Designing vibratory linear feeders through an inverse dynamic structural modification approach

Abstract

The design of vibratory feeders ensuring effective product feeding is particularly demanding since the flexibility of the device components severely affects the dynamic response. Traditional design approaches are based on expensive and time-consuming trial and error iterations, which include building and testing tentative devices. In order to overcome these limitations, this paper proposes a novel systematic approach for designing linear vibratory feeders, based on an inverse dynamic structural modification approach. After synthesising a reduced-order model, the design is cast as an inverse eigenvalue problem and solved numerically through the minimization of a convex quadratic function. Constraints on the design variables, i.e. inertial and elastic parameters, are represented through a convex domain and included in the optimization problem. The numerical and experimental results obtained prove the effectiveness of the method and its ease of application, that make is suitable for both the design of new feeders and the optimization of existing one

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

“…Vibration generators are widely employed in manufacturing plants to exert vibrations with prescribed frequency, amplitude, and spatial shape, as required by the process. Meaningful examples are vibratory feeders, often adopted to convey small parts in manufacturing plants, packaging lines, or flexible assembly cells [1][2][3][4] by exploiting the forced vibrations of a surface (named tray or trough) where the conveyed objects are placed. The vibration frequency should be consistent with the features of the conveyed objects [5,6].…”

“…For example, a uniform flow of the product can be obtained by ensuring uniform vibrations of the trough. Actually, bending of the trough at the frequency of excitation might cause large elastic deformation that severely compromise the part flow, if the design and the control of the feeder do not account for this issue [1]. Other examples are ultrasonic sonotrodes (horns) adopted for welding, atomizing, deagglomerating, machining, cleaning, or cutting [7][8][9][10].…”

“…All the approaches proposed in this paper, both involving just FS and FS with DSM, are original. The effectiveness and the comparison of the results they provide is proposed through a meaningful test case taken from the literature, that is, the optimization of the response of an industrial vibratory feeder employed in manufacturing plant proposed in [1].…”

“…Uniform flow along the tray is obtained by imposing uniform vibration of the tray, despite its flexibility. Vibratory feeders are usually driven by electromagnetic actuators [1,30,31], linear actuators [32,33], and rotating motor with eccentric masses [34], although some new promising techniques are being investigated in the literature, such as actuators based on dielectric elastomers [35]. Regardless of the technology adopted for actuation, it is here assumed that the force amplitude of each actuator can be set to the desired one.…”

“…The linear vibratory feeder assumed for validation is sketched in Fig. 1, and its parameters are taken from [1] and summarized in Table 1. Small vibratory feeders are often modeled in the literature as single-DOF [35,36] or twomass [7] systems.…”