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Helical gears at non standard center distance

Helical gears at non standard center distance

Helical gears at non standard center distance

I am reviewing the design of a set of helical gears used in an old industrial engine. These have been around since before I was born. We are changing suppliers and the new supplier is claiming the gear data is all wrong and the gears will have to be redesigned.

As far as I can see, these gears were designed to fit a center distance which is not standard. The center distance determines the operating pitch diameters, and the diametral pitch is specified as 10. The original designers specified a 20 degree pressure angle at the operating pitch diameter, and calculated helix angle, OD, root diameter, and thickness in reference to this pitch diameter. Was this approach wrong? Am I missing something?

My experience is mostly with spur gears. From what I could find about helical gears, they are commonly designed to fit the space. I fail to understand how gears that have been used this long can now not be made.

John Woodward

RE: Helical gears at non standard center distance


Is a non-standard cutting tool issue here the reason for the supplier balking?

I'm anxious to hear others responses to your question.


RE: Helical gears at non standard center distance

They may have used non-standard cutting tools, but then a gear "expert" told me that a hob of any pressure angle could be used (????). I have not been able to obtain any reliable information yet.


RE: Helical gears at non standard center distance

Can you post the basic gear data for the existing gears (approx. at least):
No's of teeth
center distance
approx. helical angle
approx. pressure angle

I am almost positive, that the new gears have to be redesigned using the (I believe) fixed center distance and no's of teeth.

In any case, more data will help to make some preliminary calculations.


RE: Helical gears at non standard center distance

Without seeing the information that you
have it is difficult is knowing how to
answer your question.
Can you list the data that you have
lead, helix anlge, cd, pressure angle,
no of teeth, etc?

RE: Helical gears at non standard center distance

I think you missed to give the profile shift of the designed gears as long as you design for non-standard center distance, which is very important to manufacturer

RE: Helical gears at non standard center distance

Gear systems can be based on the pitch being a whole number when helix is 0, and pressure angle a standard, such as 20, or when the helix is a certain amount, or anything in-between. The only rule for involute gears is that the circular pitch, on the base diameter, is the same for mates. We call this the base pitch.

When gears are put on centers, a tangent line drawn between base diameters will be at the operating pressure angle to a line drawn perpendicular to the line of the center distance. The base diameters=No_teeth*cos(pressure angle)/DP.

Any pressure angle will work, standards such as 20 degrees are done for standardization of tools. In the automotive world, companies make their own standards, since design of a new tool is insignificant for the production volume.

Bottom line, you need to have someone reverse engineer the set, then design the tools or go with the gearset redesign.

RE: Helical gears at non standard center distance

Here is the gear data:

Normal diametral pitch 10
Pressure angle 20
Helix angle 18.7667
Center distance 3.802

Pinion- 24 teeth, 2.733 od, 2.215 root, 2.7680/2.7650 over .1728 pins

Gear- 48 teeth, 5.269 od, 4.750 root, 5.3060/5.3030 over .1728 pins

Thanks for any help,
John Woodward

RE: Helical gears at non standard center distance

using your data I checked the basic geometry of your gears.
I assume that the 20 degree pressure angle is in the normal plane:

The calculated center distance = 3.802135197

Gear 1 , 24T
The calculated normal tooth thickness =  0.1539212/0.1526743
The calculated transverse tooth thickness  = 0.1625637/0.1612468
Radius where tooth thickness is checked  = 1.267378399

Gear 2, 48T
The calculated normal tooth thickness gear2 = 0.1543968/0.1532193
The calculated transverse tooth thickness gear2 = 0.1630660/0.1618223
Radius where tooth thickness is checked = 2.534756798

I did not make more detailed analysis, but it seems to me  that whoever designed the gears, did relatively good job.
Personally I would resist to use the exact 1:2 ratio unless really necessary.
The 24 and 48 teeth gears will mesh every two spins of the small gear with the same tooth of one gear hitting the same space on the other ( = "not hunting" mesh). If you use the 23/48 or 24/49 teeth, the situation would be better ("hunting"). The wear on the gears  would be more consistent.   

I hope this helps little bit!

RE: Helical gears at non standard center distance


Thanks for the calculations. I think you are right that the pressure angle is for the normal plane, although the drawing doesn't say. I assumed that it is also at the operating pitch diameters since it yields the specified helix angle. These gears are for a camshaft drive, thus the ratio.

When I get back to the office later this week I will pull the drawings and check the tooth thickness. Your numbers sound right as they give a backlash around .007.

One issue with these gears is the root diameter. I can verify the OD but I don't know how they arrived at the root diameter. A potential supplier is claiming the gears cannot be made to print and that the root diameter on some of the gears is off by as much as .300 (?????). I wonder how they have worked all these years.

John Woodward

RE: Helical gears at non standard center distance

looks like gearguru did a solution for
you.  Almost all gear manufacturers would
cut helicals gears with standard tools and
maybe make addendum and dedendum shifts to
strengthen or eliminate involute interference.
The hunting tooth myth is right on for cutting
gear teeth but not so in gear mesh.  It may be
advantageous to have the same teeth stay in
cycle rather than possibly take a chip or
error to all teeth.  Also for tracking it is
better to have an even ratio and the error will
always appear the same way thru the mesh cycles.
Sometimes the manufacturer will shorten or stub
the addendum of the gear to prevent involute
interference and then the whole depth is not
standard but can be cut with standard cutters, i.e.
you could have a profile shift and a stubbed addendum
or k m factor as used in european standards (module system.
I would check with another source to cut your gears and
see if the same questions surface.

RE: Helical gears at non standard center distance

the tooth thickness is always calculated for the (operating) pitch diameter and is measured as the length of an arc.
The root diameter can vary,as long as you have enough clearance between OD on one gear and root on the other.
For generic gears, the "standard rack" is used to calculate and/or manufacture the gear. In metric (module based, but very similar to pitch based rack) the standard addendum = module (in your case module = 25.4/DP = 25.4/10 = 2.54mm = ) and the dedendum = 1.25*module, for your gears 2.54*1.25
Adding the 2 addendi to the pitch dia you'll get the OD, subtracting 2 dedendi you'll get the root dia. In this "standard" situation there is the 0.25*module (0.25*2.54 in your case) root clearance.
These data can vary, it really depends on the tool and some other criteria (like profile shift, but it looks like you do not have any). To make the gears more robust, more deviations from tha standard tooth form can occur. Thicker tooth on small gear, thinner on larger, to compensate for stresses etc...

RE: Helical gears at non standard center distance

The tooth thickness checks out the same as what Gearguru calculated. I just checked the root diameters and found that they clear at this center distance. The root diameters are actually cut deeper than the theoretical dedendum, but either way, they clear. So far I would have to conclude that there is nothing wrong with these gears.

Thanks for all the help,
John Woodward

RE: Helical gears at non standard center distance

to be sure that the gears are correct, you also need to check if the tip of one gear in the worst situation does not interfere with the root fillet of the second gear. If you have chamfered tooth tips, situation is better but still needs to be checked.
If the hunting ratio's advantage is a myth or not, the smarter brains have to decide. In the vehicle transmissions almost all higher speed gears (3rd, 4th, 5th) use the mythical hunting ratios.

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