# Multi-Body Model of Agricultural Tractor for Vibration Transmission Investigation
## 4 Conclusions  
The multi-body model of the agricultural tractor presented in this article is composed of rigid bodies connected with idealised joints. As demonstrated, validating this idealised model with experimental data and achieving a minimal discrepancy between the model and the measurements is possible. However, using measured non-linear characteristics for stiffness and damping characteristics and a complex tyre model with real test stand data was necessary. Several steps were taken to find a correlation between the simulation and the experiment for validation. At first glance, at the location of the right bushing, the acceleration curves differ the most because of the movement of fuel, which significantly decreases the acceleration amplitude. However, the maximum peak values are very similar; the correlation for these values reaches circa 80 % at all locations. Also, the correlation coefficient for acceleration curves in the time domain when the front and rear axles pass the bump is very high (see Table 5). This leads to the conclusion that the model is suitable for driving comfort investigations. A combination of modal analysis and ride simulation result analysis in the one-third octave spectra was used to analyse vibration transmission. The resonance of tyres is always associated with the mode shape of the tractor body; their stiffness and damping properties affect the tractor body's natural frequencies. Lower stiffness of tyres leads to lower natural  
Figure 18: One-third octave spectra of the acceleration signal during the ISO track ride (no frequency weighting) on the tractor cabin at the location of the left spring-damper for three different spring-damper damping values. frequencies of the tractor body (see Figure 16). Spring-dampers' natural frequencies are present in the lower frequency bands. They are sufficient in reducing vibrations in the 3.15, 4, and 5 Hz frequency bands (see Figure 15: left spring-damper and right spring-damper: body to cabin mount increment). In higher frequencies, the effect of front bushings, which amplify vibrations transferred from body to cabin, is present (see Figure 15: left bushing and right bushing: body to cabin mount increment). This amplification is present in the 6.3 Hz frequency band and higher frequency bands. This leads to the conclusion that front bushings are inappropriate suspension elements for reducing vibrations transferred to the driver. They cause an increment in the vibration level even at the locations of spring-dampers. Because of this, the change in stiffness and damping properties of the spring-dampers does not affect comfort as much as expected. The driver seat suspension design is sufficient to reduce vibrations in the 2.5 Hz frequency band and higher frequency band (see Figure 15: cabin floor to driver seat increment). Still, the effect of front bushings is so strong that at specific frequency bands (6.3-20 Hz), the vibration level of the driver seat is still higher than on the tractor body. This paper contributes to the understanding of suspension performance in agricultural vehicles, and its novelty lies in a unified approach to vibration transmission evaluation, which is crucial for improving driving comfort. Our solution of vibration transmission is very complex; it analyses vibrations from the road excitation to the driver, which includes vibrations of the tractor body at the suspension unit location, tractor cabin vibrations at the suspension unit location, vibrations at the cabin centre of mass, and finally, vibrations at the driver seat. This initial study aims to model vibrations generated while driving and transferred from the road to the driver. Thus, the high-frequency vibrations from the engine and driveline are not considered. The model is prepared for its extension in the future. The actuation is realised using simple motion applied to shafts connected to tractor wheels. The fuel movement in the tank, which, as it was seen, affects vibrations in reality, is not modelled in any way.