The vibrations produced by an agricultural machine are transmitted to the seat of the tractor operator and must comply with the limitations imposed by international and national regulations. An agricultural machine is generally composed of a tractor that can be linked to different machines required to perform a large number of agricultural tasks. In this paper, substructuring techniques are proposed to investigate the dynamics of the agricultural machine and to evaluate the resulting vibration exposure to the tractor driver in different configurations of the machine. These techniques allow one to couple reduced-order models or experimental models of the component subsystems to obtain the response of the whole system. In the results, the vibration exposure of the tractor operator is evaluated for different configurations of the agricultural machine, by observing the frequency response function (inertance and transmissibility) and the transient response to a given excitation. In conclusion, these techniques allow one to investigate a large number of different configurations and a wide range of operating conditions with a light computational burden and without asking the manufacturers to share sensitive design details.

Mechanical systems present several contact surfaces between deformable bodies. The contact interface can be either static (joints) or in sliding (active interfaces). The sliding interfaces can have several roles and according to their application they can be developed either for maximizing the friction coefficient and the energy dissipation (e.g. brakes) or rather to allow the relative displacement at joints with a maximum efficiency. In both cases the coupling between system and local contact dynamics can bring to system dynamics instabilities (e.g. brake squeal or squeaking of hip prostheses). This results in unstable vibrations of the system, induced by the oscillation of the contact forces. \ud \ud In the literature, a large number of works deal with such kind of instabilities and are mainly focused on applied problems such as brake squeal noise. This paper shows a more general numerical analysis of a simple system constituted by two bodies in sliding contact: a rigid cylinder rotating inside a deformable one. The parametrical Complex Eigenvalue Analysis and the transient numerical simulations show how the friction forces can give rise to in-plane dynamic instabilities due to the interaction between two system modes, even for such a simple system characterized by one deformable body. Results from transient simulations highlight the key role of realistic values of the material damping to have convergence of the model and, consequently, reliable physical results. To this aim an experimental estimation of the material damping has been carried out. Moreover, the simplicity of the system allows for a deeper analysis of the contact instability and a balance of the energy flux among friction, system vibrations and damping. The numerical results have been validated by comparison with experimental ones, obtained by a specific test bench developed to reproduce and analyze the contact friction instabilities. (C) 2015 Elsevier Ltd. All rights reserved

In complex vibrating systems, contact and friction forces can produce a dynamic response of the system (friction-induced vibrations). They can arise when different parts of the system move one with respect to the other generating friction force at the contact interface. Component mode synthesis and more in general substructuring techniques represent a useful and widespread tool to investigate the dynamic behavior of complex systems, but classical techniques require that the component subsystems and the coupling conditions (compatibility of displacements and equilibrium of forces) are time invariant. In this paper, a substructuring method is proposed that, besides accounting for the macroscopic sliding between substructures, is able to consider also the local vibrations of the contact points and the geometric nonlinearity due to the elastic deformation, by updating the coupling conditions accordingly. This allows to obtain a more reliable model of the contact interaction and to analyze friction-induced vibrations. Therefore, the models of the component substructures are time invariant, while the coupling conditions become time dependent and a priori unknown. The method is applied to the study of a finite element model of two bodies in frictional contact, and the analysis is aimed to the validation of the proposed method for the study of dynamic instabilities due to mode coupling.