Fatigue Loads

[lLouie]

Hi

I have written about fatigue here many times. I found a source that I thought might be helpful, and I have a question.
To find the stresses in each spectrum (taxi, cruise), should I consider the fuel mass used by the aircraft in that spectrum? For example, should I include the fuel mass spent during 100 flights to calculate 1g stress in cruise? Or should I take the critical mass?

You can find the source in attachment.

 

[rb1957]

wow, AFgrow and James Burd ! where did you find this ? [1] cute to see the B-26 as a model plane ...

I've only scanned it, but the pedigree is good.

Yes, it should be adequate to use the configuration of the plane at mid-segment (the mission is comprised of a sequence of segments), for example the mission has a cruise segment, I'd use the mid-mission weight for this; this may not be precisely the mid-cruise weight but good enough. For climb, approach use the mid-segment weight, for take-off and landing the take-off and landing weights are easier to use still you'll have static cases you can "leverage". For all segments, you are likely to have a static case to base your external loads on, but you'll have different "fatigue" weights. If cruise is an extensive duration, you can use multiple segments (1 hour durations instead of one 6 hr segment); the difference is very minor but you should (IMHO) figure these things out for yourself (rather than rely on "some guy on the internet said ..."). Speaking more generally, 'cause I know your interest is your UAV, there are also other reasons to define segments, eg a plane with wing and fuselage fuel may have one cruise segment finish at the exhaustion of fuselage fuel ... one cruise segment is burning fuselage fuel, the other wing fuel.

[1] notice the "propriety" notice in the footer ...

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

I have searched a lot. Thank you so much for reply.
When I search many fligth loads, the cruise segment is much more than other. It makes up 99% of the flight. As the fuel in the wing decreases, the load on the structures will inevitably increase. In that case, instead of creating a single fuel mass, I should determine a separate fuel mass for each segment and apply a 1g load like my source.

For example, I should take the average fuel mass consumed as a reference for 30 taxi data. Is that correct? or Should I take critical fuel mass?

 

[rb1957]

cruise is 99% of the flight duration, but not 99% of the damage (maybe less than 1/3). For cruise you generally need 1g and "delta_1g" flight loads, in the past "delta 1g" is the difference between 2g and 1g, and then you use this with the various gust/manoeuvre loads cases, like 1.5g loads are 1g + 0.5 delta_g ... clear as mud ?

Yes, internal loads change as fuel burnt, at least as far as the wing is concerned.

I would use take-off weight for pre-flight taxi, take-off run and initial climb ... just easier and slightly conservative and very little impact, but use as many weights as you like. As I've said, i think it's better for you to develop your own sense as to what is important and what (and when) you can skip things. but 30 taxi cases (do I have that right ?) seems pretty extreme !?

But we are talking about a very minor aspect of fatigue damage. In practice there are many variations that we "smear" over with our analysis ... we can't analyze every possible variation so we say a typical mission is (say) 80% MTO, flies for a typical mission 1hr ? and lands at whatever weight is left (80% of max landing weight makes some sense, so typical mission might burn this much fuel, yes?). At an OEM I was with we started the fatigue analysis with many different cases and analyzed our way to 1 typical mission for all the detail analysis.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

Yes you are right even if the cruise is 99% of the flight, the damage may not be critical like other spectrum (maneuever).
I gave 30 taxi conditions as an example. I just want to know, should I take the average fuel mass of all flights? If it consumes an average of 2 lt in 30 taxi conditions, I should take this into account in my analysis.

 

[rb1957]

I would run take-off take-off weight, forget accounting for the fuel burnt,
I'd run climb at the mid-climb segment weight,
I'd run cruise segment (or each cruise sub-segment) at mid segment (or sub-segment) weight,
I'd run approach at mid segment weight,
I'd run landing at the landing weight (maybe a titch unconcervative, but there are so many round-offs happening ...)

but of course you can break segments into as many sub-segments as you like ... burn 100 lbs of fuel or 1% of fuel (or all up) weight ... as you wish. Study the differences and see what is significant and what isn't (to minimize work).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

Thank you very much. Thanks to you, I have gained more useful information.

 

[lLouie]

Additionally, I would like to ask, is it important to determine delta g? I assume the plane is flying at an average of 1.5g. So should I perform an analysis in the range of +-0.5g?

 

[rb1957]

there are several approaches ...
1) calculate 1 delta_g by subtracting 1g from a 2g loadcase, then factor as needed; but delta_g is (in my experience) very close to 1g ... close enough to ignore conservatively.
2) calculate the "gust alleviation" factor. In my experience this is between 0.95 and 1 so small enough to ignore conservatively, but it may be different for UAVs. This scales static loads (like above) for dynamic.

I'd've thought this would be outlined in your attachment ? Maybe they just sprinkle some "word salad" ... without explaining the detail ??

whilst these factors may be small I'd encourage yo to calc them out at least once so you can say you know they are small (and not rely on "some guy on the internet told me ...").

you are massively simplifying one of the most major components in fatigue ... the load spectrum. I know it is massively difficult, and most of the material may not be appropriate for UAVs. I know one option we gave you was "just define a spectrum" and 1+-.5g may be a good cycle but I see that as little more than a guess. I would strongly encourage you to put a loads monitoring system on your UAV, a simple nz accel at (or near) the CG is definitely something (easy enough to do). At a minimum I'd do a sensitivity study ... 10 cycles per flight ? 1+-1g ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

I have flight spectrum data like it. I can use it to do fatigue analysis.

