Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process

Zhang, W.; Zhou, Rui; Zu, Jean W.

doi:10.1007/s11071-013-0752-8

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…Zhang et al [24][25][26][27][28][29][30][31][32] had done an in-depth study and obtained a number of results. Firstly, the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end are studied.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar

Ren

2020

Shock and Vibration

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A nonlinear dynamic analysis of the cutting process of a nonextensible composite cutting bar is presented. The cutting bar is simplified as a cantilever with plane bending. The nonlinearity is mainly originated from the nonextensible assumption, and the material of cutting bar is assumed to be viscoelastic composite, which is described by the Kelvin–Voigt equation. The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. The steady forced response of the cutting system under periodically varying cutting force is approximately solved by the multiscale method. Meanwhile, the effects of parameters such as the geometry of the cutting bar (including length and diameter), damping, the cutting coefficient, the cutting depth, the number of the cutting teeth, the amplitude of the cutting force, and the ply angle on nonlinear lobes and primary resonance curves during the cutting process are investigated using numerical calculations. The results demonstrate that the critical cutting depth is inversely proportional to the aspect ratio of the cutting bar and the cutting force coefficient. Meanwhile, the chatter stability in the milling process can be significantly enhanced by increasing the structural damping. The peak of the primary resonance curve is bent toward the right side. Due to the cubic nonlinearity in the cutting system, primary resonance curves show the characteristics of typical Duffing’s vibrator with hard spring, and jump and multivalue regions appear.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar

Ren

2020

Shock and Vibration

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“…Non linear vibrations of cantilevered shells were also studied by Zhang et al [75]. The shell was assumed to be in high speed milling process and was subjected to a harmonic transverse cutting force.…”

Section: Free and Forced Vibrations Of Shells Due To Radial Excitationmentioning

confidence: 99%

Non-linear vibrations of shells: A literature review from 2003 to 2013

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

214

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International audienceThe present literature review focuses on geometrically non linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non linear vibrations of shells subjected to normal and in plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non linear vibrations of shells and panels, including (i) fluid structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non linear normal modes and meshless methods are reviewed in depth

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“…Zhang et al analyzed the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. e dynamics of the cantilevered shellshaped workpiece was studied under time-delay effects, parametric excitation, and forcing excitation [17,18]. Zhou et al investigated the nonlinear dynamics of a thin-plate workpiece during milling process with cutting force nonlinearities [19].…”

Section: Introductionmentioning

confidence: 99%

Vibration Characteristics of Rolling Mill System under Constraints of the Nonlinear Spring Force and Friction Force from Hydraulic Cylinder

Liu

Pan

Jiang

et al. 2021

Shock and Vibration

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Considering the two kinds of nonlinear constraints of rolling mill hydraulic cylinder, spring force and friction force, the vibration model of rolling mill system is established. The amplitude frequency response equations are obtained by using the average method. Comparing the time history curves of vertical vibration displacement of rolling mill system under the nonlinear spring force and friction force, the amplitude frequency characteristic curves are simulated. The external excitation amplitude is viewed as the bifurcation parameter, and the system bifurcation response changing with the external excitation amplitude is analyzed. The influence of the external excitation amplitude on the system stability is studied. The results indicate that the increase of the nonlinear spring force makes the rolling mill system’s unstable area to become wider, and the influence on the rolling mill system of nonlinear friction force behaves as the damping characteristics; the vibration of rolling mill system is alternating between the periodic, period-doubling, and the chaotic motion. The research results provide a theoretical support for restraining the vibration of the rolling mill system in the actual production process.

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Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process

Cited by 7 publications

References 31 publications

Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar

Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar

Non-linear vibrations of shells: A literature review from 2003 to 2013

Vibration Characteristics of Rolling Mill System under Constraints of the Nonlinear Spring Force and Friction Force from Hydraulic Cylinder

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