Vibration

Owing to the low stiffness of thin-walled workpieces, disturbances can readily arise during milling, severely compromising machining accuracy and surface quality. This study proposes a new viscoelastic model of a magnetorheological elastomer (MRE) and analyzes its vibration reduction performance under dynamic cutting forces. First, the governing equations of the system are derived from Newton’s second law, and the amplitude-frequency response curves are obtained using the harmonic balance method. The analytical results are then validated by Runge–Kutta numerical integration, with good agreement between the two approaches. Next, the vibration reduction performance of the MRE-based viscoelastic nonlinear energy sink (MNES) and the effects of its parameters are analyzed. Finally, the nonlinear stiffness coefficient and damping ratio are varied simultaneously at different mass ratios to identify the optimal parameter ranges for the MRE-based viscoelastic nonlinear energy sink of magnetorheological elastomer. The results show that the maximum amplitude of the main system first decreases and then increases as the nonlinear stiffness increases. With appropriate parameter selection, the MRE-based viscoelastic nonlinear energy sink of magnetorheological elastomer provides better vibration reduction performance than the traditional nonlinear energy sink. In addition, as the mass ratio increases, the minimum attainable value of the main-system amplitude initially decreases and then approaches a constant, while the optimal ranges of the nonlinear stiffness coefficient and damping ratio widen slightly. By combining a set of calculated parameters with the differential constitutive equation of the magnetorheological elastomer, the corresponding stress–strain curve is obtained. This provides guidance for the fabrication of magnetorheological elastomers with favorable vibration-damping performance. The stability of milling chatter is also analyzed. The calculated stability lobe diagram and supplementary time-domain verification results show that a milling system with the MNES can effectively suppress chatter and allow a greater depth of cut.

Non-destructive testing of already existing structures is one of the most challenging tasks of modern engineering. In this article a homogeneous beam with a certain small, arbitrarily localized damaged section is considered. A ’damaged section’ should be understood as a certain small part of a beam, which has significantly lower elastic modulus than the rest of the structure. This small part is modeled as a specific case of functionally graded material (FGM). Based on analysis of its axial vibrations, a relation between reduced elastic modulus and a velocity of the short traveling wave is obtained. Consequently, a procedure of non-destructive testing of homogeneous beams is presented, which allows us to assess not only the position and dimension of the ’damaged’ part, but also to estimate a reduction ratio of the elastic modulus. The proposed procedure is validated in the paper by the comparison of its results with the finite element method calculations. As a consequence, its applicability limits are defined, as relative errors between results can vary (0–26%), depending on the calculation case. Such a procedure can have multiple applications in modern engineering.

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.