{"id":18794,"date":"2023-09-05T12:23:08","date_gmt":"2023-09-05T09:23:08","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=18794"},"modified":"2023-09-26T09:47:44","modified_gmt":"2023-09-26T06:47:44","slug":"modelyuvannya-dynamiky-rotoriv-zminnoyi-masy-tehnologichnyh-mashyn","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=18794","title":{"rendered":"\u041c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f  \u0434\u0438\u043d\u0430\u043c\u0456\u043a\u0438 \u0440\u043e\u0442\u043e\u0440\u0456\u0432 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u043c\u0430\u0441\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0445 \u043c\u0430\u0448\u0438\u043d"},"content":{"rendered":"<p><!--more--><\/p>\n<p style=\"text-align: center;\">MODELING OF THE DYNAMICS OF ROTORS OF VARIABLE MASS OF TECHNOLOGICAL MACHINES<\/p>\n<p style=\"text-align: center;\">\u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u0414\u0418\u041d\u0410\u041c\u0406\u041a\u0418 \u0420\u041e\u0422\u041e\u0420\u0406\u0412 \u0417\u041c\u0406\u041d\u041d\u041e\u0407 \u041c\u0410\u0421\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0406\u0427\u041d\u0418\u0425 \u041c\u0410\u0428\u0418\u041d<\/p>\n<p><strong>\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 73-81. \u041d\u043e\u043c\u0435\u0440: \u21164, 2023 (323)<\/strong> <a href=\"http:\/\/journals.khnu.km.ua\/vestnik\/wp-content\/uploads\/2023\/09\/323-73-81.pdf\"> <img loading=\"lazy\" class=\"size-full wp-image-69 alignnone\" src=\"http:\/\/journals.khnu.km.ua\/vestnik\/wp-content\/uploads\/2021\/01\/pdf.png\" alt=\"\" width=\"76\" height=\"32\" \/><\/a><br \/>\n<strong>\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong><br \/>\nGRABAR IVAN<br \/>\nPolissia National University<br \/>\nhttps:\/\/orcid.org\/0000-0002-7193-6960<br \/>\ne-mail: ivan-grabar@ukr.net<br \/>\nZHUKOVSKYI OLEXANDR<br \/>\nPolissia National University<br \/>\nhttps:\/\/orcid.org\/0009-0006-1870-1341<br \/>\ne-mail: olexandr.zhukovsky@encon.com.ua<br \/>\nSENN PHILIPP<br \/>\nNanowetlaids SENN GMBH<br \/>\ne-mail: Philipp@senn-net.de<br \/>\n\u0413\u0420\u0410\u0411\u0410\u0420 \u0406\u0412\u0410\u041d<br \/>\n\u041f\u043e\u043b\u0456\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<br \/>\n\u0416\u0423\u041a\u041e\u0412\u0421\u042c\u041a\u0418\u0419 \u041e\u041b\u0415\u041a\u0421\u0410\u041d\u0414\u0420<br \/>\n\u041f\u043e\u043b\u0456\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<br \/>\n\u0421\u0415\u041d\u041d \u0424\u0406\u041b\u0406\u041f\u041f<br \/>\nNanowetlaids SENN GMBH<br \/>\n<strong>DOI:<\/strong>\u00a0<a href=\"https:\/\/www.doi.org\/10.31891\/2307-5732-2023-323-4-73-81\">https:\/\/www.doi.org\/10.31891\/2307-5732-2023-323-4-73-81<\/a><\/p>\n<p style=\"text-align: center;\"><strong>\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e\u00a0 \u043c\u043e\u0432\u043e\u044e\u00a0<\/strong><\/p>\n<p>The dynamic parameters of rotors of variable mass of winding-unwinding machines in a non-linear setting were studied. For one of the approximations &#8211; the constant linear speed of the winding V=const, the engineering dependences on time for the following parameters were obtained in an explicit form: the current radius of the rotor r(t), the angular velocity \u03c9(t), the moment of inertia Ix(t), the moment of the amount of movement Lx(t). These dependencies are the basis for creating a software-hardware complex of dynamic control and maintenance of specified parameters of unwinding-winding<br \/>\ntechnological machines in online mode. Computer modelling of the model for the parameters of a specific technological machine &#8211; longitudinal cutting machine PRS5-201 manufactured by the Izhvazhmash plant was carried out. The simulation results were in good agreement with the experimental data obtained in the full-scale experiment. The relevance of the work is confirmed by acts of proceedings at several enterprises of the paper industry in Ukraine and Europe.<br \/>\n<strong>Keywords:<\/strong> rotor with variable mass, nonlinear dynamics, dynamic parameters, moment of inertia, moment of<br \/>\nmomentum.<\/p>\n<p style=\"text-align: center;\"><strong>\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0443\u043a\u0440\u0430\u0457\u043d\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n<p>\u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043e \u0434\u0438\u043d\u0430\u043c\u0456\u0447\u043d\u0456 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438 \u0440\u043e\u0442\u043e\u0440\u0456\u0432 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u043c\u0430\u0441\u0438 \u043d\u0430\u043c\u043e\u0442\u0443\u0432\u0430\u043b\u044c\u043d\u043e-\u0440\u043e\u0437\u043c\u043e\u0442\u0443\u0432\u0430\u043b\u044c\u043d\u0438\u0445 \u043c\u0430\u0448\u0438\u043d \u0432 \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0456\u0439 \u043f\u043e\u0441\u0442\u0430\u043d\u043e\u0432\u0446\u0456. \u0414\u043b\u044f \u043e\u0434\u043d\u043e\u0433\u043e \u0437 \u043d\u0430\u0431\u043b\u0438\u0436\u0435\u043d\u044c &#8211; \u043f\u043e\u0441\u0442\u0456\u0439\u043d\u0456\u0439 \u043b\u0456\u043d\u0456\u0439\u043d\u0456\u0439 \u0448\u0432\u0438\u0434\u043a\u043e\u0441\u0442\u0456 \u043d\u0430\u043c\u043e\u0442\u0443\u0432\u0430\u043d\u043d\u044f V=const \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u043e \u0432 \u044f\u0432\u043d\u043e\u043c\u0443 \u0432\u0438\u0434\u0456 \u0456\u043d\u0436\u0435\u043d\u0435\u0440\u043d\u0456 \u0437\u0430\u043b\u0435\u0436\u043d\u043e\u0441\u0442\u0456 \u0432\u0456\u0434 \u0447\u0430\u0441\u0443 \u0434\u043b\u044f \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432: \u043f\u043e\u0442\u043e\u0447\u043d\u043e\u0433\u043e \u0440\u0430\u0434\u0456\u0443\u0441\u0443 \u0440\u043e\u0442\u043e\u0440\u0430 r(t), \u043a\u0443\u0442\u043e\u0432\u043e\u0457 \u0448\u0432\u0438\u0434\u043a\u043e\u0441\u0442\u0456 \u03c9(t), \u043c\u043e\u043c\u0435\u043d\u0442\u0443 \u0456\u043d\u0435\u0440\u0446\u0456\u0457 Ix(t), \u043c\u043e\u043c\u0435\u043d\u0442\u0443 \u043a\u0456\u043b\u044c\u043a\u043e\u0441\u0442\u0456 \u0440\u0443\u0445\u0443 Lx(t). \u0414\u0430\u043d\u0456 \u0437\u0430\u043b\u0435\u0436\u043d\u043e\u0441\u0442\u0456 \u0454 \u043e\u0441\u043d\u043e\u0432\u043e\u044e \u0434\u043b\u044f \u0441\u0442\u0432\u043e\u0440\u0435\u043d\u043d\u044f \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e-\u0430\u043f\u0430\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u0443 \u0434\u0438\u043d\u0430\u043c\u0456\u0447\u043d\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0456\u043d\u043d\u044f \u0442\u0430 \u043f\u0456\u0434\u0442\u0440\u0438\u043c\u043a\u0438 \u0437\u0430\u0434\u0430\u043d\u0438\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 \u0440\u043e\u0437\u043c\u043e\u0442\u0443\u0432\u0430\u043b\u044c\u043d\u043e-\u043d\u0430\u043c\u043e\u0442\u0443\u0432\u0430\u043b\u044c\u043d\u0438\u0445 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0445 \u043c\u0430\u0448\u0438\u043d \u0432 \u0440\u0435\u0436\u0438\u043c\u0456 on line. \u041f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043e \u043a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u043c\u043e\u0434\u0435\u043b\u0456 \u0434\u043b\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0457 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u043e\u0457 \u043c\u0430\u0448\u0438\u043d\u0438 \u2013 \u043f\u0440\u043e\u0434\u043e\u043b\u044c\u043d\u043e-\u0440\u0456\u0437\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0441\u0442\u0430\u043d\u0443 \u041f\u0420\u04215-201 \u0432\u0438\u0440\u043e\u0431\u043d\u0438\u0446\u0442\u0432\u0430 \u0437\u0430\u0432\u043e\u0434\u0443 \u00ab\u0406\u0436\u0432\u0430\u0436\u043c\u0430\u0448\u00bb. \u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u043e\u0442\u0440\u0438\u043c\u0430\u043b\u0438 \u0433\u0430\u0440\u043d\u0443 \u0437\u0431\u0456\u0436\u043d\u0456\u0441\u0442\u044c \u0437 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u0438\u043c\u0438 \u0434\u0430\u043d\u0438\u043c\u0438, \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u0438\u043c\u0438 \u0432 \u043d\u0430\u0442\u0443\u0440\u043d\u043e\u043c\u0443 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0456. \u0410\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u0456\u0441\u0442\u044c \u0440\u043e\u0431\u043e\u0442\u0438 \u043f\u0456\u0434\u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043d\u0430 \u0430\u043a\u0442\u0430\u043c\u0438 \u043f\u0440\u043e\u0432\u0430\u0434\u0436\u0435\u043d\u043d\u044f \u043d\u0430 \u043a\u0456\u043b\u044c\u043a\u043e\u0445 \u043f\u0456\u0434\u043f\u0440\u0438\u0454\u043c\u0441\u0442\u0432\u0430\u0445 \u043f\u0430\u043f\u0435\u0440\u043e\u0432\u043e\u0457 \u0433\u0430\u043b\u0443\u0437\u0456 \u0432 \u0423\u043a\u0440\u0430\u0457\u043d\u0456 \u0442\u0430 \u0404\u0432\u0440\u043e\u043f\u0456.<br \/>\n<strong>\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0440\u043e\u0442\u043e\u0440 \u0437\u0456 \u0437\u043c\u0456\u043d\u043d\u043e\u044e \u043c\u0430\u0441\u043e\u044e, \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0430 \u0434\u0438\u043d\u0430\u043c\u0456\u043a\u0430, \u0434\u0438\u043d\u0430\u043c\u0456\u0447\u043d\u0456 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438, \u043c\u043e\u043c\u0435\u043d\u0442 \u0456\u043d\u0435\u0440\u0446\u0456\u0457, \u043c\u043e\u043c\u0435\u043d\u0442 \u043a\u0456\u043b\u044c\u043a\u043e\u0441\u0442\u0456<br \/>\n\u0440\u0443\u0445\u0443<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[82],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/18794"}],"collection":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=18794"}],"version-history":[{"count":3,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/18794\/revisions"}],"predecessor-version":[{"id":19191,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/18794\/revisions\/19191"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=18794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=18794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=18794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}