Dynamic modeling of gears: An innovative hybrid FEM–analytical approach

Abstract

Gearboxes are widely used in several applications ranging from the automotive to the industrial and robotic sectors. A planetary gearbox is a special kinematic gear arrangement that, taking advantage of a planet carrier, ensures high reduction ratios together with a very small design. Therefore, they are widely employed for transmissions which require a high power density. There are several fields of applications including, but not limited to, mechatronic, automation and wind power generation. To improve the design of new solutions, for performing monitoring activities on actual gearboxes and for the definition of maintenance schedules, the availability of physical models able to accurately describe the behavior of the system, both in healthy and damaged conditions, would represent a great support. Experimental and numerical studies of the behavior of gearboxes are already available in the literature. Nevertheless, while the experimental approaches are valid only for the specific configuration tested, the numerical techniques show limitations related to the computational effort required. This paper presents an innovative approach for the characterization of the behavior of two different geared transmissions. It is based on a hybrid approach that combines finite elements (FE) with analytical formulations. In detail, the solver computes separately the macro deformation of the bodies (numerical solution based on a coarse grid) and the contacts (solved analytically avoiding the need of mesh refinements). The computational effort is reduced significantly without affecting the accuracy of the results significantly. This approach was used to investigate and understand the vibro-dynamical behavior of a back-to-back test rig (typically used for the characterization of the surface fatigue strength of gears) and of an industrial planetary gearbox. The results obtained for the healthy -not damaged -gearboxes were compared with experimental measurements for both configurations in order to validate the hybrid approach. Once the models were validated, the same methodology was eventually used to study the effects of typical gear failures and in specifically surface fatigue (pitting), on the vibrational response. The capability to reproduce the effect of damages with the model of a gearbox represents the first indispensable step of a Structural Health Monitoring strategy. State-of-art and challenges are analyzed and discussed in the paper.

A Hybrid Finite Element Method–Analytical Model for Classifying the Effects of Cracks on Gear Train Systems Using Artificial Neural Networks

“…After obtaining the responses of the system in healthy and damaged conditions, it was observed that specific frequencies, between the range of 0 Hz and 8500 Hz, due to the harmonics considered in this work, shift given the presence of damage [50]. Indeed, the results in terms of signals from the healthy system could be validated with the signals from the experimental test.…”

“…Moreover, in order to generate good numerical results and obtain converged simulations, the flanks in the region of the gear teeth, where the main analysis take place, must be discretized with a very fine mesh. This is usually performed due to the contact position of the gears and the variation of their engaged surfaces during operation, which increases the number of equations to be solved [50]. Thus, this problem can be solved in the T3D environment.…”

Thermodynamic Modelling for Heat Analysis and Prediction in Precision Transmission Systems: A Focus on Gear Operation

“…In the realm of precision machinery, attention is consistently directed toward the performance and efficiency of transmission systems, as underscored by a wealth of scholarly inquiry [1,2]. Gears, pivotal mechanical components within these systems, are recognized as bearing a substantial portion of the power load [3][4][5][6][7][8][9][10][11][12][13]. It has been observed that during their operation, the heat generated from interactions such as meshing, sliding, and impact with adjacent gears plays a significant role in influencing the system's stability and efficiency.…”

Preliminary Evaluation of the Influence of Surface and Tooth Root Damage on the Stress and Strain State of a Planetary Gearbox: An Innovative Hybrid Numerical–Analytical Approach for Further Development of Structural Health Monitoring Models

“…Other authors use the vibrational response of the gearboxes as a trigger for detecting damage. In this regard, Concli et al [13] proposed a model of a back-to-back test rig and of a planetary gearbox [14] based on the same hybrid Finite Element (FE)-the analytical approach used in this paper. The comparison of the vibrational spectra predicted, and the experimental measurements performed at Politecnico di Milano, have fully validated the approach.…”