Gear Strength Calculation - Too Conservative? 1

[jstluise]

I have a question about using the Lewis formula for calculating the maximum torque that can be applied to a gear.

A project uses involves bevel gear sets that are subject to high torques. Our concern was whether or not the bevel gear set could withstand the high torques.

Our independent calculations using the Lewis formula for bevel gears gave us very low numbers. We were skeptical, but after contacting the gear manufacturer, they gave us the same numbers.

Still skeptical, I fabricated an apparatus to do some static loading on the gear set. At a torque 5x that of the calculations, the apparatus failed before the gear teeth (due to the high separation force between the gears). So we know the gear set can withstand at least that much.

So my question...why is the calculations so conservative? I realize the dynamic loading is greater, but I couldn't really find anything about the Lewis formula that talks about this. What does the Lewis formula assume? What safety factors are incorporated into the formula? Is there a better way to calculate gear strength?

 

[dinjin]

Testing is the best way and the sample size should be
significant and from different lots if possible.
Most folks cannot afford to do it. There are safety
factors to consider depending on the application as well
as the amount of wear that will take place thru the years.
I have seen worn teeth down to one half their size in
some applications and still operating. Safety factor
guideline were developed in different industries and
applications from the past. I would guess that most
start out as a 2.5 minimum. Repeated stresses do weaken
or allow cracks to propogate, so you need service factors
as well as safety factors.

 

[FeX32]

There will always be safety factors in engineering. Hence Safe.


Fe (IronX32)

 

[tbuelna]

jstluise,

As others noted, the Lewis formula is a greatly simplified method of analyzing gears for tooth bending strength, and like any other simplified analytical approach it will naturally give very conservative results. In reality, the Lewis formula is of limited value when designing gear meshes since it only considers simple tooth bending. A proper gear mesh design would closely evaluate factors like contact stress, scoring, fatigue cycles, etc.

For reasons of safety, it is common practice to design gears with sufficient tooth bending strength/fatigue life such that they will fail due to contact stress or pitting before losing a tooth. Pitting failures are much more benign and detectable than tooth breakage, which tends to be catastrophic.

If you want a more precise method of analyzing your gears, refer to the AGMA documentation. The AGMA documents give extensive equations for the analysis you want to perform. If you do not wish to slog through the AGMA equations on your own, you can buy commercial software applications (like KISSoft or UTS) that will do the work for you and give very accurate results.

Good luck.
Terry

 

[jstluise]

Excellent response, Terry! Just what I was looking for!