scholarly journals Forced Vibration in Cutting Process considering the Nonlinear Curvature and Inertia of a Rotating Composite Cutter Bar

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yongsheng Ren ◽  
Donghui Yao
Keyword(s):  
Cutting Force ◽  
Forced Vibration ◽  
Multiple Scales ◽  
Damping Ratio ◽  
Three Dimensional ◽  
Forced Response ◽  
Cutting Process ◽  
Response Curves ◽  
Rotating Speed ◽  
Cutting System

Forced vibration of the cutting system with a three-dimensional composite cutter bar is investigated. The composite cutter bar is simplified as a rotating cantilever shaft which is subjected to a cutting force including regenerative delay effects and harmonic exciting items. The nonlinear curvature and inertia of the cutter bar are taken into account based on inextensible assumption. The effects of the moment of inertia, gyroscopic effect, and internal and external damping are also considered, but shear deformation is neglected. Equation of motion is derived based on Hamiltonʼs extended principle and discretized by the Galerkin method. The analytical solutions of the steady-state response of the cutting system are constructed by using the method of multiple scales. The response of the cutting system is studied for primary and superharmonic resonances. The effects of length-to-diameter ratio, damping ratio, cutting force coefficients, ply angle, rotating speed, and internal and external damping are investigated. The results show that nonlinear curvature and inertia imposed a significant effect on the dynamic behavior of the cutting process. The equivalent nonlinearity of the cutting system shows hard spring characteristics. Multiple solutions and jumping phenomenon of typical Duffing system are found in forced response curves.

scholarly journals Nonlinear Dynamics of Cutting Process considering Higher-Order Deformation of Composite Cutting Tool

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Donghui Yao ◽  
Yongsheng Ren ◽  
Yuhuan Zhang ◽  
Bole Ma
Keyword(s):  
Cutting Force ◽  
Nonlinear Dynamic ◽  
Cutting Tool ◽  
Primary Resonance ◽  
Higher Order ◽  
Forced Response ◽  
Cutting Process ◽  
Structural Damping ◽  
Superharmonic Resonance ◽  
Cutting System

In this paper, the nonlinear dynamic analysis of the cutting process of composite cutting tool is performed. The cutting tool is simplified to a nonplanar bending rotating shaft. The higher-order bending deformation, structural damping, and gyroscopic effect of cutting tool are considered. It is assumed that cutting tool is subjected to a regenerative two-dimensional cutting force containing the first and second harmonic components. Based on the Hamilton principle, the motion equation of nonlinear chatter of the cutting system is derived. The nonlinear ordinary differential equations in the generalized coordinates are obtained by Galerkin method. In order to analyze the nonlinear dynamic response of cutting process, the multiscale method is used to derive the analytical approximate solution of the forced response for the cutting system under periodic cutting forces. In the forced response analysis, four cases including primary resonance and superharmonic resonance, i.e., Ω ¯ = ω 1 , Ω ¯ = ω 2 , 2 Ω ¯ = ω 1 , and 2 Ω ¯ = ω 2 , are considered. The influences of ratio of length to diameter, structural damping, cutting force, and ply angle on primary resonance and superharmonic resonance are investigated. The results show that nonlinearity due to higher-order bending deformation significantly affects the dynamic behavior of the milling process and that the effective nonlinearity of the cutting system is of hard type. Multivalued resonance curves and jump phenomenon are presented. The influences of various factors, such as ratio of length to diameter, ply angle, structural damping, cutting force, and rotating speed, are thoroughly discussed.

