ACI 351.3R-04 - Centrifugal Mine Fan - Need some help 2

[ARS97]

I'm designing a block foundation for a centrifugal mine fan. The preliminary sizing for the main block is 37' long x 15' wide x 5' thick. On top the block, there are two pedestals roughly 6' tall - one supports the motor and drive bearing,the other supports the non-drive bearing. (There's a gap in between the pedestals that allows passage of ductwork.)

Everything is getting checked in accordance with ACI 351.3R-04.

My plan is to first complete hand calcs. Next, I have two possible computer-based solutions - Staadpro and Staad Foundation Advanced. First off, Staad Foundation Advanced has a machine block wizard built right into it, and it's perfectly geared for this application, but there seems to be some bugs with it. Bentley has already confirmed one of the bugs (output displays frequency in units of rad/s, not Hz like it says). I'm also getting abnormally high vibration amplitudes that just don't make sense. So, I'll likely just use it as reference. The other computer solution will be a Time-History analysis in Staadpro.

There are various input parameters and recommendations:
- Impeller assembly (which I assume includes the shaft) is balanced to ISO G2.5
- Impeller = 7,845 lbs (WK^2 = 70,407 lb-ft^2)
- Shaft = 12,645 lbs (WK^2 = 3,111 lb-ft^2)
- Motor = 2,000 HP, 894 RPM, 12,790 lbs (directly coupled to shaft)
- Bearings = approx. 1,300 lbs each
- DYNAMIC LOAD = 7,031 lbs in vertical or horizontal direction (in-plane of motion)
- Minimum foundation stiffness = 5,000,000 lb/in
- Minimum foundation mass = 339,675 lbs
- Vibration amplitude is limited to 0.2 in/s
- Foundation frequency should be 1.5 times HIGHER than operating frequency (894 rpm = 14.9 Hz)

I have calculated the vertical and horizontal impedance per Section 4.2:
Vertical = 5,799 k/in
Horizontal = 8,231 k/in
*Ignored damping
*Ignored rocking and torsion

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So.....first question deals with the dynamic load. In Section 3.2.2 of ACI 351, there are several methods for calculating the dynamic load for a rotating machine. Obviously in this case the manufacturer has already supplied the dynamic load, and I will use it for my calculations. However, for the sake of comparison, I wanted to also look at the other three methods.

Machine unbalance provided by Manufacturer (3.2.2.1b)
Equation 3-3:
mr = 7,845 + 12,645 = 20,490 lbm
e = ? Since Q = eω, then (0.1 in/s) = (e)(93.6 rad/s), then e = 0.1 / 93.6 = 0.00107”
ωo = 894 rpm = 93.6 rad/s
Sf = 2
Fo = (20,490)(0.00107”)(93.62)(2) / 12 = 32,013 lbs

Machine unbalance meeting industry criteria (3.2.2.1c)
Equation 3-4:
Fo = (20,490)(0.1)(93.6)(2) / 12 = 31,964 lbs

Machine unbalance by empirical method (3.2.2.1d)
Equation 3-6:
Fo = (20,490)(894 rpm) / 6,000 = 3,053 lbf

As you can see, equations 3-3 and 3-4 predict a dynamic load on the order of 32,000 lbs, while equation 3-6 predicts roughly 1/10 of that. I have to be doing something wrong. It's likely something simple, such as units, but I've already looked at too much already and nothing is jumping out at me. Perhaps a second set of eyes will find it. Does anybody see an error?

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The next question deals with the vibration amplitude. I just need some peer review to see if these calcs make sense.

For the vertical displacement:
Refer to equation 4-44
Fo = dynamic force amplitude = use Manufacturer load = 7,031 lbs
k = vertical stiffness = 5,799 k/in
ωo = 93.6 rad/s
ωn = (5,799 k/in * 32.2 ft-s^2 / 600k)^0.5 = 61.1 rad/s
A = 0.901 mils
For peak-to-peak, use 2A = 1.802 mils (use Fig 3.10 - "fair")

For the horizontal displacement:
Refer to equation 4-44
Fo = dynamic force amplitude = use Manufacturer load = 7,031 lbs
k = horizontal stiffness = 8,231 k/in
ωo = 93.6 rad/s
ωn = (8,231 k/in * 32.2 ft-s^2 / 600k)^0.5 = 72.8 rad/s
A = 1.308 mils
For peak-to-peak, use 2A = 2.62 mils (use Fig 3.10 - "fair")

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I'll hold off on my last question, which deals with the proper definition of the Time History within Staadpro. I need to study this a bit and make sure I'm specifying the correct input.

