon steel (medium carbon steel) or AISI 1060 steel (high carbon steel). The outline of the gear set tooth was divided into involute and trochoid curves. First, it is necessary to identify the gear set tooth that has an involute gear tooth outline. If gear parameters such as the module, teeth number, pressure angle, and radius of pitch circle are specified, the involute gear tooth outline can be determined using the gear parameters and function of the involute curve [16]. Before starting the FEA simulation, the individual three-dimensional crack and cam gear set geometry were generated. The general contact assembly was used to make contact \begin{table}
\begin{tabular}{c c} \hline
**Notation** & **Definition, Unit and Value** \\ \hline \(L\) & Lifespan of transplanter, years \\ \(N\) & Number of cycles, integer \\ \(D\) & Damage sum, integer \\ \(n_{i}\) & Number of cycles of measured data at the \(i\)th stress level \\ \(N_{c}\) & Number of cycles of the S-N curve at the \(i\)th stress level \\ \(L_{f}\) & Predicted fatigue life, h \\ \(L_{a}\) & The service life of the tractor, h \\ \(C_{f}\) & Predicted fatigue life cycles, integer \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline
**Material** & \begin{tabular}{c} **Poisson** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Modulus of** \\ **Elasticity, MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Tensile** \\ **Strength, MPa** \\ \end{tabular} &
\begin{tabular}{c} **Endurance** \\ **Limit, MPa** \\ \end{tabular} \\ \hline Medium-carbon steel & & & & \\ (SCM 420H) & 0.30 & 210 & 1158 & 579 \\ High-carbon steel (AISI 1060) & 0.29 & 212 & 1105 & 552.50 \\ \hline \end{tabular}
\end{table} 
Table 2: Material properties of the gear used for stress analysis. between the master (gear) and slave (pinion). For the assembly discretization and stress distribution, the three-dimensional geometry was meshed using mapped face meshing to obtain a uniform mesh structure. After completing the mesh, the boundary conditions, including self-weight, displacement, supports, loads (torque), and degree of freedom, were applied to the model as the pinion rotated in an anti-clockwise direction. The center of the gear shaft was set in the longitudinal direction of the gear tooth surfaces. The value of load (torque) was applied to the gear for the same angular position of the pinion in each set. A non-linear static analysis with the Newton-Raphson method was used to estimate the contact stress and determine the maximum stress location. In the post-processing section, the [PERSON] stress distribution technique was applied to obtain the stress in 10 increments. Figure 3 shows the procedure of the FEA simulation to determine the gear contact stress. Figure 4 shows the diagram of application of meshing and boundary conditions, and the position of maximum stress for both gear sets. The load (torque) was applied to the gear shaft, and the maximum stress was established at the teeth contact point of the gear and pinion. In order to perform a suitable stress analysis of the gear, the specifications of the two gear sets in the simulation were considered, as illustrated in Table 3.  
Figure 4: (**a**) Application of meshing and boundary conditions, and (**b**) position of the maximum stress. Figure 3: Block diagram showing the FEA simulation procedure to determine the gear contact stress. In order to encourage picking device gears to revolve continuously, the previous contact point of the gear teeth should be introduced before the current teeth-point contact is completed. The contact ratio represents the ratio of the average number of gear tooth pairs in contact for a pair of contact gears [16].