Conceptual Design and Numerical Dynamic Analysis of a Bowl-Type Vibratory Finishing Machine

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Abstract
This study presents the conceptual design and numerical dynamic analysis of a bowl-type vibratory finishing machine through CAD development and simulation. The methodology integrates a literature review of process and design variables, definition of operating requirements, selection of the abrasive system, mechanical sizing of critical components, and formulation of a numerical model for modal and transient dynamic analysis. The proposed machine was configured as a bowl-type system with eccentric-mass excitation, spring suspension, and a compact support structure. The specific contribution of this work lies in integrating, within a single design-oriented framework, the definition of the main machine variables, the mechanical sizing of critical components, and the modal and transient dynamic analysis of a proposed architecture prior to prototyping. The modal assessment retained ten modes, with the closest relevant frequencies remaining separated from the nominal 25 Hz excitation within the adopted screening framework. For the refined transient case, synchronized X(t) and Y(t) histories permit direct reconstruction of the bowl-edge X–Y trajectory. Over the selected late-time interval of 0.6–1.0 s, the directional half-range displacements were 1.119 mm in X and 1.095 mm in Y, while least-squares harmonic amplitudes at 25 Hz were 1.047 and 1.046 mm, respectively. These values provide directional structural-response metrics for numerical screening and a reference for subsequent experimental radial-amplitude comparison. A targeted spring-stress sensitivity study yielded local von Mises maxima of 504.84, 2111.2, and 2978.2 MPa across progressively refined global and local adaptive configurations; the large changes in magnitude and hotspot location indicate pronounced sensitivity of the spring-end peak to local adaptive refinement. Accordingly, this quantity is treated as a model-dependent local hotspot. The abrasive-loaded configuration is used as a first-order structural-inertial representation of operating mass for machine-level screening.

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