Fatigue User’s Guide > Validation Problems > Problem 7: Vibration Fatigue Analysis

Problem 7: Vibration Fatigue Analysis
This section is concerned with the validation of the vibration fatigue methodologies described in Vibration Fatigue (Ch. 8). These techniques presently employ the S-N method of fatigue life estimation as validated in Problem 1: Analysis of a Keyhole Specimen, 1179. Here we are concerned not with the validation of the S-N method, but with the comparison of time domain results with frequency domain results. Three examples are provided ranging from a simple hand calculation, to measured responses, to finite element model frequency versus time domain results.
A Simple Worked Example
These pages describe a simple worked example for a wide band spectrum comprising 1 Hz and 10 Hz frequency components. A predicted fatigue life is hand calculated for both a frequency and a time domain approach, and compared with an equivalent calculation performed using MSC.Fatigue tools. This brings together many of the topics discussed in Vibration Fatigue (Ch. 8) and shows how the theory is applied using MSC.Fatigue programs.
The worked example is based upon a PSD comprising two spectral components, 10,000 MPa2/Hz at 1 Hz and 2,500 MPa2/Hz at 10 Hz, with a 1 Hz spectral bandwidth. The stress life (S-N) material properties used are for a typical steel, of the form,

 b 4.2 K 1.0 x 1015
And in the form required by MSC.Fatigue materials data manager, MDM,

 b1 -0.238 SRI1 3728 MPa
Hand Calculation - From a PSD in the Frequency Domain
The idealized form of the input PSD is shown in Figure 14‑16 below.
Figure 14‑16 An Idealized PSD
In the time domain the PSD shown above is equivalent to a summation of two sine waves:
`sine wave 1 at 1 Hz with stress range √10,000 x 1.41 x 2= 282 MPa`
`sine wave 2 at 10 Hz with stress range  √2,500 x 1.41 x 2=141 MPa`
The following hand calculation establishes the necessary moments of this PSD to calculate the narrow band (NB) and Dirlik predicted life.
`	Mn = 40,000 x 1n + 10,000 x 10n`
`	Mo = 12,500`
`	M1 = 35,000`
`	M2 = 260,000 `
`	M4 = 25,010,000`
RMS =
Equivalent sine wave magnitude = 112 x 1.41 x 2 = 315 MPa
P-M damage
This corresponds to a fatigue life of 3,265 seconds or 0.9 hours
Damage NB = 1,472 seconds (0.409 hours)
Damage Dirlik = 7,650 seconds (2.125 hours)
MSC Fatigue Calculation - From a PSD in the Frequency Domain
The MSC Fatigue module MCOE is used to create the PSD described above. Define the Y-axis label as “RMS Power” with units “MPa2/Hz”. With a sample rate of 1.0, define the value at 1 Hz = 10,000 and 10 Hz = 2,500, all other points should remain zero, and exit when the two values have been defined. Use MQLD in tower display mode to obtain the output shown below.
The steps are outlined in the table below:

 Operation Comments mcoe Invoke MCOE from the system prompt. Create Select the Create option. Input Filename: simple.psdOK/OK Enter a file name such as simple.psd. Then click the OK button twice to accept it. The file will be created on completion of the exercise in MCOE. Sample Rate: 1 Enter 1 as the sample rate. X-axis Label:Frequency Change the X-axis label to Frequency. X-axis Units:Hz Change the X-axis label to Hz. Y-axis Label:RMS Power Change the Y-axis label to RMS Power. Y-axis Units:MPa2/Hz Change the Y-axis label to MPa2/Hz. OK Press OK. A spreadsheet will appear. 1 Hz: 10000; 10 Hz: 2500 Enter 10,000 in the 1 Hz row and 2,500 in the 10 Hz row for the Y value. Enter zero for all other up to say 11 Hz. File/OK Under the File pulldown menu, select OK. This will save the file. mqld Invoke MQLD from the system prompt. The default file to display should be simple.psd. Display | Towers Change the display to plot as towers as opposed to joined. You should see a plot similar to that in the above figure. File | Exit Quit from MQLD.
Now perform the frequency life analysis in MFLF. The file created above in MCOE, is the input filename. The “Cut-off Frequency” will correctly default to 11 Hz, and ensure that the units selected are “MPa2/Hz”. Choose “128” for the number of bins required, this high number will help to reduce rounding errors due to bin widths enabling a more accurate comparison with the above hand calculation. Use the List file browser button to select any material data set and request to edit the material the data. Edit the material data and insert the values defined above, SRI1=3728 and b1 = -0.238. The transition life NC1 can remain at 1E8, and the second slope b2 can remain as is since no input cycles exist below the stress at the 1E8 transition life. The surface finish is polished, and there is no surface treatment.
The steps are as follows:

