Machine Resonance: How to Identify It and What to Do

Resonance occurs when an external force acts at a frequency that matches the natural frequency of a machine or structure, and the vibration is amplified many times. Its signs are a vibration peak at a certain speed, a phase shift and a strong dependence of the level on direction. It is confirmed with a bump test and a coast-down or run-up recording. It is corrected by separating the frequencies: changing stiffness, mass or speed, or adding an absorber.

What resonance is

Every machine and structure has natural frequencies. Resonance is the result of an external force vibrating at the same frequency as the natural frequency of the system (Pellegrino, ReliablePlant). At that frequency vibration is amplified significantly, which can cause equipment failure and downtime. Pellegrino calls resonance a very common cause of excessive machine vibration.

What happens physically is easy to see on a rotor (Mobius Institute):

• up to about 60% of the natural frequency the rotor acts as a rigid rotor, and the "heavy spot" and "high spot" nearly coincide;
• at the natural frequency the stiffness and mass forces cancel, leaving a force proportional to damping; the high spot lags the heavy spot by 90°;
• above the critical speed the lag reaches 180°.

The lower the damping, the greater the amplification at resonance and the more abruptly the phase changes: in a lightly damped system the phase barely changes until the frequency is close to the natural frequency.

The exact frequency is not the only danger. According to Vibration Research, frequencies within about ±10% of the natural frequency also cause noticeable amplification.

Signs of resonance

Sign	What you see
Speed dependence	Vibration is high at one speed and drops noticeably when the speed changes
Peak on coast-down	When stopping, the level does not fall steadily but rises and passes through a maximum at a certain speed
Phase	A 90° shift at the natural frequency; passing through resonance the phase changes by 180°
Directionality	The level in one direction is many times higher than in the others
Spectrum	A high narrow peak; when the speed changes, the peak stays at the same frequency

On directionality: Mike Fitch (Ludeca) gives an example where the horizontal component was 75–100 times the vertical and axial, and calls it almost unquestionably a resonance problem. The reason is that stiffness, and therefore natural frequencies, differ between directions: on a pump, according to Ludeca, the natural frequency in line with the discharge pipe is usually higher than at 90° to it.

A 1x peak on its own looks like unbalance, so resonance is easily mistaken for it. How to tell unbalance, misalignment and looseness apart in the spectrum is covered in How to read an FFT spectrum.

Test 1. Bump test

EASA calls a simple bump test on a stopped machine a good first step in identifying the natural frequency.

1. Mount an accelerometer on the component of interest, in the direction where vibration is high.
2. Strike the structure with a mass: a soft-tipped hammer (modal hammer) or a block of wood. The impact delivers a small force over a wide range of frequencies at once.
3. Record the response spectrum. Its peaks are the natural frequencies.
4. Repeat in other directions. For a pump, Ludeca recommends at least two: in line with the discharge pipe (usually a higher frequency, the pipe stiffens the structure) and at 90° to it (usually a lower frequency).
5. Compare the frequencies found with running speed and its harmonics, vane pass frequency and other exciting frequencies.

Pellegrino notes that all of a structure's resonant frequencies can always be measured by impacting at one location, and recommends taking both drive point and transfer point measurements. With an instrumented hammer (with a force sensor) the analyzer sees both the force and the response; the natural frequency is where the phase between them shifts by 90°.

Test 2. Coast-down and run-up: Bode plot and waterfall

A bump test shows the natural frequencies of the machine at rest. A coast-down or run-up recording shows what happens in operation.

Simple version (coast-down peak hold). The instrument in peak hold mode records the level while the machine stops. Without resonance the level drops at a steady rate. If at some speed the amplitude starts to rise, that speed is a possible natural frequency.

Version with phase. A piece of reflective tape on the shaft and a photo tachometer let you track both the amplitude and the phase of 1x. A Bode plot is built: amplitude and phase versus speed. If a peak in amplitude coincides with a phase shift at the same frequency, resonance is likely. The natural frequency lies in the middle of the 180° phase transition.

Waterfall (cascade of spectra). Spectra are taken at small speed steps and stacked. Brüel & Kjær explains how to read it: running speed harmonics lie on radial lines through the point "0 Hz, 0 rpm", while structural resonances lie on constant-frequency lines. Where the 1x or 2x line crosses a resonance line, vibration rises. In B&K's turbogenerator coast-down example, a resonance near 1000 rpm with its peak at 16.9 Hz was excited by both the first and second harmonics, and the increased level at 2700 rpm matched the critical speed of 45.8 Hz stated by the manufacturer.

Pellegrino advises confirming a natural frequency with at least two tests, for example a bump test and a coast-down, before changing anything on the machine.

Operating deflection shape (ODS)

Once the frequency is found, the next question is what exactly is vibrating: the frame, a support, piping or the rotor itself. For this an operating deflection shape (ODS) is built: an animation of how the machine and structure move in operation.

• You need the amplitude and phase at each point relative to all the others.
• With few channels, one reference accelerometer stays in place while another is moved between points and directions. This method works for frequency or order domain data.
• The points are mapped to a geometry model, and the software shows the animation.

The animation shows which element moves most and where stiffness should be added.

What to do about resonance

The goal is to separate the exciting frequency from the natural frequency or to reduce the amplification.

Method	How it works	Example
Change speed	The operating frequency moves away from the natural frequency	Pellegrino: change the speed by 20–30%
Increase stiffness	The natural frequency rises	Stiffen the resonating support or frame
Change mass	More mass lowers the natural frequency, less mass raises it	Add or remove mass on the support
Dynamic absorber	A spring-mass system creates an out-of-phase force	Installed on the resonating component
Damping	Reduces amplification at resonance	The more damping, the lower the peak
Reduce excitation	Less force, less response	Balancing, alignment

Where to move the frequency is decided from the test results: the new natural frequency must not end up next to another exciting frequency, such as the next harmonic. Vibration Research gives a design rule of separating driving forces and natural frequencies by a factor of two.

Balancing reduces only the force, not the amplification: a machine near resonance will be sensitive even to a small residual unbalance. When balancing really helps and when the cause lies elsewhere is covered in On-site rotor balancing.

Which instrument to use

A bump test, coast-down and phase measurements need an analyzer with a phase reference. According to the manufacturer's datasheet, the Bently Nevada vb7 records two channels simultaneously and offers coast-down and run-up, bump test, cross-channel phase and orbit plots, a laser speed sensor and Keyphasor tach mode; modal analysis is available as an add-on option. KEG TRK supplies Bently Nevada equipment in Kazakhstan. Price on request.

Sources

• Alain Pellegrino, Laurentide Controls. How to Identify, Correct a Resonance Condition, ReliablePlant.
• Jim Cahill, Emerson. Spotting and Fixing Resonance in Plant Equipment.
• Mobius Institute. Vibration Matters newsletter on system dynamics, Maintworld.
• Vibration Research. Data Analysis for Identifying Resonances.
• Brüel & Kjær. Technical Review No. 2-1995: Order Tracking Analysis.
• Siemens. What is an Operational Deflection Shape (ODS)?.
• Ludeca. Pump resonance: bump test and run-up/coast-down.
• Mike Fitch, Ludeca. Location, Location, Location: Vibration Sensor Placement Is Crucial.
• EASA. How to Conduct a "Bump Test" for Resonance.
• Bently Nevada. vb7 Portable Data Collector, Analyzer and Balancer, datasheet 116M5255 Rev. F.