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20deg. Vs 14.5deg.

20deg. Vs 14.5deg.

20deg. Vs 14.5deg.

What could happen to the pinion/gear teeth if you have a 20deg pressure angle pinion driving a 14.5 deg. gear?

RE: 20deg. Vs 14.5deg.

It'll be hard to assemble, hard to turn, and grind the teeth all to hell.

Kansas City

RE: 20deg. Vs 14.5deg.


We use AGMA 6 gears. As a test I assembled a gearbox with 20 deg Vs 14.5 and it assembled and turned just fine, sounds OK also. I was wondering what the affect it will have on tooth wear and roll.

RE: 20deg. Vs 14.5deg.

I believe that they'll run well if the following three
conditions are met:

(i) the two base circle pitches are equal

(ii) the contact ratio is larger than 1

(iii) the center distance is set properly so that there
      is no interference

RE: 20deg. Vs 14.5deg.

I'd agree with eromlignod. They might feel OK by hand turning but under load they'd get destroyed.

RE: 20deg. Vs 14.5deg.

What size and number of teeth
are in these gears?  How fast
do they operate?  

RE: 20deg. Vs 14.5deg.

I do not understand why are you guys even try to answer this question. I would refer multiproducts to the literature to gain a basic knowledge before asking questions which shouldn't be asked at all. I do not dare to think what was the question if this was a gentic or stem cells forum.

RE: 20deg. Vs 14.5deg.

I can't find anything written about mixing pressure angles.

We have a 12T 48 pitch pinion driving a 48T 48 pitch gear. The pinion is at 400 RPM.

RE: 20deg. Vs 14.5deg.

You will not find anything written about mixing pressure angles because this is not done. Look for the basic law of gearing, i.e. the properties of the involute, the tout string etc.

You could as well use pin gear system as seen in the old western movies to pump water but these don't follow the laws or gearing.

To keep the laws of gearing the pressure angle has to be the same in order to get constant transmission ratio along the tooth action even with variable center distance.

RE: 20deg. Vs 14.5deg.


We had a 20deg Vs 14.5deg mix-up that was fortunatly cought at first piece inspection. Afterwords the question came up "what happens when you mix pressure angles?" and I could not find a specific answer.

RE: 20deg. Vs 14.5deg.

I had always been taught that you could
not mix pressure angles and I was curious
why they worked for you at 400 rpm and
I assume it was on the same center distance.
Were these plastic gear in that you did
hear any disturbances?  Really strange.

RE: 20deg. Vs 14.5deg.

Let's look at it geometrically.  

Two involute gears with the same pressure angle result in the two curved gear faces contacting at a point where the line of centers of the two gears intersects the pitch circle.  The pressure angle is perpendicular to the common tangent plane.  

Now, if one gear's pressure angle is different, that means its involute tooth profiles are generated from a different base circle diameter.  For a larger base circle (smaller pressure angle) the teeth would be wider at the crest and narrower at the base than teeth generated by a smaller base circle, which makes narrow crests and wide bases.   

Teeth with thicker bases also have narrower root widths between them at the same pitch, so you're mating a tooth with a wider crest in a slot with a skinnier width, which won't work.  When the pair is rotated half a pitch more, to where the skinny top mates with the wide gap, then you have backlash.

That's why if you mate two gears of differing angle, the resulting motion vibrates and grinds as alternating interference and clearance occur at each tooth.

Kansas City

RE: 20deg. Vs 14.5deg.

Well Gentlemaen - none of the answers given so far have gotten to the crux of the issue.

It is customary to design gears that mesh with the same pressure angle, only because it is also customary to design gears with the same Normal Modules or Normal Diameteral Pitches.  ie  a 20 degree pressure angle pinion meashes with a 20 degree pressure angle gear.  This is due to simplicity in design.

The real criteria however is that the pinion has the same base pitch or in the case of helical gears; normal base pitch.

