Drive shaft calculations. 1

[linamar]

Here's the problem I'm facing:
I'm working on a development project for a low power wind turbine.
The concept has been defined and a couple prototypes were built but no calculations heve been made to size the transmission shaft, housing and bearings. The prototype has a straight shaft with the rotor attached through compression rings, the bearings were selected using probably empirical methods and no stress calculations were made, at least not to my knowledge.
Since my job is to make it manufacturable in some quantities I have to start from scratch and redesign the shaft, rotor, housing and connector to the tower.
I only know the torque required to drive the generator, the weight of the rotor and this is all about it.
I haven't done such calculations in the last decade or so and I'm little rusty, and I would start with the shaft but I need to get a starting poing. We don't have FEA capabilities (can be outsourced for a fee) but there are analytical ways to calculate a shaft. I would appreciate if somebody could lend me a hand letting me know where and how should I start.
Thanks.

 

[CoryPad]

Get a free copy of NASA RP 1123 Design of Power-Transmitting Shafts here:

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19840018973_1984018973.pdf

 

[linamar]

Great! Thank you very much.

 

[cbrn]

Hi,
well, I don't know what extent of precision you want/need to achieve.
Basically, the shaft will have to be statically verified for the transmission of torque (torsion shear stress) + bending effects (own weights + radial forces such as magnetic pull or unbalances in wind force, for example). I suppose your shaft will be stepped in some way, so fatigue may become relevant because of stress-concentrations. The SCFs can be determined with Peterson or Roark-Young.
Bearings, if of some commercial type, can be calculated using manufacturer's tables or other analytical methods (see, for example, SKF). If of oilfilm-type (sleeve bearings), once again the bearings supplier may do these calculations for you, once you give him the loads diagrams (vectorial "force-and-direction" loads schemas). I suppose in your case axial load will be enough important as to force the adoption of a dedicated thrust bearing.
Last but not least, it could be a nice thing to check the critical speeds of the rotor, or at least the bending natural frequencies, and also the torsional natural frequencies: unless you want to determine hundreds of frequencies (unuseful in your case), analytical methods can easily be used, and even a simple FE formulation can be hand-made.
Just a few thoughts...

Regards

 

[linamar]

Thanks cbrn.
The rotor will turn at max 3-400rpm, however knowing the critical speeds and natural frequencies would be nice.
I'm not an aerodynamicist, a static calculation I can do but more than that is beyond my reach, and the dynamic behaviour of the rotor and dynamic stresses in the shaft, bearing housings and supporting structure are my major concern as the turbine will operate in populated areas.

 

[MartinSr00]

I assume you're using steel shafting. Steel has an endurance limit. That's good.

If you want quick and dirty, size the shaft for 5000 psi shear, and use a 410HT or 4140HT shaft.

Tau=Tr/J. It will tend to be overdesigned. That's a quick and dirty industrial way for pumps. Done this way, you don't have to be that picky about notches and fillets on the shaft, etc. If you have large overhung loads, this method may be found wanting.

The alternate way, especially if you hate the overdesign, is to calculate the maximum stresses, and apply stress concentration factors to get peak stresses. Then you need to apply a bunch of f factors to adjust for factors related to finish, reliability, environmental factors, etc. You want to keep these stresses below the endurance limit by a factor of 2-4. I suspect Shigley or Juvinal would have something on how to do this. I use Faupel and Fisher, but that may be hard to come by these days. This second way is the correct way. The first way is a fudge. For stress concentrations, use Peterson's stress concentration factors.

Just so you know, the endurance limit for steels is usually about 1/2 ultimate if I recall. But to do it perfectly right, you need to find fatigue data on the shafting material you're using.

As noted, that will tell you if it's strong enough assuming loads are stable and there are no resonances. Critical speed analyses could confirm this.

This can be done with hand calc's. FEA will give you a bunch of stresses, but you must make judgements about them.

 

[tbuelna]

linamar,

I've seen compression rings commonly used for the attachment between the rotor shaft and gearbox input, but I've never seen them used to attach the rotor (hub) to the rotor shaft. These are usually bolted flange connections, and I'd assume it's like this for safety reasons. The hydraulically assisted compression ring shaft attachment is attractive because it is less labor and time intensive to install in the field than a bolted flange joint with dozens of bolts and nuts that must be systematically torqued.

