Dynamics of a Variable-Mass, Flexible-Body System

2000 ◽  
Vol 23 (3) ◽  
pp. 501-508 ◽  
Author(s):  
Arun K. Banerjee
Keyword(s):  
Variable Mass ◽  
Flexible Body ◽  
Body System

Analysis for Effect of Key Parts on Precision of High Precision Machine Center

2011 ◽  
Vol 189-193 ◽  
pp. 2107-2111 ◽  
Author(s):  
Feng Tao Wang ◽  
Lu Tao Song ◽  
Bin Zhang
Keyword(s):  
Machine Tools ◽  
Dynamic Stiffness ◽  
Dynamics Simulation ◽  
Precision Machining ◽  
Flexible Body ◽  
Body System ◽  
Flexible Coupling ◽  
Machining Precision ◽  
Machining Center ◽  
Multi Body

Increasing the machining precision of machine tools has imposed higher demands for dynamic characteristics of the key components. Taking the MDH50 precision machining center as a example, this paper established the flexible body of five key components, bed, column, spindle boxes, slipway and worktable, and built the rigid-flexible coupling systems of whole machine, based on the basic theory of multi-body system dynamics. Then the cutting force reference to the actual constraints was applied to the system and the dynamics simulation was carried out. The effect of every component on machining precision was effectively identified. Dynamic stiffness testing of the machine is based of principles of testing the transmission components dynamic stiffness, and further analysis of the each component dynamic stiffness is conducted, which can verify the accuracy of flexible body analysis.

Study on the Dynamics Response of Ultra-Precision Single-Point Diamond Fly-Cutting Machine Tool As Multi-Rigid-Flexible-Body System Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Hanjing Lu ◽  
Xiaoting Rui ◽  
Gangli Chen
Keyword(s):  
Machine Tool ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Flexible Body ◽  
Body System ◽  
Dynamics Model ◽  
Ultra Precision ◽  
Dynamics Response

The dynamics response optimization of an ultra-precision machine tool system is the key to improve machining accuracy. Based on the transfer matrix method for multibody systems (MSTMM), the dynamics model as multi-rigid-flexible-body system is established. The overall transfer equation, overall transfer matrix, eigenfrequency equation and dynamics equation with respect to generalized coordinates are derived in this paper. Considering the environmental micro-vibration, cutting force and spindle centrifugal force during the machining process as external excitations, the vibration characteristics and dynamics response are simulated by using MSTMM. The computational results are in good agreement with test results, which validates the proposed method and dynamics model used in this paper.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

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