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I know it's long-winded, but if anybody could help out, I'd greatly appreciate it!

 

[JedClampett]

I don't know anything about STAAD Foundation Advanced, but in looking at your numbers, you should have no problems. You have a foundation (I get 416,000 lb.) that weighs more than 15 times your machine and 20 times the rotating parts. The speed is not very high.
In the old days we tried to size foundations based on weight using rules of thumb, such as 3 times the machine weight or 10 times the rotating parts. There's a lot of foundation out there that are successfully performing based on that type of design, with no fancy computer models.
But numbers don't lie. There's something wrong with the model. Is soil stiffness part of it? That's a tough unit conversion.

 

[JoshPlumSE]

You might also check your damping assumptions.... If you don't have any damping in your STAAD model, then you're going to have problems. I've seen that before where the user didn't enter in any damping values. It took a surprising amount of time to realize what happened. Because the output looked perfectly reasonable.... most of the time. Then looked crazy when it wasn't reasonable.

 

[WARose]

Something seems wrong with your unbalanced force calculation. The equation is: F=m*e*ω².

Be sure you are using the right mass (and that you are using mass (not weight)) for this equation. I've seen people use the whole motor weight when it should just be the rotating part.

I don't know anything "Staad Foundation Advanced".....but I use STAAD Pro for dynamic analysis all the time and I highly recommend it. Speaking of that, you say that you ignoring rocking. (At least for the hand calcs.) STAAD can be a big help there. (And in many instances, rocking turns out to be critical.)

 

[ARS97]

JedClampett - yeah, I believe the fan manufacturer requires a minimum of 5 times the overall weight. The tricky part is, the customer wants the vibration limited to 0.2 in/s, and I need supporting calculations that show that.

JoshPlum - that's a good point about the damping. I might have to check that out. I was just keeping it simple for now and neglecting it, but maybe that's what is making the results haywire.

WARose - equations 3-3 and 3-4 require the rotating mass (mr) to be in terms of lbm. Equation 3-6 requires the rotating weight (Wr) to be in terms of lbf. Isn't 1 lbm = 1 lbf? That's how the examples are worked out in ACI 351 anyway. The unit conversions in ACI 351 seem to get very messy!

 

[ARS97]

Here's a copy of my calcs so far.....

 

[WARose]

[blue](andysines)[/blue]

WARose - equations 3-3 and 3-4 require the rotating mass (mr) to be in terms of lbm. Equation 3-6 requires the rotating weight (Wr) to be in terms of lbf. Isn't 1 lbm = 1 lbf? That's how the examples are worked out in ACI 351 anyway. The unit conversions in ACI 351 seem to get very messy!

It's been a while since I've messed with ACI 351, so I cannot say. However, by your own numbers the proper unbalanced force calculation would be:

F_o=(20,490/386)*(0.0017)*(93.62)²=790.9 lbs

 

[ARS97]

WARose - interesting. Looks like just a question of the weight/mass conversion. I assume the "386" term is the 32.2 ft/s^2 converted to in/s^2 (multiplied by 12)?

 

[WARose]

[blue](andysines)[/blue]

WARose - interesting. Looks like just a question of the weight/mass conversion. I assume the "386" term is the 32.2 ft/s^2 converted to in/s^2 (multiplied by 12)?

IIRC: yes. I'd like to add that the unbalanced force I came out with is about what I would expect to see with a fan of that weight. (I did a lot of fan bases for a company I worked with some years ago.)

 

[ARS97]

I am strongly suspicious that the dynamic load provided by the manufacturer (7,031 lbs) is due to a catastrophic blade loss condition, which wouldn't be the appropriate dynamic load to use for the normal operational vibration analysis. If I'm using that load in my analysis, that could be why the vibration amplitude in the output of Staad Foundation Advanced is so high.....it's roughly seven times larger than predicted by the other methods listed above. I'll get in touch with the fan manufacturer and see what the deal is.

 

[WARose]

[blue](andysines)[/blue]

I am strongly suspicious that the dynamic load provided by the manufacturer (7,031 lbs) is due to a catastrophic blade loss condition, which wouldn't be the appropriate dynamic load to use for the normal operational vibration analysis.

I've seen them come up with all sorts of end-of-the-world criteria that they want you to use. Some years back, I did one where they anticipated some sort of failure where the machine would take off at 4 times its normal operating RPMs. For such a case, you can typically talk them (and the client) into letting the criteria be much less stringent in such a case. (I.e. allowing it falling into the "Correct in 2/10 days" category of machinery performance. See Fig. 3.9 in ACI 351.3R-04.)

