Analysis on Hydraulic Dynamic Stiffness Characteristics and Experimental Research of Asymmetric Valve-Controlled Asymmetric Cylinder System

Analysis on Hydraulic Dynamic Stiffness Characteristics and Experimental Research of Asymmetric Valve-Controlled Asymmetric Cylinder System | 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 Article Analysis on Hydraulic Dynamic Stiffness Characteristics and Experimental Research of Asymmetric Valve-Controlled Asymmetric Cylinder System Li Weiwei, Han He yong, Liu Chuiyi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7412169/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 15 You are reading this latest preprint version Abstract Asymmetric cylinders are widely utilized due to their simple structure and high load-carrying capacity. However, their structural asymmetry leads to significant differences in performance between the piston’s extension and retraction motions. Additionally, Hydraulic dynamic stiffness directly influences the hydraulic natural frequency, which is the lowest frequency in servo systems and thus governs the system’s dynamic response speed. Traditional nonlinear modeling of asymmetric valve-controlled asymmetric cylinder systems（AVCACS）relies on a unified transfer function for both extension and retraction, failing to account for the cylinder’s motion asymmetry. Additionally, load pressure and load flow are defined exclusively based on the extension motion, overlooking load force variations during retraction. Moreover, conventional hydraulic dynamic stiffness models also only consider cylinder parameters, neglecting the influence of connected asymmetric valve parameters, thus failing to accurately reflect the dynamic stiffness variation mechanism. To address these limitations, this study proposes a novel segmented transfer function model. Grounded in the motion asymmetry of the cylinder piston and the power matching principle of valve-controlled cylinders, the model defines forward and reverse load pressure/flow separately and establishes the corresponding mathematical model for AVCACS. It analyzes the effects of system parameters including piston position, rod-to-cap area ratio（RTCAR），and valve port area gradient ratio（VPAGR）on hydraulic dynamic stiffness. Special focus is placed on the minimum hydraulic dynamic stiffness, which limits the system’s dynamic response speed. Additionally, a comparison is conducted on the minimum forward and reverse hydraulic stiffness of AVCACS under the condition of complete matching between the valve orifice area gradient and piston area. Theoretical and experimental results demonstrate that as the matching coefficient increases, the minimum forward hydraulic dynamic stiffness increases, the minimum reverse hydraulic dynamic stiffness first decreases slightly and then increases, and the minimum reverse hydraulic dynamic stiffness is always greater than the minimum forward hydraulic dynamic stiffness, when the matching coefficient equals 1 (symmetric valve-controlled symmetric cylinder), the minimum forward and reverse hydraulic dynamic stiffness values are equal. Compared with traditional hydraulic stiffness models, the segmented transfer function model exhibits greater generality and accuracy. It provides a more precise theoretical basis for the design of control strategies in valve-controlled cylinder systems. Physical sciences/Engineering Physical sciences/Mathematics and computing Hydraulic dynamic stiffness Asymmetric valve-cylinder system Valve orifice area gradient Characteristics analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 26 Sep, 2025 Reviews received at journal 24 Sep, 2025 Reviewers agreed at journal 15 Sep, 2025 Reviewers agreed at journal 14 Sep, 2025 Reviews received at journal 11 Sep, 2025 Reviews received at journal 09 Sep, 2025 Reviewers agreed at journal 02 Sep, 2025 Reviewers agreed at journal 01 Sep, 2025 Reviewers agreed at journal 27 Aug, 2025 Reviewers agreed at journal 27 Aug, 2025 Reviewers invited by journal 27 Aug, 2025 Editor invited by journal 26 Aug, 2025 Editor assigned by journal 21 Aug, 2025 Submission checks completed at journal 20 Aug, 2025 First submitted to journal 19 Aug, 2025 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7412169","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":508823863,"identity":"3d907e49-78ee-4487-82a5-da0b77bfb863","order_by":0,"name":"Li Weiwei","email":"","orcid":"","institution":"Taiyuan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Weiwei","suffix":""},{"id":508823864,"identity":"c2ff0ce4-5387-4420-b978-96c89960865d","order_by":1,"name":"Han He yong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYFCCM2wMDAY2dvzMzAcfkKClIC1Zsp0t2YBILTxALR8OM244z2MmQJQGg4Nnjz3mMWBmNj7MYMbAUGMTTVjLgXPpxjwGbHxmhxnSHjAcS8ttIKTF7MAZM2keAx5moJbjBowNh4nWIsG4uZmxTYIULQaMG5iZ2YjTYg/UIjnHICFZ4jAbs0ECMX6RnHHGTOLNn/92/P3nPz74UGNDWAuDxAEGJh4YJ4GgchDgb2Bg/EGUylEwCkbBKBixAAAoPz4vD+HH0gAAAABJRU5ErkJggg==","orcid":"","institution":"Taiyuan University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Han","middleName":"He","lastName":"yong","suffix":""},{"id":508823865,"identity":"32c4b126-fa1a-4b01-9260-e01d672865f3","order_by":2,"name":"Liu Chuiyi","email":"","orcid":"","institution":"Taiyuan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Liu","middleName":"","lastName":"Chuiyi","suffix":""}],"badges":[],"createdAt":"2025-08-20 00:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7412169/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7412169/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-33521-6","type":"published","date":"2026-01-27T15:59:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":101690753,"identity":"de7bfa96-b276-4b8b-a760-82e2850e4942","added_by":"auto","created_at":"2026-02-02 16:08:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":914105,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7412169/v1_covered_ad8cc6a6-255e-4a7f-a956-921d4818ff51.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analysis on Hydraulic Dynamic Stiffness Characteristics and Experimental Research of Asymmetric Valve-Controlled Asymmetric Cylinder System","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Hydraulic dynamic stiffness, Asymmetric valve-cylinder system, Valve orifice area gradient, Characteristics analysis","lastPublishedDoi":"10.21203/rs.3.rs-7412169/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7412169/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Asymmetric cylinders are widely utilized due to their simple structure and high load-carrying capacity. However, their structural asymmetry leads to significant differences in performance between the piston’s extension and retraction motions. Additionally, Hydraulic dynamic stiffness directly influences the hydraulic natural frequency, which is the lowest frequency in servo systems and thus governs the system’s dynamic response speed. Traditional nonlinear modeling of asymmetric valve-controlled asymmetric cylinder systems（AVCACS）relies on a unified transfer function for both extension and retraction, failing to account for the cylinder’s motion asymmetry. Additionally, load pressure and load flow are defined exclusively based on the extension motion, overlooking load force variations during retraction. Moreover, conventional hydraulic dynamic stiffness models also only consider cylinder parameters, neglecting the influence of connected asymmetric valve parameters, thus failing to accurately reflect the dynamic stiffness variation mechanism. To address these limitations, this study proposes a novel segmented transfer function model. Grounded in the motion asymmetry of the cylinder piston and the power matching principle of valve-controlled cylinders, the model defines forward and reverse load pressure/flow separately and establishes the corresponding mathematical model for AVCACS. It analyzes the effects of system parameters including piston position, rod-to-cap area ratio（RTCAR），and valve port area gradient ratio（VPAGR）on hydraulic dynamic stiffness. Special focus is placed on the minimum hydraulic dynamic stiffness, which limits the system’s dynamic response speed. Additionally, a comparison is conducted on the minimum forward and reverse hydraulic stiffness of AVCACS under the condition of complete matching between the valve orifice area gradient and piston area. Theoretical and experimental results demonstrate that as the matching coefficient increases, the minimum forward hydraulic dynamic stiffness increases, the minimum reverse hydraulic dynamic stiffness first decreases slightly and then increases, and the minimum reverse hydraulic dynamic stiffness is always greater than the minimum forward hydraulic dynamic stiffness, when the matching coefficient equals 1 (symmetric valve-controlled symmetric cylinder), the minimum forward and reverse hydraulic dynamic stiffness values are equal. Compared with traditional hydraulic stiffness models, the segmented transfer function model exhibits greater generality and accuracy. It provides a more precise theoretical basis for the design of control strategies in valve-controlled cylinder systems.","manuscriptTitle":"Analysis on Hydraulic Dynamic Stiffness Characteristics and Experimental Research of Asymmetric Valve-Controlled Asymmetric Cylinder System","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-04 04:48:26","doi":"10.21203/rs.3.rs-7412169/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-26T18:38:19+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-24T08:36:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"161403854109357298760158013247636719966","date":"2025-09-15T11:26:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"60760143845703230435571677419069686916","date":"2025-09-15T02:15:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-11T08:37:35+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-09T09:44:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"53433848119520356646471205565055099808","date":"2025-09-02T04:06:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"59084684260876121495312656891686494874","date":"2025-09-02T03:53:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"264876322953668154761037549745437877831","date":"2025-08-28T03:39:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"318260648303218396897892481016737961078","date":"2025-08-28T03:31:30+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-28T03:12:35+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-08-26T10:47:10+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-21T08:43:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-21T02:46:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-08-20T00:09:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"819ad2de-e664-4ace-aa6c-85bf616e345c","owner":[],"postedDate":"September 4th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":54036168,"name":"Physical sciences/Engineering"},{"id":54036169,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-02-02T16:05:04+00:00","versionOfRecord":{"articleIdentity":"rs-7412169","link":"https://doi.org/10.1038/s41598-025-33521-6","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-27 15:59:05","publishedOnDateReadable":"January 27th, 2026"},"versionCreatedAt":"2025-09-04 04:48:26","video":"","vorDoi":"10.1038/s41598-025-33521-6","vorDoiUrl":"https://doi.org/10.1038/s41598-025-33521-6","workflowStages":[]},"version":"v1","identity":"rs-7412169","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7412169","identity":"rs-7412169","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}