Physics-Based Modeling and Friction Parameter Identification of a Proportional Spool Valve

Physics-Based Modeling and Friction Parameter Identification of a Proportional Spool Valve | 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 Physics-Based Modeling and Friction Parameter Identification of a Proportional Spool Valve Marian Ledvoň, Lumír Hružík, Adam Bureček, Tomáš Polášek, David Kolář This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7703407/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 31 Mar, 2026 Read the published version in Scientific Reports → Version 1 posted 14 You are reading this latest preprint version Abstract This paper presents the development of a physics-based model of a proportional directional valve with the aim of describing its dynamic behavior while accounting for the influence of friction forces acting on the spool. The model is derived from the spool’s equation of motion, and in order to achieve accurate parameter tuning, an experimental analysis of the individual forces acting on the spool was carried out. Particular attention is given to the parameters of the friction force, as this component represents a key factor affecting the dynamic response of the system. Due to the difficulty of direct measurement, the identification of friction parameters was performed through a combined numerical–experimental comparison of the system’s response to step control inputs. A significant advantage of the proposed model lies in its capability to parameterize the individual force components independently, which facilitates straightforward adaptation to different operating conditions or valve types. For experimental validation, a series of dynamic measurements was conducted on a specialized hydraulic test rig. The acquired data were used both to identify the friction model parameters and to validate the simulation model. A comparison of the simulation results with experimental data demonstrates good agreement across a wide range of operating conditions. The proposed model therefore provides a flexible and accurate tool for predicting the behavior of proportional directional valves, applicable both in the design of control algorithms and in the optimization of valve construction. Physical sciences/Engineering Physical sciences/Mathematics and computing proportional directional valve step response frequency response physics-based model friction force parameter identification Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 31 Mar, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 15 Dec, 2025 Reviews received at journal 08 Dec, 2025 Reviews received at journal 04 Dec, 2025 Reviewers agreed at journal 20 Nov, 2025 Reviewers agreed at journal 16 Nov, 2025 Reviewers agreed at journal 15 Nov, 2025 Reviews received at journal 30 Oct, 2025 Reviewers agreed at journal 10 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers invited by journal 08 Oct, 2025 Editor invited by journal 29 Sep, 2025 Editor assigned by journal 26 Sep, 2025 Submission checks completed at journal 25 Sep, 2025 First submitted to journal 24 Sep, 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-7703407","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":531638388,"identity":"5f229bd3-1fa4-4e45-9b3d-8270b8f044d0","order_by":0,"name":"Marian Ledvoň","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYJCCA0Asw8CQAKQqGBgMiNXCA9FyhkgtDHAtjG1EaNFtP/vwwM8dDDz87DmGjwvnHbY3Z2B+/AGfFrMz6QYHe88w8Ej2vDE2nrntcOLOBjYDvDaZHUhjOMDbxsBjcCMtTZp3W1qCwQEesLdwazn/jOHgX6AWe7CWOWn2IC0H8Gq5kcZwGGyLRPIxad4GG8YNB3gYG/BrecZwWLZNgkfizOPDxjzHbBJ3NrMZ49MBdFga88e3bTZy/O2JjY95aiTszdmb8YcYFEggsZmJUD8KRsEoGAWjAD8AACBgRLqtj1gTAAAAAElFTkSuQmCC","orcid":"","institution":"VSB – Technical University of Ostrava","correspondingAuthor":true,"prefix":"","firstName":"Marian","middleName":"","lastName":"Ledvoň","suffix":""},{"id":531638389,"identity":"14acf3bd-bf6e-4efc-a55f-ef1924614527","order_by":1,"name":"Lumír Hružík","email":"","orcid":"","institution":"VSB – Technical University of Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Lumír","middleName":"","lastName":"Hružík","suffix":""},{"id":531638390,"identity":"2b942ed0-a538-4c6e-bf9c-d4a59684ba8e","order_by":2,"name":"Adam Bureček","email":"","orcid":"","institution":"VSB – Technical University of Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Adam","middleName":"","lastName":"Bureček","suffix":""},{"id":531638391,"identity":"9fb4bf4e-0952-4109-a50a-c7a60551b876","order_by":3,"name":"Tomáš Polášek","email":"","orcid":"","institution":"VSB – Technical University of Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Tomáš","middleName":"","lastName":"Polášek","suffix":""},{"id":531638392,"identity":"62dc9e8f-3d25-44a9-bb74-df198b4b9269","order_by":4,"name":"David Kolář","email":"","orcid":"","institution":"VSB – Technical University of Ostrava","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"Kolář","suffix":""}],"badges":[],"createdAt":"2025-09-24 