Numerical Analysis and Validation of Eccentricity-Induced Unbalancing Mass in Rotational Systems: Rail Wheel

Numerical Analysis and Validation of Eccentricity-Induced Unbalancing Mass in Rotational Systems: Rail Wheel | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Perspective Numerical Analysis and Validation of Eccentricity-Induced Unbalancing Mass in Rotational Systems: Rail Wheel Jeetender Singh Kushawaha This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5909644/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study explores an efficient method for analyzing and mitigating unbalance in railway wheel sets using MATLAB and Computer Aided Design based simulations. The novelty lies in the combined use of simplified mathematical model using the above two approaches. Sensitivity analysis confirms the model's accuracy and industrial applicability. The work demonstrates that unbalance can be reduced significantly by marking the light and heavy spots on the wheel, aiding maintenance and enhancing operational efficiency in the workshop environment. The study underscores the practicality of computational tools in resolving critical industrial challenges. The study investigates and proposes to rail wheel manufacturer’s that the provision for process control for utilizing the light and heavy spot on the rail wheel shall be adapted as being done for road tires, to aid in the better assembled railway wheel set. Dynamic balancing Balancing mass Rail wheel Eccentricity Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction 1.1 Background Unbalanced railway wheels can lead to increased vibration, wear, and noise, ultimately compromising passenger comfort and system safety while escalating maintenance costs. The dynamic behavior of wheels during operation is significantly influenced by mass distribution, and geometrical eccentricity is a prominent source of unbalance in the railway wheel sets. The UIC code 510-2 OR, 4th edition, May 2024, specifies the axial run-out on the inside surface of each wheel operating below the maximum speed of 200 kmph, to be less then 0.5 mm. Addressing these issues requires an effective methodology to identify and mitigate unbalance [ 1 ]-[ 4 ]. This paper provides a simplified analytical model and validates it through MATLAB simulations and CAD-based results. The proposed approach emphasizes the practical implementation of light and heavy spot markings to enhance balance. Rotational systems are integral to numerous industrial applications, including automotive, aerospace, and manufacturing sectors. Imbalances in such systems can lead to detrimental effects, including increased wear, vibration, and reduced operational efficiency. This study investigates the influence of axis offsets (eccentricity) on un-balancing mass using Eq. ( 1 ), and evaluates, improves and validates it through computational techniques, using MATLAB and CAD on the residual imbalance i.e. un-balancing mass, introduced in the railway wheel Fig. 1 (a). $$\:Un-Balancing\:Weight=0.8\times\:\pi\:\times\:\rho\:\times\:eccentricity\:\times\:({R}_{o}\times\:{W}_{o}-{R}_{i}\times\:{W}_{i})$$ 1 Where \(\:\rho\:\) , \(\:ecentricity\) , \(\:{R}_{o}\) , \(\:{R}_{i}\) , \(\:{W}_{o}\) and \(\:{W}_{i}\) , are the density of wheel material, amount of eccentricity of finished wheel from its initial axis as in semi-finished wheel, inner radius at wheel rim, outer radius at hub, thickness of wheel rim and wheel hub, respectively. The approximations provided by this equation could help to alleviate the requirements of counter balancing masses and reduce it by 95.9%, in the study conducted the author. The simplified version of rail wheel, with same dimensions used in this work and generated using NX software, is presented in Fig. 1(b), the width of web is considered to be 14 mm. This Eq. ( 1 ), was empirically developed and used to approximate the amount of un-balance introduced due to eccentricity in the railway wheel. 