{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:54:11Z","timestamp":1787028851395,"version":"build-2736575974"},"reference-count":27,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T00:00:00Z","timestamp":1730937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In the literature on rotating machinery, many articles discuss the analysis of various rotor and bearing defects, including both sliding and rolling bearings. Defects in the rotor supporting system are investigated much less frequently. In rotor-bearing-supporting structure systems, where there are couplings between the individual sub-systems, damage to the supporting structure can significantly impact the dynamic properties of the entire machine. The authors of this article have, therefore, focused on analysing the defects that can occur in the supporting system of the rotor and bearings. This article presents the results of a numerical analysis of two common defects in the supporting structure: cracks in the bolted joints attaching the machine body to the foundation and a decrease in foundation stiffness. The research object was a test rig that accurately reproduced the dynamic phenomena occurring in rotating machinery, such as vapour and gas turbines. In the numerical model of the rotating machine, a three-dimensional linear model of the supporting structure was combined with a beam model of the rotor line via a nonlinear fluid film-bearing model. The developed model allowed for the analysis of two different failures in the supporting system over a wide range of rotational speeds. The calculations showed that damage to the supporting structure can significantly impact the dynamic characteristics of the entire rotating machine.<\/jats:p>","DOI":"10.3390\/ma17225444","type":"journal-article","created":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T12:12:13Z","timestamp":1730981533000},"page":"5444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Numerical Investigation of the Impact of Cracks and Stiffness Loss in the Supporting System for the Dynamic Characteristics of a Rotating Machine"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6848-5732","authenticated-orcid":false,"given":"Grzegorz","family":"\u017bywica","sequence":"first","affiliation":[{"name":"Institute of Fluid-Flow Machinery, Polish Academy of Sciences, 80-231 Gda\u0144sk, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan","family":"Kici\u0144ski","sequence":"additional","affiliation":[{"name":"Institute of Fluid-Flow Machinery, Polish Academy of Sciences, 80-231 Gda\u0144sk, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2501","DOI":"10.1007\/s11071-023-09164-5","article-title":"Dynamic modeling and vibration analysis of double row cylindrical roller bearings with irregular-shaped defects","volume":"112","author":"Li","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_2","unstructured":"Kici\u0144ski, J. (2006). Rotor Dynamics, IFFM PAS Publishers."},{"key":"ref_3","first-page":"111","article-title":"Parametric Approach to Rotating Machinery Diagnostics Under Transient Operating Condition","volume":"34","author":"Czop","year":"2005","journal-title":"Diagnostyka"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ymssp.2004.04.001","article-title":"An Investigation on the Influence of the Supporting Structure on the Dynamic of the Rotor System","volume":"19","author":"Cavalca","year":"2005","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","unstructured":"Feng, N.S., and Hahn, E.J. (2006, January 18\u201320). Difficulties in Predicting Vibrations in Turbomachinery with Hydrodynamic Bearings. Proceedings of the ISMA International Conference on Noise and Vibration Engineering, Leuven (Belgium), Heverlee, Belgium."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"111293","DOI":"10.1016\/j.ymssp.2024.111293","article-title":"Automated Modal Parameter Estimation for Coupled Rotor\u2013Foundation Systems Using Seal Forces as Excitation Source","volume":"212","author":"Paulsen","year":"2024","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1006\/jsvi.2000.3510","article-title":"An Improved Rotor Model with Equivalent Dynamic Effects of the Support Structure","volume":"244","author":"Choi","year":"2001","journal-title":"J. Sound Vib."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Moroz, L., Romanenko, L., Kochurov, R., and Kashtanov, E. (2017, January 26\u201330). Prediction of Structural Supports Influence on Rotating Machinery Dynamics. Proceedings of the ASME Turbo Expo 2017 Conference, Charlotte, NC, USA.","DOI":"10.1115\/GT2017-63035"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"118612","DOI":"10.1016\/j.jsv.2024.118612","article-title":"Vibration analysis of the propulsion shaft system considering dynamic misalignment in the outer ring","volume":"589","author":"Li","year":"2024","journal-title":"J. Sound Vib."