Frequency Domain Fatigue Analysis: The need for good resonance determination and frequency matching between the Solver FRF Analysis and the Input PSD


The following will explain the need for good frequency definition in both the Solver FRF analysis and the Input PSD so proper resonances are found for the Transfer Function and the frequency content is matched between the FRF analysis and the Input PSD.  Understanding these concepts will ensure that the intended conditions are defined to calculate accurate fatigue damage in the Frequency Domain using CAEfatigue VIBRATION (CFV).

Let’s use the example below:

In order to calculate fatigue damage and fatigue life in the frequency domain, we first need to generate the RESPONSE PSD that is the result of multiplying the TRANSFER FUNCTION by the INPUT PSD. The Transfer Function is calculated within CFV using the solver FRF stress data, and the Input PSD is defined directly within CFV. Below is an example of the three PSDs as shown by the PSD Plotter in the CFV GUI (CFG).

As can be seen in the plot, the shape and frequency content of the Response PSD is heavily dependent on the shape and frequency content of the Transfer Function.  If care is not taken in the Solver FRF calculation, it would be very possible to miss, for example, the peak amplitude (resonance) at 14 Hz in the Transfer Function and thus, it would completely change the shape and content of the Response PSD.  We will look at this more closely below.

Frequency Resolution for Resonance Detection

To the left are two Transfer Functions that were generated within CFV from two different Solver FRF analyses.  In one case, the peak amplitudes (resonances) near 40-45 Hz are recognized and accounted for by the User (blue, solid line) whereas, in the second case, the User failed to recognize the peak contribution and bypassed the 40-45 Hz frequency in the FRF analysis settings (orange, dashed line).

If we now use these Transfer Functions with a simple Input PSD, we can see the influence this mistake has on the shape and frequency content of the Response PSDs (see image to the right).

It is clear to see that the Response PSDs have different shapes and peak values.  Using the correct Transfer Function (blue, solid line), the frequency resolution in the FRF analysis has picked up the response peaks at 40-45 Hz and the correct amplitude values are passed through to the Response PSD.

However, in the second case (orange, dashed line), the Response PSD falsely shows that the max peak response is at 25 Hz and completely misses the significant resonances at 40-45 Hz.

This mistake by the User, will likely cause a significant difference in the fatigue damage and life calculations because the cumulative areas under both curves are very different, which significantly changes the Mvalue used by the Dirlik method (most common damage calculation method used in frequency domain fatigue calculations). Most solvers have parameters (like FREQ4 in Nastran), which guide the User in choosing correct frequency points around such resonances.

Frequency Matching

A keen observer may also have notice something else that is incorrect in our example above. Although the blue, solid line Transfer Function does accurately reflect the response of the model, the User failed to recognize that the points in the Transfer Function do not match up well with the points in the Input PSD, especially around 5 Hz, i.e. there is no Transfer Function frequency point at 5 Hz; nearest points are at 0.5 Hz and 25 Hz.

Within CFV, the Response PSD is generated by multiplying the value of the Transfer Function PSD point by the corresponding value of the Input PSD point.  When a Transfer Function point does not align with an Input PSD point, the nearest points are interpolated to generate a new value at the frequency from the Transfer Function (creates green dot on Input PSD).

However, the reverse does not happen; i.e. if a point on the Input PSD does not line up with a point on the Transfer Function, that Input PSD point is ignored in the Response PSD calculation (red arrow, empty red circle on Response PSD).

CFV does not change the Solver FRF stress results to add in or take away points to account for the Input PSD frequencies.  This could, in theory, be attempted for single input (real) PSD’s with corresponding real transfer functions but there would be difficult theoretical issues to resolve. However, it cannot be done for multi-input PSDs because of the difficulty to interpolate across complex cross PSD’s and the corresponding complex transfer functions. Hence, CFV requires the User to ensure the frequency resolution is sufficient in the FRF to match the Input PSD.

In this example, the Transfer Function does not have a defined point at 5 Hz so the contribution of the Input PSD at 5 Hz is ignored. Hence, this frequency mismatch produces an incorrect Response PSD at 5 Hz. Effectively, the Input PSD is changed based on the Transfer Function frequency points to create a modified Input PSD where the red dots line up with the Transfer Function points and the blue dots are ignored.