 

[ARS97]

Just heard from manufacturer. The initial balance quality is ISO G2.5 (Q = eω = 0.1 in/s), but the dynamic load is figured based on ISO G6.3 (Q = eω = 0.25 in/s) to account for potential unbalancing over time. In addition, they used an incorrect "fan arrangement coefficient" (whatever that is), and now the recommended dynamic load is 3,483 lbs, not 7,031 lbs. (They have some sort of internal procedure/equation.)

So, for comparison purposes, ACI 351 equation 3-4 now yields a dynamic force 2,482 lbs, which is comparable to the recommended value of 3,483 lbs. I need to reconfigure some calcs and see where this leads me.

Thanks for the help so far!

 

[ARS97]

UPDATE.......

I've developed a Staadpro Time-History model and I have some interesting results.

I mentioned in my first post that the manufacturer requires that the foundation frequency to be a minimum of 1.5 times HIGHER than the operating frequency of the fan (894 rpm = 14.9 Hz) This means that the primary vibration modes of the foundation should be 22.4 Hz or higher. Based on the Time-History results, which are based on initial soil assumptions (G = 10 k/in^2), shows the following:

Primary X mode (in plane of rotation) = 6 Hz
Primary Y mode (vertical) = 9 Hz
Primary Z mode (transverse) = 14 Hz

So......these initial results are showing me that achieving that level of natural frequency will be quite difficult. Better soil conditions will obviously change these results, however, even if I assume a "G" value that is double the initial assumption, the following results are obtained:

Primary X mode (in plane of rotation) = 10 Hz
Primary Y mode (vertical) = 16 Hz
Primary Z mode (transverse) = 13 Hz

Even with substantially better soil, I'm still falling well short. So, my question - what remedial measures are available? Would isolation (Fabreeka) pads placed under the bearings be an option? Are my assumptions for the Dynamic Shear Modulus (G) out of this world or something? (The soil investigation started today. I'll have results in a few weeks.) I'm just brainstorming possible remedial measures because I have a feeling that I may need ideas.

If anybody is interested, I attached the Staadpro model.

 

[WARose]

Comments (based on the update and looking at your STAAD Model):

1. The value for the dynamic shear modulus seems a little high. I don't know what soil type you have but I am use to seeing about half that (or less). That being said, your spring constants (if I am understanding this correctly) don't seem that far out of line. (Although you might want to adjust once more geotechnical info comes in.)

2. Good you are getting Geotechnical info. Be sure they get Poisson's ratio, current relative density of the soil, shear wave velocity (preferably with cross-hole testing), and all the normal info for static loading.

3. The model looks ok.....although I think you could have used plate elements for the mat rather than solids. (At this point however, STAAD's solid elements are about as flexible as the plate elements. That use to be a big no-no.)

4. In the model, you have the point loads at just a few locations. I would think it would be more spread out than that. For example, the unbalanced forces would be divided by the bolt locations.

5. You may want to consider running the mat with cracked section properties (if analysis shows it to be cracked). I usually do it by using a reduced modulus of elasticity. I doubt it would make much of a difference though.

6. I noticed you are using 5% damping. That may be too conservative in cases where the primary mass participation is due to support motion.

7. Speaking of that, the frequencies you call out above don't exactly cover the situation. You say that the "X-Mode" has a frequency of 6 Hz. But when I run it myself I get 6.915 cps with 55.7% mass participating at Mode 1, and an additional 44.1% of mass participating (for a total of 99.9%) at Mode 6 (the frequency at that mode being 17.5 cps).

8. Your forcing function call out does not have the Phase angle for one of them. I think you intended for it to be zero and I think the default value is zero.....but I'd call it out all the same.

 

[canwesteng]

Not sure if it is reasonable to high tune an equipment foundation. In theory, won't making the foundation bigger increase the vibrating mass, lowernig the frequency? Then of course this is potentially offset if it reacts against more soil resulting in a stiffer system. I've only done a few of these, but my experience I'll low tune by a factor of two or high tune by a factor of two (1.5 if two isn't reasonable). Would like to hear from WARROSE if he's done the same.

 

[WARose]

Additional info for andysines:

I don't know when your issue dates/deadlines are.....but if you've got geotechnical info on the way, I'd hold off on doing anything until then. (Because at that point you will really know what you have.)

