Effects of modal truncation and condensation methods on the Frequency Response Function of a stage reducer connected by rigid coupling to a planetary gear system

Abstract

The present paper is aimed at the application of a substructure methodology, based on the Frequency Response Function (FRF) simulation technique, to analyze the vibration of a stage reducer connected by a rigid coupling to a planetary gear system. The computation of the vibration response was achieved using the FRF-based substructuring method. First of all, the two subsystems were analyzed separately and their FRF were obtained. Then the coupled model was analyzed indirectly using the substructuring technique. A comparison between the full system response and the coupled model response using the FRF substructuring was investigated to validate the coupling method. Furthermore, a parametric study of the effect of the shaft coupling stiffness on the FRF was discussed and the effects of modal truncation and condensation methods on the FRF of subsystems were analyzed.

Effect of elastic couplings on the dynamic behavior of transmission systems

“…Therefore, the proposed method of FRF applied to gearbox is validated. Furthermore, the effectiveness of this method in reducing the computation time is proved in [20].…”

Modal energetic analysis and dynamic response of worm gear drives with a new developed dynamic model

“…The mesh stiffness matrix I 11 The inertia of the motor µ, λ Constants of proportionality of the damping matrix I 12 The inertia of the worm F 0 The vector of external static forces I 21 The inertia of the worm gear T The modal kinetic energy I 22 The inertia of the receiver U The modal strain energy δ…”

“…Bevel gears were modelled by Driss et al [20]. Planetary gears were modelled by various researchers such as Hammami et al [21], Bouslema et al [22], and Feki et al [23]. With the same approach, the new dynamic model is composed of two blocks and it has fourteen degrees of freedom.…”

Numerical modeling and dynamic characteristics study of coupling vibration of multistage face gearsplanetary transmission

“…The meshing forces were obtained by means of a double approach which combined numerical and analytical aspects (Fernandez-Del-Rincon et al, 2017). Bouslema et al (2017) aimed at the application of a substructure methodology, based on the Frequency Response Function (FRF) simulation technique, to analyze the vibration of a stage reducer connected by a rigid coupling to a planetary gear system. The computation of the vibration response was achieved by using the FRF-based substructuring method.…”

“…First of all, the two subsystems were separately analyzed and their FRF were obtained. Then, the coupled model was analyzed indirectly using the substructuring technique (Bouslema et al, 2017). Zhang et al (2016) first presented a translational-rotational dynamic model of a twostage closed-form planetary gear set under consideration of the rotational and translational displacements to investigate the dynamic response and avoid resonance (Zhang et al, 2016).…”