An improved implicit method for mechanical systems with set-valued friction

Zhang²,

Zanoni

et al. 2022

Multibody Syst Dyn

Self Cite

An explicit cosimulation scheme is developed to study the coupling of smooth and nonsmooth systems using kinematic constraints. Using the force-displacement decomposition, the coupling constraints are formulated at the velocity level, to preserve consistency with the impulse-momentum equations for frictional contacts in the nonsmooth solver, which however potentially leads to instability of the explicit cosimulation. To improve the stability of the cosimulation without affecting the format of the coupling constraints, guidelines for the modification of the prescribed motion are developed following the spirit of Baumgarte’s stabilization technique and the characteristics of the proposed integration scheme, which prescribes a combination of position, velocity, and acceleration to the constrained bodies. Using modified inputs, the stability of the cosimulation is tested using a rigidly connected two-mass oscillator model, which shows clear improvement compared to that with unaltered inputs. The performances of the cosimulation with modified inputs are further illustrated using a double-pendulum system and a complex flexible multibody system coupled with a particle damper. It follows that cosimulation results well agree with those obtained using monolithic simulation or simplified models, verifying the explicit smooth/nonsmooth cosimulation. The results also show a higher efficiency of the explicit cosimulation scheme, which requires much less computational time to obtain similar results, compared to the implicit smooth/nonsmooth cosimulation.

Section: Formulation Of Nonsmooth Subsystemmentioning

confidence: 99%

Explicit smooth/nonsmooth cosimulation using kinematic constraints

Zhang²,

Zanoni

et al. 2022

Multibody Syst Dyn

Self Cite

“…boldWN1 and boldWN2 are the first-order partial derivative of the coordinate of the bilateral constraints of the first and the last nodes, with the left and right bushing constraints. boldWT is the matrix of tangential force direction 14 where ΦT denotes tangential displacement vector of the left and right bushing constraints…”

Section: Dynamic Equation Of Balance Ropementioning

confidence: 99%

“…Zhang et al. 14 provided a mechanical systems with friction which dynamic equations are established using the augmented Lagrangian formulation and based on Coulomb’s friction law, and set-valued friction forces are described by projection functions.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of balance rope under multiple constraints with friction

Proceedings of the Institution of Mechanical Engineers, Part C:

Cao

Yang

2021

Dynamic model of balance rope under multiple constraints with friction is established via using non-equal-length element division method (NEL-EDM) based on absolute nodal coordinate formulation. Then, the natural frequency of balance rope under multiple constraints is derived by the proposed method. The KDP generalized-alpha scheme is expanded to differential algebraic equations (DAEs) with friction constraint equations and used to solve the DAEs proposed by this paper. Compared with the frequencies, lateral vibration displacements at four observation points, the analysis of the NEL-EDM is carried out by MATLAB, ANSYS, and RECURDYN software, and the feasibility of NEL-EDM is verified. The frequencies of balance rope with installed bushing constraints will occur frequency veering phenomenon when the balance rope moves up and down with the conveyance. Last, free responses of the balance rope under multiple constraints due to the effects of conveyance vertical motion, and those of in-plane excitation on forced responses of balance rope under multiple constraints with friction are investigated.

“…The generalized‐

α

method is known as second‐order accurate for smooth systems, but previous studies 34,35 show that discontinuities in velocity or acceleration caused by impacts or friction can reduce its accuracy to first‐order. For this reason, it is necessary to discover the accuracy order of this method for systems with piecewise linear characteristics.…”

Section: Numerical Examplesmentioning

confidence: 99%

A generalized approach for implicit time integration of piecewise linear/nonlinear systems

Int Journal of Mech Sys Dyn

Zanoni

et al. 2021

Self Cite

A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed. The piecewise linear characteristic has been welldiscussed in previous studies, in which the original problem has been transformed into linear complementarity problems (LCPs) and then solved via the Lemke algorithm for each time step. The proposed scheme, instead, uses the projection function to describe the discontinuity in the dynamics equations, and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration. Compared with the LCP-based scheme, the new scheme offers a more general choice by allowing other nonlinearities in the governing equations. To assess its performances, several illustrative examples are solved. The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems, but also exhibits substantial efficiency advantages over the LCP-based scheme when applied to piecewise linear systems.