Articles
Publication Date: 2024
Measurement: Journal of the International Measurement Confederation (02632241)224
The mesh stiffness is a necessary and influential parameter in system dynamics modeling and vibration analysis of straight bevel gear systems (SBG). A new experimental method, employing a laser extensometer (LE) and an innovative setup, is developed to calculate the mesh stiffness in both healthy and cracked systems. An analytical method based on potential energy and tooth root crack modeling is also proposed. Both methods were implemented on healthy and cracked gear systems with varying crack depths. The new LE experimental method's results are compared with those obtained from the proposed analytical method. The results showed good agreement between both methods, indicating that the newly proposed experimental method considers all parts of mesh stiffness and is suitable for measuring mesh stiffness in both healthy and cracked SBG systems. © 2023
Publication Date: 2024
Measurement: Journal of the International Measurement Confederation (02632241)238
The mesh stiffness plays a crucial role in influencing the performance and behavior of straight bevel gear (SBG) systems. Precisely determining the mesh stiffness enables to assess the SBG system's dynamic behavior more accurately and anticipate potential concerns such as crack identification and noise reduction. A novel experimental method is developed, employing experimental modal analysis associated with metaheuristic algorithms and an innovative setup. This method effectively determines the mesh stiffness in healthy and cracked systems. Additionally, an analytical method based on the potential energy associated with crack modeling is proposed. Both methods are implemented on SBG systems with varying crack depths. The results obtained from the experimental method are compared with those from the analytical method, revealing good agreement between them. This demonstrates that the newly proposed experimental method effectively considers all parts of mesh stiffness and is appropriate for determining the mesh stiffness in healthy and cracked SBG systems. © 2024
Publication Date: 2024
Journal of Sound and Vibration (10958568)570
Non-uniformity and damage are the two primary subjects in studying the vibrations of the beam-type elements. An exact closed-form explicit solution for the transverse displacement of a non-uniform multi-cracked beam with any type of boundary conditions is introduced. The generalized functions and the distributional derivative concepts are adopted. Four fundamental functions are introduced. These functions make the boundary conditions' process and compute the frequency equation more convenient. By introducing the non-dimensional parameters, the non-dimensional motion equation of the damaged beam with an arbitrary count of cracks is derived, and its exact closed-form explicit solution is obtained based on the four introduced fundamental functions. The standard method of computing these functions is presented, and the closed-form of these functions is determined for eight cases like uniform and conical beams. The closed-form of the frequency equation and mode shapes of the non-uniform multi-cracked beam are derived for several boundary conditions. The influence of the count of cracks, their location and intensity, and the boundary conditions on the natural frequency and mode shape are assessed by running a numerical study. The first and second frequencies of a conical beam are computed to verify the obtained results by applying this newly presented closed-form solution and the Differential Quadrature Element Method. A good agreement is evident when the obtained results are compared. © 2023
Publication Date: 2024
Nonlinear Dynamics (0924090X)112(14)pp. 11945-11970
The tooth crack identification through the effect of the tooth root crack on nonlinear vibration behaviors in a straight bevel gear (SBG) system is sought. The mesh stiffness is evaluated through an analytical method based on the potential energy and Tredgold approximation associated with tooth root crack modeling. A 10-dof model is developed for the SBG system where the backlash nonlinearity is of concern. To assess the nonlinear vibration behaviors of the SBG system, first, the dynamic response is extracted analytically with the proposed dynamic model, and experimentally with a designed setup, then the extracted response is assessed based on the different crack identification statistical factors. Results indicate that the Skewness is the most effective factor in identifying the crack in the SBG system with backlash nonlinearity, compared to other investigated factors. The nonlinear vibration response as a time history, phase diagram, Poincaré map, modal analysis, and mesh stiffness FFT spectrum is analyzed and recommended as an appropriate indicator for tooth root cracks. The modeled mesh stiffness and simulated SBG system are verified by applying FEM and the experimental method. Graphical abstract: (Figure presented.) © The Author(s), under exclusive licence to Springer Nature B.V. 2024.
