3Rainflow Cycle CountingJ Problem Description 62J Set Up the Fatigue Analysis 63J Run the Fatigue Analysis 69J Review the Results 72J Concluding Remarks 78MSC Fatigue 2005 QuickStart Guide62Problem DescriptionProblem DescriptionThis example is an extension of the previous example where the simple constant amplitude loading isreplaced with a more complex randomly varying time signal.Invoke Pre&Post or MSC Patran by typing the following symbols at the system prompt or from a DOSwindow:fXX or fatX or fatigue where XX is the version numberp3or patranIf you have not already, open the same database that you created in the previous example working in thesame directory from the File | Open menu. The name of the database should be keyhole.Objective•To predict the life of the keyhole subject to a varying load signal.•To understand how to normalize the FE stresses.•To introduce the concept to rainflow cycle counting.•To introduce the concept of damage summation.•To investigate the effect of mean stress.•To investigate the probabilistic nature of fatigue.Note:The geometry and materials information are identical to that of the previous exercise.Chapter3: Rainflow Cycle Counting63Set Up the Fatigue Analysis Set Up the Fatigue AnalysisTo begin setup for a fatigue analysis press the Analysis switch in Pre&Post (or from the Tools pulldown menu in MSC Patran, select MSC Fatigue and then Main Interface). This will bring up the MSC Fatigue main form from which all parameters, loading and materials information, and analysis control are accessed.Load the Previous S-N Analysis ParametersMSC Fatigue 2005 QuickStart Guide Set Up the Fatigue Analysis 64Instead of defining all the analysis parameters again, let us begin from the last analysis. Once the form is open, type the jobname of the previous example in the Jobname databox (simple_sn ) and issue a carriage return (Return or Enter). You will be prompted to read in an old analysis setup file (it detects a file called simple_sn.fin in your local directory and reads in the parameters).Now change the jobname and the title:1.Jobname: rf_cycle2.Title: Simple S-N Analysis, Variable LoadingLoading InformationOpen the Loading Info... form. Then press the Time History Manager button. This will launch PTIME. The time variation of the load will be defined by a signal called SAETRN which is stored in the loading central database in the MSC Fatigue installation directory.Hint:You can do the same thing in the Job Control... form with the Action set to Read SavedJob.Chapter3: Rainflow Cycle Counting65Set Up the Fatigue Analysis Copy SAETRN from the Central DatabaseWhen PTIME comes up, select Add an entry... and then Copy from central as the method of input. A form will appear that will ask for a name. Use the List button to select SAETRN from the central database.Scale the Time History LoadFrom the PTIME main menu, select Change an entry... and then Polynomial transform. We are goingto scale up the time history to represent the actual loading applied to the component. You will be asked for the Database Entry to transform and a new target file. Use the same name (SAETRN) for both and allow overwrite. The transformation from will then appear. We simply want to scale the load up so all that is needed is to input a scale factor of 10 in the second databox. Press OK when done.Finally a form appears allowing you to change any details associated with this time history. Enter the following:MSC Fatigue 2005 QuickStart Guide66Set Up the Fatigue Analysis1.Description 1: Leave as is2.Description 2: Blank this out3.Load type: Force4.Units: Newtons5.Number of fatigue equivalent units: 16.Fatigue equivalent units: Repeats7.Life results will be reported as the number of Repeats of this entire loading sequence and not asindividual stress cycles as in the previous exercise.Plot the Time HistoryPTIME returns to its main menu where you can select Plot an entry. Accept the default file, SAETRN.Note that the maximum value is close to 10,000 Newtons. As a comparison to the previous example,which oscillated in a fully reversed fashion between positive 10kN and negative 10kN, this signal variessignificantly with a very positive mean and only occasionally reaches or nears the 10kN maximum. Wetherefore would expect this loading to be less damaging with all else the same.Select File | Exit to close the plot and press or double click the eXit switch in PTIME.67Chapter 3: Rainflow Cycle Counting Set Up the Fatigue AnalysisAssociate the FE Load to its Time VariationNow back on the Loading Info... form you must associate the time variation of the load that you just created to the static FE load case. Go to the spreadsheet as was done in the previous example. Two things need to be changed on this form.1.Time History: SAETRNSelect the middle cell to make it active. Another spreadsheet (now with two rows) appears at the bottom of the form from which you select the time history file. Click on the SAETRN row anywhere with the mouse. This will replace the cell with the new time history file name.2.Load Magnitude: 10,000The next cell becomes