Compreendendo o chicote de eixo em máquinas rotativas
Chicote de eixo — known as batedor de óleo when it originates in hydrodynamic bearings — is a severe form of instabilidade do rotor marked by violent vibração autoexcitada. It appears when a rotor running in fluid-film bearings exceeds a critical threshold speed, typically around twice the first velocidade crítica. Once whip takes hold, the vibration frequency “locks” onto the rotor’s first frequência natural and stays there regardless of any further speed increase, with amplitude limited only by bearing clearance — or by catastrophic failure. It is one of the most dangerous conditions in high-speed machinery because it develops suddenly, grows to destructive levels within seconds, and cannot be cured by balanceamento or any other conventional correction. It demands immediate shutdown followed by changes to the bearing system to prevent recurrence.
1. The Progression: From Oil Whirl to Shaft Whip
Whip rarely arrives without warning — it is the end point of a four-stage progression that an attentive analyst can intercept long before the destructive stage.
Stage 1 — Stable Operation
- The rotor runs below the instability threshold.
- Only normal vibração forçada de desequilíbrio is present.
- The bearing oil film provides stable, well-damped support.
Stage 2 — Oil Whirl Onset
As speed climbs past roughly 2× the first critical speed, redemoinho de óleo begins:
- A subsíncrono vibration appears at about 0.43–0.48× shaft speed.
- A amplitude é inicialmente moderada e dependente da velocidade
- The whirl frequency rises proportionally with shaft speed.
- It may be intermittent or continuous.
- It can coexist with the normal 1× vibration from unbalance.
Stage 3 — The Whip Transition
When the rising oil-whirl frequency climbs far enough to match the first natural frequency, the behaviour changes character abruptly:
- Frequency lock-in: the vibration frequency stops tracking speed and pins itself to the natural frequency.
- Resonant amplification: amplitude grows dramatically because the system is now in ressonância.
- Sudden onset: the jump from whirl to whip can be effectively instantaneous.
- Independência em relação à velocidade: further speed increases no longer change the frequency — only the amplitude.
Stage 4 — Shaft Whip (Critical Condition)
- Vibration sits at a constant frequency — the first natural frequency, typically 40–60 Hz.
- Amplitude reaches 5–20 times the normal unbalance vibration.
- The shaft may strike its bearing-clearance limits.
- Bearings and oil heat rapidly.
- Catastrophic failure can follow within minutes if the machine is not stopped.
2. O mecanismo físico
Whip is driven by the fluid dynamics of the bearing oil film itself, which is why it cannot be balanced away — the destabilising energy comes from the lubricant, not from a heavy spot. The sequence runs as follows:
- Oil-wedge formation: the rotating shaft drags lubricant around the bearing, building a pressurised wedge.
- Tangential force: that wedge pushes on the journal in a direction perpendicular to the radial offset — a cross-coupled, tangential force.
- Orbit motion: the tangential force drives the shaft centre to whirl in an órbita at roughly half shaft speed.
- Energy extraction: the orbiting motion draws energy out of the shaft’s rotation to sustain itself — the hallmark of a self-excited vibration.
- Resonance lock: when the orbit frequency coincides with the natural frequency, resonance amplifies the motion.
- Limit cycle: amplitude grows until it is bounded by bearing clearance or by failure.
Because the exciting force scales with the lubricant’s behaviour, anything that raises the oil-film stiffness or the system amortecimento raises the speed at which instability begins.
3. Identificação do diagnóstico
Shaft whip leaves an unmistakable fingerprint in vibration data, which makes early recognition possible if the right plots are reviewed.
Assinatura de vibração
- Espectro: a large peak at the sub-synchronous (first natural) frequency that stays put regardless of speed changes.
- Terreno em cascata: the sub-synchronous component shows up as a vertical line (constant frequency) rather than the diagonal line of a speed-proportional component.
- Análise de pedidos: a fractional order that diminui as speed rises — for example drifting from 0.5× to 0.4× to 0.35× — because the frequency is fixed while speed climbs.
- Órbita: a large circular or elliptical orbit at the natural frequency.
A Diagrama de Bode taken on desaceleração further separates a true resonance from a whip, since the locked sub-synchronous line behaves quite differently from the synchronous critical-speed peak.
Velocidade de início
- Typical threshold: 2.0–2.5× the first critical speed.
- Bearing-dependent: the exact threshold varies with bearing design, pré-carga, and oil viscosity.
- Sudden onset: a small speed increase can trip the rotor from stable to fully unstable.