Suppressing the nonlinear vibrations of a compressor blade via a nonlinear saturation controller

2016 ◽  
Vol 24 (8) ◽  
pp. 1488-1504 ◽  
Author(s):  
Ali Kandil ◽  
Hany A El-Gohary
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Perturbation Technique ◽  
Time History ◽  
Nonlinear Saturation ◽  
State Equations ◽  
Response Curves ◽  
Rotating Speed ◽  
Main System ◽  
Nonlinear Saturation Controller

A nonlinear saturation controller (NSC) is applied in this work to reduce the oscillations of a rotating blade dynamical system running at unsteady rotating speed. The controller is coupled quadratically to the main system by designing its natural frequency to be one half of the main system natural frequency. This is done to setup an energy bridge between them to make use of saturation phenomenon. That phenomenon is advantageous when the excitation force increases; the whole energy in the main system is channeled to the controller. The two system modes of vibrations are found to be linearly coupled powerfully, so the controller is applied only to the first mode and, consequently, the second mode tracks it. The multiple scales perturbation technique (MSPT) is adopted to derive the steady state equations that describe the modulations of amplitudes and phases of the system before and after control. Then, a stability analysis is achieved via Lyapunov’s indirect method to determine the stable and unstable solutions depending on the real parts of the Jacobian matrix eigenvalues. Time history and different response curves of the controlled system are included for showing the controller effect. Eventually, validation curves and comparison with previously published work are included.

scholarly journals Investigating Vibration Acceleration of a Segmented Piezoelectric Ciliary-Like Body Beam for a Tactile Feedback Device

2020 ◽  
Vol 10 (15) ◽  
pp. 5362
Author(s):  
Jichun Xing ◽  
Huajun Li ◽  
Ian Howard
Keyword(s):  
Theoretical Analysis ◽  
Forced Vibration ◽  
Damping Ratio ◽  
Forced Response ◽  
Tactile Feedback ◽  
State Response ◽  
Study Results ◽  
Previous Published Study ◽  
Touch Sensation ◽  
Tactile Sensations

A piezoelectric Ciliary-like body beam of a tactile feedback device can realize a touchpoint of different tactile sensations under simple control when the finger movement changes to the opposite direction. In a previous published study, the friction of touch sensation was shown to depend on the acceleration of forced vibration of the ciliary-like body beam. For investigating the system parameters’ effect on vibration accelerations, the dynamic model of forced vibration of the touch beam is established, and the steady-state response of the touch beam excited by piezoelectric sheets is deduced. The influence of instantaneous acceleration and average acceleration of the touch beam on skin was analyzed, and an experiment was conducted to prove the theoretical analysis. The study results show that larger excitation voltage, larger piezoelectric constants, smaller elasticity modulus, and smaller damping ratio would enhance the displacement and acceleration of the forced response of the touch beam. Through the experimental results, the working mode and frequency of the touch beam was obtained, and the correctness of the theoretical analysis was verified.

scholarly journals Stability Analysis of Cutting Process with Internally Damped Rotating Tapered Composite Cutter Bar

2020 ◽  
Vol 2020 ◽  
pp. 1-23
Author(s):  
Yuhuan Zhang ◽  
Yongsheng Ren ◽  
Jinfeng Zhang
Keyword(s):  
High Speed ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Cutting Process ◽  
Internal Damping ◽  
Chatter Stability ◽  
Rotating Speed ◽  
High Speed Cutting ◽  
Cutting Chatter ◽  
Cutting System

Using the cutter bar made with composite rather than metal in high rotating speed milling or boring operations is a new attempt for suppressing chatter of the cutting system. This is because composite material has much higher specific stiffness and damping as well as dynamic stiffness compared to metal. But, for a rotating composite cutter bar, larger internal damping (or rotational damping) occurs, and such damping may cause the rotor instability in the perspective of rotor dynamics. On the other hand, the effect of internal damping of a rotating composite cutter bar on the chatter stability in high speed cutting process is also an important issue worthy of concern. In this paper, a new dynamic model of the cutting system with a rotating composite cutter bar is presented. The cutter bar is modelled as a rotating, cantilever, tapered, composite Euler–Bernoulli shaft, subjected to a regenerative cutting force. Modal damping loss factors are described based on the viscoelastic constitutive relation of composite combined with an energy approach. The governing equations of the system are obtained by employing Hamilton principle. Galerkin method is used to discretize the partial differential equations of motion. The frequency-domain solution of stability proposed by Altintas and Budak [14] is extended and used to predict the chatter stability of the cutting system. The results reveal the inherent relationship between internal damping instability and cutting chatter. The effects of the geometry parameters of the cutter bar, ply angle, stacking sequences, and internal and external damping are examined.

