Brezplačno inženirsko orodje
Kalkulator naravnih frekvenc
Izračunajte naravno frekvenco sistema masa-vzmet. Vnesite maso in togost vzmeti, da dobite frekvenco v Hz, kotno frekvenco, periodo, ekvivalentne vrtljaje in statični odklon.
Rezultati
Naravna frekvenca sistema masa-vzmet
Naravna frekvenca nedušenega sistema masa-vzmet z eno stopnjo svobode:
- k — togost vzmeti (N/m). Če je podana v N/mm, jo pomnožite s 1000.
- m — masa (kg)
Kotna frekvenca
Perioda in statični poves
Kje g = 9,81 m/s², k pa je v N/mm za rezultat povesa v mm.
Praktični primer
Dano: Masa stroja = 150 kg, skupna togost vzmeti k = 300 N/mm
k v N/m = 300 × 1000 = 300.000 N/m
f_n = (1/2π) × √(300.000/150) = (1/6,2832) × 44,72 = 7,12 Hz
ω_n = 2π × 7,12 = 44,7 rad/s
T = 1/7,12 = 0,140 s
Ekvivalent vrtljajev na minuto = 7,12 × 60 = 427 RPM
δ_static = 150 × 9,81 / 300.000 × 1000 = 4,9 mm
⚠️ Opomba: Zagotovite, da je delovna hitrost vsaj 20–30% oddaljena od naravne frekvence, da se izognete resonanci. Če obratujete blizu resonance, dodajte dušenje ali spremenite togost/maso.
Natural frequency is the frequency at which a system oscillates freely after being displaced from its equilibrium position and released. For a mass-spring system, it depends only on the mass and the spring stiffness.
Every mechanical structure has one or more natural frequencies, and they are fundamental properties used in vibration analysis, structural design, and machine diagnostics.
Knowing the natural frequency of a machine or its components is critical because if the operating speed (excitation frequency) coincides with the natural frequency, resonance occurs.
Resonance causes dramatically amplified vibrations that can lead to excessive wear, fatigue failure, bearing damage, and even catastrophic structural collapse. Engineers design machines so that operating speeds are well separated from natural frequencies.
Spring stiffness (rate) can be measured by applying a known force to the spring and measuring the resulting deflection. Stiffness k = Force / Deflection.
For example, if a 100 N force compresses a spring by 2 mm, the stiffness is 100/2 = 50 N/mm. You can also use a compression testing machine for accurate results, or consult the manufacturer's datasheet for the spring rate specification.
When the operating speed (excitation frequency) matches the natural frequency of the system, resonance occurs. At resonance, vibration amplitudes increase dramatically — theoretically to infinity in an undamped system, and to very high levels in real (lightly damped) systems.
This can cause rapid fatigue failure, excessive noise, bearing damage, and structural collapse. This is why vibration analysis always checks for proximity to resonance.
There are several strategies to avoid resonance:
- Change the operating speed so it is at least 20–30% away from any natural frequency
- Modify the stiffness by adding braces, stiffeners, or changing spring rates
- Change the mass of the vibrating component
- Add damping using vibration dampers, rubber isolators, or tuned mass dampers
- Use variable-speed drives to avoid dwelling at critical speeds during startup or shutdown
Postopki, opisani na tej strani, so bili razviti in terensko preizkušeni s strani ekipe Vibromera z uporabo naprave Balanset-1A, prenosnega dvokanalnega uravnoteževalnika in analizatorja vibracij za uravnoteženje rotorjev na mestu uporabe.
Profesionalni prenosni uravnoteževalniki, analizatorji vibracij in sistemi za spremljanje stanja, ki se uporabljajo v več kot 50 državah. Prepoznajte težave z resonanco in uravnotežite rotorje na kraju samem.
Nikolai Shelkovenko
Nikolai Shelkovenko je inženir vibracijske analize ter ustanovitelj in izvršni direktor podjetja Vibromera. Že več kot 15 let uravnotežuje vrtečo se opremo na terenu, in ne na preizkuševališču: mulčerje, industrijske ventilatorje, drobilnike, centrifuge, gredi in vretena. Prav iz tega dela so nastali instrumenti Balanset — zasnovani so bili kot orodje, ki ga strokovnjak lahko prinese do stroja in ga uporabi sam, na mestu samem, ne pa kot laboratorijska oprema. Vibromera je bila ustanovljena leta 2017, od leta 2023 pa ima sedež v Portu na Portugalskem. Tu potekajo razvoj, sestavljanje in podpora za linijo Balanset. Vodilni instrument je Balanset-1A, prenosni analizator za enoravninsko in dvoravninsko uravnoteženje ter za vibracijsko diagnostiko. Nikolai osebno sodeluje pri podpori strankam, pri reševanju zahtevnih primerov uravnoteženja in pri razvoju programske opreme. S strankami dela po vsem svetu, v katerem koli jeziku.
