. . . "Kritiskt varvtal avser det varvtal vid vilket en axel b\u00F6rjar vibrera mer eller mindre kraftigt p\u00E5 grund av resonans L\u00E4gre varvtal kallas underkritiskt varvtal (/rotation), h\u00F6gre varvtal \u00E4r \u00F6verkritiskt varvtal (/rotation). Alla roterande axlar deformeras under rotation. Hur mycket beror av: \n* Axelns och lagrens styvhet \n* Den totala massan av de roterande delarna \n* Massans f\u00F6rdelning med avseende p\u00E5 centrumaxeln \n* Eventuell d\u00E4mpning av eller i det roterande systemet Vid konstruktion av maskiner med roterande delar m\u00E5ste det kritiska varvtalet ber\u00E4knas f\u00F6r att undvika missljud och vibration. Man efterstr\u00E4var d\u00E5 att h\u00E5lla vibrationsfrekvensen 25% under systemets egenfrekvens eller tillr\u00E4ckligt mycket \u00F6ver (i m\u00E5nga fall >200% av kritiskt varvtal. Den svenske industrimannen och uppfinnaren Gustaf de Laval var f\u00F6rst i v\u00E4rlden att konstruera maskiner som var avsedda att \u00F6verskrida det kritiska varvtalet Alla f\u00F6rs\u00F6k att skapa styvare axlar f\u00F6r att klara de h\u00F6ga varvtalen gavs upp f\u00F6r att ist\u00E4llet g\u00E5 den andra v\u00E4gen och f\u00F6rvaga axeln f\u00F6r att den skulle h\u00E5lla. Genom att den mindre styva axeln ledde till ett l\u00E4gre kritiskt varvtal \u00F6kades marginalen (/avst\u00E5ndet till resonansregistret) n\u00E4r man arbetade med \u00F6verkritisk rotation, s\u00E5 upph\u00F6rde problemen med brustna axlar. Vid bruk av maskiner med \u00F6verkritisk rotation \u00E4r det som regel bra att uppvarvningen sker hastigt s\u00E5ledes att man passerar det kritiska varvtalet snabbt och inte resonanserna hinner v\u00E4xa till alarmerande niv\u00E5er."@sv . . . . . . . . . . . . "Dynamika rotor\u016F"@cs . . . "Kritiskt varvtal avser det varvtal vid vilket en axel b\u00F6rjar vibrera mer eller mindre kraftigt p\u00E5 grund av resonans L\u00E4gre varvtal kallas underkritiskt varvtal (/rotation), h\u00F6gre varvtal \u00E4r \u00F6verkritiskt varvtal (/rotation). Alla roterande axlar deformeras under rotation. Hur mycket beror av: \n* Axelns och lagrens styvhet \n* Den totala massan av de roterande delarna \n* Massans f\u00F6rdelning med avseende p\u00E5 centrumaxeln \n* Eventuell d\u00E4mpning av eller i det roterande systemet"@sv . "Dynamika rotor\u016F sjednocuje oblasti dynamiky tuh\u00FDch t\u011Bles (rotor\u016F), dynamiky tekutin (olejov\u00E9ho filmu kluzn\u00FDch lo\u017Eisek), pop\u0159\u00EDpad\u011B i problematiku dynamiky magnetick\u00FDch lo\u017Eisek mechatronick\u00FDch syst\u00E9m\u016F. Dynamika rotor\u016F popisuje mimo jin\u00E9 : Dynamika rotor\u016F se jako in\u017Een\u00FDrsk\u00FD obor v\u00FDznamn\u011B rozvinula na konci devaten\u00E1ct\u00E9ho stolet\u00ED spolu s v\u00FDvojem a v\u00FDrobou parn\u00EDch turb\u00EDn."@cs . . . . "Rotordynamics, also known as rotor dynamics, is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotor dynamics is concerned with one or more mechanical structures (rotors) supported by bearings and influenced by internal phenomena that rotate around a single axis. The supporting structure is called a stator. As the speed of rotation increases the amplitude of vibration often passes through a maximum that is called a critical speed. This amplitude is commonly excited by imbalance of the rotating structure; everyday examples include engine balance and tire balance. If the amplitude of vibration at these critical speeds is excessive, then catastrophic failure occurs. In addition to this, turbomachinery often develop instabilities which are related to