Miha Boltežar

Damping identification using a continuous wavelet transform: application to real data

A continuous wavelet transform (CWT) based on the Gabor wavelet function is used to identify the damping of a multi-degree-of-freedom system. The common procedures are already known, especially the identification with a Morlet CWT. This study gives special attention to the following: a description of the instantaneous noise, the edge-effect of the CWT, the frequency-shift of the CWT, the bandwidth of the wavelet function and the selection of the parameter σ of the Gabor wavelet function of the CWT. The procedures are demonstrated using several numerical examples and on signals acquired from the lateral vibration of a uniform beam. The study demonstrates the advantages of using the amplitude and phase methods, both of which provide information about the instantaneous noise. The procedures presented are appropriate for automating the identification process.

The norms and variances of the Gabor, Morlet and general harmonic wavelet functions

Abstract This paper deals with certain properties of the continuous wavelet transform and wavelet functions. The norms and the spreads in time and frequency of the common Gabor and Morlet wavelet functions are presented. It is shown that the norm of the Morlet wavelet function does not satisfy the normalization condition and that the normalized Morlet wavelet function is identical to the Gabor wavelet function with the parameter σ=1. The general harmonic wavelet function is developed using frequency modulation of the Hanning and Hamming window functions. Several properties of the general harmonic wavelet function are also presented and compared to the Gabor wavelet function. The time and frequency spreads of the general harmonic wavelet function are only slightly higher than the time and frequency spreads of the Gabor wavelet function. However, the general harmonic wavelet function is simpler to use than the Gabor wavelet function. In addition, the general harmonic wavelet function can be constructed in such a way that the zero average condition is truly satisfied. The average value of the Gabor wavelet function can approach a value of zero but it cannot reach it. When calculating the continuous wavelet transform, errors occur at the start- and the end-time indexes. This is called the edge effect and is caused by the fact that the wavelet transform is calculated from a signal of finite length. In this paper, we propose a method that uses signal mirroring to reduce the errors caused by the edge effect. The success of the proposed method is demonstrated by using a simulated signal.

Typical Bearing-Fault Rating Using Force Measurements-Application to Real Data

In contrast to the commonly used acceleration measurement, this research discusses the use of force measurements to identify bearing faults. A force sensor is fixed between the rigid surroundings and the bearing to measure all of the reactive forces due to the vibration excitation. Using a force measurement, systematically prepared samples with the five typical faults that can occur during the assembly process (axial, radial, bending moment, contamination and shield defect) were investigated. The samples were prepared with low, medium and high fault ratings. The force measurement, with its relatively simple signal processing based on an envelope detection, was shown to be successful in correctly identifying both the fault rating and the fault type. The presented approach was successfully applied to high-series assembly production and is relatively easy to apply to similar applications.

A comparison of strain and classic experimental modal analysis

This research is focused on a comparison of classic and strain experimental modal analysis (EMA). The modal parameters (the natural frequencies, the displacement mode shapes (DMSs) and the damping) of real structures are usually identified with classic EMA, where the responses are measured with motion sensors (e.g. accelerometers). Strain EMA is a special approach in the field of EMA, where the responses are measured with strain sensors. Classic EMA is the preferred method, but strain EMA offers advantages that are important for particular applications: for example, the direct identification of strain mode shapes (SMSs), which is important in the vibration-fatigue and damage-identification models. The next advantage is that strain EMA can sometimes be used, for experimental/geometrical reasons, where classic EMA cannot. There are also drawbacks: for example with strain EMA only, the mass-normalization of the DMSs and SMSs cannot be performed. This study researches the theoretical similarities and differences of both EMA approaches. Furthermore, the accuracy of both approaches for the case of a free–free supported beam and a free–free supported plate is investigated. Classic and strain EMA were performed with a piezoelectric accelerometer and the piezoelectric strain gauges, respectively. The results show that the accuracy of strain EMA results (the natural frequencies, DMSs and the damping) is comparable to the accuracy of classic EMA.