 

[rb1957]

ok, so looking at that the small cycles on ground are pretty meaningless; so you can say the ground stress is -5ksi (or maybe -6ksi, the minimum of the ground stresses. But the flight stresses show several cycles ... there is a flight mean stress of about 8ksi and several cycles of 1 (or 0) to 15 (or 16) ksi.

you will have heard of the GAG (or Ground-Air-Ground) cycle. This is strictly the ground mean to the flight mean stress, but is often taken (conservatively) as ground minimum to flight maximum. So I would characterise this spectrum as 1 GAG cycle of -5 to 8 and maybe 10 cycles of 1 to 15. By now I think you know the importance of alternating stress ... the GAG has an alternating stress of 6.5, and the flight cycles 7ksi ... so they'll be about equally significant (I had expected the flight stresses to be much lower), so the spectrum is about 11 cycles equally damaging (yes, there is an effect of R = min/max, and yes there is something in removing the -ve stress (calling it zero and fatigue is predominately a tension stress phenomenon).

Recognise that this is the stress on the lower wing skin, and other structures will be quite different, like the Horizontal stabilizer (the upper skin is critical, and the ground stress is pretty much zero).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

That was just a sample.
Thank you for your reply.

 

[lLouie]

I would also like to ask, with your permission, the aircraft flies at an average of 1.2g. How much does its lifespan shorten if it sees 2.5g once, twice or 10 times? Do you have an example of this? How can I write it in Excel without analyzing it?

For example, the lifespan of an aircraft flying at an average of 1.2g is 50,000 hours, how much will its lifespan be reduced if the aircraft sees 2g twice or 5 times? How can I determine this?

 

[rb1957]

ok, a plane will fly at an average of 1g (1.2g would mean it's climbing, manoeuvreing ...) Of course you could mean that the lift is equivalent to 1.2g 'cause the wing lift include the H. tail "lift" (being down) ... ie the wing lift is higher than the weight of the plane.

A typical flight will have cycles, like your previous sketch showed, so there are flight cycles 1.5g to 0.5g.
So there's a GAG cycle of 0-1g, and manoeuvre cycles of 0.5-1.5g ... so the same delta load (1g) and the same alternating load (0.5g) although different R (min/max) of 0 and 1/3. R has a small impact on things.

So very roughly if the plane is good for 200000 cycles (of 0-1g) then it would have a safe life of somewhere between 20000 and 50000 cycles. If 1 cycle per flight then 20000 to 50000 flights; if 2 cycles per flight (1 GAG and 1 manoeuvre) then 10000 to 25000 flights.

Now if your test was 0-1.5g, this is an alternating load of 0.75g. A cycle of 0.5g alternating load could be expected to have a life factor of (0.75/0.5)^4 = 1.5^4 or 4* (rounding 1.5^2 = 2). Thus you could say that your test load covers the safe life factor. Clear as mud ??

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

Actually, I want to learn this. For example, a flight profile of mine is exposed to the current maximum of 1.5g and has a lifespan of 100,000 hours. If the plane sees 2g 10 times, I want to calculate how many hours its lifespan decreases without analysis. Does this make sense? The user may also have a different flight profile than my flight profile. I hope I was able to explain it this time.

 

[rb1957]

have you heard of "Miner's rule" ?

if you are saying ...
1) I have a plane/wing that I have fatigue tested to 100000 cycles of 0-1.5g (alternating load = 0.75g).
2) If I subject the plane/wing to 10 cycles of 0-2g (alternating load = 1g) scattered throughout the life of the plane/wing, then
3) how many 0-1.5g cycles are equivalent to the original ?

damage is proportional to load^4 (or 5th power)*number of cycles.

original test damage is proportional to 0.75^4*1000000 ... the math may work but I'm suspicious of fractions < 1 so lets say the damage from the test is proportional to 1^4*100000 = 100000 (normalising the loads to your original test load).
then you have 10*1.33^4 + N*1^4 = 100000 ... N = 100000 - 3.16*10 = 99968 (or -42 if you want to use the more conservative 5th power). You should be able to find this, search for "fatigue damage power law".


"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

Yes, I have heard the Miner's Rule before.
damage is proportional to load^4 (or 5th power)*number of cycles. Is the there any source for it? I did not hear this formula.
Actually, I'm not talking about the test, I'm interested in the flight status of the aircraft in general

 

[rb1957]

experience, supported by the power coefficients in MMPDS or Mil Hdbk 5; and to a lesser extent the power coefficients in the typical da/dN curve ... 4 is a typically conservative value (and much easier to work with).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[lLouie]

Normally I would do it like this;
Damage after 1st flight + Damage after 2nd flight + ....
If I use the method you mentioned, I must do (Damage after 1st flight)^4 + (Damage after 2nd flight)^4 + ...
I understood you correctly, did not I? If it is correct, can I calculate it without analysis?
I want to write code for this. My goal is to make a calculation tool that allows damage calculation after each flight, without the need for analysis, using certain stresses and others.

 

[rb1957]

no ... damage is proportional to load^4 ... double the load, the damage is 16x; 1.2*load is 2*damage
why damage of flight 1 +damage of flight 2 + damage of flight 3 ?

you have 1000 flight 1 and 10 flight 2 ?

I understood to to ask if I have a life of 100000 of 0-1g flights then how maybe 0-1g flights can I have if I also have 10 0-2g flights (or something like). so a 0-1g flight has a damage of 1/100000 (yes?), and a 0-2g flight has a damage of 16 0-1g flights = 16/100000 so its 10*16/100000 + N*1/100000 = 1 ... N = 100000 - 160.

If you want 10 flights of 0-1g + 0-2g then damage of this flight is 17/100000, and recalc.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.