State space modeling of non-proportional passive damping in machine tools

Neugebauer, Reimund; Scheffler, Christian; Wabner, Markus; Schulten, Markus

doi:10.1007/s00170-010-2902-1

Cited by 5 publications

(3 citation statements)

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“…The viscous damping model is one of the most commonly used damping models. Several researchers have suggested that combined with the state-space method, a complex mode superposition method based on the viscous damping model can be realized, which can be applied to nonproportionally damped systems (De Domenico and Ricciardi, 2019; Foss, 1958; Igusa et al, 1984; Neugebauer et al, 2011; Papageorgiou and Gantes, 2010).…”

Section: Complex Mode Superposition Methods For a Nonproportionally Damped Systemmentioning

confidence: 99%

“…Thus, the viscous damping motion equations of these systems can be transformed to first-order differential equations by state-space modeling. The corresponding complex mode superposition method is obtained as a result of complex modal orthogonality (De Domenico and Ricciardi, 2019; Foss, 1958; Igusa et al, 1984; Neugebauer et al, 2011; Papageorgiou and Gantes, 2010). However, the construction of a reasonable damping matrix is very difficult (Clough and Penzien, 2003).…”

Section: Introductionmentioning

confidence: 99%

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Complex mode superposition method of nonproportionally damped linear systems with hysteretic damping

Sun

Yang

Deng

2020

Journal of Vibration and Control

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The vibration response of a damped linear system is always calculated based on the mode superposition method. However, the construction of the damping matrix is difficult for the conventional mode superposition methods based on the viscous damping model, and this problem is much more serious for nonproportionally damped linear systems. The damping matrix based on the hysteretic damping model is easy to construct and unique, which is determined only by the structural stiffness and material loss factor. The time-domain motion equation of a multi-degree-of-freedom nonproportionally damped linear system is easily constructed based on the hysteretic damping model. According to the characteristics of external excitation, the general solution of the corresponding homogeneous equation and special solution of the corresponding nonhomogeneous equation can be solved. By the aid of the easiness of the damping matrix, a complex mode superposition method based on the hysteretic damping model is proposed for the nonproportionally damped linear system. Based on the proposed method, a user subroutine in ANSYS and MATLAB is developed to calculate vibration responses in time-domain dynamic analyses. A shaking table test of a cantilever plate composed of host and damping layers is conducted to validate the proposed method. The method proposed in this article is unconditionally convergent, and its convergence is independent of the time step of time-domain analyses. Compared with the common complex mode superposition method based on the viscous damping model, the simulation results of the proposed method are closer to the test results, and its accuracy and efficiency are higher. In addition, the calculation results of the proposed method are unique, which is irrelevant to the choice of vibration modes.

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Section: Complex Mode Superposition Methods For a Nonproportionally Damped Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex mode superposition method of nonproportionally damped linear systems with hysteretic damping

Sun

Yang

Deng

2020

Journal of Vibration and Control

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“…These variables are not only the material properties, but also the technical decisions, the design constraints, and the technological limits that might be accurately analysed using the real prototypes. [16,[25][26][27][28][29][30][31][32] Starting from the kinematic analysis of a milling machine that highlighted the main critical factors to damp vibrations, the static and dynamic properties have been analysed by using both finite element (FE) simulations and experimental tests. In particular, FE simulations allowed to improve the structure design, increasing structural indices and avoiding technical issues in prototype fabrication.…”

Section: Introductionmentioning

confidence: 99%

Vibration Damping Analysis of Lightweight Structures in Machine Tools

Aggogeri

Borboni

Merlo

et al. 2016

Preprint

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Abstract:The dynamic behaviour of a machine tool (MT) directly influences the machining performance. The adoption of lightweight structures may reduce the effects of undesired vibrations and increase the workpiece quality. This paper aims to present and compare a set of hybrid materials that may be excellent candidates to fabricate the MT moving parts. The selected materials have high dynamic characteristics and capacity to dampen mechanical vibrations. In this way, starting from the kinematic model of a milling machine, this study evaluates a number of prototypes made of Al foam sandwiches (AFS), Al corrugated sandwiches (ACS) and composite materials reinforced by carbon fibres (CFRP). These prototypes represented the Z-axis ram of a commercial milling machine. The static and dynamical properties have been analysed by using both finite element (FE) simulations and experimental tests. The obtained results show that the proposed structures may be a valid alternative to the conventional materials of MT moving parts, increasing machining performance. In particular, the AFS prototype highlighted a damping ratio that is 20 times greater than a conventional ram (e.g., steel). Its application is particularly suitable to minimize unwanted oscillations during high-speed finishing operations. The results also show that the CFRP structure guarantees high stiffness with a weight reduced by 48.5%, suggesting effective applications in roughing operations, saving MT energy consumption. The ACS structure has a good trade-off between stiffness and damping and may represent a further alternative, if correctly evaluated.

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