Application of the nonsmooth dynamics approach to model and analyze the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini’s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.This work is supported by the Portuguese Foundation for the Science and Technology under the research project BIOJOINTS (PTDC/EME-PME/099764/2008). The first author expresses his gratitude to the Portuguese Foundation for the Science and Technology for the postdoctoral scholarship (SFRH/BPD/40067/2007). This research was conducted during a post-doctoral stay of the first author with Professor Christoph Glocker at the Center of Mechanics, ETH Zurich

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Analysis of collocated feedback controllers for four-bar planar mechanisms with joint clearances

International audienceThis article presents an analysis of two-dimensional four-bar mechanisms with joint clearance, when one joint is actuated by collocated open-loop or state feedback controllers (proportional-derivative, state feedback linearization, passivity-based control). The study is led with numerical simulations obtained with a projected Moreau-Jean's event-capturing algorithm. The contact/impact model uses kinematic coefficients of restitution, and Coulomb's friction. The focus is put on how much the performance deteriorates when clearances are added in the joints. It is shown that collocated feedback controllers behave in a very robust way

Physics-informed neural network for friction-involved nonsmooth dynamics problems

Friction-induced vibration (FIV) is very common in engineering areas. Analysing the dynamic behaviour of systems containing a multiple-contact point frictional interface is an important topic. However, accurately simulating nonsmooth/discontinuous dynamic behaviour due to friction is challenging. This paper presents a new physics-informed neural network approach for solving nonsmooth friction-induced vibration or friction-involved vibration problems. Compared with schemes of the conventional time-stepping methodology, in this new computational framework, the theoretical formulations of nonsmooth multibody dynamics are transformed and embedded in the training process of the neural network. Major findings include that the new framework not only can perform accurate simulation of nonsmooth dynamic behaviour, but also eliminate the need for extremely small time steps typically associated with the conventional time-stepping methodology for multibody systems, thus saving much computation work while maintaining high accuracy. Specifically, four kinds of high-accuracy PINN-based methods are proposed: (1) single PINN; (2) dual PINN; (3) advanced single PINN; (4) advanced dual PINN. Two typical dynamics problems with nonsmooth contact are tested: one is a 1-dimensional contact problem with stick-slip, and the other is a 2-dimensional contact problem considering separation-reattachment and stick-slip oscillation. Both single and dual PINN methods show their advantages in dealing with the 1-dimensional stick-slip problem, which outperforms conventional methods across friction models that are difficult to simulate by the conventional time-stepping method. For the 2-dimensional problem, the capability of the advanced single and advanced dual PINN on accuracy improvement is shown, and they provide good results even in the cases when conventional methods fail.Comment: 38 Pages, 24 figure

A constraint-stabilized time-stepping approach for piecewise smooth multibody dynamics

Rigid multibody dynamics is an important area of mathematical modeling which attempts to predict the position and velocity of a system of rigid bodies. Many methods will use smooth bodies without friction. The task is made especially more difficult in the face of noninterpenetration constraints, joint constraints, and friction forces. The difficulty that arises when noninterpenetration constraints are enforced is directly related to the fact that the usual methods of computing the distance between bodies do not give any indication of the amount of penetration when two bodies interpenetrate. Because we wish to calculate vectors that are normal to contact, and because it is necessary to determine the amount of penetration, when it exists, the classical computation of the depth of penetration when applied to convex polyhedral bodies is inefficient.We hereby describe a new method of determining when two convex polyhedra intersect and of evaluating a measure of the amount of penetration, when it exists. Our method is much more efficient than the classic computation of the penetration depth since it can be shown that its complexity grows only linearly with the size of the problem. We use our method to construct a signed distance function and implement it for use with a method for achieving geometrical constraint stabilization for a linear-complementarity-based time-stepping scheme for rigid multibody dynamics with joints, contact, and friction which, before now, was not equipped to handle polyhedral bodies. During our analysis, we describe how to compute normal vectors at contact, despite the cases when the classic derivative fails to exist.We put this analysis into a time-stepping procedure that uses a convex relaxation of a mixed linear complementarity problem with a resulting fixed point iteration that is guaranteed to converge if the friction is not too large, the time step is not too large, and the initial solution is feasible. Finally, we construct an algorithm that achieves constraint stabilization with quadratic convergence.The numerical results proved to be quite satisfactory, implying that the constraint stabilization holds, and that quadratic convergence exists

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor