Editorial

2 pages, 149 KiB

Open AccessEditorial

Special Issue on Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements

by Jaroslav Zapoměl

Appl. Sci. 2023, 13(20), 11551; https://doi.org/10.3390/app132011551 - 22 Oct 2023

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Rotors and shafts are essential, often used, and highly loaded components of rotating machines and machine devices [...] Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

Research

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21 pages, 5896 KiB

Open AccessArticle

A Numerical Analysis for Ball End Milling Due to Coupling Effects of a Flexible Rotor-Bearing System Using GPEM

by Chun-Jung Huang, Jer-Rong Chang, Ting-Nung Shiau and Kuan-Hung Chen

Appl. Sci. 2023, 13(12), 7252; https://doi.org/10.3390/app13127252 - 17 Jun 2023

Cited by 1 | Viewed by 921

Abstract

In this paper, the tool-tip responses for ball end milling, due to the coupling effects of a flexible rotor-bearing system, are investigated numerically. The milling machine tool spindle is modelled as the flexible rotor-bearing system. The critical speeds, natural modes, and unbalance responses [...] Read more.

In this paper, the tool-tip responses for ball end milling, due to the coupling effects of a flexible rotor-bearing system, are investigated numerically. The milling machine tool spindle is modelled as the flexible rotor-bearing system. The critical speeds, natural modes, and unbalance responses of the system are calculated by applying the generalized polynomial expansion method. This generalized polynomial expansion method expresses the displacement as a series formed by the product of generalized coordinates and axial coordinate polynomials. According to the dynamic cutting force obtained by some scholars in the past, combined with the characteristics of the flexible rotor, the dynamic response of the tool-tip for ball end milling is numerically analyzed. The responses, including time histories, orbits, and FFT diagrams, are plotted to analyze the dynamic behaviors of the tool-tip. The coupling effects of the flexible rotor-bearing system on the system for ball end milling are first studied using the generalized polynomial expansion method. Unlike previous studies, the natural frequency varies with spindle speed and which of the different modes are included in the tool-tip response depends mainly on the spindle speed. Thanks to the gyroscopic effect, the critical speeds and responses of tool-tips can be discussed with respect to various spindle speed and tool flutes. The natural modes are accurately determined, and will excite critical speeds for certain modes, including forward and backward modes, thereby significantly affecting tool-tip response. In addition, the cutting force component associated with the tool-tip response affects the rotor-bearing system parameters, complicating the issue. Milling at higher spindle speed (2160–19,950 rpm), an important new result is found that the tool-tip oscillates with the cutting-force frequency, accompanied by a longer period vibration of the first backward mode of the rotor-bearing system. It can also be seen from the frequency spectrum analysis that, as the spindle speed increases, the peak amplitude of the first backward mode becomes larger. Milling at lower spindle speed (960, 1320 rpm), the in-plane vibration trajectory of the tool-tip gradually expands outwards clockwise around the origin until a stable loop is reached. This is because only the first backward mode of the rotor-bearing system is excited. Considering the coupling effect of the rotor-bearing system to perform the vibration analysis of the milling machine system, the parameters of the system can be designed or the spindle speed can be selected to avoid severe vibration during machining. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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18 pages, 6337 KiB

Open AccessArticle

Experimental Study of the Thermal and Wear Characteristics of a Foil Bearing Lubricated with a Low-Boiling Liquid

by Bartosz Moczulak, Grzegorz Żywica, Wojciech Miąskowski, Wojciech Kiński and Paweł Bagiński

Appl. Sci. 2023, 13(11), 6766; https://doi.org/10.3390/app13116766 - 02 Jun 2023

Cited by 1 | Viewed by 1094

Abstract

Developing high-speed rotating machines, such as microturbines, requires new solutions for bearing systems. Foil bearings are one of the fastest-growing high-speed bearing technologies. This article presents the results of experimental studies on foil bearings conducted on a test rig reflecting the operating conditions [...] Read more.

Developing high-speed rotating machines, such as microturbines, requires new solutions for bearing systems. Foil bearings are one of the fastest-growing high-speed bearing technologies. This article presents the results of experimental studies on foil bearings conducted on a test rig reflecting the operating conditions of the target machine. The tested bearings were therefore placed in a chamber filled with a low-boiling medium used as a working fluid in vapour microturbines. The experiments were carried out for several test cycles following a repeatable procedure. To carry out the tests under specific environmental conditions, a measurement cycle according to the developed test procedure and a temperature stabilization system for long-term measurements were proposed. The research involved determining the thermal characteristics of four foil bearing variants and assessing the impact of operating conditions on their wear. Additional research has shown that the operating characteristics are highly dependent not only on the materials and geometry of the bearing but also on the surface roughness of the mating parts. This study is part of ongoing work to select appropriate designs and material packages for foil bearings operating under conditions involving lubricating film formation and heat dissipation. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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20 pages, 5905 KiB

Open AccessArticle

A Numerical Analysis of the Nonlinear Dynamics of Shimmed Conical Gas Foil Bearings

by Marian Sarrazin and Robert Liebich

Appl. Sci. 2023, 13(10), 5859; https://doi.org/10.3390/app13105859 - 09 May 2023

Cited by 2 | Viewed by 998

Abstract

Conical gas foil bearings (CGFBs) have the potential to halve the number of necessary bearings in a conventional rotor system supported by gas foil bearings. Transient simulations of gas foil journal bearings and gas foil thrust bearings have proven their necessity to accurately [...] Read more.

Conical gas foil bearings (CGFBs) have the potential to halve the number of necessary bearings in a conventional rotor system supported by gas foil bearings. Transient simulations of gas foil journal bearings and gas foil thrust bearings have proven their necessity to accurately predict the safe operating range of such bearings. This work presents the first transient model able to simulate the three-dimensional dynamics of CGFBs. The static behaviour of a single CGFB with a uniform bearing clearance is compared to a CGFB modified by thin metal shims and the resulting advantages of shimmed CGFBs are discussed. An investigation of the linear stability behaviour shows that the axial load of the bearing determines the stability of the equilibrium position. Furthermore, three transient simulations demonstrate the capability of the presented model to describe the nonlinear dynamics of a shimmed CGFB such as the occurrence of stable limit cycles and self-excited sub- and super-synchronous vibrations with and without a rotor unbalance. Additionally, waterfall diagrams are used to investigate the frequency response for different rotational speeds. The novel findings of this work are the importance of a non-uniform bearing clearance for the functionality of a CGFB and the identification of the axial force as a critical factor in maintaining bearing stability. These findings are specific to CGFBs and have not been discussed or mentioned in previous works. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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14 pages, 4481 KiB

Open AccessArticle

Investigation on Pivot Rolling Motion Effect on the Behavior of Rocker Back Tilting Pad Journal Bearings

by Alberto Betti, Paola Forte, Daniele Panara and Enrico Ciulli

Appl. Sci. 2023, 13(9), 5563; https://doi.org/10.3390/app13095563 - 30 Apr 2023

Cited by 1 | Viewed by 1045

Abstract

The rolling motion of the pads with rocker back (RB) and ball and socket pivots is normally neglected in common software programs for the study of the rotor dynamic behavior of tilting pad journal bearings (TPJB). In other words, the theoretical contact point [...] Read more.

The rolling motion of the pads with rocker back (RB) and ball and socket pivots is normally neglected in common software programs for the study of the rotor dynamic behavior of tilting pad journal bearings (TPJB). In other words, the theoretical contact point of the pivot is considered fixed. The aim of this work is to provide a novel way to implement in commercial software the effect of the variation of the circumferential coordinate of the theoretical contact point due to the pad rolling motion in RB TPJB. This is done by introducing an equivalent pivot rotational stiffness evaluated with an analytically derived formula, validated through finite element analysis. Such a stiffness is a function of the pad load and the radii of the contact pair, increasing with the load, the radii, and the degree of conformity of the contact. The static and dynamic characteristics of a five pad RB TPJB are then evaluated with a commercial software with and without the rotational stiffness contribution for two different pivot geometries. Non-negligible differences were found, particularly regarding the cross-coupled dynamic coefficients that show the higher sensitivity to the rotational stiffness. The inclusion of a pivot rotational stiffness among the data of commercial software for simulation of RB TPJB could contribute to fill the gap between numerical and experimental results. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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15 pages, 4874 KiB

Open AccessArticle

The Influence of Bearing Clearance on the Load Capacity of Gas Polymer Bearings

by Gregor Schilling and Robert Liebich

Appl. Sci. 2023, 13(7), 4555; https://doi.org/10.3390/app13074555 - 03 Apr 2023

Cited by 2 | Viewed by 1578

Abstract

In this paper, the influence of a nominal bearing clearance on the lift-off behaviour and the load-carrying capacity of gas polymer bearings (GPBs) is investigated. For this purpose, an experimental study with five different bearing gap configurations and a range of static loads [...] Read more.