 Operation Comments mflf Invoke MFLF from the system prompt. Input Filename: simple.psd Select the file just created and click the OK button twice. Bins Required: 128 Change the bins to 128 and click OK. Dataset Name: Press the List button here and select any dataset. Edit Data: Yes Turn on the Edit Data switch by setting it to Yes and then press the OK button. SRI1: 3728 Change Stress Range Intercept to this value. b1: -0.238 Change the First Slope to this value and then press the OK button twice. The calculation will proceed. Press the End button after the results are displayed. Analysis method Press the Analysis method button from the main menu options. All Select All as the analysis method. Press OK when the next form is presented. The number of bins should still be set to 128. Recalculate life Press the Recalculate button. The results from all analysis types will be presented. End | eXit Quit from MFLF when you are ready.
After performing the analyses a results screen is presented with results for each analysis option. The first thing that should be noticed is that the Tunna method predicts a significantly longer life (unconservative) than all the other methods which are within a factor of 4 of each other.
The two important results to note are the Narrow Band = 0.4091 hours, and the Dirlik = 2.104 hours, which compare to 0.409 hours and 2.125 hours respectively from the above hand calculation.
Hand Calculation - From a PSD in the Time Domain
In the time domain, the PSD described above is equivalent to a summation of two sine waves; with stress range 282 MPa at 1 Hz and 141 MPa at 10 Hz. The actual fatigue calculation is done by hand, though MSC.Fatigue tools are used to Rainflow count the cycles. With a sample rate of 200 Hz, and a time period of one second, use PTIME to create and sum these sine waves. Use MQLD to obtain the output shown below.
This time series is rainflow counted using PTIME, into 10 cycles, and displayed using MP3D in “view left” mode to obtain the output shown below.
The histogram editor is used to obtain the range and the mean for the 10 cycles in one second of this time series. Using these values in the MSC.Fatigue S-N materials equation give the following life values at the various bin center stress levels. No mean stress correction is applied.
N(range,mean) = life
N(129,-134) = 1.375E+6
N(116,-115) = 2.148E+6
N(103,-82) = 3.539E+6
N(103,-43) = 3.539E+6
N(96,-3.3) = 4.757E+6
N(420,3.3) = 9.642E+3
N(103,43) = 3.539E+6
N(103,82) = 3.539E+6
N(116,115) = 2.148E+6
N(129,134) = 1.375E+6
A conventional Palmgren-Miner damage calculation on these cycles gives:
E[D] = 1.074E+4
which corresponds to a fatigue life of 9308 seconds, or 2.59 hours.
MSC.Fatigue Calculation - From a PSD in the Time Domain
Use the MSC.Fatigue S-N time series fatigue analyzer (MSLF), with the following inputs/parameters:
input file is the single parameter file created by summing the sine waves
equivalent units are 0.016667 and hours (to convert results in respect of a one second file to hours)
Define the material information in a similar manner as described above and run the analysis.
The predicted fatigue life should be 2.6 hours.
The steps are as follows:

 Operation Comments ptime Invoke PTIME from the system prompt. Add an Entry: Waveform creation Select the Waveform creation option. Filename: sinewaves Enter a new filename such as sinewave. A file called sinewaves.dac will be created. Description 1 Enter an descriptions you wish. Number of fatigue equivalent units: 0.0166667 This is the conversion factor for reporting a one second signal in hours. Fatigue equivalent units: Hours Change this to hours and click the OK button. Do not worry about the units of the actual time series. MPa will be assumed even though the load type is set to Force and the units to Newtons. These are really just labels in most cases. Sample Rate: 200 Change the sample rate to 200. Frequency: 1 Change the frequency to 1. Amplitude: 282 Enter 282 for the amplitude of the first sine wave at 1 Hz and press the OK button. Summation Press the Summation button. Next Frequency: 10 Enter 10 as the next frequency. Next Amplitude: 141 Enter 141 for the amplitude at 10 Hz. Press the OK button when done. Finish Press the Finish button to indicate that no more are to be added. Plot an entry Plot the new time history. Select sinewaves as the input. File | Exit | eXit Exit from MQLD and exit from PTIME. mslf Invoke the S-N single shot fatigue analyzer MSLF. Jobname: test Enter a jobname. It can be anything. Filename: sinewaves Enter the newly created time history as the filename. Press OK twice. Dataset Name Again enter any valid S-N dataset name. Edit Data: Yes Again turn on the Edit Data switch. SRI1: 3728 Enter 3728 as the Stress Range Intercept value. b1: -0.238 Enter this value as the first slope. Press the OK button three times. The results will be displayed. End | eXit Quit from MSLF when you are ready.
Measured Responses
In this section we look at actual measured stress responses. From these responses we predict fatigue lives using the S-N method. The responses are then converted to response PSDs of stress with a subsequent vibration fatigue analysis performed using the S-N method. The predicted lives from the time domain and the frequency domain approaches are then compared for the various vibration fatigue methodologies.
Stress Response Descriptions
Three time domain stress responses are used. They are aptly named 1pk.asc, 2pk.asc and 3pk.asc and can be found in your delivery in
`<install_dir>/mscfatigue_files/examples`
These signify one peak, two peaks, and three peaks. These names are chosen since if you convert these three time signals to the frequency domain you will see that they have 1, 2, and 3 peaks in the resulting PSDs which is an indication of the type of frequency content they contain. These are stress time histories which could be representative of the stress time histories at the critical location of a FE model.
To import these responses do the following in PTIME from an empty directory:

 Operation Comments ptime Invoke PTIME either from the system prompt (or do it from the MSC.Fatigue Loading Info form by clicking on the Database Manager button). ASCII convert + load Select the “ASCII convert + load” option to read in the ASCII response files. ASCII Filename Use the List button to show the available time histories stored as ASCII files. Select 1pk.asc. Sample Rate: 50 Enter 50 as the sample rate. This is important that you enter the proper sample rate. Otherwise the subsequent conversion to a PSD will be erroneous. Equally Spaced Data: X-y pairs Change this entry to X-y pairs. Press OK. Description 1 Enter a description such as “1 Peak Stress Responses.” Load Type: Pressure This is a stress response time history so enter Pressure as the load type. Even though it is not actually a load type, this is the best equivalent. Units: MPa Give SAETRN the new name, SAETRN15, and also new description. Press OK. The time history SAETRN will be duplicated and will be called SAETRN15. Fatigue Equivalent Units: Hours One repeat of the response is equivalent to 1 hour. So enter Hours as the equivalent units. OK Press the OK button to start the conversion. This operation could take some time since it is a very large response history. Plot an entry Select the Plot option and accept the default. eXit Repeat this exercise for 2pk.asc and 3pk.asc if desired. Then exit from PTIME.
Time Domain Solution
The fatigue life from the three time domain signals can be determined quite easily if we select a material - say RQT501 from the MSC.Fatigue materials database. To calculate fatigue lives from these responses, we use the MSC.Fatigue single location stress fatigue life analyzer MSLF. This module accepts a response history directly as opposed to combining loads and FE stress results to determine the response history.

 Operation Comments mslf Invoke MSLF from the system prompt. Jobname Enter a jobname, say “1pk” for the first response history. Since it does not exist you will be prompted to create it. Filename On the next screen that appears, enter 1pk as the file name. This is the binary converted response time history. Accept all defaults on the rest of this input page. OK Accept all defaults on the next page, Model Parameters, also. Database Name: RQT501 On the Material S-N Analysis form enter RQT501 as the S-N curve. Accept all other defaults. OK Accept all defaults of the next page, Geometry. OK / End / eXit Accept all defaults on the next page, Results Setup. At this point the analysis will proceed. Permit overwrite If asked for overwrite permission. The analysis results should give approximately 3600 repeats. You can repeat this for 2pk and 3pk or exit from MSLF.
PSD Responses of Stress
The corresponding PSDs of these three signals are shown in Figure 14‑17. A single peak is generally called a narrow band signal since it only has one predominate frequency. The other signals are called wide band since they have more frequency content.
Figure 14‑17 Stress Responses and Corresponding PSDs
To create these PSDs of stress from the response time histories, use the MSC.Fatigue module MASD. Follow these instructions:
:
 Operation Comments masd Invoke MASD from the system prompt. Input Filename Use the List button to select the file 1pk.dac. Accept all other input on this form by clicking the OK button. OK Accept all defaults on the next input screen, Parameter Input. OK Accept all defaults on the next input screen, Output Parameters, also. End At this point the PSD has been calculated by the program. By pressing the End button the PSD will be plotted. File/Exit Quit from the graphics program, MQLD, and repeat for the other responses, 2pk and 3pk, if desired.
Vibration Fatigue Solution
With the vibration fatigue analyzer, the fatigue life from the PSDs can easily be calculated also with a variety of different methods, and very quickly relative to the time domain. Follow these steps to reproduce results:

 Operation Comments mflf Invoke MFLF (frequency life fatigue) from the system prompt. Input Filename Use the List button to select the file 1pk.psd. Accept all other input on this form by clicking the OK button. OK Accept all defaults on the next input screen, Intermediate Rainflow Options. Dataset Name: RQT501 On the Material S-N Analysis form enter RQT501 as the S-N curve. Accept all other defaults. OK Accept all defaults on the next input form, Geometry. End At this point the program proceeds with the calculations. You should see a life of approximately 3800 hours. eXit You can quit from MFLF and then repeat the exercise for 2pk and 3pk, if desired.
Comparison of Results, 1pk, 2pk, 3pk
Table 14‑14 a chart comparing the 1pk, 2pk, and 3pk with the time domain from all the frequency vibration methods. The Dirlik method is the default and generally gives the best results. The Narrow Band gives good results for the narrow band signal (1pk), but becomes too conservative when the signal is wide band. Tunna breaks down completely for a wide band signal. Wirshing is unconservative and then too conservative, as is Steinberg. Hancock and Kam & Dover do reasonably well but not as well as Dirlik. One of the major problems with most of these methods except Dirlik is that they are modifications of the Narrow Band method. When the signal is wide band, the Narrow Band method tends to turn any signal into a narrow band signal making the resulting fatigue prediction very and sometimes overly conservative.
Also it should be noted that there is nothing magical about the time signals or corresponding PSDs in this example. The only consideration should be when using with other material types that the relative intensity of the signal is compatible with the chosen material and should be scaled accordingly.

 Time Domain Dirlik Narrow Band Tunna Wirshing Hancock Kam & Dover Steinberg 1pk 3626 3815 3762 4485 5771 3839 3352 5765 2pk 1549 1360 1015 15637 1695 1303 1367 1648 3pk 1032 1027 570 62440 964 870 1077 936
Comparison of Results, Wind Energy
Another example is given of responses from of a wind turbine blade. In Table 14‑15 below the various methods are compared to the time domain by normalizing the frequency domain result by the time domain result. Therefore a value of unity would signify a one-to-one correspondence between frequency and time domain solutions.
Figure 14‑18 Frequency/Time Domain Normalization

 Load Case Narrow Band Dirlik Wirshing Bishop Chaudhury Hancock y12a 5.14 1.03 3.91 1.52 2.13 2.75 y19a 5.15 1.00 3.92 1.54 2.14 2.77 y27a 14.34 1.59 10.91 1.74 5.12 5.83 y35a 81.87 2.34 62.23 1.95 30.08 25.08 y12b 1.91 0.77 1.46 1.13 0.98 1.25 y19b 1.98 0.81 1.50 1.22 1.04 1.31 y27b 3.67 1.07 2.79 1.29 1.47 1.92 y35b 18.34 1.48 13.95 1.84 5.68 6.10 y12c 1.98 0.76 1.51 0.86 0.95 1.25 y19c 1.87 0.73 1.43 0.86 0.92 1.20 y27c 2.03 0.74 1.54 0.72 0.87 1.14 y35c 3.22 0.76 2.45 0.66 1.15 1.42 y12d 2.09 0.84 1.59 1.15 1.03 1.33 y19d 2.03 0.83 1.54 1.17 1.02 1.31 y27d 2.92 1.01 2.22 1.15 1.23 1.62 y35d 7.50 1.12 5.70 1.23 2.75 3.29 y12e 2.80 0.99 2.13 1.27 1.50 1.95 y19e 3.06 1.01 2.33 1.27 1.50 1.95 y27e 3.50 1.03 2.67 1.53 1.65 2.16 y35e 8.81 1.11 6.71 1.99 3.31 4.15 y12f 3.86 0.98 2.93 1.43 1.66 2.18 y19f 3.97 1.00 3.02 1.61 1.78 2.33 y27f 3.96 1.01 3.01 1.57 1.76 2.31 y35f 5.59 0.98 4.25 1.65 2.17 2.80 Average: 7.98 1.04 6.08 1.36 3.08 3.32
The following is noted about the results from Table 14‑15:
1. The worst load case is out by approximately 81 times for the Narrow Band method whereas the Dirlik method is out by only two times.
2. Dirlik does the best overall with an average of 1.04.
3. The Bishop method is a theoretical based method used to validate the Dirlik method which is an empirically based solution. The reason that Dirlik does better than the theoretical equivalent is that the response signals are assumed to be random, stationary and gaussian in nature for the theoretical solution. Not all these measured signals completely achieve these assumptions making the empirically fit solution give better answers.
Comparison of Results, Sine Waves
This is another simple example that can be reproduced quite easily by following the steps below. The exercise creates a time history by summing sine waves of very nearly the same frequency. We want to create a time history that will give a corresponding PSD with a single peak near 10 Hz. To accomplish this:

 Operation Comments ptime Invoke PTIME from the system prompt. Waveform Creation Select the Waveform Creation selection under Add an Entry or if no entries currently exist select if from the main menu. Filename: wave Give it a name. Call it “wave.” Also give it some description. Load Type: Pressure Give it a load type of pressure to signify stress. Units: MPa Give it units of MPa. Number of Fatigue Equivalent Units: 5.5556e-3 Enter 0.005556 as the number of fatigue equivalent units for a single block of the time history that will be created. Equivalent Units: Hours Enter hours as the equivalent units. Twenty seconds of time history will be defined below but we want the life to be reported to us in hours. Press OK when done. Sample Rate: 200 Enter 200 as the sample rate. This will ensure enough points will be made to define a 10 Hz signal with the proper amplitude. Total Time of Signal: 20 Enter 20 seconds as the total time of the signal. Frequency: 10 Enter 10 Hz as the frequency. Press OK and accept all other defaults. SummationNext Frequency: 9.9 Press the Summation toggle. This will allow you to define another sine wave with a different frequency to be added to the one just created. Enter 9.9 Hz, press OK accepting the defaults. SummationNext Frequency: 10.1 Do it again with 10.1 Hz as the next frequency. Finish Press the Finish toggle to end. Plot an Entry You may plot it to see a varying sine wave very similar to a narrow band signal. Change an Entry Now we will scale the load up to some realistic stress level. Since we are using MPa as the stress units and with the material to be used, RQT501, a scale factor of 50 will do the trick. Filename Accept “wave” as the file name and overwrite it. New Value = For the multiplication value enter 50. This is the second entry. Leave the others at zero. Press OK twice to accept the new scale factor. Note the RMS of the signal is about if you plot it again 61.23. eXit Exit from PTIME.
Now convert the time history to a PSD using the MASD program.

 Operation Comments masd Invoke MASD from the system prompt. Filename Enter wave as the input file. Press OK four times accepting the default each time. The resulting PSD will be plotted after accepting the result page. Note that the RMS is around 55, very close to the original time signal. File/Exit Exit from MASD.
Now run the single location stress-life fatigue analyzer MSLF using the material RQT501 and the input file wave.dac.

 Operation Comments mslf Invoke MSLF from the system prompt. Filename: wave Enter “wave” as the input file. Press OK twice accepting the default each time. Dataset Name: RQT501 Enter RQT501 as the material on this form. Press OK three times and allow overwrite. The result should be calculated. Note that it is a very large number (~2E8 Hours). End Leave MSLF running for now and move on to the next step.
Now run the single location frequency-life fatigue analyzer MFLF using the material RQT501 and the input file wave.psd.

 Operation Comments mflf Invoke MFLF from the system prompt. Filename: wave Enter “wave” as the input file. Press OK twice accepting the default each time. Ignore any warning message. Dataset Name: RQT501 Enter RQT501 as the material name. Press the OK button accepting the defaults until the analysis runs. Note the life is close to 6 years. End Leave MFLF running for now and move on to the next step.
The comparison between the time domain and frequency domain results in this case does not look good (1.25E6 Hours or 142 years versus 6 years). This was done on purpose to illustrate a point. The problem is in the material data. For the time domain solution the number of cycles has become so high that we have gone right off the curve or the valid portion of the curve. In other words the stress levels we are dealing with are not realistic for the material chosen. We are past the endurance limit. Valid regions on the S-N curve for this type of analysis range between 103 and 107. To verify this go back to both MSLF and MFLF and scale up the loads as follows:

 Operation Comments mflf or mslf Both these programs should still be running. Loading Environment Enter the Loading Environment menu. Scale Factor Change the scale factor to 2 and accept all other defaults. Recalculate Press the recalculate button. eXit Leave MSLF/MFLF or repeat this exercise for the table of scale factors in Table 14‑16.
Note that the lives are beginning to converge. Repeat the above process for each scale factor if desired.