11:54:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7703407/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7703407/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-46361-9","type":"published","date":"2026-03-31T15:59:50+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":93984618,"identity":"41190f21-31ce-4be3-86f0-e7b070252857","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4221236,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptPhysicsBasedModelingandFrictionParameterIdentificationofaProportionalSpoolValverevised.docx","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/ec9cf49cfa964f73f44921bc.docx"},{"id":93984605,"identity":"ad5e15b8-5466-436a-854a-58cf71f54128","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":7216,"visible":true,"origin":"","legend":"","description":"","filename":"74adf4d812024e968b1fd3237a2966f9.json","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/889ac2247f5885711461cb64.json"},{"id":93984608,"identity":"b24ec141-1841-48d0-8888-4c36dd3c5a2b","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":174161,"visible":true,"origin":"","legend":"","description":"","filename":"74adf4d812024e968b1fd3237a2966f91enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/7fecfe996e0ade7c35258c03.xml"},{"id":93984927,"identity":"fa0723de-a8b7-4aba-b8b5-4dc01aebe96b","added_by":"auto","created_at":"2025-10-21 04:04:29","extension":"jpeg","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":131700,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/88927b907efd3555c0dfba51.jpeg"},{"id":93984928,"identity":"0fb9dc68-09f6-49ea-b33e-068f8aeade59","added_by":"auto","created_at":"2025-10-21 04:04:29","extension":"jpeg","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":340836,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/d8317e12533266edb6f74626.jpeg"},{"id":93984606,"identity":"152582d4-8d40-428d-9f46-a900b700d56d","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"jpeg","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":119142,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/d7fb44533ce71bbe2436520c.jpeg"},{"id":93984609,"identity":"de72e5a0-fbbb-4c01-8c44-b82984fa7b21","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"jpeg","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":200328,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/9e60aa664cd8ca6de58868e1.jpeg"},{"id":93986108,"identity":"d60a27db-310f-43de-893f-80624bb109ef","added_by":"auto","created_at":"2025-10-21 04:12:29","extension":"jpeg","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":303588,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/0c8886ee7c73e5dea421feee.jpeg"},{"id":93986109,"identity":"f2173e46-ff61-4292-a4a9-b38505c1ee20","added_by":"auto","created_at":"2025-10-21 04:12:29","extension":"jpeg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":256456,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/bfc5039dec319e27d9d9b1b4.jpeg"},{"id":93984610,"identity":"7eab90bb-5fed-439b-a71b-8263224f69d6","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"jpeg","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":310040,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/e05f6cb05d0265e367553bef.jpeg"},{"id":93984615,"identity":"54ecb99f-fd94-4d8f-abda-2d13c3b56394","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"jpeg","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":260284,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage16.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/f9fd4236473257283cecbc88.jpeg"},{"id":93986111,"identity":"9ff5fff2-6f0b-4916-942e-c9908ceadc92","added_by":"auto","created_at":"2025-10-21 04:12:29","extension":"jpeg","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":298084,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage17.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/5cb8e076b81b13c35f73cc19.jpeg"},{"id":93984624,"identity":"9853ca2f-8161-4908-8e80-7963124d95aa","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"jpeg","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":148894,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/e8abe1bddbcb5b5aaf707b7e.jpeg"},{"id":93984620,"identity":"310d1667-4d17-4eed-ad70-14ecc8c451c0","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"jpeg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":136288,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/bb11d4621ebd1934cb0f74c6.jpeg"},{"id":93984631,"identity":"547a4524-df49-44bd-9e79-e7e2166a3adf","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"jpeg","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":267732,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/373b1eab9ee24be9916fa670.jpeg"},{"id":93984937,"identity":"c62e739f-b7d1-4750-929e-1c04eeb570b6","added_by":"auto","created_at":"2025-10-21 04:04:30","extension":"jpeg","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":224990,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/23056ccfe3fb34fcddd5ed34.jpeg"},{"id":93986527,"identity":"629e2689-fd39-48b4-8ec6-5d4d759b8219","added_by":"auto","created_at":"2025-10-21 04:20:29","extension":"jpeg","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":781685,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/d0032577a86e1e68c0917d18.jpeg"},{"id":93984932,"identity":"2b993928-4717-48a6-a56d-5f59dab6b33d","added_by":"auto","created_at":"2025-10-21 