# Modal Case Study

Determining the Cause of Cracks with Operational Modal Analysis

by Marc Marroquin, Brüel & Kjær North America Inc.

Just a few years ago, the field of modal analysis was very stable and well known. There was a well-defined, industry-accepted way of determining mode shapes and damping values – either use a force hammer or shaker to excite a structure, measure the responses at many locations, calculate the FRFs, and finally perform curve fitting. This process relied on many assumptions and also required a fair degree of setup time and operator skill.

Today an exciting new technique has been introduced that holds promise of replacing the traditional modal test of yesterday. Operational Modal Analysis (sometimes called 'Output Only Modal') is the technique that allows accurate identification of resonances, mode shapes, and damping values without the need of measuring the input force (i.e., hammer or shaker) or special boundary conditions. To perform an Operational Modal Analysis (OMA for short), all that is required is the raw time data of the output responses at several points. That's it! Some examples of how OMA can be measured are:

• For an aircraft wing – simply line up a series of accelerometers on the wing and fly the aircraft as normal.
• For an automobile chassis – mount accelerometers on the car chassis and drive the car down the road.
• For an engine component – place accelerometers on the component itself and operate the engine naturally.
• For a computer hard drive – mount the accelerometers on the hard drive and operate the computer normally.

The natural excitation of the product is used as the excitation of the resonances. Using special curve fitter algorithms, the resonances are extracted and animated. The OMA technique eliminates the need for special boundary conditions, elaborate test setups, and time-consuming procedures. So it is possible (as seen in the previous examples) to perform an OMA of a product in-situ retaining all natural boundary conditions.

Recently, I had an opportunity to perform OMA for a vehicle accessory manufacturer.The motor was mounted on a box-shaped pedestal. The pedestal was in turn mounted onto two guide bars that were hard mounted to the shell of a large component. During endurance testing, the pedestal would sometimes develop stress cracks along the base, cracks that could damage the shell of the adjacent component.To prevent possible problems when the product actually shipped, it was important to determine if a resonance(s) existed and what the mode shape(s) would look like Figure 1.

It was important to measure the true mode shapes in the actual set up since the pedestal supported a heavy motor (over 100 pounds) and was mounted on several sides to the guide bars. The weight of the motor and the mounting of the pedestal substantially changes the mode shapes and resonant frequencies. Simply measuring the resonances of the pedestal in a 'free-free' condition would not suffice. To add to the complexity, the motor was located in a hard-to-reach location, making it impossible to perform traditional modal analysis using a hammer or shaker. OMA was the only option available to perform the analysis needed.

The test would entail:

• The measuring of 14 locations
• The use of 2 triaxial accelerometers (one remaining in a stationary location, the other roving across 13 points)
• The excitation force being the actual motor running up from 1300 RPM to 2400 RPM in 5 seconds

The equipment used consisted of:

• Seven-channel Bruel & Kjær PULSE™ systems (Type 3560C)
• Bruel & Kjær Modal Test Consultant™ software option for PULSE (Type 7753)
• Bruel & Kjær Operational Modal Analysis software (Type 7760)
• Two ENDEVCO triaxial accelerometers

The measurements were made in about one hour with the guidance of the Modal Test Consultant.

The data was transferred from PULSE to OMA and curve fitting was performed. After the number crunching was complete, three modes were identified – 44.6 Hz, 55.2 Hz, and 95.3 Hz. It was quickly realised that the 44.6 Hz mode was the problematic mode since the normal operation of the motor was between 2600 to 2700 RPM. When looking at the actual mode shape it is also obvious why the stress cracks occurred at the base (see Figure 2).

As seen in this very brief case study, OMA proved to be an invaluable tool. A simple set of data was recorded in-situ, with natural boundary conditions using the normal operation of the product as excitation. Accurate results were achieved giving insight to the customer as to the failure of a component. All of this was accomplished without any special setups or measuring the actual excitation force. Wow!