Vibration Analysis for Industrial Machinery: Modal, Harmonic and Random Vibration Explained

Every structure has natural frequencies, set by its stiffness and mass. Problems start when an excitation frequency lands on one of them. Common sources in machinery are:

• Rotating unbalance at the running speed, and misalignment, which often shows at twice the running speed.
• Gear mesh at the number of teeth times the shaft speed.
• Blade and vane pass in fans, pumps, compressors and turbines.
• Electromagnetic forces in motors and generators, including vibration at twice the line frequency.
• Impacts and reciprocating motion in presses, punches and robots stopping and starting.

Simulation can predict these excitations too: an electromagnetic FEA of a synchronous machine gives the torque and magnetic behaviour of a motor, and a CFD analysis of a wind turbine gives the rotor speed that sets its forcing frequencies.

Modal analysis is the starting point. It calculates the natural frequencies of the structure and shows the shape it takes at each one.

• The model has to include how the machine is really supported: its foundation, mounts and bolted connections all change the frequencies.
• A common rule of thumb is to keep natural frequencies at least 10 to 20 % away from the excitation frequencies.
• The mode shapes show where the structure moves most, which is exactly where stiffening is most effective.

For machines that run at different speeds, a Campbell diagram plots the natural frequencies against the running speed, together with the excitation lines (1×, 2×, gear mesh and so on). Where they cross are the critical speeds to avoid or to pass through quickly. Rotor dynamics analysis adds effects such as gyroscopic forces and bearing stiffness that change with speed.

Knowing a resonance exists is not always enough; you also need to know whether it matters. Harmonic response analysis applies the real forces at their frequencies and calculates the resulting vibration.

• The results can be compared with vibration limits, such as the evaluation zones of ISO 20816 (which replaced ISO 10816) for machine vibration.
• Damping has a big effect at resonance, so realistic damping values matter.

Equipment that is transported, mounted in vehicles or launched into space sees random vibration rather than a single frequency. Random vibration analysis uses a power spectral density (PSD) input to predict stresses and fatigue, and shock analysis covers short, sharp events such as drops and impacts.

Launch vibration was one of the effects considered in our thermal-mechanical stress analysis of a 1U CubeSat, and vibration and shock are key loads for structures such as the one in our FEA of a battery module frame.

• Change the stiffness: add ribs or bracing, or thicken plates where the mode shape moves most.
• Change the mass: moving or adding mass shifts the natural frequency away from the excitation.
• Change the speed: with a variable-speed drive, skip bands can keep the machine away from critical speeds.
• Isolate: isolation mounts reduce the vibration passed on to the floor and to nearby equipment, but only well above the natural frequency of the isolation system itself.
• Add damping: tuned mass dampers and damping layers reduce the peak at a stubborn resonance.
• Reduce the source: balance rotors to a suitable grade (ISO 21940-11) and correct misalignment.

For machines in service, the most reliable approach combines measurement and simulation:

• Field measurements, such as accelerometer readings, operating deflection shapes or an impact hammer test, show the frequencies and shapes the real machine has.
• The FEA model is then tuned to match them, so it can be trusted.
• Fixes are tested on the tuned model before anything is changed on site, so the first modification is the right one.

Cover photo: Isis França on Unsplash