A separation of the rotor assembly from its shaft would be a catastrophic failure mode. A compression ring attachment relies solely on friction. It has no fault tolerance and there is no reliable way to verify that it has been installed correctly. On the other hand, a bolted flange connection is still safe even with the loss of several bolts. And proper bolt installation can verified by the fastener torques applied.

As with any large overhung rotor system, the most difficult loads to deal with are the blade flapping and lead/lag moments produced at the hub bearing system. These moments can be huge even in a "small" HAWT. The hub moments will also create shaft bending that can result in bearing element edge loading, if the bearing system is not designed to accommodate them. The rotor shaft bending can also produce undesirable gear mesh deflections in the gearbox if the shaft system and the gearbox mounting is too rigid in bending. The rotor shaft and gearbox connections are normally designed to be able to transmit torque effectively, but also provide strain isolation from the rotor moments.

Since wind turbines must operate reliably for up to 20 years, and replacing gearboxes and rotor bearings under warranty would cause your company significant financial liabilities, I would suggest that you do a detailed FEA of your entire rotor system, generator driveline, yaw drive and bedplate structure. Hand calculations must be simplified too much in order to be practical. They won't give anything close to the detailed results that can be achieved with modern FEA applications. A detailed FEA analysis of the entire turbine system for loads and frequencies, at both the individual part and total system levels, would be time and money well spent.

SKF sells compression ring attachment systems for wind turbines, so they can probably give you some guidance with your analysis:

http://www.skf.com/portal/skf/home/...&offerId=0.000336.287721.288053.288059.289493

Good luck.
Terry

 

[linamar]

thanks tbuelna
there is no gearbox in this design as there is no pitch control. The rotor blades have a fixed pitch and the rotor shaft is driving the generator directly.
The units with the compression rings attached rotors are technology demonstrators but in production another system will be used. I still have to do research into what is used on low power wind turbines, I would look at keys as a simple mean to transfer torque, maybe coupled with a tapered shaft and a large nut to hold the rotor in place.
Any suggestions will be welcomes; the shaft as it is today is 2" dia on the rotor end.

 

[unclesyd]

As you have a small size shaft I would look into using the Polygon coupling such as those by Stoffel. We have used these coupling in pretty severe mechanical services.

http://www.stoffelpolygon.com/

 

[linamar]

thanks unclesyd.
Since the turbine works exposed to the elements, what would be the most common rust protection coating for the shaft that would resist rust for an extended period of time? Is chroming a solution, or should I look into using stainless steel for the shaft? If so, what would be the best grade? I remember SS as being used for pump shafts, but not the specific material.
Thanks.

 

[unclesyd]

I would seriously look at one of the PH SS's, especially Aqualloy/Aquamet 22, used for boat shafting. It is very corrosion resistant and can take some serious loading and unloading while driving a boat. You can get it polished and straightened.

http://www.wbmetals.com/

http://marinemachiningandmanufa2.liveonatt.com/home.nxg

 

[linamar]

Don't you think that would be verly expensive? I am also considering a construction steel shaft, powder coated for rust protection, just like the automotive wheel hubs are protected.

 

[unclesyd]

Yes, it would be more expensive, how much I don't know as I'm out of loop now.
Yes, steel with powder coating would work but it will leave areas prone to rust.

If you go with alloy steels I would look at some of the proprietary grades like the one supplied by these companies.

http://www.associatedsteel.com/products-alloys.shtml#mirraloytgp

http://www.pennsylvaniasteel.com/flexor.php

If you chose to use the standard grades I would definitely go with the preheat treated vanities.

 

[linamar]

unclesyd,
Do you know a supplier for Aqualoy 22? I would like to buy the raw material myself and machine the shafts.
Thanks.

 

[marcd66]

This might help.

 

[ginsoakedboy]

CoryPad,

Your link does not seem to be working. Is there an updated location for this file? Thank you.

 

[unclesyd]

Here is a supplier of the Aquamet 22.
They were real nice people to work with.

http://www.wbmetals.com/

 

[CoryPad]

htlyst,

Go to nasa.gov, type RP1123 in the search box, follow that link.

 

[linamar]

thanks unclesid
I called the guys and they are willing to sell me the shaft, machined, not the material, and they won't disclose their source

 

[linamar]

thanks marcd66