the internal makeup of turbomachinery, and which must be corrected. This is the chief concern of engineers who design large rotors. Rotating machinery produces vibrations depending upon the structure of the mechanism involved in the process. Any faults in the machine can increase or excite the vibration signatures. Vibration behavior of the machine due to imbalance is one of the main aspects of rotating machinery which must be studied in detail and considered while designing. All objects including rotating machinery exhibit natural frequency depending on the structure of the object. The critical speed of a rotating machine occurs when the rotational speed matches its natural frequency. The lowest speed at which the natural frequency is first encountered is called the first critical speed, but as the speed increases, additional critical speeds are seen which are the multiples of the natural frequency. Hence, minimizing rotational unbalance and unnecessary external forces are very important to reducing the overall forces which initiate resonance. When the vibration is in resonance, it creates a destructive energy which should be the main concern when designing a rotating machine. The objective here should be to avoid operations that are close to the critical and pass safely through them when in acceleration or deceleration. If this aspect is ignored it might result in loss of the equipment, excessive wear and tear on the machinery, catastrophic breakage beyond repair or even human injury and loss of lives. The real dynamics of the machine is difficult to model theoretically. The calculations are based on simplified models which resemble various structural components (lumped parameters models), equations obtained from solving models numerically (Rayleigh\u2013Ritz method) and finally from the finite element method (FEM), which is another approach for modelling and analysis of the machine for natural frequencies. There are also some analytical methods, such as the distributed transfer function method, which can generate analytical and closed-form natural frequencies, critical speeds and unbalanced mass response. On any machine prototype it is tested to confirm the precise frequencies of resonance and then redesigned to assure that resonance does not occur."@en . "7517878"^^ . . . . . . "1105643637"^^ . . . . . "La velocit\u00E0 critica flessionale \u00E8 per definizione la velocit\u00E0 angolare applicata ad un rotore tale che la sua deformazione, di tipo esclusivamente flessionale, sia massima. \u00C8 importante sottolineare che \u00E8 di uso comune definire erroneamente la velocit\u00E0 critica flessionale come la velocit\u00E0 di funzionamento di un rotore che comporti la rottura di esso; infatti la rottura del rotore pu\u00F2 al pi\u00F9 essere una conseguenza della deformazione massima qualora essa superi la resistenza elastica offerta dal materiale di cui \u00E8 costituito il macchinario."@it . . . . . . "Rotordynamics, also known as rotor dynamics, is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotor dynamics is concerned with one or more mechanical structures (rotors) supported by bearings and influenced by internal phenomena that rotate around a single axis. The supporting structure is called a stator. As the speed of rotation increases the amplitude of vibration often passes through a maximum that is called a critical speed. This amplitude is commonly excited by imbalance of the rotating structure; everyday examples include engine balance and tire balance. "@en . . . "La th\u00E9orie des machines tournantes forme une branche de la m\u00E9canique du solide, et plus particuli\u00E8rement de la dynamique. Elle traite du comportement des masses en rotation, et trouve des applications aussi bien dans les moteurs et les r\u00E9acteurs, que dans les pompes, les disques durs ou le calcul des fondations."