flywheel interference fit to shaft.... allowance for ID expansion? 3

[electricpete]

Are there any thumbrules for level of interference fit which should be used between flywheel and shaft?

The flywheel of interest to me is keyed to the shaft as well as interference fit.

I have heard that under the influence of centrifugal force the i.d. of the flywheel can expand (if it becomes loose this may allow slight movement resulting in eccentricity or unbalance). Is there any easy way to estimate this expansion?

 

[EnglishMuffin]

Yes, you are correct, although intuition might suggest otherwise. The same thing happens in rolling element bearings, where you can lose the interference fit on the inner race at high speeds. If that happens, as well as eccentricity and imbalance, you will probably get fretting, which may show up even if the other effects don't. You can calculate the stress and strain effects using the equations given in Roark & Young, for example. There, you will find formulae for the interference fitting of thick cylinders, and the effect of centrifugal loads etc. By using superposition, you can combine the two effects and determine at what speed the interference fit will be lost. As for rules of thumb, I haven't personally seen any, but you could probably create some from the basic theory, were you so inclined.

 

[electricpete]

Thx EM. I would think centrifugal force would be negligible for bearing inner ring, but different story for flywheel.

I don't have Roark and Young. Is it a textbook?
Any other references?

 

[EnglishMuffin]

Yes - Roark, or "Formulas for Stress & Strain" is probably one of the most indispensible textbooks a mechanical engineer can have - often cited in these forums. I'm a little busy at the moment - as soon as I get a chance I will post the necessary formulas, unless somebody else beats me to it.

 

[electricpete]

I borrowed Roark (6th ed) it from a coworker.
I see the formula on page 704.
Thanks.

 

[EnglishMuffin]

Great - then you also need case 1a and 1c on page 638 for the inner and outer tubes (or inner cylinder and outer tube in your case probably). There is an example of a shrink fit calculation on page 637. Then superpose the centrifugal effect given on page 704. I have done this calculation a few times myself. You can see why I did not want to type all that if I could get away without doing it.

 

[electricpete]

Thx EM. Calculating the fit pressure is a little more complicated than I want. I am just looking for a gross understanding of the effect.

Can anyone check me on the following result.
Steel Flywheel 8" id and 8' od rotating at 1200rpm.
I get 0.020" of expansion which is astonishingly high. Maybe I have made an error? Here is the calculation.

From Roark p704:
deltaR0:=delta*w^2*R0/4/g/E*( (3+nu)*R^2+(1-nu)*R0^2);
where:
> # R0 = inner radius
> # deltaR0 = change in inner radius
> # R = outer radius
> # w = radian speed
> # delta = weight per volum
> # g = acceleration of gravity
> # E = Modulus of elasticity
> # n = poisson's ratio

Substitute values:
R0:=8*inch:R:=96*inch:
> w:=evalf(2*Pi*1200)/minute;
w := 7539.8/minute

> g:=32.2*lbm*ft/sec^2/lbf: #?
> E:=30E6*lbf/inch^2:
> nu:=0.3:
> delta:=7.8*62.4*lbm/ft^3; #SG=7.8
delta := 486.72*lbm/ft^3

Subbing in above gives:
deltaR0 := .17449e7/ft^4/minute^2*inch^5*sec^2

Unit Conversions:
deltaR0:=deltaR0*(ft/12/inch)^4*(minute/60/sec)^2;

This calculation gives:
deltaR0 := .23375e-1*inch

I always get a little confused by the treatment of g in equations like this. Did I mess up that part?

Thx for any assistance.

 

[electricpete]

Whoops. Should be 4" radius and 4' radius. (got my radius and diameters confused). Let me try again.

 

[electricpete]

OK, do everything the same except
> R0:=4*inch:
> R:=48*inch:

deltaR0 := .29219e-2*inch
0.003" change. More reasonable but still sounds high. Any comments?

 

[EnglishMuffin]

Without going through it all, if you are using lbm, lbf, in, sec units, then gc is 386.4, not 32.2. I wish it was not referred to as g, as Roark does, because that should be reserved for the acceleration due to gravity, but that's just a quibble. So you are probably out by a factor of 12 somewhere. Regarding the interference fit calculation, you don't of course actually have to calculate the stress at the interface if you don't want to - it can be eliminated from the two simultaneous thick cylinder equations.

