A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems

Abstract

A new approach to model and analyze flexible spatial multibody systems with clearance cylindrical joints is presented throughout this work. The flexible parts are modeled by using the absolute nodal coordinate formulation (ANCF) based elements, while the rigid parts are described by employing the natural coordinate formulation (NCF), which can lead to a constant system mass matrix for the final derived system equations of motion. In a simple way, a cylindrical joint with clearance is composed by two main elements, that is, a journal inside a bearing. Additionally, a lubricant fluid can exist between these two mechanical elements to reduce the friction, wear and increase the system’s life. For the case in which the cylindrical joint with clearance is modeled as a dry contact pair, a technique using a continuous approach for the evaluation of the contact force is applied, where the energy dissipation in form of hysteresis damping is considered. Furthermore, the frictional forces developed in those contacts are evaluated using a modified Coulomb’s friction law. For the lubricated case, the hydrodynamic theory for dynamically loaded journal-bearings is used to compute the forces generated by lubrication actions. The lubricated model is based on the Reynolds’ equation developed for the case of journal-bearings in which the length-to-diameter ratios are up to 1. With this approach, the misalignment of the journal inside the bearing can be studied. Finally, two demonstrative examples of application are used to provide the results that support the discussion and show the validity of the proposed methodologies.