04:04:29","extension":"jpeg","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":247854,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/4c8abf7f968a5dd1113ed3bc.jpeg"},{"id":93984611,"identity":"f5d8e441-0eaa-437c-830f-4f6675f97a48","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"jpeg","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":249802,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/955e6742d016281d0dbacd29.jpeg"},{"id":93984626,"identity":"a7852c8b-b07d-481f-8fec-b2a4a67874bf","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"jpeg","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":329268,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/644ddeb4e97d63a37d7f58eb.jpeg"},{"id":93984934,"identity":"84d64f63-3f0a-49da-b6c3-8cf84334fa0a","added_by":"auto","created_at":"2025-10-21 04:04:29","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":38154,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/b50b8c2efe28784669099a23.png"},{"id":93984938,"identity":"83bc3618-89cc-4e95-95d0-c29e16c663af","added_by":"auto","created_at":"2025-10-21 04:04:30","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":44906,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/c252247069f13896d532f143.png"},{"id":93984629,"identity":"79f37580-cf10-4fea-bad5-a74a838982a5","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":42249,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/5f8ac517db8e382e9f1800a0.png"},{"id":93984936,"identity":"ef0dcadd-7419-44ce-a63a-c3a3a9590c46","added_by":"auto","created_at":"2025-10-21 04:04:30","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":19817,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/de9477a0b86d51162d22794b.png"},{"id":93984633,"identity":"cccfcc75-ab44-4011-9a51-fea65b27ba30","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":47610,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/13d4e81a0c75648185c3a129.png"},{"id":93984635,"identity":"5c61bb1f-e10e-4c64-ae93-d5b9268e50aa","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":32023,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/1922b8f32e8d88c842ad5402.png"},{"id":93984636,"identity":"285afd19-ea1b-4361-bf99-34b632ad5167","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":54260,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/6d3a898e2bd8a7f99f5c8e2f.png"},{"id":93984634,"identity":"843b191d-840d-4f42-9624-fa0e0431a65d","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":34721,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/29c541d5d32a72337424361e.png"},{"id":93984622,"identity":"7ff1c9f6-01bd-4a27-aec3-9be8a3d3a094","added_by":"auto","created_at":"2025-10-21 03:56:29","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":52322,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/ce754819bbb67ef86de209b1.png"},{"id":93984640,"identity":"6dafa81f-8755-4499-b804-3359065d693c","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37402,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/e14cceba35190a2b6f9db15b.png"},{"id":93984939,"identity":"d23b8077-2644-4acb-9117-5baade31f648","added_by":"auto","created_at":"2025-10-21 04:04:30","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":34321,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/5ded4205215b98fa58c29f76.png"},{"id":93984940,"identity":"15f5f00e-36b9-48b4-870c-17047020fbef","added_by":"auto","created_at":"2025-10-21 04:04:30","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":35412,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/6d684bf981545d5451efa68c.png"},{"id":93984935,"identity":"768664bf-4ec6-4617-a23f-6eea28259cee","added_by":"auto","created_at":"2025-10-21 04:04:29","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29512,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/5f5c02e509e67ee395291108.png"},{"id":93984630,"identity":"f3c66805-7213-46ea-b5d2-42f577bd4519","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":241752,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/34b423ee3bb0382d645430cc.png"},{"id":93984642,"identity":"1c9d761b-5d55-4470-8cdf-8a9aba1fa755","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":65340,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/ec58452e5941239fb6f98efe.png"},{"id":93984632,"identity":"37110c8b-b715-48b8-a0ed-5b6f2fbbc9d3","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":61378,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/724a41625bc13f4bfc1c75c2.png"},{"id":93984639,"identity":"0cd8d4ea-9626-42c1-aad5-3a194c6ffaf8","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"png","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":57794,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/ae730cd3539636bc382e5ac8.png"},{"id":93984628,"identity":"6da531ed-5f2f-40cb-950d-5eae2177c9f6","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"xml","order_by":37,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":174691,"visible":true,"origin":"","legend":"","description":"","filename":"74adf4d812024e968b1fd3237a2966f91structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/467a159de11dcaa07c426994.xml"},{"id":93984637,"identity":"56190e87-31af-4dfe-bb8a-7d59656a9976","added_by":"auto","created_at":"2025-10-21 