# Multi-Body Model of Agricultural Tractor for Vibration Transmission Investigation
## 3 Results and Discussion
### ISO 5008 Test Track Evaluation  
The analysis of whole body vibrations (WBVs) in the agricultural sector is more complex than in the industry because it is strictly connected to the surface type and conditions, machine configuration, and the type of operation being undertaken [45]. For comparative purposes, the ISO 5008 standard [45] was established to measure driver vibrations on normalised test tracks. It defines the smooth track (100 m long) and rough track (35 m long). Based on the dimensions specified in the ISO standard, the rough track was modelled in the MBS environment. The methodology for measuring and evaluating the WBVs the driver is exposed to is specified in the standard ISO 2631-1. The acceleration sensor is positioned on the driver's seat to measure the vibrations transmitted to the seated operator's body as a whole through the supporting surface of the buttock. The standard also defines weighting factors for the vibration levels at defined frequency bands to consider the frequency sensitivity of the driver's body to WBVs. The weighted root mean square average weighted vibration A\({}_{\text{w}}\) is defined as:  
\[A_{\text{w}}=\left[\frac{1}{T}\int_{0}^{T}{a_{\text{w}}}^{2}(t)dt\right]^{1/2}, \tag{6}\]  
where \(T\) is the measurement time. It is convenient to analyse WBVs in the one-third octave spectrum in which the weighting factors are defined. The human body is most sensitive to vertical vibrations in 5-8 Hz frequencies where the weighting factors are greater than 1, which means these vibrations are amplified after weighting, and for lower and higher frequency bands, the weighting factor is less than 1, which means vibrations in these frequency bands become less significant. The weighting factors are plotted in Figure 14.  
Analysing the acceleration signals in the frequency domain can provide insights into the performance of different suspension elements. The following part systematically evaluates tractor suspension elements by comparing the one-third octave spectra before and after the suspension element (in the direction from the road excitations to the driver seat). A comparison is displayed for every location of the body-cabin mount and spectra of the cabin floor and driver seat are added to these comparisons. The acceleration levels are unweighted to assess the suspension element contributions better. The frequency spectra of the tractor body (red line in Figure 15) are very similar at all four locations, and they have a peak at the 2.5 Hz frequency band. The acceleration levels at cabin mount locations show different characteristics. A significant increase between body and cabin can be observed at all four locations. It is seen in the yellow \"body to cabin increment\" plots in Figure 15. At front cabin bushings, the vibration levels rise by more than 20 dB for 16 Hz and 20 Hz frequency bands. A considerable 5 dB or more increase is present at all frequency bands from 6.3 Hz to 125 Hz. At the rear, the increase is lower but still significant, especially for frequency bands between 6.3 Hz and 25 Hz. The blue line in Figure 15 shows vibration levels on the cabin floor between the mounting locations in the longitudinal and lateral directions. This point is also close to the seat suspension connection to the cabin. We can observe that at front bushings, the vibration levels are increased for frequencies up to 1.6 Hz; however, the levels are decreased for higher frequencies. A reverse characteristic is present for rear spring-dampers with the switch at 6.3 Hz. This suggests pitching movements of the cabin about different axes of rotation at different frequencies. Figure 14: One-third octave spectra of the ISO 2631-1 weighted driver seat acceleration (green) during the ISO 5008 rough track ride and the corresponding weighting factors (black). We see a slight increase in vibration values measured on the driver seat compared to the cabin floor for frequency bands of 1 Hz and lower. The levels are consistently lower for frequencies higher than 1.6 Hz, confirming the benefit of seat suspension.