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Transversal vibrations of a toothed belt in linear drives during operation
Author(s) -
Schnürer Dominik,
Holl Helmut J.
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000026
Subject(s) - flexural rigidity , vibration , deflection (physics) , finite element method , nonlinear system , rigidity (electromagnetism) , structural engineering , transverse plane , transversal (combinatorics) , acceleration , linear acceleration , mechanics , linear motion , engineering , linear motor , physics , mathematics , mathematical analysis , classical mechanics , acoustics , mechanical engineering , quantum mechanics
Vibrations of the toothed belt of a linear drive can affect the dynamic positioning accuracy and smoothness which is important for practical applications. An analytical, one‐dimensional model of a belt section is derived, taking into account the preload and flexural rigidity, as well as the non‐linear cable effect and the acceleration forces due to the belt mass. In addition to the case of constant belt length, the temporal change of the length as a result of the axial motion is an essential part of the modeling. The solution of the equation of motion is limited to the dominant transverse deflection of the belt. For the longitudinal extension, the assumption of a quasi‐static solution is taken. A FEM program is implemented to calculate the solution for given operation conditions. The evaluations are made for selected motions according to a path planning with trapezoidal velocity profiles. A modification of individual parameters, based on a practical parameter set, enables the analysis of the respective effects.