Contact Model Between Superelements in Dynamic Multibody Systems

Moving contact components are common in mechanical systems, and they exhibit a large rigid motion with linear‐elastic deflection under contact boundary conditions. The finite element method can capture local deformation and high gradient stresses, but finely meshed contact interfaces lead to numerous degrees of freedom. Model order reduction techniques for multibodies are effective, but moving contact interfaces also introduce multiple interface degrees of freedom. In the present method, the interface degrees of freedom are retained to ensure the accuracy of the local response induced by contacts, but the computational scale is not further enlarged. The motion of moving contact components is described by the floating frame of reference formulation. A free‐interface component mode synthesis method is proposed for model order reduction. Kept free‐interface normal modes represent global flexibility and residual modes accurately compensate for the local quasi‐static responses of omitted modes induced by contacts. The contribution of residual modes is represented by interface load coordinates, which can be directly evaluated by contact forces. The contacts are calculated with the present contact algorithm. The accuracy and efficiency of the proposed method are fully demonstrated through correlation with the finite element method in gear meshing simulations.

“…After obtaining the equivalent nodal loads of contact interfaces, the ILCs can be evaluated by Equation (25).…”

Section: Contact Force Calculationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A free‐interface component mode synthesis of moving contact multibodies and its application to gear contacts

Yao

Shu

Ren

2022

“…It is worth noticing that before K -orthogonalization, the static modes G c might have very similar contribution to strain energy so that it is very difficult to distinguish between them and, thus, to decide which ones to select. The K -orthogonal set of modes obtained after transformation (22) is such that the contribution of the lower residual modes to strain energy 779 content is now optimized. Therefore, the effect of the truncation to n r < n c static modes on the quality of the solution can be better controlled.…”

Section: Computation Of the Modal Reduction Basismentioning

confidence: 99%

“…The problem of properly choosing the modal content of the superelement remains, specially the static modes injected in the representation, so as to properly describe the interaction with adjacent elements with a minimum of DOFs in the system. The problem becomes particularly acute when attempting to apply the modal reduction concept to systems such as gears where intermittent unilateral contact occurs between constantly changing pairs of nodes .…”

Section: Introductionmentioning

confidence: 99%

A ‘nodeless’ dual superelement formulation for structural and multibody dynamics application to reduction of contact problems

Géradin

Rixen²

2015

Self Cite

Summary A ‘nodeless’ superelement formulation based on dual‐component mode synthesis is proposed, in which the superelement dynamic behavior is described in terms of modal intensities playing the role of intrinsic variables. A computational scheme is proposed to build an orthogonal set of static modes so that the system matrices can have a diagonal or nearly diagonal form, providing thus high computational efficiency for application in the context of structural dynamics as well as flexible multibody dynamics. Connection to adjacent components is expressed through kinematic relationships between intrinsic variables and local displacements. The efficiency of the method is demonstrated on a simple example involving multiple unilateral contact. Copyright © 2015 John Wiley & Sons, Ltd.

“…The component mode synthesis (CMS) as, for example, presented in retains only the dynamically reacting eigenvectors and augments these with static shape vectors such as constraint or attachment modes to compensate for the omitted high‐frequency eigenvectors. The guaranteed static completeness of CMS has brought numerous researchers to use the method for solving contact problems, both in gear and bearing simulations. However, the addition of a static shape vector for each boundary degree of freedom that can possibly be loaded during the simulation results in reduced‐order models having several hundreds or even thousands degrees of freedom (DOF), particularly in the case of highly refined FE meshes.…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

A nonlinear parametric model reduction method for efficient gear contact simulations

Blockmans

Tamarozzi

Naets

et al. 2014

A novel nonlinear parametric model order reduction technique for the solution of contact problems in flexible multibody dynamics is presented. These problems are characterized by significant variations in the location and size of the contact area and typically require high-dimensional finite element models having multiple inputs and outputs to be solved. The presented technique draws from the fields of nonlinear and parametric model reduction to construct a reduced-order model whose dimensions are insensitive to the dimensions of the full-order model. The solution of interest is approximated in a lower-dimensional subspace spanned by a constant set of eigenvectors augmented with a parameter-dependent set of global contact shapes. The latter represent deformation patterns of the interacting bodies obtained from a series of static contact analyses. The set of global contact shapes is parameterized with respect to the system configuration and therefore continuously varies in time. An energy-consistent formulation is assured by explicitly taking into account the dynamic parameter variability in the derivation of the equations of motion. The performance of the novel technique is demonstrated by simulating a dynamic gear contact problem and comparing results against traditional model reduction techniques as well as commercial nonlinear finite element software. Copyright NLPMOR METHOD FOR EFFICIENT GEAR SIMULATIONS 1163 meshes. These approaches separate the bulk deformation of the interacting components from the nonlinear local displacement field at the contact surfaces, computing the former using linear FE on a coarse mesh and obtaining the latter from classical contact theory. Most notably, Vijayakar [3] combines traditional FE with the Boussinesq solution for a point-load acting on an infinite halfspace, whereas Andersson and Vedmar [2] compute the local deformation due to Hertzian contact pressure using a formula derived by Weber and Banaschek [4]. Although these approaches require significantly less degrees of freedom as compared to traditional FE-based contact simulations, the procedure of matching the analytical and FE solutions at a certain depth below the contact surface is computationally involved, resulting in relatively high costs per time increment [5]. Moreover, an energy-consistent adaptation of these approaches to the formalism of flexible multibody dynamics (FMBS) has yet to be pursued. Finally, the question as to whether an infinite half-space serves as a good approximation of the actual contact zone is highly case-specific.The use of conventional FE to represent flexible bodies in multibody simulations can be rendered practical with the aid of model order reduction (MOR) techniques. These techniques originated from the fields of control theory [6] and structural dynamics [7] and were primarily designed for reducing the sizes of, respectively, first-order and second-order linear systems. Using the floating frame of reference formulation [8], the linear elastic deformation of a flexible body is separate...