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

Abstract

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.

Robust Assignment of Natural Frequencies and Antiresonances in Vibrating Systems through Dynamic Structural Modification

“…e proposed method relies on the idea of homotopy optimization that has been adopted by the authors and their co-workers, in solving PEA problems similar to equation (7) [28,52], antiresonance assignment [22,52], as well as to the response optimization of underactuated multibody systems [37]. In this paper, the technique is extended to solve equation ( 15), i.e., the PEA problem embedding a robustness condition.…”

“…In the third test case, it is required to keep the same natural frequency of the original system, while increasing its robustness with respect to some parameters. is problem could be of interest in resonators (such as feeders [37] or sonotrodes [38]) that are excited by an external tuned harmonic force matching one resonance frequency. Since the system parameters might slightly change during operation, a robust design of these devices is of great importance to ensure that the resonance frequency is robust to parameter variations that could mistune the system and hence downgrade the system performances.…”

“…is goal is of practical interest in structures and machines in the presence of either wanted or unwanted vibrations. For example, ensuring insensitive natural (or resonance) frequencies is of great importance in the design of resonators (such as feeders [26,37] or sonotrodes [20,38]), where the resonance frequency should match the excitation frequency regardless of the changes in some parameters, to ensure large motion with small actuation effort. In the case of vibration absorption of harmonic excited systems, assigning antiresonances at the excitation frequency is an effective approach ( [39][40][41]), that should be ensured even in the case of changes of some system parameters.…”

Integrated Inverse Dynamics and Optimized Mechanical Design in Underactuated Linear Vibratory Feeders Under Periodic Excitation

“…Traditionally, structural modification has been widely adopted over the decades to assign natural frequencies [18][19][20], mode shapes [21,22] and antiresonance frequencies [23][24][25]. Recently, DSM has been adopted also to increase the robustness against the system uncertainties in motion planning [26] and to improve the subspace of the allowable motion in linear vibratory feeders excited through harmonic excitation [27]. In addition, a mechanical design approach to convert non-minimum phase systems into minimum phase has been proposed in [4].…”

Desensitized motion planning for underactuated multibody systems

“…Since m < n, the system is underactuated. The dynamic model in (1) can be rewritten by partitioning q into the vector of m actuated generalized coordinates, and the vector q u of the n − m unuactuated ones [21]:…”