An overview of the ANCF approach, justifications for its use, implementation issues, and future research directions

Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.

/pdf/a-review-of-flexible-multibody-dynamics-for-gradient-based-1rwuzuu2yo.pdf

A review of flexible multibody dynamics for gradient-based design optimization

Resonant vibration generators, such as vibratory feeders or ultrasonic sonotrodes, are often employed in manufacturing to generate harmonic vibrations with suitable amplitude, spatial shape, and frequency, in order to meet the process requirements. These underactuated systems are usually excited in open loop by few actuators, and therefore, it is not ensured that the desired response is correctly achieved, since the feasible motions should belong to the subset of the allowable motions. To achieve the closest approximation of the desired vibrations, some new solutions are here proposed. The first strategy is the optimal shaping of the harmonic forces exerted by the actuators, by solving an inverse dynamic problem through a coordinate transformation and the projection of the desired response onto the subspace of the allowable motion. By exploiting the formulation of such a subspace, a second approach that involves concurrently both the force shaping and the modification of the inertial and elastic system parameters is proposed. The idea of this approach is to exploit the modification of the elastic and inertial parameters to properly shape the allowable subspace in such a way that it spans the desired response. A solution method is developed, and analytical sensitivity analysis is proposed to choose the design variables. Validation is proposed through a linear vibratory feeder with a long flexible tray, taken from the literature. The results show the effectiveness of the proposed strategies that lead to a very precise approximation of the desired response.

/pdf/response-optimization-of-underactuated-vibration-generators-1qvrcywcuo.pdf

Response optimization of underactuated vibration generators through dynamic structural modification and shaping of the excitation forces

Utilizing orthoses and exoskeleton technology in various applications and medical industries, particularly to help elderly and ordinary people in their daily activities is a new growing field for research institutes. In this paper, after introducing an assistive lower limb exoskeleton (RoboWalk), the dynamics models of both multi-body kinematic tree structure human and robot is derived separately, using Newton's method. The obtained models are then verified by comparing the results with those of the Recursive Newton-Euler Algorithms (RNEA). These models are then augmented to investigate the RoboWalk joint torques, and those of the human body, and also the floor reaction force of the complete system. Since RoboWalk is an under-actuated robot, despite the assistive force, an undesirable disturbing force exerts to the human. So, optimization strategies are proposed to find an optimal design to maximize the assistive behavior of RoboWalk and reduce joint torques of the human body as a result. To this end, a human-in-the-loop optimization algorithm will be used. The solution of this optimization problem is carried out by Particle Swarm Optimization (PSO) method. The designed analysis and the optimization results demonstrate the effectiveness of the proposed approaches, leading to the elimination of disturbing forces, lower torque demand for RoboWalk motors and lower weights.

RoboWalk: Explicit Augmented Human-Robot Dynamics Modeling for Design Optimization

Reducing the weight of a system leads to lower forces being exerted, which in turn allows for lower requirements and an even lighter system. This “virtuous circle of lightweight engineering design” can especially be present when designing dynamic systems. Design optimization is a tool to enable and exploit this favorable phenomenon. This work introduces a unified approach to reap the benefits of optimally designed lightweight systems in structural dynamics and multibody dynamics. An efficient gradient-based optimization framework has been implemented and this is explained and demonstrated. The centerpiece of this optimization methodology is the design sensitivity analysis applied to the time integration with a nonlinear solver. A semi-analytical approach is chosen to balance computational effort and implementation effort, where the sensitivities are derived via direct differentiation with numerical differences for the sensitivities of the system parameters. Nomenclature is introduced to simplify these equations for a more lucid description showing the intrinsic equivalence of the solving routines of structural dynamics and multibody dynamics. The method is shown on the practical example for the optimal design of a hydraulic engineering mechanism.

Lightweight Engineering Design of Nonlinear Dynamic Systems with Gradient-Based Structural Design Optimization

In this study, the optimal design of a mechanism consisting of multiple bodies including a hydraulic cylinder as actuator, is carried out Multibody dynamics enable the analysis of motion and forces and build the base for numerical design optimization of such systems To consider also the hydraulic behavior of the actuator, hydraulic equations are included into the system equations Direct sensitivity analysis is applied by a semi-analytic approach in combination with Newmark- Open image in new window time integration with the Newton–Raphson method The introduced methodology is applied to a Tyrolean weir cleaning mechanism and design optimization of the mechanism is shown The approaches are general and therefore can be applied to other multibody systems or can be further extended to other fields of multiphysics simulations

Multiphysical Design Optimization of Multibody Systems: Application to a Tyrolean Weir Cleaning Mechanism

Analytical derivatives of flexible multibody dynamics with the floating frame of reference formulation

The vibrational behavior of components in mechanical systems like drives and robots can become critical under changes in the system properties or loading in operation. Such undesired vibration can lead to detrimental conditions including excess wear, fatigue, discomfort, and acoustic emissions. Systems are designed to avoid certain frequencies to avoid such problems, but system parameters can change during operation due damage, wear, or change in loading. An example is the change in system properties or operation state that then activates resonance frequencies in our system. Therefore, this work has the goal of modifying the modal behavior of a system to avoid vibrational problems. Methods of design optimization are applied to find a new optimum design for this altered condition. Here, this is limited to the addition of mass in order to move the resonance frequency out of critical ranges. This though requires a new formulation of the optimization problem. We propose a new constraint formulation to avoid frequency ranges. To increase efficiency, a reduced analytical sensitivity analysis is introduced. This methodology is demonstrated on two test cases: a two-mass oscillator followed by a test case of higher complexity which is a gear housing considering over 15,000 design variables. The results show that the optimization solution gives the position and amount of mass added, which is a discrete solution that is practically implementable.

Optimal In-Operation Redesign of Mechanical Systems Considering Vibrations—A New Methodology Based on Frequency-Band Constraint Formulation and Efficient Sensitivity Analysis

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