# How to Diagnose and Prevent Resonance

June 7th, 2016

#### By: Grant Slinger - Mechanical Engineer II

As vibration consultants at Pioneer Engineering we are frequently called out to investigate machinery that exhibits excessive vibration. Often it is assumed that simply balancing the rotor will make the vibration problem go away. However, upon further investigation it is not uncommon to find that a structural resonance is the root cause of excessive vibration, and balancing is not a viable or long term solution to the problem. This is particularly common in variable speed equipment or equipment that has recently undergone a running speed change. But what is resonance and how do you properly diagnose and correct the problem?

##### What is Resonance?

There are two types of vibration that need to be considered when investigating a potential resonance problem; forced vibration and free vibration. Forced vibration occurs when an object is forced to vibrate at a particular frequency by an oscillating input or force (such as an unbalance force). Free vibration occurs when an object is given an initial displacement and then allowed to “ring down” with no external force acting to keep it in motion. The frequency that this free vibration naturally wants to occurs at is known as the natural frequency. If an object is being forced to vibrate at its natural frequency, resonance will occur. This is what causes large amplitudes of vibration when a machine’s running speed is at or near a natural frequency even if the force inputs are low.

##### How to Identify Resonance

Several different field tests can be performed to verify that resonance is in fact the cause of excessive vibration in a system. Two of the most common tests are a modal impact test and a startup or coastdown data collection.

###### Startup and Coastdown Analysis

Vibration data collected during a machine startup or shutdown provides a wealth of information that is not available from steady-state data. Most importantly, it provides the ability to compare vibration amplitude and phase throughout the entire operating speed range. Different sources of vibration behave differently with changing speed. For instance, unbalance typically causes vibration amplitudes that increases exponentially with increasing speed. Misalignment typically causes vibration that increases linearly with increasing speed. Resonance however, is characterized by a large increase in vibration at the resonant frequency but generally lower amplitudes at all other speeds. The cascade plot below shows an example of typical vibration exhibited during startup of a machine with a structural natural frequency in its operating speed range.

###### Modal Impact Test

Often known as an impact test or a modal analysis, this is a method that allows us to experimentally determine the natural frequencies, mode shapes, and damping of a test structure. If any one of the calculated natural frequencies are within or near the operating speed range of a machine, there is the potential for a resonant condition to occur. Typically field modal testing is performed with a calibrated modal impact hammer. The hammer contains a load cell in the tip which provides a direct measurement of the impact force of applied to the system. Accelerometers are placed throughout the test structure to measure the response, or ringdown, of the system to the hammer’s impact. A spectrum of this ringdown can be used to determine the natural frequencies of the system. This test is typically performed with the machine turned off, however advanced signal processing can also be used to average out running condition vibration and identify only the free vibration.

##### How to Avoid Resonance

As we’ve seen, resonance occurs when the natural frequency of a system coincides with any expected forced vibration frequencies (such as unbalance) which can lead to severe levels of vibration. If it is determined that resonance is in fact the cause of excessive vibration, what can be done to stop or minimize the effect of a resonant condition?

The natural frequency of a system is dependent upon two main factors; stiffness, and mass. If the natural frequency is w, w = sqrt(k/m).

Where k is the stiffness and m is the mass. Therefore, in order to change the natural frequency, we need to change either k or m or both. Typically, the objective is to increase the natural frequency such that it is above any expected vibration frequencies. If the natural frequency is above or significantly far away from any expected vibration frequencies the resonance will likely no be excited. This theory forms the basis for any structural redesigns implemented to avoid resonance.

In practice, the following rules can be used to shift a natural frequency and minimize the vibration response of a system;

- Adding stiffness increases the natural frequency
- Adding mass decreases the natural frequency
- Increasing damping reduces the peak response but widens the response range
- Decreasing damping increases the peak response but narrows the response range
- Reducing forcing amplitudes reduces response at resonance

If changing the natural frequency is determined to be the best solution, it is important to fully characterize the system before attempting any structural redesigns. Recently we performed a startup vibration analysis on a small building adjacent to a 200 MW natural gas power turbine. On startup it was noted that there was a large increase in vibration in the building when the turbine went through the 700 rpm range. A modal impact test of the building showed a natural frequency at the same 700 cpm frequency, confirming the presence of a resonant condition. One could easily assume just adding stiffness to the support structure of the building would reduce vibration amplitudes. However, it was known that the first shaft critical of the rotor was around 1500 cpm. If stiffness were blindly added to the structure it could easily shift the natural frequency into the 1500 cpm range thus making the vibration significantly worse. In this instance it may actually be better to add mass to the system and shift the natural frequency down to a frequency where the forces are lower.

At Pioneer Engineering we recommend using a validated finite element analysis (FEA) model of a structure to determine the optimal design changes in order to fix and avoid resonant conditions. This allows us to test various different potential design changes in a computer simulation first before recommending any structural changes. Watch Pioneer’s feed for the next article entitled “Importance of validating FEA models” for more information about how Pioneer Engineering validates and tests structural redesigns to guarantee resonance is avoided.

Pioneer Engineering has extensive experience with performing modal analysis to diagnose resonance issues as well as doing theoretical computer FEA models to recommend validated structural redesigns. For more information on how modal analysis and FEA can be implemented at your facility, please contact us at 970-266-9005 or here.