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 of cylindrical joints is presented in this work. The flexible parts are modeled by using 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 derived system equations of motion. In a simple way, a cylindrical joint with clearance is composed of 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 and wear and increase the system's life. For the case in which the joint 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 the form of hysteresis damping is considered. Furthermore, the frictional forces developed in those contacts are evaluated by 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 with length-todiameter ratios up to 1. Using this approach, the misalignment of the journal inside the bearing can be studied. Finally, two demonstrative examples of application are used to provide results that support the discussion and show the validity of the proposed methodologies.

Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

“…Such an algorithm has exhibited good applicability to even more tough problems solved by Tian et al [25][26][27][28] and by Liu et al [29] to study the dynamics of a flexible multibody system with clearance joints. Readers can also gain an insight into the efficient parallel computation strategy in the work by Liu et al [29].…”

“…The arc-length method [20,21] is used to accurately trace the nonlinear equilibrium path, and the bifurcation analysis without introducing any imperfections into structures is performed via the approach of mode injection [22]. Then, for the dynamic simulations of thin shell systems, the generalized-alpha algorithm, which has been studied in many studies [23][24][25][26][27][28][29], is employed to solve the dynamic equations. In Sect.…”

Dynamic computation of flexible multibody system with uncertain material properties

“…Tian et al [11] proposed a novel methodology for modeling and analysis of flexible multibody system with clearance and lubricated revolute joints by using the ANCF. The ANCF was also incorporated with the Natural Coordinate Formulation (NCF) to build the dynamic model of the rigid-flexible multibody systems by Tian et al [12], who derived a new general and comprehensive approach for a spatial flexible multibody system with cylindrical clearance joint. Liu et al [13] used the ANCF-NCF combined method to compute the dynamic response of a large scale rigid-flexible multibody system composed of composite laminated plates.…”

A Comparative Study of Joint Clearance Effects on Dynamic Behavior of Planar Multibody Mechanical Systems

“…The numerical simulation results were compared with experimental data, which revealed that the method could effectively describe the dynamic response of the mechanical systems. And then, Tian et al (2011) proposed a new methodology to model and describe the multibody mechanical system with joint clearance. They also observed that the methodology could effectively describe the misalignment of journal inside the bearing.…”