Zorlanmış Titreşimi Anlamak
Zorlanmış titreşim is oscillatory motion caused by an external periodic force acting on a mechanical system. The vibration occurs at the frequency of the applied force — the forcing frequency — and its amplitude is proportional to the magnitude of that force and inversely proportional to the system’s resistance to motion at that frequency. The overwhelming majority of titreşim in rotating machinery is forced vibration, with the usual culprits being dengesizlik (a rotating centrifugal force), yanlış hizalama (coupling forces), and aerodynamic or hydraulic pulsations. Forced vibration is fundamentally different from kendi kendini uyaran titreşim, where the system generates and sustains its own oscillation, and from free vibration, the transient ring-down that follows an impulse. Grasping these principles matters because they explain how vibration amplitude relates to fault severity and how vibration can be controlled — either by reducing the forcing or by modifying the system’s response.
1. Characteristics of Forced Vibration
Frequency matching
- The vibration frequency equals the forcing frequency — force the system at 30 Hz and it vibrates at 30 Hz.
- This is unlike self-excited vibration, which locks onto a doğal frekans regardless of the driving rate.
- The frequency is therefore predictable directly from the forcing source.
Amplitude proportionality
- Amplitude is proportional to the forcing magnitude: double the force and (in a linear system) you double the vibration.
- Remove the forcing and the vibration stops — which is precisely why it is controllable.
Phase relationship
- There is a definite faz relationship between force and response.
- That phase depends on the forcing frequency relative to the natural frequency:
- Rezonansın altında: the vibration is essentially in phase with the force.
- Rezonansta: a 90° phase lag.
- Above resonance: a 180° phase lag.
İstikrar
- The system is stable: the vibration is bounded and does not grow without limit.
- Amplitude is set by the forcing and the system response together — the opposite of unstable self-excited vibration, which can run away until a nonlinearity arrests it.
2. Common Forcing Functions in Machinery
Unbalance — 1× forcing
- Güç: a rotating centrifugal force from mass eccentricity.
- Sıklık: once per revolution (1× shaft speed).
- Büyüklük: F = m·r·ω², so it rises with the kare of speed.
- Önemi: the primary vibration source in most rotating equipment.
That ω² dependence is worth dwelling on: doubling the running speed quadruples the unbalance force, which is why a rotor that runs quietly at low speed can shake violently when brought up to duty. You can put numbers to it with our Dengesizlikten Kaynaklanan Merkezkaç Kuvveti Hesaplayıcısı.
The other principal sources
- Misalignment — 2× forcing: coupling forces from angular or parallel offset, producing vibration at twice shaft speed and a characteristically high eksenel bileşen.
- Aerodynamic / hydraulic (blade or vane passing): pressure pulsations from blade–stator interaction at the number of blades × shaft speed — the signature of fans, pumps and compressors, driven by aerodinamik ve hidrolik kuvvetler.
- Gear mesh forces: tooth engagement creating periodic loading at the number of teeth × shaft speed (the dişli örgü frekansı), with a magnitude tied to transmitted torque and tooth quality.
- Elektromanyetik kuvvetler: magnetic-field pulsations in motors and generators at 2× line frequency (120 Hz on a 60 Hz supply, 100 Hz on 50 Hz) — notably independent of mechanical speed, an asynchronous forcing.
3. Response to Forcing: How the System Behaves
The same force produces wildly different amplitudes depending on where the forcing frequency sits relative to the system’s natural frequency. Three regimes describe it.
Below natural frequency (stiffness-controlled)
- Amplitude ≈ Force ÷ Sertlik.
- Response is in phase with the forcing.
- For speed-dependent forces, amplitude rises with speed.
- The typical operating region for most sert rotorlar.
At natural frequency (resonance)
- Amplitude ≈ Force ÷ (Damping × Natural Frequency).
- Amplified by the Q-factor, typically 10–50×.
- A 90° phase lag, and small forces now create large vibration.
- Sönümleme is the only thing limiting the amplitude — the practical importance of rezonans.
Above natural frequency (mass-controlled)
- Amplitude ≈ Force ÷ (Mass × Frequency²).
- A 180° phase lag — the vibration moves opposite to the force direction.
- Amplitude falls as frequency rises.
- The operating region for esnek rotorlar running above their kritik hızlar.
4. Forced Vibration vs Other Types
Forced vs free vibration
- Zoraki: Sürekli zorlama, titreşim sürdürülür, zorlama frekansında
- Özgür: an impulse response that decays, at the natural frequency.
- Örnek: A çarpma testi produces free vibration; a running machine produces forced vibration.
Forced vs self-excited vibration
- Zoraki: an external force, amplitude proportional to that force, stable.
- Self-excited: an internal energy source, amplitude limited only by nonlinearity, unstable.
- Örnekler: unbalance is forced; petrol girdabı is self-excited.
5. Control and Mitigation
Reduce the forcing (usually the best route)
- Dengeleme: reduces unbalance forcing directly and is the most common corrective action.
- Hizalanma: reduces misalignment forces.
- Repair defects: fix the mechanical problems generating the forces.
- Most effective: eliminating or minimising the forcing source at its origin.
Modify the system response, or avoid resonance
- Change stiffness or mass: Doğal frekansları zorlayıcı frekanslardan uzaklaştırın
- Add damping: blunt the resonant amplification.
- İzolasyon: reduce force transmission into the supporting structure.
- Avoid resonance: keep forcing frequencies clear of natural frequencies, with a separation margin of about ±20–30%, verified by design-phase analysis and enforced with speed restrictions if a clash is unavoidable.
6. Practical Significance and Diagnosis
Because almost all machinery vibration is forced — unbalance, misalignment, gear mesh and the rest — it is also predictable and controllable, and the standard maintenance actions of balancing and alignment work precisely because they attack the forcing. The diagnostic approach follows directly: identify the forcing frequency from the spectrum, match it to a known source (1×, 2×, gear mesh, vane passing), diagnose that source, and reduce the forcing with the appropriate maintenance.
This is where field instrumentation earns its place. A portable two-channel analyser such as the Denge-1a measures the vibration genlik and phase at the running speed, lets you read the spectrum to separate a 1× unbalance peak from a 2× misalignment peak, and — having identified unbalance as the dominant forcing — corrects it on the spot by alan dengeleme the rotor in its own bearings. Measuring phase as well as amplitude is what distinguishes a forcing problem from a resonance problem, since the two behave very differently as speed changes.
Forced vibration is the fundamental vibration type in rotating machinery, arising whenever an external periodic force acts on the system. Understanding its principles — frequency matching, amplitude proportionality, and the stiffness-, damping- and mass-controlled response regions — is what enables correct diagnosis of vibration sources, the right corrective action (reduce the forcing or modify the response), and design strategies that keep vibration low through forcing reduction and resonance avoidance.
