See you at NAFEMS World Congress NWC19 – Quebec City, Canada


CAEfatigue Limited will be involved in presenting 4 papers at the NAFEMS World Congress in June 2019.

Our tentative presentation schedule is as follows:

Tuesday, June 18th – MORNING – J1 Dynamics & Vibration 1

Frequency Domain Spot Weld & Seam Weld Analysis.  Bishop, N. (CAEfatigue-USA), Murthy, P. (CAEfatigue-EU), Roemelt, P. (Ford-Germany), Meehan, T. (Ford-USA).

 

Tuesday, June 18th – AFTERNOON – J2 Dynamics & Vibration 2

Loads Conditioning for Frequency Domain Analysis.  Kerr, S. (CAEfatigue-USA), Datta, S. (FCA-USA).

Loads Enveloping. Bishop, N.(CAEfatigue-USA), Kerr, S. (CAEfatigue-USA), Costa, E. (Ford-Brasil), Meehan, T. (Ford-USA).

 

Wednesday, June 19th – AFTERNOON – H7 Fracture & Fatigue 3

Two-Wheeler Fatigue and Random Response.  Sethi, M. (Hero MotoCorp-India), Sharma, A. (Hero MotoCorp-India), Bishop, N. (CAEfatigue-USA), Harsha, K. (CAEfatigue-India).

 

Link to the NAFEMS AGENDA HERE

 

*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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Duration of a PSD: What does that mean?


Recently, we posted a blog about calculating fatigue damage in the Frequency Domain and how the process was not dissimilar to fatigue damage calculations in the Time Domain. That blog raised the same question by Users several times: What time duration does a PSD have?

This is an interesting question.

For those who work in the Time Domain, the concept of a “time duration” is simple. The time signal is captured for a specific period of time and that is, by definition, the “time duration” of the signal.

However, in the Frequency Domain, a PSD has NO time duration. A PSD is simply a snapshot of the frequency content and magnitude of the time signal and also provides the statistical properties of the time signal, presuming the time signal is (1) Stationary, (2) Random, and (3) Gaussian.

Single Input PSD

To calculate the damage from a single input PSD, we use the “rainflow” cycle count formula for n(S) to generate a histogram of stress ranges. This was explained in the previous blog. This calculation is done at every element / node location throughout the model using the appropriate Response PSDs, with or without deterministic loading and are summed together to generate a histogram of stress ranges.

Where;

n(S) is the TOTAL number of rainflow cycles or perhaps a better term, stress range cycles for a given stress value. When plotted for all stress values, this produces a stress range histogram.

E[P] is number of stress cycles per second calculated from the Response PSD. This is also called the Expected Number of Peaks of the Response PSD.

T is the duration of the Event loading in seconds. By default, CFV uses 1 second.

P(S) is the probability density function (pdf) of stress cycle ranges (peak to peak). By default, CFV uses the Dirlik Method to calculate this function, which tells us how to distribute the stress cycles from E[P].

For a single input PSD, CFV assumes that the duration of the Event (T) is 1 second. Hence, the PSD stress histogram is created, and the damage calculated for a time duration of 1 second. The PSD itself does not have a time duration.

Multi Input PSD

To calculate the damage from multiple input PSDs, we use the same “rainflow” cycle count formula for n(S) to generate the histogram of stress ranges for each PSD. Once again, the default is 1 second for each histogram and hence damage is also calculated for 1 second.

HOWEVER, there is a difference when we use PSDs converted from known time histories; which is often done in the automotive industry. In these cases, the converted PSD actually represent a converted time history, which has a time duration.

As shown below, the actual raw time signals in section (1) from the upper plot, were conditioned first as shown in the middle plot, prior to their conversion to PSDs, as shown in the lower plot. The CONDITIONED time signals in the middle plot have a time duration of 11 seconds. Hence, the PSDs in the lower plot should be applied in the fatigue damage calculation for 11 seconds to match the application time period of the conditioned time signals. This would mean that T in the n(S) formula should be set to 11 seconds. The PSD itself does not have a time duration but the damage calculated from the PSD will assume a event duration of 11 (not 1 second).

CONCLUSIONS:

To be clear, a power spectral density (PSD) itself does not have a time duration. However, the damage calculated from the PSD assumes a damage resulting from 1 second but this must be changed if the PSD is converted from a known time signal with a known duration.

