Meshing Dissimilar Pressure Angles 1

[ZCHSC]

I am dealing with a Chinese supplier / gear designer whose proposal for a geartrain includes several pairs of meshing spur gears with dissimilar diametral pitches and dissimilar pressure angles. I have found no reference in Dudley's Gear Handbook, our company's internal references, my college textbooks, or online, that discuss any methods for designing gears to run on each other with different pressure angles. This flies in the face of everything I've learned about gearing, and the language barrier between us is making a fundamental explanation difficult.

These gears will be powdered metal, so nonstandard pressure angles and diametral pitches are not uncommon, but non-matching DP and PA for a pair of meshing gears is something that blows my mind. Can anyone provide some insight into this??

 

[Matt51]

Yes,

It can work if done correctly. It is not uncommon for manufacturers to use a "short pitch" or "short lead" hob to manufacture gear teeth. For example, if they are hobbing a 20 degree gear, they may use something like a 16 degree PA on the cutter, as this lowers the trochoid to involute intersection (smaller form diameter). There may also be cutting time advantages but you would have to ask someone with gear cutting experience.

The Buckingham Manual of Gear Design, sections 2 and 3, has these calculations. For example, section 2, spur gears, page 30. As a check, base pitch is always the same for mating gears. Calculation of base pitch is shown in different gear handbooks.

If you can post your basic gear data, I can run software and tell you if the gears run together ok.

 

[ZCHSC]

Interesting...here is the data that the supplier has provided so far:

Pinion = 19 Teeth ; D.P = 9.69 ; P.A. = 30.57181
Gear = 31 Teeth ; D.P. = 10.2 ; P.A. = 25.0000

Operating on a center distance of 2.5000

That is exactly as he has specified. Hope you can make sense of it, and thanks for the help.

 

[Matt51]

They match, I did a hand calc of the base pitch. Gears mate ok.

 

[ZCHSC]

I just did the same, and you are right. I'm surprised the Dudley Gear Handbook doesn't make mention of this technique. I couldn't believe what I was seeing from this supplier at first, but it looks like I should get myself a copy of the Buckingham book and learn something new...

If it's not too much to explain here, (the Buckingham book is on the way, but I'm curious) Are there any other checks required when considering a dissimilar pressure angle design?

It appears that the objective is to achieve equal base pitches while maintaining one point of contact between the two pitch circles. (i.e. no pitch circle overlap or seperation). Is there more to it?

 

[mfgenggear]

I would tread carefully even thou it will technically work
there are caveats in using mixed pitch & pressure angles.
My previous disscussion with other gear engineers problems could a rise. like self distruction. then again it will work.

I would recommend Lots of acual testing.

also in addition it will require special tools to cut the gears, since it is not standard.

My opionion "if this is a new design".I would stick with the same DP & PA.

 

[ZCHSC]

This is not actually my design; I am working on a similar geartrain myself, using AGMA design standards that I understand. I like to stick with 20 and 25 degree pressure angles, and achieve strength through addendum shift and material choice.

But I have also been asked to evaluate this proposal, and it was very unfamiliar to me.

Please see above, these will be powdered metal gears. No cutting tools necessary.

 

[Matt51]

Hi,

You will find everything you need when the Buckingham book arrives.

As one example, lets say you use a 20 degree pressure angle hob to cut a pinion and a gear. Lets say you have positive profile shift (addendum modification coefficient, rack shift, or whichever term you prefer), and you increase the center distance. The operating pressure angle will be greater than 20 degrees.

As another example, lets say you have two gears in an existing gearbox. You want to keep the centers the same and one of the gears the same, but add or drop a tooth from the other gear. You push or pull the cutter into the gear, until backlash is adequate when mounted. All the numbers become non-standard.

My guess is the Chinese engineer you have been working with has a preferred way of optimizing a gear mesh, and what he sent you is his end result. The design would probably appear to be very logical if he documented his entire design process, but he may view that as proprietary.

The only other checks you need to make sure of is to verify there is correct backlash when the gears are meshed, the contact ratio is adequate, and there are no interferences between the tips and roots as the gears roll through mesh. An autocad plot is one convenient way to do this, plot both teeth, and roll them through different positions. Or have the Chinese engineer do it. All the equations you need to do these checks are in commerical software packages, or in the Buckingham book. The more I read Buckingham's books, the more I realize he truly was a genius. Analytical Mechanics of Gears is always in print and very affordable.

Don't be afraid to uses non-standard geometry when it is beneficial to do so.

 

[ZCHSC]

I'm looking forward to the Buckingham book. Hopefully it will clarify all these issues.

The design requirements are to run a 19 and 31 tooth gear at a 2.50 center distance; by my logic, I would set the diametral pitch to (19+31)/2*2.5 = 10 , check strength, and adjust addendums accordingly. My own design uses the same ratio, center distance and tooth count, and by my calculations a set running at 20 degrees will be sufficient even without a profile shift. Granted, my design is meant to last half the number of hours as his.

 

[mfgenggear]

I would sample verify the gears with a master gears simulate the mating gear make sure there is no Tooth to Tooth errors (which would indicatate interference), and making sure the gears meet the specified AGMA quality level prior to testing.

I made lots of gear with bastard pitch & pressure angle
and non std center distance but the gear trains where the same DP & PA.