In this paper, the influence of a nominal bearing clearance on the lift-off behaviour and the load-carrying capacity of gas polymer bearings (GPBs) is investigated. For this purpose, an experimental study with five different bearing gap configurations and a range of static loads is carried out. Furthermore, the test rig for the clearance and friction torque measurements is illustrated and discussed from a practical point of view. The experimental gap measurement results of all the bearing configurations and the method used are explained and discussed. Finally, the friction torque during the lift-off and run-up phases is measured for a range of static loads. A method that uses the time derivative of the measured friction torque during the run-up tests as a criterion for the lift-off detection is explained and applied to the measured data. The results of this study indicate that there are large differences between the most studied bump-type and gas polymer bearings in terms of the dependence of the load-carrying capacity on the bearing gap. Furthermore, the recorded effects are described, and possible explanations are given. Finally, the differences in characteristics from those of bump-type bearings are described and their importance for the design process of rotors supported in GPBs is explained. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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21 pages, 32974 KiB

Open AccessArticle

The Numerical Identification of Basins of Attraction for the Vibration Response of the Rigid Rotor with Squeeze Film Dampers

by Michal Molčan, Petr Ferfecki and Jaroslav Zapoměl

Appl. Sci. 2023, 13(5), 2864; https://doi.org/10.3390/app13052864 - 23 Feb 2023

Cited by 1 | Viewed by 1005

Abstract

The article deals with the computational study of the rigid rotor coupled with squeeze film dampers. Various techniques such as the method of computation of the synchronous response with a circular centred orbit, the harmonic balance method, and the direct time integration method [...] Read more.

The article deals with the computational study of the rigid rotor coupled with squeeze film dampers. Various techniques such as the method of computation of the synchronous response with a circular centred orbit, the harmonic balance method, and the direct time integration method are used to analyse the nonlinear behaviour of the rotor system. The results indicate that the rotor system can exhibit both a synchronous circular response with a large orbit radius and a nonsynchronous response with a quasiperiodic character. However, both responses are undesirable in rotating machinery and should be avoided. The new results are presented to provide insight into the impact of initial conditions on the vibration response via basins of attraction. The simulations show that: (i) the basins of attraction are more sensitive to the choice of the initial velocities than displacements, (ii) the basins of attraction are noticeably dependent on the rotor speed in the region of a nonsynchronous response, and (iii) the border between the basins of attraction can be smooth or without a clear structure. The research brings clear conditions defined by parameters such as the dimensionless SFD constant, unbalance, and rotational speed for the suppression of undesirable nonlinear phenomena. The results suggest that the damper can effectively improve the vibration response of high-speed rotating machinery, but its design must be chosen appropriately. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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16 pages, 18174 KiB

Open AccessArticle

The Influence of Rotor Adjustment Parameters on the Dynamic Balance of a Scale-Model Rigid Variable Speed Rotor

by Liang Li, Ming Chen, Fang Wang and Anan Xu

Appl. Sci. 2022, 12(23), 12125; https://doi.org/10.3390/app122312125 - 27 Nov 2022

Cited by 4 | Viewed by 1330

Abstract

In this paper, the dynamic balance of a rigid variable speed rotor is tested and analyzed. The vibration acceleration is measured by vibration analyzer instrumentations. The rotor adjustment parameters of counterweight, pitch, and trailing-edge flap are considered. The amplitude and phase of the [...] Read more.

In this paper, the dynamic balance of a rigid variable speed rotor is tested and analyzed. The vibration acceleration is measured by vibration analyzer instrumentations. The rotor adjustment parameters of counterweight, pitch, and trailing-edge flap are considered. The amplitude and phase of the 1 Ω vibration acceleration are analyzed through an all-phase fast Fourier transform. The experiments are conducted using two rigid rotors with the same geometry. The accelerations of the fuselage in the

x, y

, and

z

directions are measured. Through a waterfall diagram of the auto-power spectrum, it is found that the imbalance of counterweight, pitch, and trailing-edge flap causes an obvious increase in 1 Ω and 2 Ω acceleration. The hub counterweight mainly causes the lateral and longitudinal vibration in the disc plane, and the aerodynamic factors such as pitch and trailing-edge flap mainly affect the vertical vibration. In order to achieve dynamic balance for variable speed rotors, the counterweight adjustment should be given the highest priority for the vibration in the disc plane, and the pitch and trailing-edge flap adjustment should be given the highest priority for the vertical vibration. The results obtained from this experiment may be helpful toward reasonable designs of variable speed rotor helicopters. Full article

(This article belongs to the Special Issue Rotor Dynamics: Theoretical Analysis, Computer and Experimental Modelling, Measurements)

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