Co-Simulation of Multibody Systems With Contact Using Reduced Interface Models

Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem remain undisclosed and are generally not accessible to the rest of the simulation environment. In noniterative co-simulation schemes, commonly used in real-time applications, this may lead to the instability of the numerical integration. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of one or more subsystems that provide physically meaningful input values to the other subsystems between communication points. This work describes such an interface model that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction. The dynamics of the system is initially formulated as a mixed linear complementarity problem (MLCP), from which the effective mass and force terms of the interface model are derived. These terms account for contact detachment and stick–slip transitions, and can also include constraint regularization in case of redundancy in the system. The performance of the proposed model is shown in several challenging examples of noniterative multirate co-simulation schemes of a mechanical system with hydraulic components, which feature faster dynamics than the multibody subsystem. Using an interface model improves simulation stability and allows for larger integration step-sizes, thus resulting in a more efficient simulation.

Interface Models for Multirate Co-Simulation of Nonsmooth Multibody Systems

Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Complex engineering applications can be simulated in co-simulation setups, in which each subsystem is solved and integrated using numerical methods tailored to its physical behaviour. Co-simulation implies that the communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem are generally not accessible to the rest of the simulation environment. In non-iterative co-simulation schemes, this may lead to the instability of the integration. Increasingly demanding requirements in the simulation of machinery have led to the coupling, in real-time co-simulation setups, of multibody models of mechanical systems to computational representations of non-mechanical subsystems, such as hydraulics and electronics. Often, these feature faster dynamics than their mechanical counterparts, which leads to the use of multirate integration in non-iterative co-simulation environments. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of the multibody system, to provide meaningful input values to faster subsystems between communication points. This work describes such interface models that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction.

Thermomechanical Component Mode Synthesis for Blade Casing Interaction Prediction

Increasing the efficiency of turbomachines is a major concern as it directly translates into lower environmental impact and improved operational costs. One solution is to reduce the blade-casing operating clearance in order to mitigate aerodynamic losses at the unavoidable cost of increased structural unilateral contact and friction occurrences. In centrifugal compressors, the dynamic behaviour of the structures interacting through unilateral contact and friction is not yet fully understood. In fact, the heat generated during such events may affect the dynamics through thermal stresses. This paper presents a complete thermomechanical modelling strategy of impeller rotor and casing, and of blade-tip/casing contact events. A fully coupled thermomechanical modal synthesis technique is introduced and applied to turbomachinery-related models. The blisk is reduced via a hybrid modal synthesis technique combining the Craig-Bampton method and the characteristic constraint mode method. The casing model is reduced using an axisymmetric harmonic modal synthesis. Both strategies involve thermomechanical modes embedding thermal dilatation effects. The contact modelling algorithm is then introduced. It handles unilateral contact and friction occurrences together with heating effects. This algorithm uses the above mentioned reduced-order models as input data to avoid CPU-intensive simulations. The results show that the thermomechanical behaviour of the structures is well preserved by the reduction strategy proposed. Contact simulations on simple cases show qualitative results in accordance with expectations. Further work is needed in order to validate the strategy based on experimental results. However, this methodology opens the way to extended multiphysics simulations of contact events in turbomachinery.

Nonsmooth Modal Analysis: Investigation of a 2-DOF Spring-Mass System Subject to an Elastic Impact Law

The well-known concept of normal mode for linear systems has been extended to the framework of nonlinear dynamics over the course of the 20th century, initially by Lyapunov, and later by Rosenberg and a growing community of researchers in modal and vibration analysis. This effort has mainly targeted nonlinear smooth systems — the velocity is continuous and differentiable in time — even though systems presenting nonsmooth occurrences have been increasingly studied in the last decades to face the growing industrial need of unilateral contact and friction simulations. Yet, these systems have nearly never been explored from the standpoint of modal analysis. This contribution addresses the notion of modal analysis of nonsmooth systems. Developments are illustrated on a seemingly simple 2-dof autonomous system, subject to unilateral constraints reflected by a perfectly elastic impact law. Even though friction is ignored, its dynamics appears to be extremely rich. Periodic solutions are sought for given numbers of impacts per period and nonsmooth modes are illustrated for one and two impacts per period in the form of two-dimensional manifolds in the phase space. Also, an unexpected bridge between these modes in the frequency-energy plots is observed.

A Qualitative Numerical Analysis of Rotor-Casing Interactions in Centrifugal Compressors of Helicopter Engines

In experimental and numerical investigations of unilateral contact and friction induced rotor-casing interactions, a variety of complex phenomena is expected. Although most of the features of the structural responses can be explained within a simplifying linear framework, the nonlinear nature of contact and friction forces induce complicated responses which require an appropriate methodology to be conveniently analyzed. The presented work focuses on a thorough numerical exploration of such undesired events in an attempt to provide a dedicated systematic method of analysis. Interaction simulations are carried out on the centrifugal compressor of a modern helicopter engine, for which it is assumed that the casing is rigidly distorted along a mathematical shape exhibiting distinct nodal diameters. The proposed work focuses on linear geometric aspects, such as cyclic symmetry and spatial aliasing of engine orders on nodal diameters as well as nonlinear attributes, such as sub- and super-harmonic participations in the response, in order to properly characterize the dynamics of the interaction. The results are presented as space and time two-dimensional Fourier transforms of the numerically predicted response. Dominant responses are visible along time harmonics of the forcing frequency imposed by the assumed shape of the casing. It is observed that the participation of some nodal diameters in the response is a consequence of both the aliasing effect and superharmonic forcing terms.

Study of the Residual Strength of an RC Shear Wall with Fractal Crack Taking into Account Interlocking Interface Phenomena

In the present paper, the postcracking strength of an RC shear wall element which follows the construction practices applied in Greece during the 70s is examined by taking into account the complex geometry of the crack of the wall and the mixed friction-plastification mechanisms that develop in the vicinity of the crack. Due to the significance of the crack geometry, a multiresolution analysis based on fractal geometry is performed, taking into account the size of the aggregates of concrete. The materials (steel and concrete) are assumed to have elastic-plastic behaviour. For concrete, both cracking and crushing are taken into account in an accurate manner. On the interfaces of the crack, unilateral contact and friction conditions are assumed to hold. For every structure corresponding to each resolution of the interface, a classical Euclidean problem is solved. The obtained results lead to interesting conclusions concerning the influence of the simulation of the geometry of the fractal crack on the mechanical interlock between the two faces of the crack, a factor which seems to be very important to the postcracking strength of the lightly reinforced shear wall studied here.

Dynamics of Large Scale Finite Element Models With Multiple Unilateral Constraints

Determination of the response of mechanical structures with complex geometry requires application of the finite element method. This leads frequently to models with a relatively large number of degrees of freedom, which may also possess nonlinear properties. Things become more complicated for systems involving unilateral contact and friction. In classical structural dynamics approaches, such constraints are usually modeled by special contact elements, with characteristics selected in a delicate manner. This study presents a systematic numerical methodology, which is suitable for determining dynamic response of large scale finite element models of mechanical systems involving multiple unilateral constraints. The method is based on a proper combination of results from two classes of direct integration methodologies. The first one includes standard methods employed in determining dynamic response of structural models with smooth nonlinearities, while the second class includes specialized methodologies that simulate response of dynamical systems with unilateral constraints. The validity and effectiveness of the methodology developed is illustrated by numerical results.