A PSD only gives you the frequency content and magnitude to be applied as input loading to the structure. This loading, along with the transfer function, will generate a Response PSD that is then used to calculate the fatigue damage / life. The damage calculation assumes a T value equalling 1 second in the rainflow cycle count formula, n(S).   Hence, if the specification is to apply the Input PSD for say, 10 hours in the X direction, followed by 20 hours in the Y direction and finally 50 hours in the Z direction, then the math is simply. Apply an Input PSD to the appropriate X direction solver subcase for 10 hours or (10 x 60 x 60) 36,000 seconds; meaning multiply the damage generated for 1 second by 36,000. We would then apply an Input PSD to the Y direction subcase for 20 hours or (20 x 60 x 60) 72,000 seconds, followed by applying an Input PSD to the Z direction subcase for 50 hours or (50 x 60 x 60) 180,000 seconds. The X, Y and Z damage will be added together to give a total damage expected for the structure at each element.

If the PSD is converted from a known time signal, then the PSD gives you the frequency content and magnitude to be applied as input loading to the structure. PLUS, you must also use the time duration of the conditioned time history as the T value in the rainflow cycle count formula, n(S).

In most cases, there are several time signals making up an Event of loading. When converted to the Frequency Domain, the time signals become a PSD matrix (PSDM) of loading comprising direct PSD and cross PSDs. This PSDM will accurately reflect the time signal loadings plus the influence of loading A on location B (i.e. phasing between loads). The entire PSDM “Event” will be given the duration of the conditioned Event and in many cases, the required loading in the fatigue calculating will be applied not in minutes or hours but in repeats of the PSDM Event duration.

*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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Frequency Domain Fatigue Damage Calculation Process: Is it really that different?


If you are new to the Frequency Domain, it is understandable that you may think that this “stuff” is way different than the Time Domain. This is especially true when we ask folks to do material damage calculations in the Frequency Domain. You may hear that this is a whole new way of thinking … or, is it?

During our onsite and online training sessions, we often see a look of total confusion in the eyes of our students when we start to talk about the Frequency Domain. Many have some comforting, albeit, vague memories of the Fourier Series from past days at college, but many have been working in the Time Domain for so long that any thoughts about changing to Frequency Domain are very daunting.

However, are we really changing that much … especially when it comes to a fatigue damage calculation? Below is an image we often use to convince students that there really is not that much difference.

The material fatigue calculation process, in the image below, has 6 steps regardless of if you start with a Time Signal or PSD. You start with (1) a stress time signal or PSD then (2) you do some sort of cycle counting process to eventually generate (3) the stress range histogram. From here, (4) you refer to the fatigue material properties, (5) use Miners Rule to generate cycles to failure and (6) present the damage / life results.

If you look at the images below, you will see that steps (3), (4), (5) and (6) are identical whether you are working in the Time Domain or Frequency Domain. So, we really need to only focus on steps (1) and (2).

 

STEP 1: Conversion of the Time Signal to a PSD

We like to call this “conditioning” of the time signal because you cannot simply convert a time signal to a PSD without properly conditioning (or correcting) the time signal to satisfy the 3 key assumptions that must be meet.

Most often we see issues with STATIONARY: which is the need for the signal to have the same statistical properties regardless of what time slice you look at within the time signal.

Below are multiple time signals belonging to the same Event that are non-stationary. The time signals have several low intensity sections as well as sections that appear to have different frequency content. The statistical properties across these time signals are different depending on the time slice you select to analyze.

Since we are interested in the damage that these signals will cause to a structure, we cannot simply convert the signals “as is” because the non-stationary sections will add time to the duration of the loading, which is not appropriate since the time of the loading should only reflect the parts of the signals that do the damage and not the low intensity section that cause little to no damage.

In this case, the Event should be broken into 3 separate (and shorter) Events that only reflect the parts of the time signals that cause significant damage (see below). The remaining parts of the signals can be ignored as they cause little to no damage.

CAEfatigue Limited provides conversion / conditioning tools called TIME2PSD (manual) and CAEfatigue CONDITIONING – CFC (automatic) that do this work for our Users. Below is an image of the first “new / shorter” Event 1 from above, that has been conditioned (second plot) and converted into PSDs (third plot). These properly converted PSDs are then brought into a CFV fatigue analysis.

STEP 2: Cycle Counting the PSDs

We use the term “cycle counting” just to make new students a little more comfortable. In fact, we really do not cycle count but follow a new process that eventually produces a stress range histogram similar to what is produced when you cycle count a time signal.

The process starts with calculating the “spectral moments”. These spectral moments are then used in a “fatigue modeler” to generate a probability density function (pdf) that gives us the distribution of the stress cycles across the stress range. We use this pdf to distribute the total number of cycles calculated from the Response PSD to calculate a histogram of stress cycles.

CFV provides multiple methods to calculate the pdf of stress cycles in the frequency domain. However, the CFV software currently uses the DIRLIK approach as the default method. This method works well for all forms of random input (both wide band and narrow band PSDs) and will also work well when random input PSDs are mixed with deterministic loading (i.e. sine on random analysis).