@fr . . . . . "Rotordynamics"@en . . . . "La velocit\u00E0 critica flessionale \u00E8 per definizione la velocit\u00E0 angolare applicata ad un rotore tale che la sua deformazione, di tipo esclusivamente flessionale, sia massima. \u00C8 importante sottolineare che \u00E8 di uso comune definire erroneamente la velocit\u00E0 critica flessionale come la velocit\u00E0 di funzionamento di un rotore che comporti la rottura di esso; infatti la rottura del rotore pu\u00F2 al pi\u00F9 essere una conseguenza della deformazione massima qualora essa superi la resistenza elastica offerta dal materiale di cui \u00E8 costituito il macchinario. Per poter fornire una pratico esempio si pu\u00F2 considerare il rotore di Jeffcott."@it . . . . . . "Dynamika rotor\u016F sjednocuje oblasti dynamiky tuh\u00FDch t\u011Bles (rotor\u016F), dynamiky tekutin (olejov\u00E9ho filmu kluzn\u00FDch lo\u017Eisek), pop\u0159\u00EDpad\u011B i problematiku dynamiky magnetick\u00FDch lo\u017Eisek mechatronick\u00FDch syst\u00E9m\u016F. Dynamika rotor\u016F popisuje mimo jin\u00E9 : \n* N\u00E1r\u016Fst amplitudy rotorov\u00E9ho chv\u011Bn\u00ED p\u0159i naj\u00ED\u017Ed\u011Bn\u00ED na provozn\u00ED ot\u00E1\u010Dky a brzd\u011Bn\u00ED z provozn\u00EDch ot\u00E1\u010Dek u syst\u00E9mu tvo\u0159en\u00E9ho rotorem a lo\u017Eisky. V d\u016Fsledku buzen\u00ED s ot\u00E1\u010Dkovou frekvenc\u00ED (1\u00D7) (od nev\u00FDva\u017Eku) je t\u0159eba p\u0159i naj\u00ED\u017Ed\u011Bn\u00ED a brzd\u011Bn\u00ED p\u0159ekon\u00E1vat ot\u00E1\u010Dkov\u00E1 p\u00E1sma, v nich\u017E m\u016F\u017Ee p\u0159i tzv. kritick\u00FDch ot\u00E1\u010Dk\u00E1ch doch\u00E1zet k rezonanci. \n* Stavy rezonance p\u0159i buzen\u00ED rotoru v\u00EDce r\u016Fzn\u00FDmi ot\u00E1\u010Dkov\u011B-harmonick\u00FDmi frekvencemi. Pokud je nap\u0159\u00EDklad rotor buzen ot\u00E1\u010Dkovou frekvenc\u00ED (1\u00D7) (od nev\u00FDva\u017Eku) a z\u00E1rove\u0148 dvojn\u00E1sobnou frekvenc\u00ED (2\u00D7) (nap\u0159\u00EDklad p\u0159i jednostrann\u00E9 trhlin\u011B), pak dojde k rezonanci tak\u00E9 p\u0159i polovi\u010Dn\u00ED hodnot\u011B ka\u017Ed\u00FDch kritick\u00FDch ot\u00E1\u010Dek. Ob\u011B\u017En\u00E9 lopatky axi\u00E1ln\u00EDch turb\u00EDn a disky rotor\u016F parn\u00EDch turb\u00EDn pak mohou b\u00FDt vybuzeny do rezonance i daleko vy\u0161\u0161\u00EDmi ot\u00E1\u010Dkov\u011B-harmonick\u00FDmi frekvencemi. \n* Zv\u00FD\u0161en\u00ED vlastn\u00EDch frekvenc\u00ED rotoru gyroskopick\u00FDm efektem disk\u016F rotoru a radi\u00E1ln\u00EDch ob\u011B\u017En\u00FDch kol. Zm\u011Bna vlastn\u00EDch frekvenc\u00ED rotoru a vlastn\u00EDch tvar\u016F kmit\u016F s ot\u00E1\u010Dkami, kv\u016Fli ot\u00E1\u010Dkov\u00E9 z\u00E1vislosti tuhosti kluzn\u00FDch lo\u017Eisek. \n* V\u00FDskyt subsynchronn\u00ED slo\u017Eky rotorov\u00E9ho chv\u011Bn\u00ED p\u0159i dosa\u017Een\u00ED a p\u0159ekro\u010Den\u00ED meze stability, p\u0159i n\u00ED\u017E se rotorov\u00E9 chv\u011Bn\u00ED vyvolan\u00E9 nev\u00FDva\u017Eky ( tzn. chv\u011Bn\u00ED s ot\u00E1\u010Dkovou frekvenc\u00ED) st\u00E1v\u00E1 nestabiln\u00ED. Dynamika rotor\u016F se jako in\u017Een\u00FDrsk\u00FD obor v\u00FDznamn\u011B rozvinula na konci devaten\u00E1ct\u00E9ho stolet\u00ED spolu s v\u00FDvojem a v\u00FDrobou parn\u00EDch turb\u00EDn. Probl\u00E9my dynamiky rotor\u016F je v\u0161ak nutno \u0159e\u0161it nejen p\u0159i v\u00FDvoji tepeln\u00FDch a vodn\u00EDch turb\u00EDn a gener\u00E1tor\u016F, ale objevuj\u00ED se nap\u0159\u00EDklad i p\u0159i v\u00FDvoji odst\u0159edivek, rychlob\u011B\u017En\u00FDch h\u0159\u00EDdel\u016F tkac\u00EDch stroj\u016F , bezkontaktn\u011B ulo\u017Een\u00FDch h\u0159\u00EDdel\u016F zubn\u00EDch vrta\u010Dek, nebo u pevn\u00FDch disk\u016F po\u010D\u00EDta\u010D\u016F."