 Scale Factor Time Domain Dirlik Narrow Band 1 1.25E6 51,290 67,381 2 20 13 13 2.25 5.4 3.5 3.4 2.5 1.6 1.06 1.04 2.75 2025 Seconds 1303 Seconds 1279 Seconds 3.0 762 Seconds 490 Seconds 1.7 Seconds 3.1 451 Seconds 339 Seconds 1.7 Seconds 3.2 221 Seconds 237 Seconds 1.7 Seconds
You may find it interesting to compare the other frequency domain solution types also. This signal composed of three similar sine waves summed together does not satisfy the requirement that the signal be random. Even without fully satisfying this, the Dirlik method still gives excellent correlation for realistic stress ranges showing the robustness of the technique. As a final verification the cycle histogram plots are shown for the time and frequency domain solutions in Figure 14‑19 and Figure 14‑20 below. Note that the maximum stress range between the two is very similar (~1000 MPa) for the load case with the highest scale factor (3.2).
Figure 14‑19 Cycle Histogram Results of Time Domain
Just as a note of point, this exercise would not work with a pure sine wave. This is because of the fact that any PSD analysis must realistically use a random signal. A pure sine wave is not a random signal. As an exercise you could perform the same operations as above but on a pure sine wave at 10 Hz. When you compare the resulting cycle histogram plots you will note that the stress ranges predicted by the PSD solution are twice as large as they actually are from the time domain solution.
Figure 14‑20 Cycle Histogram Results of Frequency Domain
Finite Element Model Responses
Now we compare fatigue life predictions in a similar manner as done in the previous section but the responses are determined from finite element modeling. Again the time domain responses and fatigue predictions will be compared to the frequency domain responses and life predictions.
A simple model will be used first in a quasi-static method by running a static analysis of a single load case and associate it’s time variation via an external time history. The same model will then be run through a frequency response analysis and the time signal used in the quasi-static method will be converted into an input load PSD that will be applied to the same location of the model. The fatigue predictions from each will then be compared.
The model is a simple bracket shown in Figure 14‑21 subject to random excitation in the direction of the applied loading. MSC.Nastran is used as the solver and two FE analyses are performed. For the static analysis a unit load is applied at the indicated location and direction. The bracket is fixed at the circular hole. A frequency response analysis is also performed with a unit load at the same location and subject to a frequency range from around zero to 25 Hz.
Figure 14‑21 A Simple Bracket Subject to Random Excitation
Step 1 - Quasi-Static Model
The first step is to perform a fatigue analysis using the quasi-static S-N method to establish a baseline. The excitation is provided by the 1pk response previously used in this section, except it is scaled and the units are modified. It is assumed that this response signal is available. The following operation modifies the signal:

 Operation Comments ptime Invoke PTIME from the system prompt or from MSC.Patran. It is assumed that the 1PK, 2PK, and 3PK signals are loaded into PTIME already from the previous exercise. If not, load them now or import the ASCII versions as described earlier. Change and entry | Polynomial transform Select this option from the main menu. Database Entry to Transform:1PK Select 1PK as the signal to modify. Target Filename:1PK_PSI Enter a new name such as 1PK_PSI. We are going to change the descriptive units to PSI since they are the units of the FE model. New Value = 0.15 x Enter 0.15 in the second databox to act as a multiplier and scale loading history. Press OK. Units: lbs force Change the units to lbs force. Number of fatigue equivalent units: 1.3889 Change this to 1.3889 which is how many hours are in 5000 seconds, the length of the signal. Fatigue equivalent units: Hours Change this to report the life in hours. Press the OK button. eXit Exit from PTIME.
Now set the fatigue analysis up using either MSC.Patran or MSC.Fatigue Pre & Post.