active and a databox appears below the spreadsheet. Change this entry to 10,000. You must press a carriage return (Return or Enter) to accept the value in the databox and fill the cell in the spreadsheet. Forgetting to do this is a common error.The time variation of the loading is now associated to the static FE results. Press the OK button to close the Loading Info... form.The load magnitude acts as a divisor to normalize the stresses to obtain a stress distribution due to a unit load as in the equation σij (t)=P(t)σij /P fea , where σij and P fea are the stress tensor and load magnitude from the FE analysis, P(t) is the externally defined time variation of the loading, and σij (t) is the resulting timeNote:In the previous example we entered unity for the Load Magnitude accepting the FE load asbeing the true representation of the load and thus the stresses. The time history, UNITLOAD, scaled the stress distribution between 1 and -1 to signify the time variation of the loading. This time the time history SAETRN is used to define the actual loading as it changes with time. The FE load magnitude is therefore simply an arbitrary number used to obtain the stressdistribution. The stresses in the FE analysis need to be normalized by this FE load magnitude of 10kN, to simulate the stress distribution due to a unit load.MSC Fatigue 2005 QuickStart Guide68Set Up the Fatigue Analysisvariation of the stress tensor (at any particular location in the component). This can be done because theanalysis is linear elastic. Using linear elastic FE analysis and associating an external time variation of theloading for fatigue analysis is called the “pseudo-static” method. “It might be said that all stress analysesare basically fatigue analyses, the differences lying in the number of cycles of applied stress.” - quotefrom Carl C. Osgood, Fatigue Design (1982).Chapter3: Rainflow Cycle Counting69Run the Fatigue Analysis Run the Fatigue AnalysisYou are ready to run the fatigue analysis. Open the Job Control... form, set the Action to Full Analysis and press the Apply button. The database will close momentarily as the results information is extracted. When the database reopens, the job will have been submitted. You can then set the Action to Monitor Job and press the Apply button from time to time to view the progress. When the messageFatigue analysis completed successfullyappears, the analysis is complete. Close down the Job Control... form when done.Rainflow Cycle CountingThis analysis takes a few minutes to run to completion. The reason it takes longer than the previous example is due to the complex nature of the time signal. The program is performing a procedure called rainflow cycle counting, referred to as “preprocessing” in MSC Fatigue. Cycle counting is a mechanismto extract and count the number of stress cycles in a signal.MSC Fatigue 2005 QuickStart Guide70Run the Fatigue AnalysisThe term Rainflow is attributed to two Japanese gentlemen, Matsuishi and Endo, who invented themethod. It is based on the concept of rain drops flowing off Japanese style pagoda roofs. Time historysignals are stood on end and rain is visualized to run off of each peak or valley. Various rules wereadopted to count cycles and reversals which is beyond the scope of this text; but suffice it to say that theend result of rainflow cycle counting is a set of constant amplitude signals and a count of the number ofcycles in each. Cycle counts can be visualized as probability density functions (PDF) or as 3-dimensionalhistogram matrices as you will see later.Damage SummationIt is important to break up a variable signal into a number of constant amplitude signals in order to assessthe life from the S-N curve. The curve itself is created by a series of constant amplitude tests. So for eachcycle in the signal you must look up the proper stress from the S-N curve. What stress to look up is thejob of rainflow cycle counting. The next challenge to tackle is the summation of the damage from eachcycle in order to report a total life due to all cycles. This is accomplished by way of the Palmgren-Minerlinear damage summation law.This states that damage can be summed by determining the ratio of the number of cycles experienced tothe number of cycles to failure for a given stress range or level and then summing all the ratios for everystress range. When this number, known as Miner’s Constant, reaches unity, failure is said to haveoccurred. The predicted life is then determined by summing the percentage of life used by each stresslevel for the entire time signal. Life is then reported back as to the number of times the given time signalcan be applied before failure.71Chapter 3: Rainflow Cycle Counting Run the Fatigue AnalysisSpeeding up the AnalysisThere are two ways that you could speed up this analysis.1.First, since we already know where the failure location will be (at the point of highest stress) because of the simplicity of this model, we could have defined a Group with only this node (Node1) and specified it in the Materials Info... form. This however, would only