Hypoid Gear Pressure Angles

[iv2jm]

Hey Folks,

There seems to be lots of scattered information about hypoid gearsets and I'm trying to grasp some basic understanding. I'm using equations from the Timken website (attached) to resolve gear forces back to bearing support loads.

They don't relate the tangential forces to the pressure angle and it seems fairly important. They do relate the tangential forces to spiral angle, but that seems far more relevant to the thrust and separating loads.

Is the tangential force completely unrelated to pressure angle or is it so small that its not worth including?

Also, what are appropriate pressure angles for hypoid pinion and gears? That's the only piece of data I don't have (yet) for my gearset and I'm curious if I'm close.

Thanks in advance for your help,
Jimmy

 

[tbuelna]

iv2jm,

The separating force is a function of pressure angle.

Typical normal design pressure angles would be 20 to 25 deg. The operating pressure angles are slightly different, as are the pressure angles between drive and coast flanks. But probably not enough to be concerned with in a bearing load calc.

Hope that helps.
Terry

 

[iv2jm]

Thanks for you help, Terry. That makes a lot of sense... especially after I simplified my thought process and considered plain ol' spur gears.

If you're up for more, now I'm fighting myself with the tangential load on the gear.

Im trying to compare the values from those Timken equations to the manufacturers multiplication factors (input torque x separating factor, etc). The equations match the factors (within 4%) for all pinion values, but the gear values are way off. The errors are within 1% of each other, but 75% different from the factors.

Because of that, I think my tangential load on the gear is strange (and I rearranged the Timken equation relating the two tangential loads to each other with cosines of the spiral angles).

Two questions:
-Does it make sense the the tangential load on the gear would be about 1/3rd the tangential load on the pinion? (thats what it takes to get the factors to equal my equations.)

-Is there a good resource available that would clarify how to calculate the tangential load on the gear (thats easily available online)?

Thanks again,
Jimmy

 

[tbuelna]

iv2jm,

The Timken document you linked gives the equation for tangential loads on the pinion and gear if you know the spiral angle (p.A23, left column, midway down the page). Use 35deg for the spiral angle.

I don't know why your manufacturer's recommended load factors are so different. The only thing I can suggest is to check that your driver/driven and pinion/gear relationships are common, and that your spiral directions are also common between both analysis cases. I'm not a hypoid gear expert, but I believe it's common practice to have the convex tooth surface on the drive side flank of your driving pinion, because this is a stronger arrangement.

Hope that helps.
Terry

 

[WinstonH]

Hi,
The Timken equations differ significantly from my ancient

"New Departure Handbook", that I used for many years.

The NDH equations take Pinion Pressure Angle & spiral angle into account as well as pinion drop.

These equations were for ball & double angular contact, but the forces from the gear mesh to the bearings surely would be the same?

So why does not Timken take into account the other tooth elements? Fair question, do you need a scan?

Cheers,

 

[iv2jm]

Terry, I used that equation but it comes out way off and the spiral angles (which are known) are different for each... otherwise it'd be a plain ol' spiral bevel.

Winston, I'd love to see a scan of the NDH equations if it's not too much trouble... Thanks!

To make the Timken equations = Gleason Factors, I need to divide the pinion force by 4.06 (trial and error/goalseek):

Ftg = Ftp/4.06

Ftg= Tangential Force, Gear
Ftp= Tangential Force, Pinion

My gears are a 4.10:1 ratio- I'm trying to decide if thats a coincidence with a little rounding... Seems like the Ft's should balance somewhere, and shaft torque would maintain that ratio, so I'm not convinced thats totally correct.

But I'm running with the manufacturer's specs for now!

Thanks for all the help so far,
Jimmy

 

[WinstonH]

Jimmy,

Here you go, the spiral data is included, as it's referenced by the hypoid equations.

Cheers, Winston.

 

[tbuelna]

iv2jm,

I just took a very quick look at the ND handbook pages WinstonH posted. The tangential force (P) is calculated for both components at their mean pitch radius. So in simple terms, they would appear to be equal and opposing. As for bearing loads in the example shown, the pinion is cantilevered and the gear is straddle mounted. So there would obviously be differences there.

Hypoid gears and pinions have both radial and thrust loads. In the example shown in the ND handbook with an overhung pinion, the single row ball bearing next to the teeth only takes radial loads. But those radial loads are very high, due to this bearing's small axial offset from the pitch plane. The other pinion bearing is a duplex ball bearing, which takes all of the axial loads (regardless of direction) plus the small radial moment reaction about the front bearing.

The example shown in Timken is for a pair of single row tapered rollers on the overhung pinion. In this example, the thrust load can be taken by one bearing or the other, depending upon the direction of the thrust load. And the direction of the pinion thrust is dependent upon which component is the driver or driven, direction of rotation, and direction of tooth spiral. The pinion bearing loads are based on the combined radial and axial loads, and the worst case bearing loads would be an inboard pinion bearing that had to take both radial and thrust loads.

Once again, if you're using "factors" to compare the relative strength or capacity of a large ratio gear and pinion, you need to understand what those "factors" represent. While the tangential force the pinion and gear teeth in mesh are subject to should be equal and opposing, the capabilities (such as bending strength) of the pinion and gear teeth are not the same. Due to the smaller pitch diameter in the pinion, its teeth tend to be weaker in bending than the more truncated teeth in the gear, unless profile shift is used compensate. The smaller number of teeth in the pinion also means that each pinion tooth sees many more fatigue load cycles than each gear tooth, or 4.10 times as many in your example. So you would have to take these things into account when using "factors".

Hope that helps.
Terry

 

[iv2jm]

Winston, thanks for the scan, and Terry, thanks for the input. Understanding the 'factors' is exactly why I started the equation comparison.

The funny part is the discrepancy between NDH and Timken regarding the tangential load on the gear. For the Timken equations to match the Gleason factors, I had to divide the Timken tangential load by 4.06 (my gear ratio is 4.10). That's exactly what the NDH equation says to do...

Now that I've seen the derivation of that tangential load, I feel more confident in understanding the factors and believe there is an error in the Timken equation.

I appreciate all the help from both of you,
Thanks,
Jimmy