 Operation Comments patran Invoke MSC.Patran (or MSC.Fatigue Pre & Post) if you have not already done so. File / New... Open a new database from the File pull -down menu. Call it “vibration.” Set the analysis preference to MSC.Nastran if asked. Ignore any warning messages. Analysis Open the Analysis application (or Import in MSC.Fatigue Pre & Post) from the main form of MSC.Patran. Action: Read Output2Object: BothMethod: Translate Set the Action, Object, and Method accordingly. Select Results File... Select the MSC.Nastran OUTPUT2 file to import for the static analysis. It is called bracket_stat.op2. Apply Press the Apply button to import the model into the database. Tools / FATIGUE...(Analysis) Invoke MSC.Patran’s FATIGUE interface by selecting it from under the Tools pull-down menu (or the Analysis application switch in MSC.Fatigue Pre & Post.) General Setup Parameters: Analysis: S-N Set the analysis type to S-N on the main form. Res. Units: PSI Set the units to PSI. Jobname: static Give the job a name. Use “static.” Title: Static Example Give the job a title. Solution Parameters Form: Mean Stress Correction: None Set the parameter to None. The mean of the random response loading is essential zero, so no mean stress correction is necessary. Materials Information Form: Material: MANTEN Place the cursor in the cell under the word Material and click on the mouse. A listbox will appear. Select the material MANTEN from this listbox. Finish: Polished Select Polished from the option menu that appears. The word polished appears in the Finish cell. The SAE specimen was a polished specimen with no surface treatment. Treatment: No Treatment Select No Treatment from the option menu that appears. Region: default_group Select the default group as the region. This contains the node we created at the beginning of this exercise. The Materials Information form can be closed down now by clicking the OK button. You may wish to create a group with only Node 47 in it to expedite the analysis since this is the critical node which we will be looking at in more detail later. If you do, reference this group here. Loading Information Form: Results Transformation: Transform to Basic Set the transformation to Basic so that proper averaging of the element nodal stress results occurs. Load Case ID Activate this cell to make the widgets at the bottom of the form appear. Get/Filter Results Open this form to get the results. Select All Results Cases The easiest way to get the results is to press this toggle and then press the Apply button. Select a Results Load Case: Select the only Results Case that appears in this list box. Select a Stress Tensor: Select the result that says “Stress Tensor.” Fill Cell Press this button to fill the spreadsheet cell with the Results Case ID. Time History: 1PK_PSI Select 1PK_PSI which we created earlier. Load Magnitude: 1.0 Accept the default here by pressing the RETURN key. Job Control Form: Full Analysis Set the action to Full Analysis and press the Apply button. This could take some time if you analyzer the entire model. Monitor Monitor the job if you wish.
Step 2 - Vibration Model
The second step is to perform a fatigue analysis using the vibration capability and then compare against the baseline. The excitation is provided by the 1pk response previously used in this section, except it is converted to a loading input PSD. The following operation modifies the signal:

 Operation Comments ptime Invoke PTIME from the system prompt. Add an entry... | creaTe psd from time Select this option from the main menu. This will invoke a separate module called MASD for auto-spectral density calculations. Input Filename: 1PK_PSI When MASD starts, select 1pk_psi as the input filename. OK/OK/OK/End Press the OK button three times to invoke the action. The time signal has now been converted into a loading input PSD. Press the End button to continue. Description 1 Enter any description here. Units: lbs force Change the units. The rest of the form does not need be modified., so click the OK button. A new entry and file called 1pk_psi.psd exists. eXit Exit from PTIME.
Now set the fatigue analysis up using either MSC.Patran or MSC.Fatigue Pre & Post. It is assumed that MSC.Patran is still running and that the database is still opened.