calculate life at this one node and would ignore the rest of the model.2.Second, on the Job Control... form you can turn on the Simplified Analysis toggle. As an exercise after you finish this problem, turn this toggle ON , change the Jobname to something else and re-run the problem. Note how much faster the analysis proceeds relative to the first time. What is happening is that for a normal analysis, the rainflow procedure is being applied to each location once its stress time variation is determined. When the Simplified Analysis toggle is turned ON, the rainflow procedure is applied to the loading time history first and the FE stresses are used to scale the rainflow histogram matrix. This speeds up the analysis significantly for a complex time signal for a single load. It does however, produce slightly less accurate results. Notice the slightvariation in predicted life when you do this.Hint:This is where user-defined fatigue equivalent units come in handy, because rarely does onewant life reported in “repeats” of the time signal, but rather in more meaningful units suchas hours, miles, years, laps, missions, etc. This is accomplished by defining these user-defined units in the PTIME, loading database manager, utility. Use the Change an entry | Edit details option.MSC Fatigue 2005 QuickStart Guide72Review the ResultsReview the ResultsOpen the Results... form on the main MSC Fatigue setup form (not to be confused with the Resultsapplication switch on the main Pre&Post or MSC Patran form). With the Action set to Read Results,press Apply. The fatigue analysis results have been read into the database. You can review the lifecontour plot as you did in the previous exercise if you wish. The contour will look similar but themagnitudes will be different.Tabular ListingOn the MSC Fatigue Results... form, change the Action to List Results and press Apply. This will startthe module PFPOST which tabularly lists the fatigue analysis results. Accepting the jobname and thedefault filtering values by pressing OK a couple of times will get you to the main menu. Press or doubleclick the Most damaged nodes switch to view a tabular listing. Note the life value of approximately105.26=184,000 repeats of the signal on Node 1. This is significantly less damaging than the previousexample considering the life is reported in repeats of the time history and not as individual cycles. To getthe number of cycles, we would have to multiply the life result by the rainflow cycle count. Press Cancelto quit the listing and press or double click eXit to leave PFPOST.Chapter3: Rainflow Cycle Counting73Review the Results Histogram MatrixLet us take a look at the results of a rainflow cycle count. From the Results... form, change the Action to Optimize and press Apply (you do not need to enter a node number) on the Results... form. This will launch the module FEFAT in its design optimization mode. When it comes up, press Worst Case to automatically select the node with the lowest life prediction. Enter a Design Life of 1E6 (a million) repeats. Press the OK button. The analyzer will re-analyze the fatigue life at Node 1 and will report the life value to you. Pressing the End button will put you into the main optimization menu.Select results Display and then plot Cycles histogram. This will display a histogram plot showing the results of the rainflow cycle count for the critical location on the model. It looks a little bit like a city skyline. Note that there are quite a few cycles that have low stress ranges and that there are fewer with high stress ranges. The height of each tower represents the number of cycles at that particular stress range and mean. Each tower is used to look up damage on the S-N curve and damage is summed over all towers.A histogram cycle plot from our first example would yield only a single tower of unit height with a meanof zero.MSC Fatigue 2005 QuickStart Guide Review the Results 74Now convert the cycle histogram plot to a damage histogram plot. This is done by either returning to the main menu and selecting results Display | plot Damage histogram or with the cycle histogram plot still displayed, select Plot_type | Damage . Now you can see the damage caused by each bin. Notice that the lower stress ranges produced zero damage. All damage came from cycles in the higher stress range, which is to be expected. Select File | Exitwhen done viewing the graphics.Hint:The accuracy of the fatigue calculation is dependent on the number of towers allowed in therainflow histogram. Typically it is broken up into what are called bins which is the matrixsize. These bins can be 32x32, 64x64, or 128x128. If you want to increase the accuracy, youcan run FEFAT interactively at the critical location and specify a larger bin size.75Chapter 3: Rainflow Cycle Counting Review the ResultsEffect of Mean StressNow let us investigate the effect of mean stress on the fatigue life predictions. First remember that the S-N curve we are using was produced for an R-ratio of minus one, or no mean stress in other words. The time history used in this example has a