In this paper an improved bearing model is developed in order to investigate the vibrations of a ball bearing during run-up. The numerical bearing model was developed with the assumptions that the inner race has only 2 DOF and that the outer race is deformable in the radial direction, and is modelled with finite elements. The centrifugal load effect and the radial clearance are taken into account. The contact force for the balls is described by a nonlinear Hertzian contact deformation. Various surface defects due to local deformations are introduced into the developed model. The detailed geometry of the local defects is modelled as an impressed ellipsoid on the races and as a flattened sphere for the rolling balls. With the developed bearing model the transmission path of the bearing housing can be taken into account, since the outer ring can be coupled with the FE model of the housing. The obtained equations of motion were solved numerically with a modified Newmark time-integration method for the increasing rotational frequency of the shaft. The simulated vibrational response of the bearing with different local faults was used to test the suitability of the envelope analysis technique and the continuous wavelet transformation was used for the bearing-fault identification and classification.
COBISS.SI-ID: 12119579
A mechanical system's modal parameters change when fatigue loading is applied to the system. In order to perform an accelerated vibration-based fatigue test these changes must be taken into account in order to maintain constant-stress loading. This paper presents an improved accelerated fatigue-testing methodology based on the dynamic response of the test specimen to the harmonic excitation in the near-resonant area with simultaneous monitoring of the modal parameters. The measurements of the phase angle and the stress amplitude in the fatigue zone are used for the real-time adjustment of the excitation signal according to the changes in the specimen's modal parameters. The presented methodology ensures a constant load level throughout the fatigue process until the final failure occurs. With the proposed testing methodology it is possible to obtain a S-N point of the Woehler curve relatively quickly and to simultaneously monitor the changes of the specimen's natural frequency and damping loss factor. The presented methodology with real-time control is verified on an aluminium Y-shaped specimen (10exp6 load cycles are achieved in 21 minutes) and is applicable to a specimen with arbitrary geometry. Besides the faster completion of the fatigue test the methodology can be adopted for the validation of the vibrational fatigue analysis.
COBISS.SI-ID: 12402971
The characterization of vibration-fatigue strength is one of the key parts of mechanical design. It is closely related to structural dynamics, which is generally studied in the frequency domain, particularly when working with vibratory loads. A fatigue-life estimation in the frequency domain can therefore prove advantageous with respect to a time-domain estimation, especially when taking into consideration the significant performance gains it offers, regarding numerical computations. Several frequency-domain methods for a vibration-fatigue-life estimation have been developed based on numerically simulated signals. This research focuses on a comparison of different frequency-domain methods with respect to real experiments that are typical in structural dynamics and the automotive industry. The methods researched are: Wirsching–Light, the alfa_0.75 method, Gao–Moan, Dirlik, Zhao–Baker, Tovo–Benasciutti and Petrucci–Zuccarello. The experimental comparison researches the resistance to close-modes, to increased background noise, to the influence of spectral width, and multi-vibration-mode influences. Additionally, typical vibration profiles in the automotive industry are also researched. For the experiment an electro-dynamic shaker with a vibration controller was used. The reference-life estimation is the rainflow- counting method with the Palmgren–Miner summation rule. It was found that the Tovo–Benasciutti method gives the best estimate for the majority of experiments, the only exception being the typical automotive spectra, for which the enhanced Zhao–Baker method is best suited. This research shows that besides the Dirlik approach, the Tovo–Benasciutti and Zhao–Baker methods should be considered as the preferred methods for fatigue analysis in the frequency domain.
COBISS.SI-ID: 12402715
When estimating a structure's fatigue life during vibrational test the stress frequency- response function (SFRF) to the base excitation is required.The response to this base excitation can be numerically obtained by solving the equilibrium equations for each frequency of interest. In this research we propose a new method, that can be used to obtain the SFRFof a base-excited structure using the modal model of the unconstrained structure, only. By further developing the idea of a structural modification using the response function this research significantly reduces the computation time and the amount of data sent to the fatigue-analysis software.The new method is presented on two numerical examples: a simple beam structure and a Y-shaped structure. Using numerical examples, the effects of the modal truncation, the matrix singularity and the damping are discussed.
COBISS.SI-ID: 12882459
When dealing with small and light structures, difficulties occur when measuring the modal parameters. The resonant frequencies are usually relatively high and therefore a wide frequency range is needed for the measurement. Furthermore, the mass that is added to the structure by the sensors causes structural modifications. To overcome these difficulties, an improved method using an operational modal analysis instead of an experimental modal analysis is proposed in this study. It is derived from the sensitivity-based operational mode-shape normalisation with a consideration of the mode-shape variation. The measurement of the excitation force is not needed, because the operational modal analysis is used and only two simultaneous response measurements at an unknown excitation are required. The proposed method includes the cancellation of the added mass, resulting in mode shapes and resonant frequencies of the unmodified structure. The numerical and experimental results on small and light structures are compared with the results of the experimental modal analysis. The comparison shows that the proposed approach allows measurements over a wide frequency range and increases the accuracy of the results compared to the sensitivity-based operational mode-shape normalisation and also compared to the particular experimental modal analysis method that was used in this study. The advantages of the proposed method can be seen whenever the mass that is added to the structure by the accelerometer is not negligible and therefore a variation of the mode shapes occurs.
COBISS.SI-ID: 13110043