Are gears with the same Diametral Pitch (DP) guranteed to mesh?

[YYCHM]

@francist , @Brent H I agree with what you're saying about the order of operations, but I'm going to let @RobinHood guide me through this one.

G-Day is Friday

 

[YYCHM]

Spent a GREAT day with @RobinHood making my gear today. 10am-4pm actually... Thanks Rudy



When I arrived Rudy had the dividing head and gear cutter all setup on the mill already.



Some initial measurements on the mill indicated excessive runout on the gear blank, so Rudy chucked it up in the lathe and cleaned it up, in particular, he re-drilled the centering hole on one end of the mandrel.



Here we are taking the first tooth cut.



I tried to capture an image of the smoke wisps coming off the cutter here. We used lots of cutting fluid per pass.



This is the last of the initial 0.1" pass. It was 1 full turn of the dividing head + 21 holes. per cut, and I think we did that 28 times? Rudy will correct me if I'm wrong.



And done after a second pass of 0.035". So that was 56 times around the dividing head total? Rudy had setup the table power feed such that each pass was simply a matter backing the cutter up, setting the dividing head, activating the power feed and doping on lots of cutting fluid.



A mesh test.... looking good.



I asked Rudy to show me how to bore it out to final dimension properly. This is his 4J setup. Aluminium strips to protect the teeth. Note the parallels (clamped) to hold the gear parallel to the chuck face.



And the final result... Needs a bit of burr cleanup and a keyway.

Thanks for a GREAT day Rudy, I learned a lot today...

 

[Mcgyver]

Nice work!

 

[RobinHood]

Yes, 28 divisions/indexes per one turn of the dividing head spindle. Interesting factoid about this particular 28T gear: after each 7 divisions, you end up in the same starting position - that is a good check as every 90* of rotation you know if you are still on track.

When I made the 127T metric transposing gear for the SM1340, I did not know if I made an error until the end - that was nerve racking.

Here are the calculations of how far to move on the dividing plate. I have the original documentation for the dividing head and there is a table to look it up, but I do the math just fo practise... The internal ratio is 40:1

 

[DPittman]

So how come you didn't cut the tooth depth all in one pass?

 

[YYCHM]

So how come you didn't cut the tooth depth all in one pass?

That's ultimately a @RobinHood question, but I'll take a stab at it.

As the cutter progresses to target depth, you're taking a wider and wider cut, so the initial cut can have a greater DOC than later cuts in terms of the amount of material removed per cut.

It also gives one a chance to see how things are reacting vibration wise etc. etc.

 

[RobinHood]

You got it @YYCHM.

Also, depends on the type of material. In softer stuff like aluminum, brass, delrin, etc, one could take the whole depth in one go.

 

[YYCHM]

And now with keyway....

 

[DPittman]

Interesting, I haven't exhaustively researched the subject (obviously), but I was under the understanding that when cutting gears the entire depth is cut in one sweep, because you gradually move into the blank and the geometry of the cutter, means you are taking progressive cuts anyhow. I believe I've read similar recommendations for slitting saws also. But I can imagine just like almost everything else..."it all depends".
Nice job gentlemen.

 

[RobinHood]

@DPittman , I think that is a good way of doing things as well.

It also depends on the type of machine, the rigidity of the set-up, etc. Too light cuts do not usually cause a problem whereas too heavy ones can cause all kinds of issues and parts can get wrecked in a hurry.

Was our operation optimized - absolutely not. Probably not even close, if it were for production.

 

[PeterT]

Looks great guys, Bravo. Looking at the whole operation, I think I agree with whoever made the comment ^upstairs^ that getting the bore established beforehand would make me breath easier because so much work goes into cutting the teeth & then re-establish center again to remove some more ID material. Maybe taking that one step further - also do the key way slot before teeth cutting too, because its presence doesn't affect anything on the shaft fixture. One more operation to get out of the way beforehand.

So is the tooth cutting job done when you went to arrived at target depth or how did you measure pitch diameter? I was particularly interested in that aspect.

 

[RobinHood]

I do agree with making the bore to the final size and a mandrel to suit (and even the key way) before cutting the gear teeth is the most optimized way of doing things.

We were trying to use stock material that was on hand and leave room for material removal because of the uncertainty of size and fit of the mating stub shaft/part.

Looking at off-the-shelf gears from suppliers, it is very common to see ID bores that are undersized so the end user can bore to fit. Reboring an ID is an easier task than making the gear itself as far as complexity and tooling required is concerned.

Yes, it was an extra step for us, albeit an easy one in the grand scheme of things.

As far as the measuring the pitch diameter after machining the teeth: we did not. It is not usually measured because it depends only on the number of teeth and the diametral pitch (or module, if metric) and it never changes or has a tolerance for a given gear. See attached PDF for an engineering explanation.

