How CAESAR is calculating NEMA23 moments about resoltn point

hi to all,
Thank you for your time in replying and answering my questions.

while performing NEMA 23 check.

1) How CAESAR is calculating moments about resolution point
Mx =
My =
Mz =

When we enter the input distance from resolution point?

Thanks

Runner,

Please use "Search" function.

Regards,

danb,
In NEMA "Factor for allowable increase" (optional), if client have no information about this, Default value is 1 as said by CAESAR II (F1 help)
Question is if I consider Factor for allowable increase as 2.0 I get pretty good result then 1.0, whom should I consult rather then client?
I could not understand HOW CAESAR II is calculating MOMENTS ABOUT RESOLUTION POINT? ( I searched in CAESAR tech doc and help but couldn't find any information on it)

Moments About Resolution Point
(Algebraic addition of the moments above)
MX= -524 ft.lb.?
MY= -3428 ft.lb.?
MZ= 5986 ft.lb.?

Runner,

1. It is the manufacturer you have to contact.

2. See Aplication Guide, Example 10 - Nema SM 23.

Regards,

Moments about the resolution point are calculated due to loads applied to each nozzle, and summed to give the net value. Typically moments in X direction for one nozzle:

MX components from one nozzle = MX + FY.dZ + FZ.dY

Where dX dY and dZ are the vectors from nozzle to resolution point.

Danb is right about the NEMA factor. If it's not in the data, and it should be, contact the vendor.

Unfortunately, the NEMA documentation uses the word "resolve" or "resolution". The example clearly shows that is not the case.
I believe you'll find other discussion on this topic in this Forum. Use the search feature.

Thank you for your time in replying,
its very much help full, I have read from turbine vendor dwg Factor for allowable increase twice so I used 2.0.

Thanks
arun

Dear Mr. Diehl,

I'm just curious why the current interpretation of SM 23 and API 617 seems to miss the next words after "resolved". In both documents appear "resolved at the centerlines".

By "mechanics", I would interpret the intention of this reference is to ask "resolving" the resultant moment based on the notion of "moment of force about a line". By definition, this one is the (vector) projection on that axis of the (vector) "moment of force about a point" when point belongs to that axis.
It can be proved that the moment of force about the line remains the same when point is "moving" along the line.

My best regards.

Mariog,

We, too, are puzzled by the wording. A few years ago we asked for an "interpretation" and our request has not been satisfied.

I don't have the code in front of me now but I agree that it looks like that sentence is missing a few words.

I find it unfortunate that that code uses the term "resolved". These forces and moments are not resolved about a point as we would expect.

But in the end, the mechanics of resolution is inappropriate anyway. There is no load path to this intersection between nozzle line and shaft, is there? But as long as the machines work, then it's good enough for me.

Dear Mr. Diehl

I guess everybody was puzzled by the problem of missing resolution point. What I understand now, after accidental refreshing my "mechanics" and revisiting the sentences of standards, is they are not asking to calculate moments about a point but about a centerline.

Presuming their intention was indeed to "resolve" the moments of forces about a line (and, exactly as you said, avoiding to ask myself why this procedure is enough for machine), there are several practical methods to do it. One can find in books a specific way to develop such calculation without a resolution point.

Other method- more appropriate for computers calculation- is to consider a point on that line, to calculate -as a vector- the resulting moment about that point and to get vector projection on the line. The result is the resultant moment about the line and -by "mechanics"- the result does not depend on the chosen point. In other words, we can choose any point on line when calculate the moment about the line.

The only doubt may be....indeed was the intention of SM-23 to calculate the moments about a line? just because in their examples was not the case...

Thanks and my best regards.

I’ve tried to understand the logic by which SM-23 does not mention a resolution point. I think there is an explanation for the missing point reference in SM-23 and I try to explain it.

I guess their approach without mentioning a resolution point for combining forces and moments of inlet, extraction and exhaust connection was to proceed as following:
- Consider a system of coordinates as in figure 8-15, where Y="vertical up" is centerline of the exhaust connection, Z is perpendicular on Vertical and on Turbine shaft, X is parallel to Turbine shaft and pass thru Y and Z intersection;
- Calculate the forces and moments about axes X, Y and Z (SM-23 says -rather cryptic- "resolve at the centerlines" and I interpret as "calculate moments about axis") and limit to the values given in 8.4.6.2 b;
- Consider previous calculated Fx, Fy, Fz, as components of Fc=sqrt(Fx^2+ Fy^2+ Fz^2)
and Mx, My, Mz as components of Mc=sqrt(Mx^2+ My^2+ Mz^2)
and comply with 8.4.6.2 a, limit 2

I would observe that:
- The coordinate system is not ambiguous; however it has an "origin" which is not on turbine shaft and makes the system a little bit "uncomfortable" vs. expectations;
- In order to calculate moments about X, Y, Z we don’t really need a unique resolution point (for example "Mechanics" explain that Mx remains the same when we consider any reference point on X and the result Mx=Sum(Mxi-zi*Fyi+yi*Fzi) does not depend on xi)
- Calculating Fc and Mc means to use formulas and we don’t need any reference point.

That means that we are able to calculate without a reference point?
Yes and no… better said there is a way to develop calculation without an explicit reference point. In fact it is something tricky and hidden in formula Mc=sqrt(Mx^2+ My^2+ Mz^2) where we assume in back that Mx, My and Mz exist together as components in a point; this is happening only on intersection of X, Y and Z, so at origin of coordinate system.

So in my understanding we may calculate without a reference point or using a reference point which is the origin of coordinate system- the results should be the same.

Probably I failed to convince you all on subject "moments about centerlines" and everybody prefers to refer to a more familiar "moment about a point". But I think this aspect is not really important- because the things are equivalent- just SM-23 complicated the matter not referring to a point.

I think the root of the problem is the common perception that SM-23 coordinate system is not completely defined and the origin is not specified. Not true- but unfortunately true with API 617 figure 4.E1…

However looking to SM-23 figure 8-15, the axis Z is perpendicular on Y (because the system is orthogonal) and Z is perpendicular also on turbine shaft (as figure describes).
The vertical Y (exhaust centerline) and the turbine shaft are two lines in space that do not lie in a plane, and Z is the line intersecting both of them at right angles. It is "the common perpendicular" and it is known that "any two skew lines have a unique common perpendicular".
So Z axis is unique and the intersection between Z and Y gives the origin of coordinate system.

Now having a point clearly defined as origin of coordinate system, is there anything more needed?
Maybe yes, because the first impulse in calculation is to use the origin as "resolution point" but after it is the question if that's what SM-23 has asked for.
In my interpretation the answer is "yes" because calculating moments Mx,My and Mz by other method and combining them as components is equivalent with calculating the moment about "origin" of coordinates. But looking to the Samples Problems of SM 23 the answer is "God knows"…

Best regards.