Damped Vibration Response of an Axially Moving Wire Subject to an Oscillating Boundary Condition and the Application to Slurry Wiresaws

2020 ◽  
pp. 1-37
Author(s):  
Liming Li ◽  
Imin Kao
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Traveling Waves ◽  
Solution Space ◽  
Vibration Response ◽  
Temporal Variables ◽  
Rocking Motion ◽  
Vibration Responses ◽  
Oscillating Boundary ◽  
Axially Moving

Abstract This paper presents the analysis of a new class of differential continuum system with a solution of traveling waves containing coupled spatial and temporal variables. Herein, we derive the analytical solution of the damped vibration response of a longitudinally moving wire with damping, subject to an oscillating boundary condition. The vibration response is the outcome of combining four traveling waves, induced by a wave initiating from the oscillating boundary, and traveling between the two boundaries. The four different traveling waves are the independent bases of the vibration responses that span the solution space of vibration of such continuum system. The combination, or the interference, of these traveling waves in the undamped condition produces nodal points in the vibration response, which can be formulated through the analytical solution. The impacts of wire speed, oscillating frequency at the boundary and damping factors on the vibration response are investigated. Furthermore, the vibration induced by the oscillating motion of the boundary has a profound impact on the effectiveness of slicing ingots with rocking motion of oscillating wire guides in wiresaw manufacturing processes.

Study on the Vibration Response of Axially Moving Continua

2013 ◽  
Author(s):  
Chunhui Chung ◽  
Imin Kao
Keyword(s):  
Wave Propagation ◽  
Transfer Function ◽  
Review Paper ◽  
Adjoint Equation ◽  
Equation Of Motion ◽  
Vibration Response ◽  
Advantages And Disadvantages ◽  
Vibration Responses ◽  
Axially Moving ◽  
Mathematical Derivation

Axially moving continua such as belt, chain, and conveyer are common transmission components. The study of the vibration response of axially moving continua is an essential topic to understand the fundamentals of vibration and improve the performance of the machines. However, it typically requires more rigorous effort in mathematical derivation to obtain the analytical forced vibration responses of the axially moving continua because of the characteristics of non-self-adjoint equation of motion. The methods utilized to obtain the analytical solutions include the modal analysis, canonical form, wave propagation, Laplace transform, and transfer function. In this review paper, these methods will be reviewed and presented. The advantages and disadvantages of different methodologies are discussed as well.

Analysis of vibration response and machining quality of hybrid robot based UD-CFRP trimming

2021 ◽  
pp. 095440542098609
Author(s):  
Yan Zhang ◽  
Hao Li ◽  
Xuda Qin ◽  
Jie liu ◽  
Zhuojie Hou
Keyword(s):  
High Performance ◽  
Vibration Response ◽  
Industrial Robots ◽  
Force Characteristic ◽  
Surface Waviness ◽  
Machined Surface ◽  
Machining Quality ◽  
3D Surface Roughness ◽  
Machined Surface Quality ◽  
Vibration Responses

To fulfill the demands of higher precision, better quality, and more flexibility, the usage of high-performance industrial robots is rapidly increased in aerospace industry. Considering the anisotropic and inhomogeneous characteristics of composite materials, this study focuses mainly on dynamic response investigation of a newly designed hybrid robot (named as TriMule) in CFRP trimming process and its influence on the machined quality. First, combined with the cutting force characteristic, the vibration responses of tool center point (TCP) under the dynamic excitation were obtained. The influences of robotic TCP vibration on machined surface quality with different fiber orientations, including surface waviness, cavity, 3D surface roughness, and depth of affected zone, are first studied by comparing hybrid robot and machine tool. From experiment results, it can be concluded the proposed TCP vibration response model has sufficient prediction accuracy. Meanwhile, it is found that larger robotic vibration response is accompanied by higher surface waviness, bigger surface cavity, and greater affected zone. Results also showed that the fiber orientation and milling style are two essential factors that affect robot vibration and machining quality during CFRP trimming.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

The Effect of Biot Number on a One-Dimensional General Conduction Solution

2021 ◽  
Author(s):  
Robert L. McMasters ◽  
Filippo de Monte ◽  
James V. Beck
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Biot Number ◽  
Analytical Solutions ◽  
Heat Fluxes ◽  
Graphical Form ◽  
Large Temperature ◽  
Convection Coefficient ◽  
General Analytical Solution

Abstract Analytical solutions for thermal conduction problems are extremely important, particularly for verification of numerical codes. Temperatures and heat fluxes can be calculated very precisely, normally to eight or ten significant figures, even in situations involving large temperature gradients. It can be convenient to have a general analytical solution for a transient conduction problem in rectangular coordinates. The general solution is based on the principle that the three primary types of boundary conditions (prescribed temperature, prescribed heat flux, and convective) can all be handled using convective boundary conditions. A large convection coefficient closely approximates a prescribed temperature boundary condition and a very low convection coefficient closely approximates an insulated boundary condition. Since a dimensionless solution is used in this research, the effect of various values of dimensionless convection coefficients, or Biot number, are explored. An understandable concern with a general analytical solution is the effect of the choice of convection coefficients on the precision of the solution, since the primary motivation for using analytical solutions is the precision offered. An investigation is made in this study to determine the effects of the choices of large and small convection coefficients on the precision of the analytical solutions generated by the general convective formulation. Results are provided, in tablular and graphical form, to illustrate the effects of the choices of convection coefficients on the precision of the general analytical solution.

Analytical Solution for Solid Cylindrical Heat Source Model With Convective Boundary Condition

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Yang Zhou ◽  
Cheng Xu ◽  
David Sego ◽  
Dong-hai Zhang
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Analytical Solution ◽  
Heat Source ◽  
Groundwater Flow ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Energy Pile ◽  
Special Cases ◽  
Scs Model

Abstract The energy pile technology has been widely used, and the solid cylindrical heat source (SCS) model is usually adopted to describe the heat transfer process between the energy pile and the surrounding soil. This paper investigates the SCS model with a convective boundary condition (SCS-3 model), and realistic conditions such as transversely isotropic ground and groundwater flow are all included in the model. An analytical solution for the problem is established using Green's function method and the theory of moving heat sources. Solutions for the SCS model with a boundary condition of the first kind (SCS-1 model) and for the line source (LS) model with a convective boundary condition (LS-3 model) are recovered as special cases of the solution in this paper. Computational examples are presented, and comparisons between different models are made. First, the SCS-1 model is compared with the SCS-3 model, showing the error caused by neglecting the surface convective effect. Second, the LS-3 model is compared with the SCS-3 model, showing the error associated with neglecting the size of heat source. The effects of groundwater flow velocity and convective heat transfer coefficient on the temporal and spatial variations of these errors are also investigated.

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