Fault Detection in DC Electro Motors Using the Continuous Wavelet Transform

Two time–frequency methods were used to detect typical faults in DC electro motors: the windowed Fourier transform and the continuous wavelet transform. Four groups containing three electro motors each were manufactured with typical faults and examined. These faults included a bearing fault, an increased unbalance, a fragmented brush and a fragmented collector. The velocity of the vibrations at selected points on the electro motors was measured with a laser probe. The parameters of both transforms were selected in order to make both methods comparable. Because of the poor frequency variance, the windowed Fourier transform was, in this case, proven to be inferior to the continuous wavelet transform. Therefore, the continuous wavelet transform was chosen as the primary tool for fault detection.Three criteria were found that successfully discriminated between the typical faults. These were the highest magnitude level, the frequency of the first and second harmonics and the time period between the magnitude pulses in the third (highest) frequency region. If the maximum magnitude levels versus the period of the pulses in the third frequency range are plotted, four distinct regions corresponding to four different faults are obtained. Since the regions do not overlap, linear classifiers can be used with the presented criteria.

The use of strain sensors in an experimental modal analysis of small and light structures with free-free boundary conditions

Small and light structures have distinctive features, which cause difficulties in the measurement of their modal parameters. The major issues are the mass, which is added to the measured structure by sensors, and the very high resonant frequencies. Those difficulties occur with a measurement of the excitation force. An innovative procedure for the experimental modal analysis of small and light structures was developed in this study. This procedure involves a measurement of the excitation force, which was performed by a piezo strain gauge that enables an analysis of the aforementioned structures with free–free support. The main advantage of this sensor in comparison with other devices used for force measurements is that it adds a very small mass to the measured structure (≈0.4 g) but at the same time enables an accurate measurement of the modal parameters in a wide frequency range (up to 20 kHz). This makes it suitable for a measurement of the frequency-response functions of light structures that have high resonant frequencies. Consequently, an experimental modal analysis can be performed. The presented approach was experimentally tested on a sample with small dimensions and mass. The results of the experiment (modal parameters) were compared with the results of the numerical model. The good agreement between the results indicates that this procedure can be used on other similar structures.

Non-linearity and non-smoothness in multi-body dynamics: Application to woodpecker toy

Abstract The introduction of the article gives a short historical overview of the modelling of multi-body dynamics with unilateral contacts. The unilateral contacts formulation as introduced by Pfeiffer and Glocker is adapted to discretely defined body shapes. By using two-step collision detection, a fast and exact collision detection is achieved. The procedures are tested on a numerical example of the woodpecker toy and the results are compared with those of other authors who used a simpler mathematical model.

Evaluation of the Frequency-Dependent Young’s Modulus and Damping Factor of Rubber from Experiment and Their Implementation in a Finite-Element Analysis

Rubbers are commonly used in industry to reduce vibration transfer and, consequently, reduce structural noise. The vibration transfer through rubber can be modelled with finite elements; however, to achieve satisfactory results it is necessary to know the viscoelastic properties of the rubber. This paper describes the commonly used theory of vibration transmission through rubber modelled as a single-degree-of-freedom (SDOF) system. Three simplified rubber models are used to identify the constant Young’s modulus and damping factor from the measurements of two different rubber specimens, and with the obtained results the theoretical transmissibilities are calculated. The frequency-dependent Young’s modulus and damping factor are also calculated from measurements. The practical use of previous measurements of dynamic material properties is presented in a finite-element analysis, where three different definitions of the dynamic material properties are carried out for four different rubber specimens, which corresponds to 12 analyses. The finite-element analyses are then compared with the measurements, and general guidelines for using dynamic material properties in ANSYS Workbench v.14 are given.

Fatigue Damage for Sweep-Sine and Random Accelerated Vibration Testing

The vibration testing of components in the automotive industry requires long testing times and the use of expensive facilities. To shorten these testing times an accelerated vibration-testing approach is usually applied. This research tries to shorten these testing times by considering the parameters that define vibration-testing techniques. With special attention to the excitation types sweep-sine and random, a damage-based approach is applied. The phenomenon of fatigue damage is closely observed from the frequency-domain point of view but also by considering the relationship between the time and the frequency domains. The Palmgren-Miner cumulative rule is applied to calculate the fatigue life. Two case studies of measured responses are used to compare the times to failure. The results show that proposed predictions can be used to compare different testing techniques, but they are not so accurate when predicting the actual times to failure.

Improved 2D model of a ball bearing for the simulation of vibrations due to faults during run-up

This paper present an improved 2D bearing model for investigation of the vibrations of a ball-bearing during run-up. The presented numerical model assumes deformable outer race, which is modelled with finite elements, centrifugal load effects and radial clearance. 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. 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 continuous wavelet transformation for the bearing fault identification and classification.