Three dimensional dynamics of pretwisted beams: A spectral-Tchebychev solution

Filiz, Sinan; Bediz, Bekir; Romero, Louis A.; Özdoğanlar, O. Burak

doi:10.1016/j.jsv.2014.01.010

Cited by 47 publications

(17 citation statements)

References 38 publications

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“…To simulate the vibrations of the measurement point, D, simulated dynamic axial forces and torques are applied on the drill and angular displacement of the point D is estimated by summing up the angular displacements generated by torques and axial forces of central and peripheral inserts as shown in Eq. (29).…”

Section: Comparison Between Simulation and Experimental Resultsmentioning

confidence: 99%

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Time domain simulation of chatter vibrations in indexable drills

Parsian

Magnevall

Eynian

et al. 2016

Int J Adv Manuf Technol

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Regenerative chatter vibrations are common in drilling processes. These unwanted vibrations lead to considerable noise levels, damage the quality of the workpiece, and reduce tool life. The aim of this study is to simulate torsional and axial chatter vibrations as they play important roles in dynamic behavior of indexable insert drills with helical chip flutes. While asymmetric indexable drills are not the focal points in most of previous researches, this paper proposes a simulation routine which is adapted for indexable drills. Based on the theory of regenerative chatter vibration, a model is developed to include the asymmetric geometries and loadings that are inherent in the design of many indexable insert drills. Most indexable insert drills have two inserts located at different radial distances, namely central and peripheral inserts. Since the positions of the central and peripheral inserts are different, the displacement and thereby the change in chip thickness differs between the inserts. Additionally, the inserts have different geometries and cutting conditions, e.g., rake angle, coating, and cutting speed, which result in different cutting forces. This paper presents a time-domain simulation of torsional and axial vibrations by considering the differences in dynamics, cutting conditions, and cutting resistance for the central and peripheral inserts on the drill. The time-domain approach is chosen to be able to include nonlinearities in the model arising from the inserts jumping out of cut, multiple delays, backward motions of edges, and variable time delays in the system. The model is used to simulate cutting forces produced by each insert and responses of the system, in the form of displacements, to these forces. It is shown that displacements induced by dynamic torques are larger than those induced by dynamic axial forces. Finally, the vibration of a measurement point is simulated which is favorably comparable to the measurement results.

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Section: Comparison Between Simulation and Experimental Resultsmentioning

confidence: 99%

“…The axial and angular deflections are coupled in drills with helical flutes [17,29], and these types of drills have a torsional-axial mode which includes axial and angular deflections simultaneously. Figure 1 shows the simultaneous angular and axial deflection of the drill when it is twisted or compressed.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Time domain simulation of chatter vibrations in indexable drills

Parsian

Magnevall

Eynian

et al. 2016

Int J Adv Manuf Technol

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“…Carnegie and Thomas extended these works to investigate the coupled bending vibration of pre-twisted beam [11]. More recently, Filiz et al [12] developed a 3-D model to investigate the dynamics of pre-twisted beam using the spectralTchebychev solution. Even though much work has been done on vibration and dynamic behavior of pre-twisted strips, not much work has been done on wave propagation in these structures, in particular.…”

Section: Introductionmentioning

confidence: 99%

Wave Propagation in Thin Pretwisted Anisotropic Strips

Thirupathi¹,

Guruprasad²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…For instance, structures that have non-coincident neutral and strain axes (e.g., pretwisted geometry with a curved cross section) exhibit coupled 3D motions, even in the absence of rotational motions [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…(2) plate/shell based modeling approaches, which are commonly used for modeling the dynamics of rotating blades [6,11]. The one-dimensional methods, such as Euler-Bernoulli [9,12,13] and Timoshenko beam theories [14][15][16] or the dynamic stiffness matrix technique [17], yield accurate results for simple geometries and low rotational speeds; however, as the geometry becomes complex (or even for rotating stubby beams) and/or as the rotational speed increases, large deviations in natural frequencies and mode shapes are observed between the experimental and theoretical calculations [10,18]. Moreover, the beam-based approaches do not enable investigation of the cross-sectional deformations (i.e., warping effects).…”

Section: Introductionmentioning

confidence: 99%

Three dimensional dynamics of rotating structures under mixed boundary conditions

Bediz

Romero

Özdoğanlar

2015

Journal of Sound and Vibration

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This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method.

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Three dimensional dynamics of pretwisted beams: A spectral-Tchebychev solution

Cited by 47 publications

References 38 publications

Time domain simulation of chatter vibrations in indexable drills

Time domain simulation of chatter vibrations in indexable drills

Wave Propagation in Thin Pretwisted Anisotropic Strips

Three dimensional dynamics of rotating structures under mixed boundary conditions

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