# Multi-Body Model of Agricultural Tractor for Vibration Transmission Investigation
## 1 Introduction  
Driving comfort is an equally important topic for agricultural tractors as it deals with commercial vehicles. The common goal of reducing vibrations transmitted to the driver remains the same. However, for a tractor, the variety of work conditions is large, and the character of road roughness is broad. The benefits of using the simulations when studying driving comfort are then amplified. In the global automotive industry, considerable effort is put into shortening the development times. Simulation models are suitable for analysing the impact of the design changes on the vehicle characteristics before producing the physical prototype [1]. Virtual prototypes are built using the multi-body method of mechanism analysis, allowing the performance of static, kinematic, and dynamic simulations [2]. In the automotive industry, multi-body simulations based on various complexity models are used in the development of suspension systems and anti-lock braking systems or for the evaluation of ride and handling characteristics of vehicles [3]. Just as importantly, multi-body models are used in the prediction of the vehicle powertrain's (or its subassembly) dynamic behaviour in order to detect critical components with the aim of decreasing the vibroacoustic response [4]. Drivers of agricultural tractors are exposed to low-frequency vibrations. The natural frequency of a person sitting in a cabin is generally 4-6 Hz [5], which interferes with the natural frequency of a tractor (1-7 Hz) [6]. The impact of the vibrations on health has beenresearched thoroughly [7], and the international standard ISO 2631 sets the endurance limits for the acceleration of the human body. Many publications describe mathematical models of tractor dynamical behaviour with different levels of complexity [5; 6; 8; 9]. In [5], a simple two DOF half-tractor model was presented. The tractor cabin's passive suspension parameters underwent optimisation concerning the target value, which is the vertical acceleration of the tractor cabin. In [6], they developed a half-tractor model to investigate driving comfort for semi-active suspension and rubber mounts. A controlling algorithm for semi-active suspension was designed. To improve ride comfort, they aimed at the vertical acceleration of the cabin, as in [5]. A semi-active cabin suspension design was investigated in [10] to observe a significant improvement in vibrational comfort compared to a passive suspension. In [8], five half-tractor models were introduced with different configurations of cabin suspension and suspensions on axles. Again, the comfort was evaluated using the vertical acceleration of the cabin. Active damping control strategies of the tractor's rear hitch were implemented in [11] to reduce the pitching motion of the tractor and improve handling stability. A self-levelling cabin suspension system was researched in [12], achieving a slight decrease in whole body vibrations (WBVs) at the driver seat. In [13], the MBS model of the tractor was created and validated using measured data by tuning the properties of the tyre model, specifically the Fiala tyre model. The correlation was surprisingly good even though the Fiala tyre model was used. This model assumes stiffness and damping characteristics to be linear, but they are not. Transmission of vibrations was analysed in [14; 15; 16]. In [14], several measurements with different drivers were performed, accelerometers were placed at the seat pan, and accelerometers were placed on the driver's head to determine seat-to-head transmissibility. The vibrations were measured in all directions. In [15], authors examined WBVs at the seat location and driver back to establish seat-to-back transmissibility in the dominant vertical direction. In [16], measurements were performed to find the transfer function between the ground profile and the motion of an unsprung agricultural tractor body. In [17], a multi-body model of an agricultural tractor, which is capable of predicting vibrations on the tractor body, cabin, and seat, was implemented.