kappa calculation

[Tmoose]

I'm headed off to a local tech school library to check out a few gear design books.
I'm looking for guidance to the basic calculations for "kappa" of gear lubrication

thanks

Dan T

 

[tbuelna]

Tmoose,

Are you sure you mean kappa? The only use of kappa in EHL contact terminology that I know of is to represent the ratio of the semi-major/semi-minor axis dimensions in an elliptical contact condition.

A simple static Hertzian contact solution between curved elastic bodies is given in Roark's, and it also gives the values for semi-major/semi-minor axis lengths at the contact zone.

Calculating the semi-major/semi-minor axis dimensions with full EHL contact is a much more complex problem, since it can involve both fluid mechanics and heat transfer. And your results will change greatly due to dynamic operating conditions.

A good rolling element bearing text (ie. Tedric Harris' Advanced Concepts of Bearing Technology, 5th ed., chapter 4) will give you all the equations you need, since EHL contact in rolling element bearings is similar to EHL contact in involute gear teeth. But you will need to supply all of the values for the variables, and they can cause a big error in your results if you don't get them right.

The only difference between EHL contact in gears and bearings is that gears meshes may tend to have more sliding, so high performance gear meshes are normally analysed for scoring probability. The relative sliding will cause heating of the EHL oil film, and when this local oil film temperature rise is severe enough the lubricant will flash and the EHL film will collapse. This results in boundary contact, which produces greater friction and heating, which then overheats the gear metal causing it to de-temper and lose strength, which then rapidly results in surface compressive stress failure and galling of the gear teeth. Scoring failures are always something to be avoided in gear meshes, since a gear mesh will fail in scoring very rapidly (within minutes) and without warning.

Good luck and have fun.
Terry

 

[Tmoose]

Hi Terry,

I based "kappa" on bearing literature and bearing software calculating parameters like those that appear on page 158 here -

http://www.bardenbearings.com/PDF CD/MACHINET.PDF

If I Google "ehd kappa" the 5th hit is a Google books reference to "Handbook of Lubrication and Tribology: Application and maintenance" - By George E. Totten.
Some stuff about the ratio of viscosity at operating temp to the viscosity "required." I'm really after the required viscosity. Even Drago seems to resort to posting a very basic table based on temperature to answer the

Kluber offers this, again for ball/roller bearings.

http://www.kluberna.com/pdfs/Tribology_Proper_Lubricant_Selection.pdf

I actually think it was during a conversation with an application engineer several years ago that I heard Kappa applies to gears too, although I certainly could have got it wrong.

 

[tbuelna]

Tmoose,

As far as I can tell, the "K" value noted in that Barden catalog is similar to the many "K" values that most simplified gear analysis techniques use. The Barden "K" value appears to be a modification that accounts for the difference between normal and kinematic viscosity characteristics of lubricants. The reason this correction is important in analysing EHL contacts is that the lower kinematic viscosity will result in a thinner EHL oil film thickness. Bearing or gear tooth contacts that operate for a greater percentage of their life in full EHL conditions (ie. a lamda value >1.0) will naturally have a much better adjusted L10 (or L2,L5, etc.) life. However, most of the "lubricant adjustment factors" that I have seen gear and bearing analysis programs use vary widely. In fact, this "lubricant adjustment factor" can affect your adjusted L10 life results by a factor of up to 3 or 4 times.

Kinematic viscosity differs from the bulk system oil viscosity due to the instantaneous temperature rise the lubricant is subject to as it undergoes shearing effects passing through the contact zone. The less efficient the contact (ie. lots of relative sliding or spinning) the more the lubricant film is heated.

A good gear software like KISSoft will give you a probability of scoring function for gear meshes, which is based on the temperature rise in the contact zone oil film. With high performance gear meshes, scoring usually ends up being the limiting factor with regards to power capacity of a gear mesh.

Regards,
Terry

 

[Tmoose]

"Fundamentals of gear design" - Drago - Chapter 9 - "WEAR predominates the low speed range, while SCORING rules the upper".

I'm interested quantifying the viscosity required to protect the gears when operating under heavy load at low/very low pitch line velocity on the inching drive. My first guess is the viscosity required to achieve EHD when on the inching drive will be unreasonably high, so what we really need is a heavy dose of EP additives.

 

[tbuelna]

Tmoose,

You seem to understand the basic issue well enough, but I would somewhat disagree with your quote from (the very highly respected gear expert) Ray Drago. Scoring is a function of transmitted power and how efficient the tooth contact motion is. Scoring can be an issue with both high and low pitch line velocities.

As for characterizing "wear", that is sort of an ambiguous term. Gears never really "wear". They typically fail in one of three basic modes: fatigue due to tooth bending, fatigue due to surface contact, or galling/smearing due to material transfer (usually due to scoring). The term "wear" would seem, to me, to imply that the gear is gradually losing material. A gear that operates in predominately EHL contact, and has a very low scoring index, will never lose material. However, a gear that is transferring (or losing) material due to the high localized surface contact stresses produced by boundary contact conditions, will quickly fail.

If your gear mesh operates with high pitch line forces and low pitch line velocities, it may never likely produce satisfactory contact conditions to create an EHL oil film. If this is the case, there is no oil on earth with a viscosity high enough to help.

As you noted, an EP additive will help in boundary contact conditions, but they are no magic cure. Most EP additives work by creating a film on the surface of the metal gear that prevents the diffusion bonding effects between the contacting asperity points of the loaded surfaces. But this protection only functions for a very limited amount of time, since it is quickly sheared away during operation.

There is actually a contact stress limit, below which the fretting/material transfer due to boundary contact will not be a problem. It is usually very low, and depends upon the material, heat treatment, surface roughness, surface operating temperature, etc. But this is the limit you should use if your gear mesh is subject to boundary contact and you want it to operate reliably.

Here's a somewhat relevant reference:

http://books.google.com/books?id=YT...=8#v=onepage&q=contact fretting limit&f=false

Good luck,
Terry