1.2. Visualization of eccentricity Visualization of eccentricity in the wheel is easily visualized by Fig. 2 , the eccentricity leaves two arc shaped volumes in the wheel rim and hub in opposite directions. The three-D visualization for un-balancing mass is presented in Fig. 2 , the difference of the two volumes contributes to the un-balancing mass. 1.3. Causes of un-balance in a rail wheel The primary causes of unbalance in a brand-new wheel include manufacturing defects, design flaws, material inconsistencies, and assembly inaccuracies. Among these, manufacturing defects play a significant role due to variations in machining operations and equipment settings. Material inconsistencies are often negligible, while design flaws, such as holes or slots, are easily identified and mitigated. However, manufacturing and assembly inaccuracies due to machine limitations are harder to detect, leading to compromised production quality. In the absence of precise problem identification, production continues with potential inefficiencies, which may result in further operational challenges down the line. 2. Methods The methodology for this work is designed to simulate the machining of a semi-finished rail wheel into a finished wheel, analyze the resulting un-balance due to varying eccentricity, and evaluate the effects using computational techniques. The following steps outline the comprehensive approach: 2.1. Wheel simplified models The simplified 3-D model of semi finished wheel was prepared using NX software [5] & [6]. This approach was adapted for easy modeling and processing as the intricate profile shape does not contribute to the un-balance, this is the assumption and justified, as these are on the outer surfaces. The semi-finished model featured a smaller inner diameter at the hub and a larger outer diameter at the rim. The finished wheel models were cut out/generated from the semi-finished model, using the eccentricity as 0, 0.025, 0.05, 0.75, 0.1, 0.125, 0.150, 0.175, 0.2, 0.225 & 0.25 mm. The variation of mass is contributed by difference of these volumes, it can be easily visualized by, and is depicted in, figure 2. 2.1.1. Effect of eccentricity on mass The finished wheel models, due to the geometry of the semi-finished wheel, had the same mass but because of the eccentricity the two halves had variation of mass. This was revealed on checking the mass property of the body, using the software’s inbuilt function “ measure” after parting the wheel models into two, as one half is presented in figure 3 (a). Figure, 3 (a) presents wheel half of the finished wheel with eccentricity of 0.062 mm, 3(b) presents the finished wheel with 0.062 mm eccentricity and 3(c) presents the perfect finished wheel. Here, it is worth to note that the center of mass for the perfect finished wheel and the one with the eccentricity differ by 0.1661 mm in the z-axis, where as the eccentricity was just 0.062 mm; this is due to the geometry of the wheel hub and rim, these are of different dimensions. The variation of mass of two halves, with eccentricity is presented in the figure 4, plotted using MATLAB programming [7]-[10]. The figure represents that the mass of one side increases and on the other side decreases. 2.1.2. Un-balance comparative analysis The difference of mass of two halves of the parted wheel halves gives the amount of un-balance contributed, due to eccentricity, in the simple averaging terms, whereas for very precise calculations the distance from the center of theses unbalance contributing areas shall also be considered. But for simplicity we will proceed with this concept. The un-balance values were evaluated using the empirical formulae of equation (1) for, eccentricity value as 0, 0.025, 0.05, 0.75, 0.1, 0.125, 0.150, 0.175, 0.2, 0.225 & 0.25 mm. Here, the values of , , , and , were considered to be as per the wheel model, i.e. 7.872e -6 kg/mm 3 , 400, 122.5, 130 & 190 mm, respectively. The obtained values are plotted in figure 5(a), it is worth noting that the values obtained by empirical formula provided good approximation to CAD model values. The coefficient 0.8 in the empirical formulae can be considered to be a variable constant depending upon the hub and rim dimensions. On increasing this variable constant to 1.1, the approximation results were perfectly aligned to the CAD model results, as presented by figure 5(b). 3. Results and Discussion 3.1. The results in reference to figure 4, can be interpreted that with increase of eccentricity the mass of one side increases is equal amount and it decreases on other side of the center line. 3.2. The results in reference to figure 5, present that the empirical equation (1) provided good approximations to aid in the resolution and decision making regarding the quantification of the eccentricity. 3.3. The empirical equation (1) can be adjusted to various designs of rotating machinery and wheels with different dimensions of rail wheels to conveniently address balancing problems, offering a clear path for future expansion of this study. 3.4. Marking the light and heavy spots on wheels helps to reduces unbalance effectively; while most rail wheel manufacturers mark the heavy spot-commonly using paint-a few manufacturers omit this step. These markings can be used by technical and supervisory staff to ensure the correctness of assembly as per the approved practice for assembly for static, dynamic or coupled balance of the wheel set. Wheel set manufacturers can incorporate this methodology into production routines, enhancing safety and operational efficiency. Additionally, this approach can extend to other rotational systems such as turbines and automotive wheels. 4. Conclusions This study presents a MATLAB and CAD based analytical framework for mitigating unbalance in railway wheels. Results demonstrate the model's applicability in industrial settings, with practical recommendations for provisioning of marking light and heavy spots on the rail wheels to optimize the wheel and wheel set balance. Future work may explore adapting the methodology for other rotating systems. Abbreviations CAD Computer aided design Declarations Availability of data and materials The models and codes used in the current study are available from the corresponding author on reasonable request. Competing interests The author declares that there is no potential conflict of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) did not receive any support from any organization. Authors’ contributions JSK conceptualized, analyzed, drafted, prepared, read, edited and approves the manuscript. Acknowledgements The author, undertaking this work as a hobby project, expresses sincere gratitude to all resource providers and tacit permission providers to use the various tools and software’s through internet. Special thanks are extended to MathWorks® for supporting the programming efforts and providing access to MATLAB® software, which greatly facilitated the solution process. The author is also deeply appreciative of the design office staff for providing a supportive and accommodating environment, contributing to the successful completion of this study. The author is thankful to the internet community for ensuring the availability of various software’s, the study and reference materials. Lastly, heartfelt thanks go to ChatGPT for its prompt and invaluable assistance in enhancing & completing the work. Authors' information https://orcid.org/0009-0005-2630-6790 Jeetender Singh Kushawaha - Academia.edu References Wang Y, Kang H, et al. (2011) Influence of dynamic unbalance of wheelsets on the dynamic performance of high-speed cars , Journal of Modern Transportation, Vol. 19(3), pp. 147–153. New T, Pimsarn M. (2021) Railway axle and wheel assembly press-fitting force characteristics and holding torque capacity , Applied Sciences, Vol. 11, Article 8862. Taneja S. (2020) Effect of tyre unbalance on performance of vehicle , International Journal of Mechanical Engineering and Technology, Vol. 11(12), pp. 12–18. Pintao B, Mosleh A, Vale C, Montenegro P, Costa P. (2022) Development and validation of a weigh-in-motion methodology for railway tracks , Sensors, Vol. 22, Article 19769. Section 6 – List of Drawings, https://www.scribd.com/document/664185101/Drawings-Section-6. Accessed 10 December 2023. NX 12 for Engineering Design , https://me5763.github.io/lab/assets/books/NX-12-for-Engineering-Design.pdf. Accessed 01 January 2024. Hunt B, Lipsman R, et al. (2001) A Guide to MATLAB for Beginners and Experienced Users , Cambridge University Press, New York. Otto S.R., Denier J.P. (2005) An Introduction to Programming and Numerical Methods in MATLAB , Springer, USA.Chapman S J (2008) MATLAB: Programming for Engineers, Fourth Edition, Thomson, Canada. Chapman S.J. (2008) MATLAB: Programming for Engineers , Fourth Edition, Thomson, Canada. MATLAB: The Language of Technical Computing (2005) MATLAB Programming MathWorks Inc. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5909644","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Perspective","associatedPublications":[],"authors":[{"id":449878831,"identity":"0af9b4ba-3b3b-4f41-9533-00fe3719932b","order_by":0,"name":"Jeetender Singh Kushawaha","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIiWNgGAWjYBACCQaGhANAmrEBSAAZB+QYGHiI0HIASYsxMVrASsFaQMzEBkJaJBsYHh7+UHFHdnv78YeHC37dSd9w/OzBBx8Y7OR0G7BrkQY77Mwz4zlncgwOz+x7lrvhTF6y4QyGZGOzA9i1yIG0HGw7nDiDIYfhMG/P4dwNB3LMpHmALtyGV8s/oBb+5w9AWtINzr/BrwXssIMNQC0SCQaHeX4cTjC4QcAWyWagljPHDhvPkHhjcJi34bDhzBtvjA1nGOD2i8TxnuQPFTWHZWfwpz/+zPPnsDzf+RzDBx8q7ORwaWFg5klAcBjbGBgUwCoNcCgHA3Zkw/4wMMg34FM9CkbBKBgFIxEAACS6b6uR41L/AAAAAElFTkSuQmCC","orcid":"","institution":"Modern Coach Factory","correspondingAuthor":true,"prefix":"","firstName":"Jeetender","middleName":"Singh","lastName":"Kushawaha","suffix":""}],"badges":[],"createdAt":"2025-01-27 05:54:00","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5909644/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5909644/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81723343,"identity":"fb70772e-15c3-4813-878c-5d5e9f975ac6","added_by":"auto","created_at":"2025-04-30 16:43:13","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":105428,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Railway wheel (Image: \u003cem\u003eCourtesy internet\u003c/em\u003e), (b) Simplified wheel\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5909644/v1/be64eeac3dc86383825276bd.png"},{"id":81722402,"identity":"0f04b173-2c22-4e08-880a-ed4ba7e83c60","added_by":"auto","created_at":"2025-04-30 16:35:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":49364,"visible":true,"origin":"","legend":"\u003cp\u003eVisualization for un-balancing mass\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5909644/v1/98fdf456ea32255a5c8304ba.png"},{"id":81723345,"identity":"745c775c-4f6d-4820-9560-765e6d72d0d4","added_by":"auto","created_at":"2025-04-30 16:43:13","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":361299,"visible":true,"origin":"","legend":"\u003cp\u003eMeasure of mass property of wheel\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5909644/v1/e1f09432edee0a67faff9962.png"},{"id":81722405,"identity":"443d4248-377b-4bd6-b10c-a3acf91de81c","added_by":"auto","created_at":"2025-04-30 16:35:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":45939,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of mass of two halves of the wheel\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5909644/v1/bfb0e3d752fbd66a1ec63b92.png"},{"id":81724522,"identity":"a843b5a6-9d1a-4718-9d64-0c44a91ebce7","added_by":"auto","created_at":"2025-04-30 16:59:13","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":92973,"visible":true,"origin":"","legend":"\u003cp\u003eUn-balance with eccentricity in the wheel\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5909644/v1/a70550b15c05dd6add93745f.png"},{"id":83569116,"identity":"81ee202a-96a3-4cf7-ae45-59708d6c8ea5","added_by":"auto","created_at":"2025-05-28 16:01:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":961371,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5909644/v1/1822ae8d-6897-4f42-bbe7-f29d7d20e6ed.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical Analysis and Validation of Eccentricity-Induced Unbalancing Mass in Rotational Systems: Rail Wheel","fulltext":[{"header":"1. Introduction","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\n \u003ch2\u003e1.1 Background\u003c/h2\u003e\n \u003cp\u003eUnbalanced railway wheels can lead to increased vibration, wear, and noise, ultimately compromising passenger comfort and system safety while escalating maintenance costs. The dynamic behavior of wheels during operation is significantly influenced by mass distribution, and geometrical eccentricity is a prominent source of unbalance in the railway wheel sets. The UIC code 510-2 OR, 4th edition, May 2024, specifies the axial run-out on the inside surface of each wheel operating below the maximum speed of 200 kmph, to be less then 0.5 mm. Addressing these issues requires an effective methodology to identify and mitigate unbalance [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]-[\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eThis paper provides a simplified analytical model and validates it through MATLAB simulations and CAD-based results. The proposed approach emphasizes the practical implementation of light and heavy spot markings to enhance balance.\u003c/p\u003e\n \u003cp\u003eRotational systems are integral to numerous industrial applications, including automotive, aerospace, and manufacturing sectors. Imbalances in such systems can lead to detrimental effects, including increased wear, vibration, and reduced operational efficiency. This study investigates the influence of axis offsets (eccentricity) on un-balancing mass using Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), and evaluates, improves and validates it through computational techniques, using MATLAB and CAD on the residual imbalance i.e. un-balancing mass, introduced in the railway wheel Fig.\u0026nbsp;1 (a).\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$$\\:Un-Balancing\\:Weight=0.8\\times\\:\\pi\\:\\times\\:\\rho\\:\\times\\:eccentricity\\:\\times\\:({R}_{o}\\times\\:{W}_{o}-{R}_{i}\\times\\:{W}_{i})$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ecentricity\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{o}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{o}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{i}\\)\u003c/span\u003e\u003c/span\u003e, are the density of wheel material, amount of \u003cem\u003eeccentricity\u003c/em\u003e of finished wheel from its initial axis as in semi-finished wheel, inner radius at wheel rim, outer radius at hub, thickness of wheel rim and wheel hub, respectively. The approximations provided by this equation could help to alleviate the requirements of counter balancing masses and reduce it by 95.9%, in the study conducted the author.\u003c/p\u003e\n \u003cp\u003eThe simplified version of rail wheel, with same dimensions used in this work and generated using NX software, is presented in Fig.\u0026nbsp;1(b), the width of web is considered to be 14 mm. This Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), was empirically developed and used to approximate the amount of un-balance introduced due to eccentricity in the railway wheel.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e1.2. Visualization of eccentricity\u003c/h2\u003e\n \u003cp\u003eVisualization of \u003cem\u003eeccentricity\u003c/em\u003e in the wheel is easily visualized by Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the \u003cem\u003eeccentricity\u003c/em\u003e leaves two arc shaped volumes in the wheel rim and hub in opposite directions. The three-D visualization for un-balancing mass is presented in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the difference of the two volumes contributes to the un-balancing mass.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e1.3. Causes of un-balance in a rail wheel\u003c/h2\u003e\n \u003cp\u003eThe primary causes of unbalance in a brand-new wheel include manufacturing defects, design flaws, material inconsistencies, and assembly inaccuracies. Among these, manufacturing defects play a significant role due to variations in machining operations and equipment settings. Material inconsistencies are often negligible, while design flaws, such as holes or slots, are easily identified and mitigated. However, manufacturing and assembly inaccuracies due to machine limitations are harder to detect, leading to compromised production quality. In the absence of precise problem identification, production continues with potential inefficiencies, which may result in further operational challenges down the line.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"2. Methods","content":"\u003cp\u003eThe methodology for this work is designed to simulate the machining of a semi-finished rail wheel into a finished wheel, analyze the resulting un-balance due to varying eccentricity, and evaluate the effects using computational techniques. The following steps outline the comprehensive approach:\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e2.1. Wheel simplified models\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe simplified 3-D model of semi finished wheel was prepared using NX software [5] \u0026amp; [6]. This approach was adapted for easy modeling and processing as the intricate profile shape does not contribute to the un-balance, this is the assumption and justified, as these are on the outer surfaces.\u003c/p\u003e\n\u003cp\u003eThe semi-finished model featured a smaller inner diameter at the hub and a larger outer diameter at the rim. The finished wheel models were cut out/generated from the semi-finished model, using the eccentricity as 0, 0.025, 0.05, 0.75, 0.1, 0.125, 0.150, 0.175, 0.2, 0.225 \u0026amp; 0.25 mm. The variation of mass is contributed by difference of these volumes, it can be easily visualized by, and is depicted in, figure 2.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e2.1.1. Effect of eccentricity on mass\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe finished wheel models, due to the geometry of the semi-finished wheel, had the same mass but because of the eccentricity the two halves had variation of mass. This was revealed on checking the mass property of the body, using the software\u0026rsquo;s inbuilt function \u0026ldquo;\u003cem\u003emeasure\u0026rdquo;\u003c/em\u003e after parting the wheel models into two, as one half is presented in figure 3 (a). Figure, 3 (a) presents wheel half of the finished wheel with eccentricity of 0.062 mm, 3(b) presents the finished wheel with 0.062 mm eccentricity and 3(c) presents the perfect finished wheel. Here, it is worth to note that the center of mass for the perfect finished wheel and the one with the eccentricity differ by 0.1661 mm in the z-axis, where as the eccentricity was just 0.062 mm; this is due to the geometry of the wheel hub and rim, these are of different dimensions.\u003c/p\u003e\n\u003cp\u003eThe variation of mass of two halves, with eccentricity is presented in the figure 4, plotted using MATLAB programming [7]-[10]. The figure represents that the mass of one side increases and on the other side decreases.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e2.1.2. Un-balance comparative analysis\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe difference of mass of two halves of the parted wheel halves gives the amount of un-balance contributed, due to eccentricity, in the simple averaging terms, whereas for very precise calculations the distance from the center of theses unbalance contributing areas shall also be considered. But for simplicity we will proceed with this concept. The un-balance values were evaluated using the empirical formulae of equation (1) for, eccentricity value as 0, 0.025, 0.05, 0.75, 0.1, 0.125, 0.150, 0.175, 0.2, 0.225 \u0026amp; 0.25 mm. Here, the values of \u003cimg width=\"10\" height=\"37\" src=\"data:image/png;base64,R0lGODlhDwA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAACwAOABEAhAAAAAAAAAAAOgAAZgA6kABmtjoAADo6ADpmtjqQ22YAAGY6AGa2/5A6AJDb/7ZmALbb/7b//9uQOtu2Ztv///+2Zv/bkP//tv//2wECAwECAwECAwECAwECAwECAwECAwVeICCK2HQEgYBQo3gtAQFhTcyS9RCJEsqMvUABiBoCLgofUSiqoHSjR5GHItxoqAQAyxRZDCnHMRn4UbvfME4NcBYpGKlALJKiwKnViKtttZBKfiNuc4JLVoZ1U4kAIQA7\" alt=\"image\"\u003e, \u003cimg width=\"19\" height=\"37\" src=\"data:image/png;base64,R0lGODlhHAA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABwAbABUAhAAAAAAAAAAAOgAAZgA6OgA6ZgA6kABmtjoAADo6OjpmkDpmtjqQ22YAAGaQ22a222a2/5A6AJA6OpDb/7ZmALaQZrb//9uQOtuQZtu2Ztv///+2Zv/bkP/btv//tv//2wWjICBySGCeQfJoYuu+InZCwEeZBgvvwGYKk1EpQOPBLqaBReRpmBhG2C1waDVNxSjTGYCKfAGltkXCij6R57gFBgI6aYFj3ZqiAgsdHW2qZpJLdABXRDVpVII9P0EAUzmCSGGBkWJrfAGPimYuHxVDCjp/JgWBhJmGXQBIVWAnj5eIIkiPPqd7aV6zenRXRTdViQAkbr3BqBA2eMYiHRImBA8tIQA7\" alt=\"image\"\u003e, \u003cimg width=\"16\" height=\"37\" src=\"data:image/png;base64,R0lGODlhGAA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABwAXABUAhAAAAAAAAAAAOgAAZgA6ZgA6kABmtjoAADo6OjpmtjqQtjqQ22YAAGaQ22a222a2/5A6AJDb/7ZmALb//9uQOtuQZtu2Ztv///+2Zv/bkP/btv//tv//2wECAwECAwECAwWVICBmR2CeAeJcYuu21fkAnGQW7PtiphCNpcBM56KYBhPRhmFaEF22gKG1NA2f1YBTxAsgn0CriANpgrm9n6YsaJxFUVQgkTuTTVPLMamzDbMzd1I6Sz5oAYYAUThvRl58jl9ggowAXUJFNyx6JgR8WZU0ZU6XmqInU2NlV28vJJKtL0ahsS02qbUtdwsWW7kARgIKFyEAOw==\" alt=\"image\"\u003e, \u003cimg width=\"23\" height=\"37\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u0026nbsp;and \u003cimg width=\"21\" height=\"37\" src=\"data:image/png;base64,R0lGODlhHwA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABwAdABUAhAAAAAAAAAAAOgAAZgA6ZgA6kABmtjoAADqQtjqQ22YAAGY6AGZmZma222a2/5A6AJDb/7ZmALb//9uQOtu2Ztv/ttv/29v///+2Zv/bkP//tv//2wECAwECAwECAwECAwWtYBSMowOc2JicgEia7Kkpo9Cw26PienDHLNdAwkrtTrnACsiajIbInpKVOUCZJ2fgajy2ptjsk5gjLI7VwiUsDqgBqUZvKYKxtepZwTKHu9dsAHgXTg5JSjkCEIEoIwUVCmqHCSkGbHV+bhQBJocID4phM6FGZm+HDGCMmSVRJFerXW8Ah6pMg6x2h7NYSUtGvId2vTrDq2xVsMd3f8uMIpbObL4US9K3AQIIFyEAOw==\" alt=\"image\"\u003e, were considered to be as per the wheel model, i.e. 7.872e\u003csup\u003e-6\u0026nbsp;\u003c/sup\u003ekg/mm\u003csup\u003e3\u003c/sup\u003e, 400, 122.5, 130 \u0026amp; 190 mm, respectively.\u003c/p\u003e\n\u003cp\u003eThe obtained values are plotted in figure 5(a), it is worth noting that the values obtained by empirical formula provided good approximation to CAD model values. The coefficient 0.8 in the empirical formulae can be considered to be a variable constant depending upon the hub and rim dimensions. On increasing this variable constant to 1.1, the approximation results were perfectly aligned to the CAD model results, as presented by figure 5(b). \u0026nbsp;\u0026nbsp;\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003e\u003cem\u003e3.1.\u003c/em\u003e The results in reference to figure 4, can be interpreted that with increase of eccentricity the mass of one side increases is equal amount and it decreases on other side of the center line.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e3.2.\u003c/em\u003e The results in reference to figure 5, present that the empirical equation (1) provided good approximations to aid in the resolution and decision making regarding the quantification of the eccentricity.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e3.3.\u003c/em\u003e The empirical equation (1) can be adjusted to various designs of rotating machinery and wheels with different dimensions of rail wheels to conveniently address balancing problems, offering a clear path for future expansion of this study.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e3.4.\u003c/em\u003e Marking the light and heavy spots on wheels helps to reduces unbalance effectively; while most rail wheel manufacturers mark the heavy spot-commonly using paint-a few manufacturers omit this step. These markings can be used by technical and supervisory staff to ensure the correctness of assembly as per the approved practice for assembly for static, dynamic or coupled balance of the wheel set. Wheel set manufacturers can incorporate this methodology into production routines, enhancing safety and operational efficiency. Additionally, this approach can extend to other rotational systems such as turbines and automotive wheels.\u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThis study presents a MATLAB and CAD based analytical framework for mitigating unbalance in railway wheels. Results demonstrate the model's applicability in industrial settings, with practical recommendations for provisioning of marking light and heavy spots on the rail wheels to optimize the wheel and wheel set balance. Future work may explore adapting the methodology for other rotating systems.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eCAD \u0026nbsp; \u0026nbsp;Computer aided design\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe models and codes used in the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declares that there is no potential conflict of interest with respect to the research, authorship, and/or publication of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author(s) did not receive any support from any organization.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eJSK conceptualized, analyzed, drafted, prepared, read, edited and approves the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author, undertaking this work as a hobby project, expresses sincere gratitude to all resource providers and tacit permission providers to use the various tools and software\u0026rsquo;s through internet. Special thanks are extended to MathWorks\u0026reg; for supporting the programming efforts and providing access to MATLAB\u0026reg; software, which greatly facilitated the solution process. The author is also deeply appreciative of the design office staff for providing a supportive and accommodating environment, contributing to the successful completion of this study. The author is thankful to the internet community for ensuring the availability of various software\u0026rsquo;s, the study and reference materials. Lastly, heartfelt thanks go to ChatGPT for its prompt and invaluable assistance in enhancing \u0026amp; completing the work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ehttps://orcid.org/0009-0005-2630-6790\u003c/p\u003e\n\u003cp\u003eJeetender Singh Kushawaha - Academia.edu\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eWang Y, Kang H, et al. (2011) \u003cem\u003eInfluence of dynamic unbalance of wheelsets on the dynamic performance of high-speed cars\u003c/em\u003e, Journal of Modern Transportation, Vol. 19(3), pp. 147\u0026ndash;153.\u003c/li\u003e\n \u003cli\u003eNew T, Pimsarn M. (2021) \u003cem\u003eRailway axle and wheel assembly press-fitting force characteristics and holding torque capacity\u003c/em\u003e, Applied Sciences, Vol. 11, Article 8862.\u003c/li\u003e\n \u003cli\u003eTaneja S. (2020) \u003cem\u003eEffect of tyre unbalance on performance of vehicle\u003c/em\u003e, International Journal of Mechanical Engineering and Technology, Vol. 11(12), pp. 12\u0026ndash;18.\u003c/li\u003e\n \u003cli\u003ePintao B, Mosleh A, Vale C, Montenegro P, Costa P. (2022) \u003cem\u003eDevelopment and validation of a weigh-in-motion methodology for railway tracks\u003c/em\u003e, Sensors, Vol. 22, Article 19769.\u003c/li\u003e\n \u003cli\u003eSection 6 \u0026ndash; List of Drawings, https://www.scribd.com/document/664185101/Drawings-Section-6. Accessed 10 December 2023.\u003c/li\u003e\n \u003cli\u003e\u003cem\u003eNX 12 for Engineering Design\u003c/em\u003e, https://me5763.github.io/lab/assets/books/NX-12-for-Engineering-Design.pdf. Accessed 01 January 2024.\u003c/li\u003e\n \u003cli\u003eHunt B, Lipsman R, et al. (2001) \u003cem\u003eA Guide to MATLAB for Beginners and Experienced Users\u003c/em\u003e, Cambridge University Press, New York.\u003c/li\u003e\n \u003cli\u003eOtto S.R., Denier J.P. (2005) \u003cem\u003eAn Introduction to Programming and Numerical Methods in MATLAB\u003c/em\u003e, Springer, USA.Chapman S J (2008) MATLAB: Programming for Engineers, Fourth Edition, Thomson, Canada.\u003c/li\u003e\n \u003cli\u003eChapman S.J. (2008) \u003cem\u003eMATLAB: Programming for Engineers\u003c/em\u003e, Fourth Edition, Thomson, Canada.\u003c/li\u003e\n \u003cli\u003eMATLAB: The Language of Technical Computing (2005) MATLAB Programming MathWorks Inc.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Dynamic balancing, Balancing mass, Rail wheel, Eccentricity","lastPublishedDoi":"10.21203/rs.3.rs-5909644/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5909644/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study explores an efficient method for analyzing and mitigating unbalance in railway wheel sets using MATLAB and Computer Aided Design based simulations. The novelty lies in the combined use of simplified mathematical model using the above two approaches. Sensitivity analysis confirms the model's accuracy and industrial applicability. The work demonstrates that unbalance can be reduced significantly by marking the light and heavy spots on the wheel, aiding maintenance and enhancing operational efficiency in the workshop environment. The study underscores the practicality of computational tools in resolving critical industrial challenges. The study investigates and proposes to rail wheel manufacturer\u0026rsquo;s that the provision for process control for utilizing the light and heavy spot on the rail wheel shall be adapted as being done for road tires, to aid in the better assembled railway wheel set.\u003c/p\u003e","manuscriptTitle":"Numerical Analysis and Validation of Eccentricity-Induced Unbalancing Mass in Rotational Systems: Rail Wheel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-30 16:35:08","doi":"10.21203/rs.3.rs-5909644/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"44234f5b-da34-4beb-831f-ca1636b18bbc","owner":[],"postedDate":"April 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-28T15:53:41+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-30 16:35:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5909644","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5909644","identity":"rs-5909644","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}