The formulae for determining the minimum tooth depth — ht=2.157/P = 2.157/16 = 0.1348” in our case — is plenty accurate enough as the working depth of the gear is hk=2.000/P = 2.000/16 = 0.125”. The minimum clearance is 0.0098” (S=0.157/P). Also, if you start with the blank’s OD a few thou under maximum of 1.875” (as we did) and touch off on it, the gear will be small enough and work for sure if the center distance to the mate is halfway accurate, it will work.

The only thing that varies now is the backlash.

 

[YYCHM]

This is a very closely coupled arrangement...….



Almost too much so. Meshing the gears while trying to align the keyway is a bit of a challenge. There is no perceived backlash. Once installed the power feed clocks away splendidly.



I'm thinking a 20-30 deg full tooth bevel(?) to the back side of this gear would aid in aligning the keyway before the gears starts to mesh. Like the top side of this gear only on the bottom side.

 

[RobinHood]

Some end relief on the contact side of each gear may help with the engagement.

 

[Canadium]

By the way I have been recently poring over calculations of my own to determine the pressure angle for gears on my own lathe. I came to the conclusion that machinists have by and large been making a simple calculation very complicated and difficult. Trying to measure the base width of a single tooth as seems to be commonly recommended on forums is a bad way to do it because it introduces huge errors.

So using my own gear as an example together with equations in the Machinery's Hanbook this is what I did.

From the handbook p619 in my 22nd edition;

DB=DcosФ where DB=Base circle diameter, D=pitch diameter, Ф=pressure angle
DB is the diameter of the circle that just touches the bottom of the gear teeth, in my case the base circle diameter can be accurately measured to be 2.936 inches. I need to find D to solve the equation.
D=N/P where N=number of teeth, P=diametral pitch
I need to find P to solve this equation;
P=(N+2)/DO where DO=the outside diameter of the gear. In my case;
P=(50+2)/3.25=16 therefore
D=50/16 =3.125 and therefore;
cosФ=DB/D=2.936/3.125=0.93952 which from cos tables is very close to the cos of 20 degrees or 0.93969

 

[YYCHM]

By the way I have been recently poring over calculations of my own to determine the pressure angle for gears on my own lathe. I came to the conclusion that machinists have by and large been making a simple calculation very complicated and difficult. Trying to measure the base width of a single tooth as seems to be commonly recommended on forums is a bad way to do it because it introduces huge errors.

So using my own gear as an example together with equations in the Machinery's Hanbook this is what I did.

From the handbook p619 in my 22nd edition;

DB=DcosФ where DB=Base circle diameter, D=pitch diameter, Ф=pressure angle
DB is the diameter of the circle that just touches the bottom of the gear teeth, in my case the base circle diameter can be accurately measured to be 2.936 inches. I need to find D to solve the equation.
D=N/P where N=number of teeth, P=diametral pitch
I need to find P to solve this equation;
P=(N+2)/DO where DO=the outside diameter of the gear. In my case;
P=(50+2)/3.25=16 therefore
D=50/16 =3.125 and therefore;
cosФ=DB/D=2.936/3.125=0.93952 which from cos tables is very close to the cos of 20 degrees or 0.93969

Didn't work for me. How are you measuring DB?

 

[Canadium]

Imagine a circle concentric to the outside diameter which just touches the bottom of the teeth. You want to measure the diameter of this inner circle. Or in other words where the teeth begin as you move out from the center of the gear.

 

[Canadium]

There is of course an even simpler method if you can assume that all the gears you are dealing with are either going to have a pressure angle of 20 degrees or 14.5 degrees. The newer more modern 20 degree gears have a rounded or radiused bottom between teeth while the older 14.5 degree gears will have a squared bottom between teeth.

There's a nice photo comparison on this Practical Machinist page:

https://www.practicalmachinist.com/vb/general-archive/measuring-pressure-angle-spur-gears-74835/

 

[YYCHM]

There is of course an even simpler method if you can assume that all the gears you are dealing with are either going to have a pressure angle of 20 degrees or 14.5 degrees. The newer more modern 20 degree gears have a rounded or radiused bottom between teeth while the older 14.5 degree gears will have a squared bottom between teeth.

There's a nice photo comparison on this Practical Machinist page:

https://www.practicalmachinist.com/vb/general-archive/measuring-pressure-angle-spur-gears-74835/

I don't think either of those techniques would have worked in this case...

Have the spaces between the teeth been under cut or deepened?

The calculation and observation does work reasonably well for the gear we cut.

 

[Canadium]

Ie...

Have the spaces between the teeth been under cut or deepened?

The calculation and observation does work reasonably well for the gear we cut.

It's an interesting question! I started examining and making calculations for every gear I could find here. I have to admit that not all the calculations work as nicely as my first example. I have a lot of South Bend lathe gears and in some cases the very same gear has slightly different dimensions which would affect pressure angle calculations considerably. For example one head stock gear measured exactly 4 inches diameter but a replica measured just 3.95 dia. If the teeth were cut a bit shallow or conversely deeper it would also affect the calculation.