The equation for normal base pitch in metric mm is:
Pi x Cos (Pressure Angle) x Normal Module

and in inches is

Pi x Cos (Pressure Angle) / Normal Diametral Pitch

For a 14 1/2 degree pressure angle pinion to properly mesh with conjugate action with a 20 degree pressure angle gear, we need to solve the equation as follows (in metric mm):

Pi x Cos(14.5) x Normal Module Pinon = Pi x Cos(20) x Normal Module Gear

Reducing we get

Normal Module Gear = Normal Module Pinion x Cos (14.5)/Cos(20)

Incidentally - this concept of gears requireing the same Normal Base Pitch to have conjugate action is the main reason why gears are noisy.  To tourbleshoot noise problems, try to measure the normal base pitches.  If the two gears match, they will will run quiet even if both gears of off spec by the same amount.


RE: 20deg. Vs 14.5deg.

belatedly, to answer the original question, the teeth could break.  And thirty five years ago, they did !  And that's when I learned about pressure angles !

RE: 20deg. Vs 14.5deg.

Go back to the typical definition of "pressure angle".  It is the angle between a tangent to the involute at the "pitch circle" and a radial line through the point of tangency.  A gear tooth that includes a 20° pressure angle also has a point closer to the root where the pressure ange is 14.5°.  If the pitch of the gears is the same at the circles where the pressure angles match, they can run fine if there are no interferences and the center distance is properly chosen.  

Using "standard" gearing, the best design practice is certainly to match DP and PA, but it is not impossible to find a combination where different PA's can be well mated with different DP's.

RE: 20deg. Vs 14.5deg.


As I understand it all you did is a mathmatical trick to get the same module. But instead of a pure rolling with no sliding you will get sliding between the tooth all over the tooth. The results are not just noise but wear.

RE: 20deg. Vs 14.5deg.

Spurs & Gearmold,

Can you give a specific combination of gears with different pressure angles that run together?  If you are
speaking only of operating pressure angles, I could agree.
I know a long addendum gear running against a standard addendum gear will operate with no problem, but at different pressure angle.  These are cut with the same standard pressure angle tooling.  I have not see a set of gears with one having a been cut with 20 pressure angle tooling that operates with a gear that is cut with 14.5 pressure angle tooling.

RE: 20deg. Vs 14.5deg.

Well, you could call this a "mathematical trick", but the mathematical truth is that the curve we know as the "involute of a circle" is really just a single curve.  There is no 14.5° involute or 20° involute or whatever.  It's just ONE curve on which we base all "involute form" gear teeth.  If pressure angles match, regardless of the "nominal" pressure angle of a specific component, then we will have the conjugate action afforded by the involute form.  This insures that noise generated by mating gears arises from
a) sliding action and hence, surface  finish
b) inaccuracies in the generation of the involute form and/or
c) tolerances in the position of the involutes (shaft sizes and positions, etc.)
Likewise, wear will depend on these factors plus lubrication.  Notice that nominal pressure angle ISN'T in the list.

The concept of "operating pressure angle" is an extension of this idea.  One of the greatest advantages of the involute profile is the fact that teeth still mesh in conjugate action even if center distance is changed a bit.  The "operating pressure angle" (angle between a normal to the line of action and the centerline of mesh), will change, but the action is still purely conjugate.  This design flexibility is not strictly applicable to cycloidal tooth form designs.

No, I cannot give a specific combination.  We don't normally design gear trains using different nominal pressure angles for mating gears, and I'm not going to spend time creating an example.  My point was only that it is conceptually possible to find such a combination.

You can see practical applications of this if you do a lot of double-flank gear rolling with non standard DP gears or both English and metric gears.  Suppose you have to check a .4 module, 20°PA gear, but don't have a .4 module master.  Do you spend $800 for a new master and wait for delivery, or just use a 64 DP master and calculate the difference?  

RE: 20deg. Vs 14.5deg.

Involute curves are based on the base circles and not pitch circles and that is why the teeth from different
pressure angle do not work with each other.

RE: 20deg. Vs 14.5deg.


