The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references.

In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

An analysis of the frictional mechanics of a steadily rotating belt drive is carried out using a physically appropriate creep-rate-dependent friction law. Unlike in belt-drive mechanics analyzed using a Coulomb friction law, the current analysis predicts no adhesion zones in the belt-pulley contact region. Regardless of this finding, for the limiting case of a creep-rate law approaching a Coulomb law, all predicted response quantities (including the extent of belt creep on each pulley) approach those predicted by the Coulomb law analysis. Depending on a slope parameter governing the creep-rate profile, one or two sliding zones exist on each pulley, which together span the belt-pulley contact region. Closed-form expressions are obtained for the tension distribution, the sliding-zone arc magnitudes, and the frictional and normal forces per unit length exerted on the belt. A sample two-pulley belt drive is analyzed further to determine its pulley angular velocity ratio and belt-span tensions. Results from this analysis are compared to a dynamic finite element solution of the same belt drive. Excellent agreement in predicted results is found. Due to the presence of arbitrarily large system rotations and a numerically friendly friction law, the analytical solution presented herein is recommended as a convenient comparison test case for validating friction-enabled dynamic finite element schemes.

In this study, an explicit time integration finite element model is used to study the effect of belt bending on the dynamic and steady-state responses of belt-drives. Three-node beam elements based on the torsional-spring formulation are used to model the belt. The pulleys are modeled as rigid circular bodies. The driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with the frictional contact governed by a Coulomb-like tri-linear friction law. Several response quantities are generated including the normal contact force and tangential friction force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt-spans mid-span tensions and transverse vibrations.

Multibody dynamics and the discrete element method (DEM) are integrated into one solver for predicting the dynamic response of ground vehicles which run on wheels and/or tracks on cohesive soft soils (such as mud and snow). Multibody dynamics techniques are used to model the various vehicle components and connect those components using various types of joints and contact surfaces. A penalty technique is used to impose joint and normal contact constraints. An asperity-based friction model is used to model joint and contact friction. A soft cohesive soil material model (that includes normal and tangential inter-particle force models) is presented that can account for soil compressibility, plasticity, fracture, friction, viscosity, cohesive strength and flow. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between the particles and polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. Numerical simulations of a typical vehicle going over a slopped soft soil terrain are presented to demonstrate the integrated solver. The solver can be used in vehicle design optimization.