## 2 Materials and Methods
### Procedures of Vibration Evaluation
#### 2.4.2 Measurement of Vibration for Operator Comfort  
Driving surface roughness and velocity of the vehicle greatly affect the intensity of vibration. The International Roughness Index (IRI), a well-recognized standard to quantify road surface roughness, is used throughout the world to describe the roughness of driving surfaces [48]. Based on the IRI parameters and previous studies [44,49,50], the roughness of the selected surfaces or roads was also calculated in this study to classify the road conditions. Equation (2) represents the relationship between the road roughness, speeds, and WBV in the vertical direction (Z-axis). \[\frac{rms_{z}}{IRI}=0.16\,\left(\frac{v}{80}\right)^{1/2} \tag{2}\]  
According to ISO 2631-1 standards, there are two methods, daily exposure value (A(8)) and the Vibration Dose Value method (VDV), to evaluate vibration exposure using the effective value of weighted acceleration. The A(8) index is measured considering the weighted \(rms\) acceleration, where one quarter of \(rms\) of the weighted acceleration is used to calculate the VDV instead of the half power. Both methods assess the vibrational exposure to an operator's body for an 8-h work cycle, and the application of frequency weighting filters for the obtained raw data is required. Table 4 shows the Equations (3)-(8) of the A(8) and VDV indices. The ISO 2631-5 standard emphasizes the daily compressive dose value (\(S_{d}^{A}\)) and risk factor (\(R^{A}\)) to evaluate the operator exposure to vibration. \(S_{d}^{A}\) (specifically, internal spinal force) is measured through two methods: the severe-condition regime and the less-severe-condition regime. Here, the regime indicates the place where the operator remains seated under all exposures. The possible ways of acceleration transmission to the operator's body are the seat, backrest, feet, and hands. The compressive dose value depends on the body mass, posture, and mass index of the operator, and the three directional raw acceleration values were used to determine the less-severe condition. On the other hand, the risk factor is estimated (Equations (9)-(12)) considering the equivalent daily compressive dose of the lumbar spine (T12/L1, L1/L2, L2/L3, L3/L4, L4/L5, L5/S1), exposure days \begin{table}
\begin{tabular}{c c c} \hline \hline
**ISO** & \multicolumn{2}{c}{**Equations for Vibration Evaluation**} \\ \hline \multirow{4}{*}{2631-1} & Daily exposure value A(8) & Vibration Dose Value (VDV) \\ \cline{2-3}  & \(rms_{us}=\left[\frac{1}{T}\int_{0}^{T}a_{w}^{2}(t)dt\right]^{1/2}\) & (3) & \(vdv_{us}=\left[\int_{0}^{T}a_{w}^{4}(t)dt\right]^{1/4}\) \\  & \(A(8)=K_{s}\,rms_{us}\,\sqrt{\frac{T_{us}}{T_{0}}}\) & (4) & \(vdv_{us}=K_{s}\,vdv_{us}\,\sqrt{\frac{T_{us}}{T_{usus}}}\) \\  & \(A(8)=\max\left[A(8)_{x},A(8)_{y},A(8)_{z}\right]\) & (5) & \(VDV(8)=\max\left[VDV_{x},VDV_{y},VDV_{z}\right]\) \\ \hline \multirow{4}{*}{2631-5} & Daily compressive dose value & Risk factor \\ \cline{2-3}  & \(S^{A}=\left(\sum_{i}\left(\frac{C_{us}}{B}\right)^{6}\right)^{1/6}\) & (9) & \(R^{A}=\left(\sum_{m=1}^{n}\left(\frac{S_{d}^{A}N_{w}^{1/6}}{S_{d}^{A}-S_{d}^{A},z}\right)^{6}\right)^{1/6}\) \\ \cline{1-1}  & \(S_{d}^{A}=\left(\sum_{i}S_{i}^{A6}\frac{t_{ij}}{t_{ai}}\right)^{1/6}\) & (10) & \(S_{stat,i}^{A}=6.765\,\text{MPa}-0.067\,\text{MPa}\times(b+i)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ISOs for evaluating operator exposure to vibration, and their relevant equations. per year, number of years, lumbar spine strength based on age, and the mean value of the compressive-decompressive force, following the methods mentioned by [48]. It is important to mention that the risk factor is not the only indication of the probability of failure. Here, R\({}^{\text{A}}\) = 1 indicates that the dynamic load of the shock reached the same order of magnitude as the ultimate strength that the vertebra is capable of resisting. In this study, the age of the onion transplanter operator was 40 years and he worked an average of 8 h daily for the previous 10 years.