Published on February 28, 2014
In this presentation, rotating equipment refers to machines like o Trommels and composters, used for waste processing o Kilns used in the production of cement o Coolers, dryers and granulators, used in processes such as fertilizer manufacture o Scrubbers and car dumpers used in the mining industry Scrubbers for removing dust from process gases Car dumpers for emptying ore cars 2
In our experience many of these machines get designed with too low a fatigue life That’s not to say that these photos show examples of badly designed machines, but Often stress ranges are too high in areas where welds have low fatigue classifications – we will discuss weld classes later in the presentation Fatigue assessments often neglect to include non-loading bearing attachment welds 3
The main areas of concern, where stress ranges are the highest, are in the vicinity of support rollers, the midspan (for uniformly loaded machines), and as mentioned earlier, attachments such as the tangent plates on this dryer 4
Non proportional multiaxial loading also needs to be considered In this composter example, for every single reversal of longitudinal bending stresses in the vicinity of the tyre, there exist three fatigue cycles in the circumferential direction as the tyre passes the trunnion rollers 5
And sometimes machines will have irregular load profiles such as in this car dumper where a fully loaded ore car is moved into position, rotated, emptied, rotated back and then driven away 6
I will now briefly give some background to calculating weld fatigue lives using stress-life, or S-N curves S-N curve analysis has been superseded by strain-life analysis for cast forged and machined components, but it is still a valid and powerful method for analysing welded joints Because of the high effective stress concentrations in structural joints, local yielding limits the effect of mean stresses, which are ignored in the analysis of welds Fatigue cracks initiate at weld toes, on the surface of components where there is no out of plane stress, so the treatment is simplified to that of plane stress 7
Welds need to be classified correctly in order to use the right fatigue data in the life calculations. In this photo for example, the two welds will have vastly different lives, for the same stress ranges, when classified correctly When using S-N curves a distinction is made between load bearing and non-load bearing members (such as attachment plates for ancillary equipment like blowers or instruments etc The environment needs to be considered, whether the weld is in air or in a corrosive environment The slopes of the S-N curves are modified depending on whether the stresses are of constant or variable amplitude Stress history derivation needs to consider whether the stresses are uniaxial or multiaxial And finally, weld improvements, such as grinding of the weld toe can yield improvements to the calculated fatigue life 8
An example of a variable amplitude stress history is shown here Rotating machine tyre FEA submodel External circumferential tyre stress history is plotted Step 1 is tensile, at the bottom of the machine Step 2, as the tyre passes over the trunnion roller, is compressive Step 3 is tensile as the shell bends, and so on Step 6 is not as compressive as step 2 because the product within the machine is heaped over the trunnion at step 2 9
Finally, there are three main approaches to using S-N curves for the fatigue assessment of welds We will now briefly look at each of these methods 10
One of the commonly used fatigue codes is British Standard 7608: Code of practice for fatigue design and assessment of steel structures Welds are grouped and each group, or class, has its own S-N curve The class depends on joint configuration, weld dressing, stress direction, weld process etc Classification of details that do not appear in the standard can be carried out using special tests or by reference to published work Calculations are based on the assumption that uniaxial S-N curves are applicable when used with equivalent stresses such as von Mises (for pressure vessel design) and principal stresses (for structural applications) 11
The standard requires consideration of axial, bending and shear stress The design stress is based on principal stress ranges The design peak of the maximum principal stress needs to be within 45 degrees of the design trough of the minimum principal stress Uniaxial cycle counting, such as rainflow, or for simple stress histories, reservoir cycle counting is used to identify cycle numbers and ranges Reservoir cycle counting involves “filling” the cycle with water and draining from the lowest trough. The next cycle is identified by draining the remaining water from the next lowest trough, and so on 12
I will now show an example of the calculation of the stress history for fatigue analysis Here is a rotating machine with an attachment plate joined with a fillet weld to the shell We will consider one full revolution of the machine and examine the stresses on this ring location 13