Atomics Simulation of Cutting Velocity Dependency in AFM-Based Nanomachining Process

2011 ◽  
Vol 80-81 ◽  
pp. 448-451 ◽  
Author(s):  
Jia Xuan Chen ◽  
Ying Chun Liang ◽  
Li Quan Wang ◽  
Xing Lei Hu
Keyword(s):  
Cutting Force ◽  
Thrust Force ◽  
Three Dimensional ◽  
Cutting Speed ◽  
Cutting Process ◽  
Nanometric Cutting ◽  
Subsurface Layers ◽  
Cutting Velocity ◽  
Dynamics Simulations ◽  
Cutting Speeds

Three-dimensional molecular dynamics simulations are performed to investigate the AFM-based nanometric cutting process of single crystal copper. The effects of cutting velocities (180, 360, and720 m/s) on the cutting force, the ratio of the thrust force and cutting force and subsurface layers. The results show that the dislocations nucleate beneath the tool, and propagate along the [-11-1] direction in the (111) plane. The effects of the nanocutting action from the tool on the subsurface damaged layers decrease gradually as the distance from the tool tip increases. With the increasing cutting speed, the cutting forces increase accordingly. However, the ratio of the the ratio the thrust force and cutting force decrease as the cutting speeds increase. With the proceeding of the cutting process, that tends to the same on the whole.

Nonlinear Periodically Forced Vibration of Stay Cables

2004 ◽  
Vol 126 (2) ◽  
pp. 245-252 ◽  
Author(s):  
Y. Q. Ni ◽  
G. Zheng ◽  
J. M. Ko
Keyword(s):  
Three Dimensional ◽  
Solution Process ◽  
Periodic Oscillation ◽  
Suspension Bridge ◽  
Element Model ◽  
Forced Response ◽  
Stay Cable ◽  
Response Curves ◽  
Stay Cables ◽  
Unstable Solutions

A new method for analyzing nonlinear steady-state dynamic response of three-dimensional sagged stay cables subject to arbitrary periodic excitation is proposed in this paper. Firstly, the nonlinear governing equation of motion of a stay cable with arbitrary sag is formulated in terms of three-node curved finite elements. Then a frequency-domain solution method to obtain the periodically forced response is developed by applying the incremental harmonic balance (IHB) technique to the finite element model. The proposed method is an accurate algorithm in the sense that it accommodates multi-harmonic components and no mode-based model reduction is made in the solution process. Both frequency- and amplitude-controlled algorithms are formulated and are alternatively implemented to obtain complete frequency-response curves including unstable solutions. The proposed method enables direct solution to the sub- and super-harmonic resonances, and gives a way to analyze nonlinear periodic oscillation under parametric excitation and internal resonance. Case study of applying the proposed method to nonlinear dynamic behavior analysis of the Tsing Ma suspension bridge cables is demonstrated. The analysis results show that the side-span free cables of the bridge display distinctly different nonlinear characteristics in the construction stage and in the final stage.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Bole Ma ◽  
Yongsheng Ren
Keyword(s):  
Differential Equation ◽  
Dynamic Analysis ◽  
Cutting Force ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Cutting Process ◽  
Cutting Depth ◽  
Resonance Curves ◽  
Cutting System

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.

Determination of cutting force of roll-formed section in shaped dies-knife guillotine

2020 ◽  
pp. 373-376
Author(s):  
S.V. Povorov ◽  
D.V. Egorov ◽  
D.S. Volgin
Keyword(s):  
Cutting Force ◽  
Cutting Process ◽  
Sheet Blank

The change in cutting force in the cutting process of roll-formed section in shaped dies-knife guillotine is studied. It is established that to calculate the cutting force in shaped guillotine, one can use formulas to determine the cutting force of sheet blank on conventional straight knives guillotine.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

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