@cs . . . "Die Rotordynamik vereint die Fachgebiete der Festk\u00F6rperdynamik von Rotoren, der Dynamik der Str\u00F6mungsvorg\u00E4nge im Schmierspalt von Gleitlagern sowie bei der Verwendung aktiver Magnetlager die Dynamik mechatronischer Systeme. Die Rotordynamik beschreibt u. a.: Die Rotordynamik nahm als technische Wissenschaft mit der Entwicklung und der Produktion von Dampfturbinen Ende des 19. Jahrhunderts einen starken Aufschwung. Probleme der Rotordynamik waren nicht nur bei der Entwicklung thermischer und hydraulischer Turbomaschinen zu l\u00F6sen, sondern traten z. B. auch auf bei der Entwicklung von"@de . "Th\u00E9orie des machines tournantes"@fr . . "Die Rotordynamik vereint die Fachgebiete der Festk\u00F6rperdynamik von Rotoren, der Dynamik der Str\u00F6mungsvorg\u00E4nge im Schmierspalt von Gleitlagern sowie bei der Verwendung aktiver Magnetlager die Dynamik mechatronischer Systeme. Die Rotordynamik beschreibt u. a.: \n* Die Amplitudenvergr\u00F6\u00DFerungen der relativen Wellenschwingung beim Hoch- und Auslauf von Rotor-Lagersystemen. Infolge der drehfrequenten (1X) Unwuchterregung werden Resonanzen bei kritischen Drehzahlen durchfahren. \n* Resonanzzust\u00E4nde bei Erregung eines Rotors durch mehrere Drehzahlharmonische. Wird z. B. ein Rotor durch die Unwucht drehfrequent (1X) und durch einen einseitigen Wellenriss mit der doppelten Drehfrequenz (2X) erregt, so herrscht Resonanz auch beim halben Wert jeder kritischen Drehzahl. Die Laufschaufeln axialer Turbomaschinen und scheibenf\u00F6rmige Bauteile von Dampfturbinenrotoren (Schirmschwingungen) k\u00F6nnen durch weit h\u00F6here Drehzahlharmonische in Resonanz angeregt werden. \n* Anhebung von Rotoreigenfrequenzen durch die Kreiselwirkung scheibenf\u00F6rmiger Bauteile von Rotoren und radialer Laufr\u00E4der. Ver\u00E4nderung der Rotoreigenfrequenzen und Eigenschwingungsformen mit der Drehzahl durch die Drehzahlabh\u00E4ngigkeit der Steifigkeit der Gleitlager. \n* Das Auftreten subsynchroner Anteile der Wellenschwingung beim Erreichen und \u00DCberschreiten der , an der die unwuchterregte (d. h. drehfrequente) Wellenschwingung instabil wird. Die Rotordynamik nahm als technische Wissenschaft mit der Entwicklung und der Produktion von Dampfturbinen Ende des 19. Jahrhunderts einen starken Aufschwung. Probleme der Rotordynamik waren nicht nur bei der Entwicklung thermischer und hydraulischer Turbomaschinen zu l\u00F6sen, sondern traten z. B. auch auf bei der Entwicklung von \n* Zentrifugen \n* schnell laufenden Spindeln von Spinnmaschinen \n* luftgelagerten Spindeln von Bohrern in der Dentaltechnik \n* in den vergangenen Jahrzehnten bei der Entwicklung von Festplattenlaufwerken."@de . "Rotordynamik"@de . . . . . . . . "Kritiskt varvtal"@sv . . "La th\u00E9orie des machines tournantes forme une branche de la m\u00E9canique du solide, et plus particuli\u00E8rement de la dynamique. Elle traite du comportement des masses en rotation, et trouve des applications aussi bien dans les moteurs et les r\u00E9acteurs, que dans les pompes, les disques durs ou le calcul des fondations."@fr . "Velocit\u00E0 critica flessionale"@it . . . . . . . . . . . . . . . . . . "19645"^^ . . . . . . .