predominately tensile mean. The initial life prediction did not take into consideration this mean stress and therefore could perhaps be giving a somewhat non-conservative answer. From FEFAT’s design optimization menu, select Sensitivity analysis | Mean stress correction (all) then press or double click the Recalculate switch. A listing showing no correction plus two mean stress correction methods appear: Goodman and Gerber. Note that both of them give more conservative answers.How is mean stress compensated for in the S-N analysis?The simple way to explain this is that for both the Goodman and Gerber methods, knowing the ultimate tensile strength (S u ) and the actual stress amplitude (σa ) and mean (σm ), an equivalent stress range with zero mean is determined. Goodman and Gerber follow these equations:σa S e -----σm S u------+ 1 Goodman =σa S e -----σm S u ------⎝⎠⎛⎞2+1 Gerber =MSC Fatigue 2005 QuickStart Guide Review the Results 76Graphically this looks like the plot to the right where, at least for Goodman, if you draw a line connecting S u to the intersection of σa and σm and then continue it on to the stress amplitude axis, this will indicate the equivalent stress S e with zero mean. This stress is then used to look up damage on the S-N curve.Probabilistic Nature of FatigueAs a final exercise in this example, let us investigate two different materials as we did in the first problem. From the main menu of FEFAT’s design optimization mode, select Material optimization . Change the material S-N curve from MANTEN_MSN to RQC100_MSN and then press or double click theRecalculate switch again. Note that RQC100_MSN , being a much higher strength steel, gives a much higher life prediction (357,000 repeats vs. 184,000 repeats) for no mean stress corrections. This means RQC100_MSN is a better material to use (or does it?). Just looking at the S-N curve might indicate this also.Press or double click the Original parameters button to put the material back to MANTEN_MSN and then press or double click the Change parameters switch and change the Design Criterion to 99. Press or double click the Recalculate switch. Note the life of approximately 85,400 repeats. Now change the material to RQC100_MSN as done earlier and press or double click the Recalculate switch. The lifeusing the higher strength steel is now only about 30,900 repeats, less than that of the lower strength steel.Note:As a stress range of a cycle becomes larger and larger, there tends to be less and less possiblevariability in the mean of that cycle. This is indicated on the cycle histogram plot since thebase of these type of plots tends to be triangular in nature, which means that as the stress gets larger, the mean stress has less of an effect on the fatigue life.Chapter3: Rainflow Cycle Counting77Review the ResultsThis is due to the probabilistic nature of fatigue and the scatter associated with the S-N curves themselves. By specifying 99 as the design criterion, we are asking MSC Fatigue to calculate a life value based on a 99% certainty of survival. The larger the scatter in the original S-N data that makes up the curve, the less certain we will be of survival and the code takes this into account by reporting a more conservative answer. The default is a 50% probability of survival (or failure)Note:Scatter is associated with S-N curves and other damage curves due to the fact that, for example, if you take 10 identical test coupons and subject them to what you think are identicaltests, you will get ten slightly different answers. The material parameters associated with S-Ncurves take this into consideration with the Standard Error of Log(N) (SE) determined byregression analysis of the raw data.MSC Fatigue 2005 QuickStart Guide78Concluding RemarksConcluding RemarksThis exercise introduced you to rainflow cycle counting, damage summation, mean stress effects, andthe probabilistic nature of fatigue by using a randomly varying load on our simple keyhole model.Though this example still did not help us identify critical locations since we already knew where failurewould occur, it did start to show the power of MSC Fatigue by being able to handle complex time signalsand to make compensation for parameters that may effect the fatigue life, something that would be adaunting task to do by hand.The next exercise will introduce the concept of a component S-N curve.Quit from Pre&Post or MSC Patran when you are through with this exerciseNote:MSC Fatigue does not take into account the frequency (speed at which cycles are experienced) or the sequence (when a particular cycle is experienced relative to other cycles) of cycles froma given signal. Rainflow cycle counting simply counts the number of cycles and determinestheir range and mean. Frequency and sequence can have an influence on the fatigue life but isa third or fourth order effect on life prediction in most cases. MSC Fatigue does provide youwith certain fatigue analysis utilities to determine if these influences are important after theinitial analysis using the MSC MSC Fatigue module MTCD (for time correlated damage).。