Uncertainty analysis of phase and amplitude of harmonic components of bearing inner ring four-point roundness measurement

Viitala, Raine; Widmaier, Thomas; Hemming, Björn; Tammi, Kari; Kuosmanen, Petri

doi:10.1016/j.precisioneng.2018.05.008

Cited by 21 publications

(8 citation statements)

References 13 publications

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“…The roundness profile was measured utilizing the four-point method. [18,23,24]. The four-point method is able to differentiate the roundness profile and the error motion of the workpiece in a reliable way.…”

Section: Bearing Waviness Measurementmentioning

confidence: 99%

Simulation of Subcritical Vibrations of a Large Flexible Rotor with Varying Spherical Roller Bearing Clearance and Roundness Profiles

et al. 2020

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In large rotor-bearing systems, the rolling element bearings act as a considerable source of subcritical vibration excitation. Simulation of such rotor bearing systems contains major sources of uncertainty contributing to the excitation, namely the roundness profile of the bearing inner ring and the clearance of the bearing. In the present study, a simulation approach was prepared to investigate carefully the effect of varying roundness profile and clearance on the subcritical vibration excitation. The FEM-based rotor-bearing system simulation model included a detailed description of the bearings and asymmetricity of the rotor. The simulation results were compared to measured responses for validation. The results suggest that the simulation model was able to capture the response of the rotor within a reasonable accuracy compared to the measured responses. The bearing clearance was observed to have a major effect on the subcritical resonance response amplitudes. In addition, the simulation model confirmed that the resonances of the 3rd and 4th harmonic vibration components in addition to the well-known 2nd harmonic resonance (half-critical resonance) can be significantly high and should thus be taken into account already in the design phase of large subcritical rotors.

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Section: Bearing Waviness Measurementmentioning

confidence: 99%

Simulation of Subcritical Vibrations of a Large Flexible Rotor with Varying Spherical Roller Bearing Clearance and Roundness Profiles

et al. 2020

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“…The principle of radial bearing force measurement is straightforward and has been presented in a previous study [18]. In the present study, the center point movement was measured by exploiting the four-point method developed by Kuosmanen and Väänänen [20] and further investigated by Viitala et al [21]. The method is a combination of two different methods: the Ozono three-point method [22], developed for roundness measurements, and the two-point method, which is a straightforward method to measure the diameter variation of the rotor.…”

Section: Test Setupmentioning

confidence: 99%

Method and device to investigate the behavior of large rotors under continuously adjustable foundation stiffness

Viitala¹

2020

J. vibroeng.

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Vibration problems have been observed after the installation of large rotating machines, such as electric machines and generators and paper machine rolls. One possible cause can be differences between the foundation stiffness of the installation location and the testing platform where the machine is balanced and optimized. Foundation stiffness exerts a significant effect on the behavior of a rotating system, and the above-mentioned differences can cause major unexpected changes at natural frequencies, and thus resonance. The problem is typical for large machines due to their large mass, which leads to low natural frequencies. This induces situations where these natural frequencies coincide with rotor excitations and cause excessive vibration. This study presents a novel method and a device for adjusting the foundation stiffness of a large rotor system, consequently enabling the investigation of the effect of foundation stiffness on rotor behavior. However, this investigation is restricted to the horizontal axis. The characteristics of the device were analyzed together with a rotor behavior measurement that consisted of versatile measurements of acceleration, force and displacement in different locations inside the rotating system. The device in the presented form is best applied in R&D laboratories and factory acceptance test cells, in which it can be used to predict the behavior of various rotors on different foundations. With the dynamic rotor behavior measurement performed with the device, the natural frequencies and their harmonic components can be presented as a function of foundation stiffness. This information can be used both to optimize rotor behavior in an installation location and also to improve the rotor system behavior in the design phase. The method and device presented in this study can be considered effective and successful, since the natural frequencies of the first two rotor modes could be manipulated freely at a range of 50-100 % by changing the stiffness.

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“…a n cos(nγ) + b n sin(nγ)) (18) Instead of original coefficients γ n determining the n-th harmonic, we obtain the new coefficients a n and b n . a n = c n cosγ n (19) b n = c n sinγ n (20) The following applies for amplitude: (21) And for phase: (22) Table 1 presents the difference between the calculated (γ c ) and the actual (γ) phases -the actual phase depends on whether the values "a" and "b" are positive (+) or negative (-). The table is supplemented by examples and graphical interpretation.…”

Section: Application Of the Fourier Series To A Roundness Profilementioning

confidence: 99%

“…They introduced two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. Viitala et al [21] analyzed the uncertainty of the four-point roundness measurement of a bearing inner ring using harmonic components of the Fourier series. Attention was drawn especially to the phase of the harmonic components, since the uncertainty of the phase is analyzed very little in the existing research studies.…”

Section: Introductionmentioning

confidence: 99%

Application of Fourier Series for Evaluation of Roundness Profiles in Metrology

Görög¹,

Görögová²

2019

Adv. Sci. Technol. Res. J.

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A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series are known as harmonic analysis. It is a useful way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical. This paper deals with the mathematical basics of Fourier series using trigonometric functions. This is the basic for a discrete Fourier transform. It allows transforming the discrete data to the frequency data or vice versa, i.e. transforming the frequency data to the discrete data. The most important part of the article is the application of the Fourier series and the Fourier transform to metrology, specifically on the roundness profile. The mathematical relationships for the practical use of harmonic analysis and the detailed method of determining the actual phase were described. General relationships do not give accurate results, due to the phase shift quadrant. The results of the harmonic analysis were applied graphically by the authors on a concrete example of a roundness profile. The individual harmonic components are shown in the linear and polar graphs as well as the resulting roundness profile. The Fourier analysis knowledge will contribute to a better analysis of the roundness profiles measured on the drawn tubes that will be investigated in the research project.

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Uncertainty analysis of phase and amplitude of harmonic components of bearing inner ring four-point roundness measurement

Cited by 21 publications

References 13 publications

Simulation of Subcritical Vibrations of a Large Flexible Rotor with Varying Spherical Roller Bearing Clearance and Roundness Profiles

Simulation of Subcritical Vibrations of a Large Flexible Rotor with Varying Spherical Roller Bearing Clearance and Roundness Profiles

Method and device to investigate the behavior of large rotors under continuously adjustable foundation stiffness

Application of Fourier Series for Evaluation of Roundness Profiles in Metrology

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