 Operation Comments patran Invoke MSC.Patran (or MSC.Fatigue Pre & Post) if you have not already done so. File / Open... Open the old database from the File pull -down menu if necessary. Analysis Open the Analysis application (or Import in MSC.Fatigue Pre & Post) from the main form of MSC.Patran. Action: Read Output2Object: Results EntitiesMethod: Translate Set the Action, Object, and Method accordingly. Select Results File... Select the MSC.Nastran OUTPUT2 file to import for the static analysis. It is called bracket_freq.op2. Apply Press the Apply button to import the model into the database. Tools / FATIGUE...(Analysis) Invoke MSC.Patran’s FATIGUE interface by selecting it from under the Tools pull-down menu (or the Analysis application switch in MSC.Fatigue Pre & Post.) General Setup Parameters: Analysis: Vibration Set the analysis type to Vibration on the main form. Res. Units: PSI Set the units to PSI. Jobname: vibration Give the job a name. Use “vibration.” Title: Vibration Example Give the job a title. Solution Parameters Form: Mean Stress Correction: None Set the parameter to None. Materials Information Form: This should be setup identically to the pseudo-static job. Loading Information Form: Results Transformation: Transform to Basic Set the transformation to Basic so that proper averaging of the element nodal stress results occurs. Frequency Resp Activate this cell to make the widgets at the bottom of the form appear. Get/Filter Results... Open this form from the Loading Information form. Select the only Result Case that appears in this top of this form. It may already be selected for you (LOAD_CASE, 58 subcases). Filter Method:Global Variable - Variable:Frequency Turn this option menu to Global Variable and set the Variable to Frequency. This may already be the default settings. Filter/Add/Close Press the Filter button. This will filter only subcases with frequency step information from the Result Case. Remember there is a static load case in these also. Press the Apply button. This will load an abbreviation of the frequency steps into the listbox on the Loading Information form which will be used in the analysis. Close the form down when done. Select a Results Load Case: Select the only Results Case abbreviation that appears in this list box. Select a Stress Tensor: Select the result that says “Stress Tensor.” Fill Cell Press this button to fill the spreadsheet cell with the Results Case IDs. Time History: 1PK_PSI.PSD Select 1PK_PSI.PSD which we created earlier. Job Control Form: Full Analysis Set the action to Full Analysis and press the Apply button. This could take some time if you analyzer the entire model. Monitor Monitor the job if you wish.
Comparison of FE Fatigue Results
Use PFPOST to view the results from the two analyses:

 Operation Comments Results... Open the Results... form from the main MSC.Fatigue form. List Results Set the Action to List Results and click the Apply button. PFPOST will be invoked. OK/OK Press the OK button twice accepting the defaults. Most damaged nodes Select this option to display a list of the most damaged nodes. Take note of the life at node 47. Cancel/Cancel Press the Cancel button twice. Jobname: static Enter “static” as another jobname to view the results from the quasi-static fatigue analysis. OK/OK Press OK twice. Most damaged nodes Again note the life at node 47. Cancel Close the report down. eXit Exit from PFPOST.
The table below (Table 14‑17) shows results from the two analyses. In all cases only the Dirlik method is compared to the time domain. Note that only the 1pk response was analyzed in this example, but the 2pk and 3pk are also reported. You can repeat this exercise using the 2pk and 3pk signals if you wish. Also reported in the table are the results using different frequency resolutions. This example corresponds to the 57f job which signifies 57 frequencies were analyzed in the frequency response analysis. Note that as the resolution of the frequency steps becomes greater, the answers tend to converge. The MSC.Nastran input deck (bracket_freq.dat) is provided if you wish to run the analysis with different frequency steps to reproduce the table below.

 Job 1pk 2pk 3pk static 295 Hrs. 136 Hrs. 97 Hrs. vibration (15f) 450 Hrs. 150 Hrs. 111 Hrs. vibration (29f) 261 Hrs. 99 Hrs. 76 Hrs. vibration (57f) 234 Hrs. 94 Hrs. 71 Hrs. vibration (141f) 229 Hrs. 90 Hrs. 68 Hrs. vibration (ALLf) 241 Hrs. 94 Hrs. 71 Hrs.
The job ALLf was run with identical frequency content as the loading input PSDs, 1pk, 2pk, and 3pk. The following notes are made about the results:
1. The results are always conservative relative to the time domain but usually with in a factor of two or less.
2. Only if the frequency resolution of the transfer function around the excitation frequencies of the loading input PSD or the natural frequencies of the model (if they are excited) is not sufficient do answers tend to be non-conservative.
3. This particular example is stiffness dominated since the excitation frequencies are well below the natural frequencies of the model. When this is the case. This gives the same structural response as a static analysis at all the analyzed frequencies in this example. For this reason you would expect to achieve the same or close to the same fatigue results as the pseudo-static method in the time domain.
4. Very high cycle tends to be misleading because of large scatter in data. The table below shows this behavior. For lower cycle fatigue the answers between frequency and time domain do tend to converge. Although the validity of the S-N method then comes into question for very low cycle problems.

 Scale Factor Time Domain Dirlik 0.5 1,290,000 518,767 0.6 78,900 57,728 0.7 13,977 10,468 0.8 3,130 2,505 0.9 906 719 1.0 295 236 1.1 108 87 1.2 43 35 1.3 15 15 1.4 3.1 6.8 1.5 0 3.3