# 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  
Gear tooth breakage or operation above the limit of the contact teeth durability harms the service life of a gear mechanism. Determination of a reasonable face width range is important to avoid micropitting of the contact teeth [29]. In this study, after selecting the face width range, an FEA simulation was performed to select the maximum stress position by applying a gear mechanism load in terms of the contact teeth, contact ratio, and roll angle [17]. A theoretical method considering the American Gear Manufacters Association (AGMA) theory was used to evaluate the FEA simulation and determine a suitable face width and material. Figure 2 shows the stress analysis procedure of the picking device gear to determine the dimension (face width) and material. Table 1 indicates the considered variables in the stress and fatigue analysis of the picking device.  
Figure 1: The overall structure of the automatic pepper transplanter under development: (**a**) picking device, (**b**) conveying device, (**c**) dibbling device, (**d**) picking gear mechanism, (**e**) crank gear set, and (**f**) cam gear set.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Definition, Unit and Value** \\ \hline \(\sigma\) & Material allowable stress, MPa \\ \(k_{p}\) & Velocity factor, integer \\ \(w_{t}\) & Full gear load, MPa \\ \(F\) & Face width, m \\ \(m\) & Gear module, m \\ \(Y\) & Lewis factor, integer \\ \(V\) & Velocity, m/s \\ \(d\) & Gear diameter, m \\ \(N\) & Rotational speed, rad/s \\ \(l\) & Length of the line of action, m \\ \(r_{o1}\) & Gear addendum circle radius, m \\ \(r_{b1}\) & Gear base circle radius, m \\ \(r_{o2}\) & Pinion addendum circle radius, m \\ \(r_{l2}\) & Pinion base circle radius, m \\ \(r_{p1}\) & Gear radius of the pitch circle, m \\ \(r_{p2}\) & Pinion radius of the pitch circle, m \\ \(\theta\) & Pressure angle, rad \\ \(P_{b}\) & Base circle, m \\ \(P_{n}\) & Pitch circle, m \\ \(\varphi_{C}\) & Roll angle, rad \\ \(\varphi_{A}\) & The angle of approach, rad \\ \(\varphi_{R}\) & The angle of recess, rad \\ \(S_{A}\) & Positions of the starting points \\ \(S_{B}\) & Positions of the endpoints \\ \(F_{m}\) & Nominal tangential force at mid-face width, N \\ \(T\) & Torque, Nm \\ \(d_{m}\) & Mean pitch diameter of the gear and pinion, m \\ \(\sigma_{H}\) & Teeth contact stress, MPa \\ \(Z_{E}\) & Elastic coefficient, MPa \\ \(K_{o}\) & Overload factor, 1.5 \\ \(K_{d}\) & Dynamic factor, 1 \\ \(K_{s}\) & Size factor, 1 \\ \(K_{H}\) & Load distribution factor, 1 \\ \(Z_{I}\) & Geometry factor for pitting resistance \\ \(N_{T}\) & Total number of load cycles \\ \(D_{i}\) & Duration at \(i\)th bin, s \\ \(D_{t}\) & Total duration, s \\ \(N_{i}\) & Rotational speed at \(i\)th bin, rad/s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Variable notations, definitions, and units for picking device stress and fatigue analysis.  
Figure 2: Block diagram showing the procedure to determine suitable gear set face width and material. AGMA: American Gear Manufacturers Association; FEA: finite element analysis.