The start and end of the cycle is identified by these peaks The red curve is the longitudinal stress history The blue curve is the circumferential stress history The green curve is the shear stress history 14
The maximum principal stress is calculated 15
The minimum principal stress is calculated 16
The angle of the maximum principal stress is added to the plot – values are on the secondary vertical axis Angles are determined using formulas derived from the Mohr’s circle 17
• The angle of the minimum principal stress is added to the plot 18
Design peaks and troughs must be within 45 degrees of each other The green bars must be placed such that the maximum ranges are determined 19
Peaks and troughs are identified - note that the actual peak of the maximum principal stress is not used The analysis is complex and time consuming The resulting direction is used to classify the weld 20
One alternative to using the methods of calculating stress ranges that are presented in the codes is to use a technique known as the critical plane technique Unlike the codes, which effectively sum damage that is occurring on different planes, damage is summed on a particular plane Especially useful for non-proportional, biaxial loading and with FEA models Stresses are resolved onto a plane lying perpendicular to the surface of the component 21
The calculation of damage is carried out on planes that are rotated by 10 degrees. Adding more intermediate planes has been shown not to produce higher damage results Cycle counting and Miner’s rule are used to calculate the damage on each plane The plane with the highest damage is termed the critical plane The direction of the critical plane is used to correctly classify the weld The example shows the critical plane normal for pure bending, at 0/180 degrees i.e. parallel to the bending stress direction. For bending and torsion, the plane is rotated by approximately 30 degrees 22
In our experience, critical plane analysis can yield ranges which are 20% higher than those calculated in accordance with BS7608 For a weld with an S-N curve with an inverse slope of 3, this results in a life reduction factor of 1.7. For a design life of 20 years, this is reduced to 12 years 23
As I mentioned earlier, the critical plane technique lends itself well for implementation into software that can process the results from an FEA stress analysis We use a package called fe-safe™ with built in S-N curves and this image depicts a tangential plate weldment for a girth gear Critical planes angles are part of the output and are used to classify the welds The software will produce plots of log-life for easy post-processing In the case of fe-safe™, the reported lives are unfactored so some manual calculations are required for different material thicknesses, environments etc 24
This image shows a submodel of a rotating shell at the product feed end The stresses are predominantly circumferential The shortest lives are identified here are in the area of greatest stress concentration, perpendicular to the dominant direction of the stress range 25
In this example, again of a submodel, but this time of tyre chair plates welded to a shell, the software identified the lowest lives to be at the ends of the welds rather than along the direction of the weld 26
We now look at the last of the methods considered in this presentation, by using the Path Dependant Maximum Range for cycle counting stresses on the critical plane for use with S-N curve data Critical plane normal and shear stresses are plotted on a normal and shear plane Beta is an equivalence factor used to relate the uniaxial to shear S-N data 27
This example will look at applying the PDMR to a uniaxial stress history 28
The PDMR will yield the same result as the Rainflow cycle counting technique 29
Now we will look at applying the PDMR to a multiaxial stress history 30
The path length, a function now of both normal and shear stress components on a critical crack plane, becomes the fatigue damage parameter Cycle counting involves summing actual and virtual paths 31
PDMR yields higher stress ranges where there is significant shear in the cycle or were the stresses are highly non-proportional such as in a driven shaft under bending 32
Research project interested in the accuracy of each method and whether the analysis can be simplified and sped up 33
The test specimen has the geometry characteristics of the machines we looked at in the introduction i.e. large diameter and thin wall The test specimen is trunnion supported Loads are also applied via rollers mounted in bogies Weights are hung from the arms to generate a constant load on the test piece As far as we are aware, this type of welded geometry has not been used to generate S-N data in the past 34
Biaxial stresses are also generated in machines other than those considered in this presentation This bucket wheel reclaimer undergoes complex loading from each digging cycle and simultaneous side loading Crane booms see large rotations in principal stress directions with each passing of the lifting trolley And excavators experience side and inertia loads that give rise to biaxial stresses All can be analysed using the techniques presented here 35
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