Dynamic Analysis of Planar Multibody Systems Considering Contact Characteristics of Ball Bearing Joint

A comparative study of dynamic analysis for planar multibody systems with ball bearing joints is conducted in this study. The transmission mechanism is used as the exemplar case for illustrating the effect of ball bearing joints on the dynamic behavior of multibody systems. To reflect the energy loss, the models of continuous contact force and modified Coulomb’s friction are considered in the kinematic equations for the multibody system with ball bearing joint. With this, the dynamic characteristics of the mechanism are studied. Meanwhile, an experimental platform is built to generate the test data for demonstrating the effectiveness and correctness of the proposed method. Moreover, the effects of driving speed and clearance size on the dynamic behavior of the multibody system are investigated. The numerical results indicate that the dynamic behavior of the mechanical system is sensitive to the variation of the design parameters and the selection of parameters can affect greatly the accuracy of the mechanism with clearance joints.

Deformation, Fracture, and Friction Processes

The main mechanical and physical quantities and concepts ruling deformation, fracture, and friction processes are recalled, with particular attention paid to the simplicity of the analysis, but without betraying the scientific validity of the arguments. We particularly discuss the difference between between elastic and plastic deformation, and quasistatic and dynamic loadings, essential in avalanche triggering mechanisms. The physical origin of Griffith’s rupture criterion that rules both fracture nucleation and propagation, and the transition between brittle and ductile failure processes, is thoroughly discussed. We also explain the physical meaning of the classical Coulomb’s friction law, showing why it can hardly apply to a non-conventional porous, brittle, and healable solid like snow.

A Study on the Mechanism of Impact between Curved Bridge Segments Using Nonsmooth Dynamics

It has been observed in many previous earthquakes that impact often occurs between the main girders in curved bridges. An earthquake can result in deck-unseating leading to catastrophic destruction of the structure. In this paper, the nonsmooth multirigid body dynamics method and the set-valued formulation were used to model and analyze the mechanism of impact between the curved bridge segments. The analysis demonstrated that these impacts are the major cause of segment rotation. The main contribution of this paper is to use Newton’s impact law and Coulomb’s friction law to describe the interaction between the curved bridge segments in the form of a set-valued function and to express impacts with friction as a linear complementary problem. For frictionless and frictional contact, the paper considers the single-point and multipoint impacts using the linear complementary formula to detect the unique actual slip-stick conditions of these states. A variety of criteria for distinguishing each case are presented and the results provide the kinetic characteristics of each contact case. The analysis has shown that the impact between the segments of a curved bridge and the tendency of the segments to rotate (and thus detach) are related to the overall geometry, the coefficient of restitution, the coefficient of friction, and the preimpact conditions in the plane of motion. Finally, a theoretical relationship diagram of the impact, rotation slip, and stick condition of the curved bridge segments at the contact point is given. The presented results will be useful for the seismic design of curved bridges.

Structurally informed design of interlocking block assemblages using limit analysis

This paper presents a computational framework to design assemblages of interlocking blocks and to analyze their structural feasibility. The core of this framework is an extension of limit analysis to corrugated interfaces with orthotropic sliding behavior. Such block interfaces are made of a number of locks (i.e. projections on the corrugated faces, locking the blocks together) with rectangular cross section. The sliding resistance at the block interfaces is governed by the shear resistance of the locks and Coulomb’s friction law, normal to and along the locks, respectively. This resistance is assumed as a function of different interface geometric parameters and the stress state on an interface is represented by using a number of contact points distributed over the lock centerlines. The abstraction model has been validated through the comparison of the torsion–shear behavior of an interface obtained by the proposed model and experimental tests reported in the literature. The extended limit analysis has been implemented to model single-layer shells. When the model is infeasible, the geometry of the overall shell, blocks, and interlocking interfaces can be adjusted by the designer to make the model structurally feasible. The performance of the framework is presented through several examples, which demonstrate the relationships between the geometry of the interlocking interfaces and the stability of the assemblages.

Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η ( γ ˙ ) , is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1 / γ ˙ .

Dynamic Responses of Planar Multilink Mechanism considering Mixed Clearances

Translational and revolute joints are the main kinds of joints in planar multilink mechanisms. Translational and revolute clearance joints have great influence on dynamical responses of planar mechanisms. Most research studies mainly focused upon revolute clearance of planar mechanisms based upon the modified Coulomb friction model, some studies investigated clearance of the pin-slot joint, and few studies researched mixed clearances (considering both translational clearance and revolute clearance) based on the LuGre friction model. Dynamic response of the 2-DOF nine-bar mechanism considering mixed clearances based on the LuGre model is investigated in this work. The dynamic model with mixed clearances is built by the Lagrange multipliers. Dynamic responses including motion output of the slider, driving torques, contact forces, shaft center trajectories at revolute clearance pairs, and slider trajectory inside the guide are analyzed, respectively. Influences of different friction models on dynamic responses are studied, such as LuGre and modified Coulomb’s friction models. Effects of different clearance values and different driving speeds on dynamic responses with mixed clearances are both analyzed. Virtual prototype model considering mixed clearances is carried out through ADAMS to verify correctness.