4. Estratégias de prevenção
Because whip cannot be balanced out, prevention focuses on the mancal de deslizamento and on how the machine is operated.
Modificações no projeto do rolamento
1. Tilting-pad bearings — the most effective fix. The pads pivot independently, eliminating the destabilising cross-coupling force; they are inherently stable across a wide speed range and are the industry standard for high-speed turbomachinery.
2. Pressure-dam bearings — a modified cylindrical bearing with a groove or dam that raises effective damping and stiffness; cheaper than tilting-pad but less effective.
3. Bearing preload — applying radial preload (often through an offset-bore design) raises stiffness and pushes the instability threshold higher.
4. Amortecedores de película comprimida — an external damping element surrounding the bearing that adds damping without redesigning the bearing itself, well suited to retrofits.
Medidas Operacionais
- Speed limitation: hold maximum speed below the threshold — typically under 1.8× the first critical.
- Gerenciamento de carga: run at higher bearing loads where possible, since load increases damping.
- Oil-temperature control: a cooler oil is more viscous and more stabilising.
- Monitoramento: contínuo monitoramento de vibração with alarms specifically watching the sub-synchronous band.
5. Consequências e danos
Efeitos imediatos
- Violent vibration: amplitudes can reach several millimetres (hundreds of mils).
- Barulho: a loud, distinctive sound quite unlike normal operation.
- Rapid bearing heating: temperatures can climb 20–50 °C in minutes.
- Degradação do óleo: high temperature and intense shearing break down the lubricant.
Falhas potenciais
- Bearing wipe: the babbitt lining melts and is wiped away.
- Danos no eixo: scoring, galling, or permanent bending.
- Seal failure: excessive shaft motion destroys seals.
- Shaft breakage: de alto ciclo fadiga from the violent oscillation.
- Coupling damage: the transmitted forces wreck couplings.
6. Related Phenomena
Redemoinho de óleo
Redemoinho de óleo is the precursor to whip: the same mechanism, but the frequency has not yet locked onto the natural frequency. Its amplitude is lower, its frequency tracks speed at ~0.43–0.48×, and in some applications it is tolerable.
Redemoinho de vapor
Turbilhão de vapor is a similar instability in steam turbines, driven by aerodynamic forces in labyrinth seals rather than the bearing oil film. It shows the same sub-synchronous vibration locking onto a natural frequency.
Dry-Friction Whip
This variant arises at seal locations or from contato entre o rotor e o estator. Friction supplies the destabilising mechanism; it is less common than oil whip but equally dangerous and calls for a different remedy — eliminating the contact or improving the seal.
7. Case Study: Compressor Shaft Whip
Cenário: a high-speed centrifugal compressor on plain cylindrical bearings.
- Operação normal: 12,000 rpm with vibration of 2.5 mm/s.
- Speed increase: the operator pushed to 13,500 rpm for more capacity.
- Início: at 13,200 rpm a sudden violent vibration developed.
- Sintomas: 25 mm/s at a constant 45 Hz; bearing temperature rose from 70 °C to 95 °C in three minutes.
- Emergency action: immediate shutdown averted a bearing failure.
- Causa raiz: the first critical speed was 2,700 rpm (45 Hz); the whip threshold at 2× critical = 5,400 rpm had been far exceeded.
- Solução: plain bearings were replaced with tilting-pad bearings, allowing safe operation to 15,000 rpm.
8. Standards, Practice, and Field Tools
- API 684: requires a rotordynamic stability analysis for high-speed turbomachinery.
- API 617: specifies bearing types and stability requirements for centrifugal compressors.
- ISO 10814: Fornece orientação sobre a seleção de rolamentos para estabilidade
- Industry practice: tilting-pad bearings are standard for equipment running above 2× the first critical speed.
In the field, the everyday safeguard is to catch the precursor before the rotor ever reaches whip. A portable two-channel analyser such as the Conjunto de equilíbrio-1a lets an engineer record amplitude, fase and spectrum during a controlled run-up and watch the sub-synchronous band directly — if a stable 1× signature suddenly grows a locked, speed-independent peak near the first natural frequency, the rotor is on the edge of whip and the speed must be backed off. The same instrument confirms afterwards that the underlying unbalance is within tolerance, ruling it out as a contributing excitation. Shaft whip remains a catastrophic failure mode best handled by correct bearing selection and design; recognising its distinctive sub-synchronous, frequency-locked signature is what enables rapid diagnosis and the decisive emergency response that protects expensive high-speed equipment.
