Gears - Hobbing gears with similar base pitch

[Marley003]

TL;DR Summary

How does Base pitch error of hob affect profile error in gear

Hi everyone

To save money on jobs we manufacture racks which insert into a holder like a hob. These are ground accurately to the stated size over pins and angle. These blades/racks also have lead angles. We regularly hob gears that have a different module or pressure angle to the cutter (as long as the base pitch is very similar). I wondered if there was an equation that stated the difference in base pitch between the blades and the gear what would that equate to in profile error of the gear. I am guessing the tooth depth plays a big role as the larger the more error will occur.

For example if I cut a gear with a 7.5 base pitch and use a cutter that was 7.48 base pitch what profile error would that equate too over whatever distance ?

Thanks

 

[Lnewqban]

Welcome, Marley!

If I understand correctly, do you need to know how the innacuracy of the hobs you fabricate affect the functioning of the gears that are cut with it?

 

[Marley003]

Hi lnewqban

In a way yes, although the blades/ racks are made accurately but we don’t make new ones for each gear. Instead we use a blade we already have in stock ( with a base pitch as close to the gear we are manufacturing ) so the pressure angle and the module don’t have to match the gear as long as the base pitch is the same.

We rough the gear out with the blades leaving 0.2mm stock per flank and finish grind. I just wanted to know if there was an equation or theory behind if the base pitch of the blades are slightly different to the gear how much profile error will that equate to in the gear. So if u hob a 7.5 base pitch gear with a 7.48 base pitch hob how much profile error would that put in the flank. Obviously I’m sure tooth depth will play a role as stated.

Be good to work out how much different we could go on the base pitch to clean up the error when grinding. We are leaving 0.2mm stock per side so how much variance on the base pitch produces say 0.2mm profile error. So we know a limit on how different the base pitch could be of the hobs in relation to the gears.

 

[Baluncore]

In a way yes, although the blades/ racks are made accurately but we don’t make new ones for each gear. Instead we use a blade we already have in stock ( with a base pitch as close to the gear we are manufacturing ) so the pressure angle and the module don’t have to match the gear as long as the base pitch is the same.

Now I am really confused.
If you rough-out the gear blank, then finish grind the gear, the accuracy of the gear produced will depend on the grinding process.

If the profile of the hob, used for the roughing-out, is far from the gear being produced, then the hob must be set to penetrate less into the gear blank, leaving more material to be removed by the grinding process.

The theory and mathematics of gear generation is solid, but we don't know where your solid ground is. You want an equation that describes the profile of a gap, but we do not know where in the system that gap actually is.

Do the blades have several tooth gaps, or only one?
I need to see a picture of the blades you use with the hob. Is there a web link to the tooling and process you use?

 

[Marley003]

Hi baluncore

Thanks for the reply,

Yes but if the error produced in the Hobbing is too much for the stock left on the flank, the gear will not clean up all the profile error at the grinding operation and be scrap.

We work out a roughing size tooth thickness we hob too which gives us a dimension over pins. This roughing size tooth thickness allows for 0.2 mm material per flank for grinding.

https://m.made-in-china.com/product...r-Shape-Gear-Rack-M4-M5-M6-M8-2010941325.html

Here is a picture of something similar. So we have the 6 teeth on a rack and we have six of those which slot into the cutter to produce the hob. The teeth are equally ground so the pitch and angle and depth are the same on them all. The pitch between teeth x cosine of the angle gives the base pitch of the hob.

So let’s say (these figures are not correct, only using this to try to explain what I am looking for) if I want to hob a 7.500mm base pitch gear and use a 7.5mm base pitch hob/blades to a roughing size it may produce 15 micron of profile error on the gear graph for the roughing op - which we can clean up when grinding (as we were leaving 0.2mm). Say we use a hob with a base pitch of 7.490 and it produces more profile error for the same distance over pins it may be 100 micron of profile error which we could still clean up at grinding as we left 0.2mm on the flanks. Say we use a rack with a base pitch of 7.42 to cut a 7.5 gear to the same roughing sizes it may produce a profile error of 300microns which would not clean up when we grind the gear and it would scrap the gear.

My question is I am trying to find an equation which helps me know how much different the base pitch of the tool can be too the gear produced and how the difference affects the profile error . If there is an equation we could work out a limit on the base pitch for the cutting racks . For example anything over 0.03mm on base pitch produces more than 200micron errors so stay within 0.03mm of the base pitch of the gear produced.

Hope this helps and sorry for the essay

 

[Baluncore]

OK, that all makes sense, but I have a couple specific questions.

So we have the 6 teeth on a rack and we have six of those which slot into the cutter to produce the hob. The teeth are equally ground so the pitch and angle and depth are the same on them all. The pitch between teeth x cosine of the angle gives the base pitch of the hob.

So your hob is six trapezoidal teeth long, with the equivalent of six gashes, (the blades), that provide the cutting edges. Each of those cutter blades will be staggered by 1/6th of a gear tooth pitch, to make effectively the single-start thread on the hob, that cuts the rotating gear.
Those cutter blades could be placed axially along the hob, (with a cutting edge relief angle), or they could be rotated to the thread lead angle so they cut square without relief.
Is it the cosine of the hob lead angle that changes the base pitch of the gear?
Is that not removed by the skew angle of the hob shaft?

Why do I ask? The deepest faces of the gear teeth are cut by the centre part of the hob, the crests of the gear teeth are cut by the ends of the hob. If the cutter blade is rotated axially, the hob is no longer truly cylindrical, it is slightly hyperbolic, so will cut deeper at the ends, overcutting the gear crests. Gears with many teeth, suffer from the pitch error problem, smaller gears with low tooth counts are less sensitive to hob pitch errors.

The search for equations seems to branch two ways at each step of the analysis.
For example, pulling the hob away from the gear will increase the material remaining that needs to be ground later, but that may preserve the tooth crests that are being over-cut by the ends of the hob. The trade-off is about 36.4%, the tangent of the gear tooth pressure angle, assumed here to be PA=20°. When you rough out the gear, to a dimension over pins, you could compensate before the overcutting by increasing that dimension over pins by 1/0.364 = 2.75 times the overcut. That would allow a greater deviation in hob pitch than is ideally permitted.

 

[Baluncore]

If we consider a worst case gear wheel with a large number of teeth, then we might jump the detail.

A six tooth hob will be correct at the centre, with a maximum accumulated error of three times the pitch error, at the ends of the hob. For a six tooth hob, your maximum acceptable base pitch error is therefore; 0.2mm / 3 = ±0.067 mm = ±67 um.

If the base pitch error exceeds 67 um per tooth then:
1. Increase the target dimension over pins by 2.7 times the excess;
2. or, make a set of new cutter inserts with a closer pitch;
3. or, relieve one face of the tips of the cutter teeth at the ends of the hob.