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"343","DOI":"10.3390\/wind3030020","article-title":"Towards an Integrated Design of Direct-Drive Wind Turbine Electrical Generator Supporting Structures","volume":"3","author":"Touw","year":"2023","journal-title":"Wind"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"116577","DOI":"10.1016\/j.oceaneng.2023.116577","article-title":"Numerical Modelling of a 1.5 MW Ttidal Turbine in Realistic Coupled Wave\u2013Current Sea States for the Assessment of Turbine Hub-Depth Impacts on Mechanical Loads","volume":"292","author":"Guy","year":"2024","journal-title":"Ocean Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"103506","DOI":"10.1016\/j.marstruc.2023.103506","article-title":"A Low-Fidelity Model for the Dynamic Analysis of Full-Lattice Wind Support Structures","volume":"92","author":"Vergassola","year":"2023","journal-title":"Mar. Struct."},{"key":"ref_13","first-page":"2024301","article-title":"Assessment of vibration isolation generated by the inertial forces of an aircraft combustion engine on a test bench","volume":"25","author":"Misztal","year":"2024","journal-title":"Diagnostyka"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4811","DOI":"10.1080\/15397734.2023.2237689","article-title":"Numerical and experimental analysis of vibration characteristics of spindle system under bearing assembly errors","volume":"52","author":"Wang","year":"2024","journal-title":"Mech. Based Des. Struct. Mach."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"104758","DOI":"10.1016\/j.ijnonlinmec.2024.104758","article-title":"An analytical method of dynamic stiffness of combined supporting structure and its effects on rotor systems: Simulation and experiment","volume":"163","author":"Luo","year":"2024","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0168-874X(02)00064-1","article-title":"Application of the Impedance Coupling Method and The Equivalent Rotor Model in Rotordynamics","volume":"39","author":"Choi","year":"2002","journal-title":"Finite Elem. Anal. Des."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"117683","DOI":"10.1016\/j.jsv.2023.117683","article-title":"Model and Experimental Analysis of a Rotor Rig Dynamics with Time-Varying Characteristics","volume":"557","author":"Wu","year":"2023","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"110921","DOI":"10.1016\/j.ymssp.2023.110921","article-title":"On the Experimental Dynamic Substructuring of Rotating Machine Foundations","volume":"206","author":"Martini","year":"2024","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"118596","DOI":"10.1016\/j.jsv.2024.118596","article-title":"Mode selection for component mode synthesis with guaranteed assembly accuracy","volume":"589","author":"Janssen","year":"2024","journal-title":"J. Sound Vib."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109920","DOI":"10.1016\/j.triboint.2024.109920","article-title":"Self-excited vibration analysis of spline rotor systems considering parallel and angular misalignments","volume":"198","author":"Huang","year":"2024","journal-title":"Tribol. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"20703","DOI":"10.1007\/s11071-024-10148-2","article-title":"Coupling Nonlinear Dynamics and Multi-Objective Optimization for Periodic Response and Reduced Power Loss in Turbochargers with Floating Ring Bearings","volume":"112","author":"Polyzos","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_22","unstructured":"(2015). Abaqus\/CAE User\u2019s Guide, Dassault Systems, Abaqus."},{"key":"ref_23","first-page":"71","article-title":"Identification of Model Support Structure of Rotor Machine","volume":"40","year":"2006","journal-title":"Diagnostyka"},{"key":"ref_24","unstructured":"\u017bywica, G. (2007, January 4\u20137). Simulation Investigation of the Effect of a Supporting Structure Defect on Dynamic State of the Rotor Supported on Slide Bearings. Proceedings of the ASME IDET\/CIE 2007 Conference, Las Vegas, NY, USA."},{"key":"ref_25","first-page":"99","article-title":"Modelling of Dynamics Reactions in Systems of Rotor-Bearings-Supporting Structure Type","volume":"31","year":"2007","journal-title":"Mach. Dyn. Probl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3195","DOI":"10.3390\/ma8063195","article-title":"Failure Mode Analysis of Aluminium Alloy 2024-T3 in Double-Lap Bolted Joints with Single and Double Fasteners: A Numerical and Experimental Study","volume":"8","author":"Fallahnezhad","year":"2015","journal-title":"Materials"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.compstruct.2017.12.048","article-title":"Numerical Failure Assessment of Multi-Bolt FRP Composite Joints with Varying Sizes and Preloads of Bolts","volume":"187","author":"Mandal","year":"2018","journal-title":"Compos. Struct."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/22\/5444\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:28:18Z","timestamp":1760113698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/22\/5444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,7]]},"references-count":27,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["ma17225444"],"URL":"https:\/\/doi.org\/10.3390\/ma17225444","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,7]]}}}