03:56:30","extension":"html","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":194836,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1/f93fff78b1dabec9ad3c207b.html"},{"id":106345033,"identity":"ff64332c-c8a0-4d34-b5d2-a2355c8c1e66","added_by":"auto","created_at":"2026-04-07 16:17:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1713215,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptPhysicsBasedModelingandFrictionParameterIdentificationofaProportionalSpoolValverevised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7703407/v1_covered_2e1df5e3-70ac-4f8e-a5ef-5402c7df70c4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Physics-Based Modeling and Friction Parameter Identification of a Proportional Spool Valve","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":"proportional directional valve, step response, frequency response, physics-based model, friction force, parameter identification","lastPublishedDoi":"10.21203/rs.3.rs-7703407/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7703407/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper presents the development of a physics-based model of a proportional directional valve with the aim of describing its dynamic behavior while accounting for the influence of friction forces acting on the spool. The model is derived from the spool\u0026rsquo;s equation of motion, and in order to achieve accurate parameter tuning, an experimental analysis of the individual forces acting on the spool was carried out. Particular attention is given to the parameters of the friction force, as this component represents a key factor affecting the dynamic response of the system. Due to the difficulty of direct measurement, the identification of friction parameters was performed through a combined numerical\u0026ndash;experimental comparison of the system\u0026rsquo;s response to step control inputs. A significant advantage of the proposed model lies in its capability to parameterize the individual force components independently, which facilitates straightforward adaptation to different operating conditions or valve types. For experimental validation, a series of dynamic measurements was conducted on a specialized hydraulic test rig. The acquired data were used both to identify the friction model parameters and to validate the simulation model. A comparison of the simulation results with experimental data demonstrates good agreement across a wide range of operating conditions. The proposed model therefore provides a flexible and accurate tool for predicting the behavior of proportional directional valves, applicable both in the design of control algorithms and in the optimization of valve construction.\u003c/p\u003e","manuscriptTitle":"Physics-Based Modeling and Friction Parameter Identification of a Proportional Spool Valve","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-21 03:56:24","doi":"10.21203/rs.3.rs-7703407/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-15T09:16:51+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-08T10:18:30+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-04T12:25:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"161403854109357298760158013247636719966","date":"2025-11-21T03:29:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"181124342674201364161091062958774344446","date":"2025-11-17T01:42:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"34488442763530022998039049470201063066","date":"2025-11-15T07:40:47+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-30T21:27:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"235829282283354343176174933409731406809","date":"2025-10-11T00:08:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"275303043076385066593342254568917118677","date":"2025-10-09T12:12:46+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-08T13:51:02+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-29T12:45:02+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-26T08:35:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-25T11:25:14+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-24T11:40:24+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":"4476607a-1e5e-46ba-a736-fffedcc7b39f","owner":[],"postedDate":"October 21st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":56522366,"name":"Physical sciences/Engineering"},{"id":56522367,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-04-07T16:15:49+00:00","versionOfRecord":{"articleIdentity":"rs-7703407","link":"https://doi.org/10.1038/s41598-026-46361-9","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-03-31 15:59:50","publishedOnDateReadable":"March 31st, 2026"},"versionCreatedAt":"2025-10-21 03:56:24","video":"","vorDoi":"10.1038/s41598-026-46361-9","vorDoiUrl":"https://doi.org/10.1038/s41598-026-46361-9","workflowStages":[]},"version":"v1","identity":"rs-7703407","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7703407","identity":"rs-7703407","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}