 

[EnglishMuffin]

Actually - I've just run the numbers and I get about the same result as you. You must have been working in feet rather than inches, which would mean gc should be 32.2 as you appear to have it. Sounds about right for the size of flywheel. A good way to mount something like that might be to use Ringfeder shrink disks - you would have a thin extension on each side of the flywheel at the inner diameter, perhaps produced by counterboring, and then the interfernce generated on the extensions by the shrink disks would be substantially immune to the centrifugal effects, and no keys are needed. This is a method I have used on smaller flywheels.

 

[JP0506]

Why not use a SPLIT TAPER LOCK BUSH, this will eliminate any chance of slippage.

 

[fredt]

I agree that using Roark will give you the a good estmate of the expansion due to centrifugal forces in most cases. However, there are some other considerations - a few that come to mind are:
Will you ever want to remove the flywheel in the future?
Manufacturing tolerance - this can be an issue with bore stress levels making selecting ideal interference difficult.
Thermal expansion effects - unlikely to be a problem with a flywheel.

There is an old rule of thumb .001" per inch of shaft diameter. Although I still advocate doing the calculation, my experience is that this guideline usually gives an acceptable result when checked by more sophisticated analysis such as FEA.

Only a small amount of residual interference will make the key redundant. Keep in mind also that with a longish hub and narrow web the stress and deflection in the hub can vary considerably along its axial length.

 

[fredt]

Further to my previous contribution you could also use a taper seating on hub and shaft. This gives better control of interference but axial positioning is less precise. Include tappings and grooves for oil injection in the hub if you need to remove it sometime. SKF have recommendations for this.

Englishmuffin's proposal for Ringfeder is also good. I understand the theory of using the compressive type but I think that the internal ones would work well. I have used both types with success and both types make removal relatively easy.

If there is never going to be reason to remove the flywheel a good heavy shrink fit is least expensive and most reliable. Fit by liquid nitrogen cooling shaft is probably easier than heating flywheel. If you do decide to heat flywheel using gas burners start by heating at rim - don't concentrate heat on hub area.

 

[EnglishMuffin]

I always prefer to use the "shrink disk" type of Ringfeder where possible and appropriate, since they produce much better concentricity than the other types. Also, in this case they are of course immune from any appreciable loss of interference due to centrifugal force, although with proper choice of interface pressure this is not necessarily a problem.

 

[electricpete]

Thanks for all the suggestions. I don't think it is likely I am hestitant to require any dramatic changes on this piece of equipment.... trying to follow OEM guidance.

There will be poosible need to remove flywheels in the future.

The flywheel is also keyed to the shaft at 3 locations spaced at 120 degrees apart.

My rough understanding is that the keys play a role in keeping the flywheel centered as follows: Each key allows the flywheel centerline to move only along the line which passes through the center of that key and center of the shaft. There is only one intersection of the three lines. Thus the keys (assuming they have a tight circumferential fit) help to keep the flywheel centered even when the interference disappears.

 

[EnglishMuffin]

Interesting, but difficult to make accurately, and very prone to fretting if it is really intended to run with clearance. I'm sure you would have been better off with some type of taper clamping device as some of us have recommeded, but it's too late now I guess.

 

[vgarzani]

Are you having step changes in 1X response even after using the 3 tangential key design? I have 8 of these things in service, but haven't installed the 3rd T key yet. When lightening strikes our switchyard, it is not unusual to see a number of step changes in 1X. The first time it happened, we initiated an exhaustive search for a common factor in the Unit 1 and Unit 2 monitoring system - there isn't one, but step changes in 1X at the same time were noted in machines on each Unit.

 

[electricpete]

Hi Vincent. Yes, I am sure we are talking about the exact same application. Can you refresh my memory which site you are at. I am in Texas ("STP&quot.

I have heard of the step increase at a plant in CT. Here is the way I understand the situation: All W machines come with the 3-key design, spaced 120 degrees apart. Originally 2 of those 3 keys are 3-piece key design and the third is a 1-piece key. An upgrade converts the third to 3-piece design. The three-piece key just makes it that much tighter when you assemble the machine initially.

We ourselves have not installed the upgrade and have not experienced any step increases in vib. However during refurbishment it was identified the flywheel was looser than OEM tolerances. That is when I first got dragged into the evaluation. A learning experience for me. I suspect the keys are more critical to preventing vib problems than the flywheel interference, but both play some role.