The formula to calculate the histogram of stress ranges, n(S), is given below. This calculation is done at every element / node location throughout the model using the appropriate Response PSDs (and/or deterministic loading) and summed together to generate the histogram of stress ranges. This data then allows the calculation of fatigue damage at every element / node location following the remaining steps (4), (5) and (6) as talked about at the beginning of the blog.

Where;

n(S) is the TOTAL number of rainflow cycles or perhaps a better term, stress range cycles for a given stress value. When plotted for all stress values, this produces a stress range histogram.

E[P] is number of stress cycles per second calculated from the Response PSD. This is also called the Expected Number of Peaks of the Response PSD.

T is the duration of the Event loading in seconds. By default, CFV uses 1 second.

P(S) is the probability density function (pdf) of stress cycle ranges (peak to peak). By default, CFV uses the Dirlik Method to calculate this function, which tells us how to distribute the stress cycles from E[P].

To calculate E[P] and p(S) we need to first calculate the spectral moments.

f is the frequency of interest

G(f) is the height of the one-sided Response PSD at the frequency of interest

Once we calculate the moments m0, m1, m2 and m4 we can calculate the expected peak rate (i.e. total number of cycles / second) using the formula

and calculate the stress cycle pdf, p(S), using the DIRLIK formula below.

Where the probability density function p(S) is solely a function of moments m0, m1, m2 and m4.

If we (again) use the comforting term “rainflow cycle”, below we see the histogram of rainflow cycles count (ns) versus a stress bin number. With a little added manipulation, this can be converted to stress range histogram.

We have now taken care of steps (1), (2) and (3), and can manage the rest of the damage calculation in the same manner as we do in the Time Domain.

 

CONCLUSIONS:

When calculating the fatigue damage / life in the Frequency Domain, we can fall back on many of the things we already know about the process from the Time Domain. Our only challenge is to:

  • Properly convert the Time Signals to PSDs by conditioning the time signals first,
    prior to the conversion.
  • With a properly converted PSD, use Spectral Moments and a Fatigue Modeler
    (like Dirlik) to calculate the pdf and stress range histogram.

Once these 2 steps are done, we can calculate damage / life in the same manner as we would do in the Time Domain.

So, is there a big difference when calculating material fatigue damage between Time Domain and Frequency Domain? Depends on who and when you ask the question. To anyone new to the Frequency Domain, the answer will be a resounding “YES!”, however, if you ask that same person after they have had the appropriate training and some experience, perhaps the answer will be “actually, not so much!”.

 

*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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Successful CFV v2019 Seminar Held in India


On Friday, November 16th, 2018, CAEfatigue Limited (India) had the pleasure to welcome nearly 50 industrial leaders to a 1 day technical seminar in Bangalore to introduce the latest release of CAEfatigue VIBRATION v2019; our flagship random response and fatigue analysis software for work in the frequency domain.

The seminar was attended by members of top companies within India that are currently working in or wish to work in the Frequency Domain.  The presentation and discussions were led by Dr. Neil Bishop (Founder and CEO of CAEfatigue Ltd) and supported by the technical team of Dr. Paresh Murthy and Mr. Harsha Kolar.

“We had a wonderful day full of challenging discussions and insightful interaction.  I want to thank Kolar and Paresh for their great work organizing the event and to the seminar Attendees for providing input to such an engaging day of technology discussions and sharing”.  Dr. Neil Bishop.

 

The seminar introduced CAEfatigue VIBRATION (CFV) v2019. This release includes improved functionality to “condition” road load data prior to PSD conversion as well as improved BASE SHAKE functionality and a complete solution for multi-input, full vehicle assessment in the Frequency Domain.  V2019 also includes the ability to request displacements, velocities, accelerations, forces and cascade these results to various component locations in the model. This release can also use relative displacements to detect the probability of component collisions (Example: exhaust hitting vehicle floor pan, headlight hitting headlight enclosure, etc.) and the probability of gaps opening up between sealed components.

CAEfatigue VIBRATION v2019 also includes an industry first!  The ability to do seam weld and spot weld analysis in the Frequency Domain. This advance in technology supports the complete, full vehicle fatigue solution in a frequency domain analysis.

Thank you Seminar Attendees, for a wonderful day!

*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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SINE SWEEP on RANDOM PSD: The need for frequency matching between the Solver FRF and the Sine Sweep


Similar to the previous blog post where we talked about frequency matching between the Solver FRF and the Input PSD loading, there is also a need to have good frequency matching between the Solver FRF and a sine sweep input loading.  Understanding this will ensure that you calculate accurate responses and, therefore, fatigue damage in the Frequency Domain using CAEfatigue VIBRATION (CFV).

Input PSD, Transfer Function and Response PSD:

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).

