SUMMARY Mechanical systems are usually subjected not only to bilateral constraints, but also to unilateral constraints. Inspired by the generalized‐ α time integration method for smooth flexible multibody dynamics, this paper presents a nonsmooth generalized‐ α method, which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions. Both the algorithm and the implementation are illustrated in detail. Numerical example tests are given in the scope of both rigid and flexible body models, taking account for both linear and nonlinear systems and comprising both unilateral and bilateral constraints. The extended nonsmooth generalized‐ α method is verified through comparison to the traditional Moreau–Jean method and the fully implicit Newmark method. Results show that the nonsmooth generalized‐ α method benefits from the accuracy and stability property of the classical generalized‐ α method with controllable numerical damping. In particular, when it comes to the analysis of flexible systems, the nonsmooth generalized‐ α method shows much better accuracy property than the other two methods. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted under (quasi-)static loadings or vibration design criteria, the proposed approach aims at considering as precisely as possible the effects of dynamic loading under service conditions. Solving this problem is quite challenging and naive implementations may lead to inaccurate and unstable results. To elaborate a robust and reliable approach, the optimization problem formulation is investigated because it turns out that it is a critical point. Different optimization algorithms are also tested. To explain the efficiency of the various solution approaches, the complex nature of the design space is analyzed. Numerical applications considering the optimization of a two-arm robot subject to a trajectory tracking constraint and the optimization of a slider-crank mechanism with a cyclic dynamic loading are presented to illustrate the different concepts.

The dynamic performance of vehicle drivetrains is significantly influenced by differentials which are subjected to complex phenomena. In this paper, detailed models of TORSEN differentials are presented using a flexible multibody simulation approach, based on the nonlinear finite element method. A central and a front TORSEN differential have been studied and the numerical results have been compared with experimental data obtained on test bench. The models are composed of several rigid and flexible bodies mainly constrainted by flexible gear pair joints and contact conditions. The three differentials of a four wheel drive vehicle have been assembled in a full drivetrain in a simplified vehicle model with modeling of driveshafts and tires. These simulations enable to observe the four working modes of the differentials with a good accuracy. INTRODUCTIONNowadays the requirements to reduce fuel consumption and environmental pollution are more and more important in automotive industry. In order to reach this goal, the current trend addresses the enhancement of reliable simulation tools in the design process. Multibody simulation techniques are often used for * Address all correspondence to this author. dynamic analysis of suspensions and engines. The link between engine and wheels of the vehicle is the drivetrain. The modeling of transmission components, such as differential, gear box or clutch would allow the global modeling of cars from the motor to the vehicle dynamics.Differentials are critical components whose behavior influences the dynamics of vehicles. They are subjected to many nonlinear and discontinuous phenomena: impact, hysteresis, contact with friction, backlash,... Some vibrations can notably be generated and transmitted in the whole car structure and decrease the comfort of the passengers. An accurate mathematical model is needed to improve the performance of these mechanical systems and decrease their weight. Nevertheless the modeling of discontinuities and nonlinear effects is not trivial and often leads to numerical problems.The literature mentions several ways to model transmission components in automotive and other application fields such as wind turbines or railway. The gear contacts can be modeled with fully elastic model of gear wheels as described in [1]. Gear pairs are sometimes represented with a purely rigid behavior (see [2]) or with modal models to study the vibrations [3]. Modeling of multi-stage planetary gears trains are available in [4] and [5]. Reference [6] presents a method to simulate impacts in gear trains following several approaches. Methods to deal with nu-1

In this paper, a new contact formulation defined between flexible bodies modeled as superelements is investigated. Unlike rigid contact models, this approach enables to study the deformation and vibration phenomena induced by hard contacts. Compared with full-scale finite element models of flexible bodies, the proposed method is computationally more efficient, especially in case of a large number of bodies and contact conditions. The compliance of each body is described using a reduced-order elastic model which is defined in a corotational frame that follows the gross motion of the body. The basis used to reduce the initial finite element model relies on the Craig-Bampton method which uses both static boundary modes and internal vibration modes. The formulation of the contact condition couples all degrees of freedom of the reduced model in a nonlinear way. The relevance of the approach is demonstrated by simulation results first on a simple example, and then on a gear pair model.

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