I did not say it would not work but you really must know
what you are designing.You must be sure it will work. In addition It would Depend on the production volume, and the fit form & function.

 

[dimjim]

You can get the same result by using the 10.2 dp
and 25 degree pressure angle for the pinion and
use 50 percent long addendum design.
If the base diameters have the same ratio as the
number of teeth, they will operate, ie the base
pitch is the same. You do not need to define the
pinion as the parameters listed by the vendor.

50 percent long addendum pinion designs are quite
common as long as the pinion is the driving member.

 

[mfgenggear]

Bingo

 

[israelkk]

Matt51

If for example you refer to the first case in Buckingham Manual of Gear Design, sections 2 page 30 and to the different operating pressures of the 1st gear and the 2nd gear then they are not arbitrary selected. If you can see the 2nd operating pressure angle = 16.315 degree is calculated from the 1st operation pressure angle = 14.5 degrees.

According to the law of gearing the standard pressure angle is the angle between the line tangent to the two base circles of the gears to the line connecting the centers of the gears and is the same for both gears. Meaning, that they have to be manufactured by the same tool (hob, rack, fellow etc).

When one use long addendum or short addendum (profile shift or rack shift or tooth correction at is is sometimes called) the actual working pressure angle for each mating gear is different from the standard pressure angle. But, both mated gears have the same standard pressure angel.

For example if you use a 20 degrees tool then all gears manufactured by this tool are 20 degrees gears no matter how much tooth correction you used. To mate a pinion manufactured by a 20 degrees rack with a gear manufactured 25 a degrees rack is to my best knowledge wrong and defies the law of gearing.

 

[israelkk]

ZCHSC

I had a similar problem with a gear designer/supplier who suggested a non standard gear system. To solve the problem I instructed him to design the gears (although they were molded gears) as though as they were manufactured by a hob or rack. Meaning, that the gears will look exactly as though they were manufactured by a hob (same trochoid at the root) to the desired AGMA class accuracy and testing radius. This way I could test it on a 2 flank 20 degree master gear machine exactly as I test machined gears

 

[Matt51]

Hi Israelkk,

I assure you, however strange it sounds, that you can use a complete range of pressure angles for generating a 20 degree pressure angle gear for example, as long as the diametral pitch of the cutter has been changed accordingly (there is one pitch that works with each pressure angle - you cannot just use any pitch). Call any hob supplier and ask him about short pitch hobs. I will find the exact calculation in Buckingham when I get back in the office next week, and I will plot the teeth tomorrow on some software and see how they look.

Regards,
Matt Hawkins

 

[Matt51]

Ok,
I agree with dimjim. To check any further, the outside diameters and root diameters would have to be given.

 

[dimjim]

Matt 51,
If both members of the long and short addendum are modified by the same amount they still operate on the
standard center distance and pressure angles.
You are right if only one is modified or they are not
modified by the same amount the operating pressure angles do change.

 

[Matt51]

Hi dimjim,

Yes, I agree with what you are saying. The point I am trying to make is that you can specify a gear as 20 degree pressure angle, 10 pitch, or almost the same gear (the trochoid is changed) can be specified with a different pressure angle and a different pitch. I believe that is what happened, the same gear, specified differently. If you keep the base cirle dia the same, and therefore the base pitch, the involute portion of the tooth is the same. The generating pitch diameters are different though with different pitch and pressure angle. If we consider three types of pitch diameter, the standard, the generating, and the operating. The generating pitch diameter has physical significance when cutting the gear. Although not when forming powdered metal gears.

We can calculate, for the Pinion = 19 Teeth ; D.P = 9.69 ; P.A. = 30.57181; what is the equivalent pitch for a 25 degree pressure angle. 1.96078 pd; 1.68822 base circle; The pd for this base cirle with a 25 pa is 1.862745. For 19 teeth, the dia pitch is then 10.200. So for whatever reason, the Chinese engineer chose to specify the same gear at a different pressure angle and pitch. Probably this is part of his optimization process, where he is watching pressure angles at different conditions, to make sure they do not exceed certain limits.

Israelkk, try Manual of Gear Design, section 3, page 19. "Given the tooth proportions in the plane of rotation of a helical gear, to determine the position of a mating rack of different circular pitch and pressure angle". Or section 2, page 30.

Regards,
Matt

 

[israelkk]

Matt51

I see what you mean. However, I prefer to work with a standard gear proportions systems either it is ISO, DIN, JIS or AGMA. It makes life much simpler and you can use standard tooling for testing even if the gears are molded or made of powder metallurgy. If you do not design the gears according to standard proportion gear tooth you will have to order special master gears, etc. As dimjim said you can achieve the same using short and or long addendum on standard and non standard center distance.

The way you work there is no meaning to standard module or diametrical pitch because each gear has different pitch or module. This is exactly why those standard module and pitches was established, to make it cheaper using standard tooling and testing tools. Toady the trend is that precision gears even plastic molded gears will be tested with master gears (especially the fine pitch gears) and the cost of non standard master gear may be in justifiable unless for very large quantities.

 

[ZCHSC]

Matt51 -

+1 to that philosophy. In my design process, I found the AGMA standards and standardized modifications to be perfectly capable of providing the needed strength in the required size envelope.