If you have to do something at this point, I think the first thing I'd try is to make the mat wider (along the X-axis). Rocking seemed to account for a lot of your movement. As a rule of thumb, I always use to make the mat as at least as wide as 1.5 x the length from the bottom of the mat to the center line of the shaft/rotor of the fan. I'm not sure what that is for you.....but just looking at it, I would assume it would make it wider.

By the way, in the interest of accuracy (it probably won't change things dramatically) you need to designate the vertical springs as compression only.

 

[ARS97]

WARose - thank you for your detailed answer. A lot of helpful feedback there. Let me try to answer some of these questions/comments...

1. The Dynamic Shear Modulus was simply an assumption used in one of the examples in ACI 351. I took that value and calculated the stiffness values. I then converted that stiffness value into a plate mat support in the following manner:

Vertical = (5,799 k/in)(12 in/ft) / (555 ft^2) = 125 k/ft^2/ft
Horizontal = (8,231 k/in)(12 in/ft) / (555 ft^2) = 178 k/ft^2/ft
(NOTE - the 555 ft^2 is the overall contact area of the block)

2. Yes, I've requested those soil values. However, we had two options to choose from for the Dynamic Shear Modulus - an on-site shear wave velocity test (which I preferred), or an empirical range for the soil type (which the contractor preferred). I was over-ruled and the contractor went with the cheaper option (empirical value). So, what they failed to pay for in testing (roughly $3,000) they'll likely pay for in extra design time and material cost.

3. I don't use solids all that often. There seems to be more support and load options for plate elements. Plus the output isn't as convenient (from what I've seen anyway). I simply used a thin negligible plate mesh on the bottom of the solids to facilitate the use of these plate features. The plate meshing and solid meshing on that bottom face was identical and connected at each node.

4. I could certainly spread the loads out. I didn't think it would make a huge difference in the end for the results, but I can look at it. I actually started off with a very detail model that had the exact load areas blocked out in the meshing, but it ran so slow it became a bit unworkable. For a final model though, perhaps I'll have to revert back to that.

5. Good point about the cracked section properties. I can incorporate that. I didn't think that far ahead.

6. The damping is something I'm not real sure on. Once again, I made an assumption based on a few ACI 351 examples.

7. Yes, I agree.....I was a bit too generic in my explanation.

8. Yeah, there are two defined forcing functions. Number 1 is the vertical load at phase 0, and number 2 is the horizontal load at phase 90. Not sure why it's not displaying...


As for the follow up post....

Making the mat wider in the X direction is definitely something I want to do. However, I'm very restricted due to the geometry. This is a twin fan, so the corner of these foundation blocks meet in the middle, and I have various structures that I want to keep isolated away from this foundation. If it were a single fan, this would be a much easier issue.

"compression only" springs - I think that's a no-no with a modal analysis. I could be wrong though....I'll have to check. If not, it's an easy fix.

Once again....thanks a ton. This has been very helpful. I'll digest your comments a bit more and see where the geo report leads me.

 

[dik]

If underground, you may have to use significantly greater load factors. I've often encountered this.

Dik

 

[WARose]

[blue](andysines)[/blue]

"compression only" springs - I think that's a no-no with a modal analysis. I could be wrong though....I'll have to check. If not, it's an easy fix.

I ran your model with it and there was no issue. (And it didn't dramatically change things as I suspected.)

When the time comes, you may want to "fine tune" the model to account for the mass of soil underneath it and embedment. (Checking to see if one or the other could possibly hurt you. They typically help.....but embedment (of the mat) in the ground is not something you can typically count on long-term. Separation develops over time.)

But at this point, everything seems too preliminary for that.

[blue](andysines)[/blue]

2. Yes, I've requested those soil values. However, we had two options to choose from for the Dynamic Shear Modulus - an on-site shear wave velocity test (which I preferred), or an empirical range for the soil type (which the contractor preferred). I was over-ruled and the contractor went with the cheaper option (empirical value). So, what they failed to pay for in testing (roughly $3,000) they'll likely pay for in extra design time and material cost.

That certainly has a familiar ring to it.

[blue](andysines)[/blue]

Once again....thanks a ton. This has been very helpful.

You are welcome.....don't forget to give my post(s) a star if you really like it. (I could use one of those once in a while. )

 

[ARS97]

The embedment is a bit tricky. See, there are other turned-down slabs that are going to be poured up next to this block. So, there really won't be much in terms of soil next to these blocks. Originally I was going to add lateral restraint to this block, but as you mentioned, separation occurs over time, and that isn't reliable. I could tie those foundations into the block, but I think I'd rather keep them separated.

Stars given.....thanks a ton!