Therefore, to ensure the fatigue damage and life calculations are accurate, the User must consider frequency resolution (to detect resonances) and frequency match between the Solver FRF analysis and the Input PSD definition.  Below are the correct Input PSD, Transfer Function and Response PSD for this example, which reflect appropriate frequency content and matching.

Good frequency content and matching can be accomplished by a careful understanding of the expected resonances in the model and the expected input loading that will be applied as part of the fatigue analysis.  Once understood, an appropriate choice of solver parameters (such as “FREQ1” and “FREQ4” entries for Nastran) can be made to ensure the desired frequency resolution to pick up resonances and where the loading changes significantly in the Input PSD, i.e. for typical road load data, the Input PSD will likely require good Solver FRF frequency resolution in the 1.0 Hz to 10.0 Hz range.

This post is intended to provide an understanding of how frequency domain fatigue analysis is conducted in CFV.  Remember, providing accurate data in will ensure accurate results out.

 

*CAEfatigue Limited (www.caefatigue.com) is a privately owned company with it’s world headquarters located in London, England.   CAEfatigue Limited is dedicate to developing random response and fatigue evaluation software for dynamic mechanical systems that is easy to use for the average Engineer or Designer.   The CAEfatigue Limited suite of products are in use across multiple industries throughout the world and have become the industry standard for use in the frequency domain. Share with:

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Why use the Frequency Domain?


We are often asked why should I use the frequency domain when doing fatigue analysis. Please let us give you a quick overview of why.

Below is a hypothetical example of damage calculations done using RLD (road load data) from automotive testing at a proving ground.  This comparison also applies to any process that uses time domain data as the input loading to their components. For those not familiar with proving ground automotive vehicle testing, the workflow is fairly straight forward. A vehicle is instrumented with accelerometers at various locations on the vehicle.  Most often each accelerometer is measuring data in the X, Y and Z direction.  So, if we have accelerometers at 4 locations on the vehicle, which are measuring accelerations in 3 directions, than we have 12 channels (RLD time histories) of information being collected at the same time as we drive the vehicle over a planned route for some period of time.  All of the channel information is combined into a single proving ground EVENT and in many cases, automotive testing collects data from multiple events throughout the proving ground with different loading conditions at different speeds.

To calculate damage using the TIME DOMAIN, we need to apply the collected road load data to an FEA model within a stress solver for EVERY event and then sum up the damages from the multiple events to calculate the total damage to the vehicle.  This is extremely time consuming and requires a significant amount of solver effort.

To calculate damage using the FREQUENCY DOMAIN, we need to run a SINGLE stress analysis and use those results as a multiplier between the collected road load data and the output response of damage. However, we need one additional step, which is to convert the road load data time histories into frequency based power spectral densities (PSD’s).  We do this within CAEfatigue VIBRATION (CFV) using a manual conversion tool called TIME2PSD or we can also use our automated conversion tool called CAEfatigue CONDITIONING (CFC).

The image above graphically represents the differences between a Time Domain and a Frequency Domain fatigue analysis using Nastran as the stress solver.  As mentioned, the key difference is the number of Nastran SOL112 runs required in the Time Domain when the testing duty cycle contains numerous proving ground events.

This is not the case with the Frequency Domain where only one SOL111 run is required.  This difference can result in significant time savings with the added benefit of better output parameters captured by the frequency domain approach.

CAEfatigue Limited have work with numerous companies to benchmark the frequency domain process against the time domain process for models directly relevant to their needs.  On all occasions, we have been able to prove the correlation between the two processes and show why it makes sense to switch.

*CAEfatigue Limited (www.caefatigue.com) is a privately owned company with it’s world headquarters located in London, England.   CAEfatigue Limited is dedicate to developing random response and fatigue evaluation software for dynamic mechanical systems that is easy to use for the average Engineer or Designer.   The CAEfatigue Limited suite of products are in use across multiple industries throughout the world and have become the industry standard for use in the frequency domain. Share with:

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CAEfatigue Ltd at WCX World Congress – Detroit, April 2018


Dr. Stuart Kerr, Chief Operating Officer for CAEfatigue Limited, announced today that CAEfatigue will be at the WCX World Congress in Detroit in early April.   “CAEfatigue Limited and our US distribution partner CAE Software Solutions LLC, are very proud to author/coauthor several papers for the World Congress this year and we are also very happy to have worked with strong partners in the advancement of this technology.  I invite all interested to come along and enjoy these presentations.”