However, we now want to apply a deterministic sine sweep to the analysis that will be included along with the random input PSD; many refer to this as “sine on random” input loading.  Within CFV, this can be easily accomplished, BUT, as you will see in this post, we must be very careful to ensure the resolution of the sine sweep is sufficient to pick up the peaks in the Transfer Function. Otherwise, the sine sweep may miss the resonant frequencies and, therefore, not provide an accurate response PSD. This is no different than ensuring a good resolution / frequency match between the random input PSD and Transfer Function as discuss in our previous post.

Frequency Resolution and Resonance Detection of the Sine Sweep

What is a Sine Sweep?

Just to be very clear, a sine sweep applies a single sine wave to a structure and after the responses are calculated, the next sine wave is applied to the structure; i.e. one after the other. This continues until all sine waves in the sweep have been applied and the responses from all sine waves have been added together.  If a random PSD is also required, it is applied every time the single sine wave is applied, i.e. at the same time as the sine wave.  Below is an example of a 9 Hz sine wave and a random PSD, which are applied together as a single EVENT in a SINE on RANDOM analysis within CFV. Note: CFV can also apply many sine waves at the same time (harmonic loading), if desired, but this would not be considered a sine sweep.

Example of SINE on RANDOM Analysis

Let’s assume that the solver FRF analysis has been correctly executed and it captures the peak FRF responses that are in the structure.  This would also ensure the Transfer Functions (created within CFV) are accurate and contains all the response frequencies of interest to our analysis. Consider the Transfer Function in the plot to the right. There is one significant peak in the Transfer Function where the worst case stress is occurring.  This peak is at 8.8 Hz.  We can use this information to define our sine sweep.

Within CFV, a sine wave sweep can be defined as a series of single sine waves using a SINGSINE entry, a DETLOAD entry or a SINESW entry.  For this example, we will define a series of single sine waves using SINGSINE applied with a random, single input PSD loading (shown as the input PSD in the plot above). This is a SINE on RANDOM example. Note: CFV will also allow the application of a sine sweep without the random PSD loading, if desired.

Our first sweep is a series of single sine waves between 2 Hz and 32 Hz with an amplitude of 1 G and a spacing of 2 Hz.  This sweep is rather course in spacing and misses the peak response at 8.8 Hz. Selecting the “worst case” element, we can see from the Event plot, that the worst damage occurs at Event 108, which corresponds to an 8 Hz sine wave with a random PSD loading. The fatigue damage at this element for this frequency is 0.09.  Total fatigue damage predicted from the application of all sine waves and random PSDs at this element is 0.12, where 1.0 would be a fail.  A User may mistakenly feel very comfortable with these results and assume the structure will not fail but the analysis had a course spacing in the sine sweep and the peak resonance was missed.

Our second sweep is a series of single sine waves between 2 Hz and 32 Hz with an amplitude of 1 G and a spacing of 1 Hz.  In this sweep we have improved the frequency spacing but still fail to include the resonant frequency of 8.8 Hz Selecting the same “worst case” element, we can see from the Event plot, that the worst damage occurs at Event 1090, which corresponds to 9 Hz.  The fatigue damage at this element, for this frequency alone is 0.45.  Total fatigue damage predicted from the application of all sine waves and random PSDs at this element is 0.69, where 1.0 would be a fail.  A User may feel comfortable that this structure will pass because the damage is under 1.00 but what happens if we actually apply a sine wave at 8.8 Hz, which is the peak response frequency.

Our third, and final sweep is a series of single sine waves between 2 Hz and 32 Hz with an amplitude of 1 G and a spacing of 1 Hz (same as above).  However, we will replace the 9 Hz sine wave with an 8.8 Hz sine wave to match the peak response frequency seen in the Transfer Function. Selecting the same “worst case” element, we can see from the Event plot, that the worst damage occurs at event 1088, which corresponds to 8.8 Hz. The fatigue damage at this element for this frequency alone is 0.80.  Total fatigue damage predicted from the application of all sine waves and the random PSD at this element is 1.04, where 1.0 would be a fail. This is significantly different from the first sweep that only predicted a total damage of 0.12 (due to a course sine wave spacing in the sweep) or the second sweep that predicted a total damage of 0.69 (but missed the resonant frequency in the sweep).

CONCLUSIONS

Under loading from a random PSD and a properly defined sine sweep (including the resonant frequency) the structure may fail from fatigue because the damage value is just above 1.00.  This possibility of failure was missed when the sweep was inappropriately spaced or did not include the resonant frequency and the User could have thought, based on incomplete data, that the structure was acceptable.

Therefore, it is imperative to understand the resonant frequencies within your model, especially within the expected operational frequency range, and to include those frequencies within the sine sweep to get the best response prediction from your analysis.

 

*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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