emadaldin sh khoram-nejad

Investigating the sound radiated from faulty rolling element bearings (REBs) in rotor-bearing systems is as crucial as studying their vibration characteristics. This approach offers experts and researchers a more comprehensive understanding of faulty REB behavior, enhancing fault diagnosis capabilities. This study examines the impact of bearing faults, pedestal looseness, and shaft eccentricity on the vibro-acoustic characteristics of REBs. Additionally, it assesses the influence of fault severity and compound fault scenarios on these behaviors. A 6-degree-of-freedom (DOF) dynamic model is developed for an SKF 6205 bearing, including the shaft, inner ring, outer ring, and pedestal. The Hertzian theory is employed to model contact between the bearing balls and inner/outer rings. The governing equations are solved using the Runge-Kutta method to determine the surface velocity of the REB components, yielding a 4.56% error compared to experimental results, demonstrating good agreement. Based on the surface velocity, the sound pressure level (SPL) is calculated by modeling the inner and outer rings as cylindrical sound sources. The results reveal that auditory and visual observation can identify shaft eccentricity, while sound is a more sensitive indicator of bearing faults. Detecting incipient faults remains challenging, regardless of whether vibration or sound measurement tools, such as accelerometers or sound level meters, are employed. Furthermore, phase portraits indicate that pedestal looseness and bearing faults, unlike shaft eccentricity, result in chaotic and unpredictable motion, which may explain the sudden failures often observed in industrial REBs.

This paper aims to discuss the vibration analysis of the post-buckled cracked axially functionally graded (AFG) beam. The nonlinear equations of motion of the Euler-Bernoulli beam are derived using the equilibrium principles. Then, these differential equations are converted into a set of algebraic ones using the differential quadrature (DQ) method and solved by an arc-length strategy. The resulted displacement field from the post-buckling analysis is assumed to be the equilibrium state of vibration analysis, and an eigenvalue problem is derived. By solving this linear eigenvalue problem, both the natural frequencies and mode shapes of the beam are calculated. The validation of results in comparison with a similar work shows a good agreement. The effect of several parameters such as the extensible and inextensible clamped-clamped boundary conditions, initial geometric imperfection, crack’s depth, and crack’s location on the natural frequencies and mode shapes are investigated in detail.