The first paper entitled “Loads Cascading in the Frequency Domain” will be presented Tuesday morning (April 10th) at 9 am during Technical Session M209 in room 140F.   The paper will be presented by Dr. Neil Bishop (CEO of CAEfatigue Ltd) and will cover the topic of transferring road load data to different parts of a full body model using our latest software module CAEfatigue RANDOM (CFR).

The second paper entitled “Frequency Domain Loads Enveloping” will be presented Tuesday afternoon (April 10th) at 3 pm during Technical Session M203 in room 140E.   The paper will be presented by Edinilson Alves Costa of Ford Motor Company Brasil and will cover the topic surrogate loads.  This work was done in collaboration with CAEfatigue Limited and will form the basis of a new software module called CAEfatigue SURROGATE (CFS) due out later this year.

Directly after the second paper presentation, Dr. Bishop will also lead a technical discussion at 3:30pm entitled Vibration Fatigue Research and Development.

The third paper entitled “Frequency Domain Fatigue Analysis of Exhaust Systems” will be presented Thursday afternoon (April 12th) at 2 pm during Technical Session M200 in room 140D.  The paper will be presented by Phillippe Leisten of Eberspacer Exhaust Technology GmbH and will cover work done in collaboration with CAEfatigue Limited.

“It was wonderful to work so closely with Ford Brasil and Eberspacer on these technical papers and we are delighted to be in Detroit to share the good work that was done”, said Dr. Neil Bishop.   “CAEfatigue Limited remains committed to the continual improvement of our product and the advancement of this field of study.”

*CAEfatigue Limited (www.caefatigue.com) is a privately owned company with it’s world headquarters located in London, England.   CAEfatigue Limited is dedicate to developing random response and fatigue evaluation software for dynamic mechanical systems that is easy to use for the average Engineer or Designer.   The CAEfatigue Limited suite of products are in use across multiple industries throughout the world and have become the industry standard for use in the frequency domain.

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CAEfatigue Ltd Plans to Launch Software Suite


It was announced today by our Founder & CEO, Dr. Neil Bishop, that CAEfatigue Limited* are launching a number of new software products in the later half of 2018.   The announcement covers a significant update to CAEfatigue VIBRATION (CFV) and CAEfatigue GUI (CFG) as well as new products including CAEfatigue CONDITIONING (CFC) – recently launched and CAEfatigue RANDOM (CFR) – recently launched. Two new additional products due for launch in late 2018 are CAEfatigue SURROGATE (CFS) for simplifying complex test loading into simple PSD loading and CAEfatigue TIME (CFT) that will provide our clients with a complete time domain fatigue solver.

“The addition of CFT will provide our customers with a complete suite of frequency domain and time domain products to evaluate the fatigue results for a dynamic system”, said Dr. Neil Bishop.   The launch of the new product suite and the recent launch of our point release Vr3.1.1, solidifies our commitment to continual improvement of our product.

  

 

*CAEfatigue Limited (www.caefatigue.com) is a privately owned company with it’s world headquarters located in London, England.   CAEfatigue Limited is dedicate to developing random response and fatigue evaluation software for dynamic mechanical systems that is easy to use for the average Engineer or Designer.   The CAEfatigue Limited suite of products are in use across multiple industries throughout the world and have become the industry standard for use in the frequency domain.

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New Distributor for Italy


CAEfatigue Limited is pleased to announce that it has agreed to a relationship with Exemplar sol with headquarters located in Torino, Italy.  Exemplar is now our primary distributor for Italy and we welcome them to the team. Please see our Partners page for further information about Exemplar srl.

*CAEfatigue Limited (www.caefatigue.com) is a privately owned company with it’s world headquarters located in London, England.   CAEfatigue Limited is dedicate to developing random response and fatigue evaluation software for dynamic mechanical systems that is easy to use for the average Engineer or Designer.   The CAEfatigue Limited suite of products are in use across multiple industries throughout the world and have become the industry standard for use in the frequency domain.

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