Well said

RE: 20deg. Vs 14.5deg.


Yes, I will spend $800 for a new master. Otherwise it is cheating. If a gear manufacturer can not afford the $800 then he should choose another business. The customer expects honesty and trusts that the gears he gets are according to spec. If one orders gears according to AGMA Q10, Q12 etc. he expects that the gears will be inspected according to AGMA spec including the use of the correct grade of the master gear, the correct load between the master gear and the gear, etc. If you were in the aerospace business and do such a stunt this will be your last job.

Once I consulted for a spring design. The customer asked for a quote for the designed spring from a well known and highly advertised company. They quoted for the spring but inquiry showed that they do not posses the equipment to test the resulted spring. Would you order from such a company that can not accurately test what they are making?

RE: 20deg. Vs 14.5deg.


One more small issue. If you look in the AGMA for fine pitch gears you will find that the tooth height of the full depth is not 2.25 X addendum as for metric gears according to ISO. It is 2 X addendum plus some constant addition.

RE: 20deg. Vs 14.5deg.

Reading these posts and trying to absorb all the info leaves me to think of a pair of racks engaged with each other and either one having different pressure angles. I don't see how it could work.

RE: 20deg. Vs 14.5deg.

......and thinking about it some more; remembering that a rack is in effect just an infinitely large gear, how could the two racks (with the same pitch but different pressure angles) mesh correctly and maintain a constant velocity?

RE: 20deg. Vs 14.5deg.

** for Gearcutter and Israelkk

RE: 20deg. Vs 14.5deg.

....and more thoughts; the two infinitely large gears, with mis-matching pressure angles, I believe would not have a constant velocity. So how can gearmold suggest that the curves would be conjugate? I thought that the law of gearing (or geometry in general) states that for two curves to be conjugate they must engage and mesh with a constant velocity?

RE: 20deg. Vs 14.5deg.

Gearmolds statement about involutes is correct.
We should not mix the operating pressure angle with the cutting tools pressure angle.
The involute gears will work at slightly changed center distance smoothly, that's one more reason why involute is used. If the center distance changes, the operating pressure angle changes; the manufacturing ("rack") angle obviously remains. And in the bearings/shaft calculations we always use the operating pressure angles. Actually when a "profile shift" is used in the design which is a common practice, the operating and manufacturing pressure angles differ - little, but they do. Try some math, you can proove it yourself.
I have seen gears designed to be cut with tools of different pressure angle and assembled so, that they worked perfectly on precalculated center distance with a common operating pressure angle. But the difference in the "rack" angles was not as big as 20 versus 14.5 degrees.

RE: 20deg. Vs 14.5deg.

paulliu's statements are correct, too.

RE: 20deg. Vs 14.5deg.

...as are the spur's...

RE: 20deg. Vs 14.5deg.

Could we please ensure that we stay within the scope of the question which began this thread which was about a pair of gears meshed together with the same pitch but different pressure angles.
 If anybody wants to talk about the difference between generating or operating pressure angles or about whether or not gears with the same base pitch will mesh correctly or not why don't you post a new thread. These topics have already been covered in several other threads previous.

RE: 20deg. Vs 14.5deg.

Well, if you did not find it to be about the topic:
If the gears have the same BASIC pitch, they can mesh.
As already stated paulliu, that's why I said that he is right.
And that's basically what the spur and gearmold told us also.
Some theory/math and explanation WHY something can or can not be done is never out of the topic.

RE: 20deg. Vs 14.5deg.


I have been away for the past week so I have not seen all of the messages in this forum.

In response to your March 16th posting;

Ironically, one of my clients asked me to review such a pair of gears (14 1/2 degree PA meshing with 20 degree PA) about a month ago.  I have seen it done one other time about 4 years ago as well.  It would not be ethical for me to share their particular designs, but it is quite easy to make up a simple example.

The following gears will mesh with proper conjugate action.

Spur Pinion
16 teeth   1.5 module 14-1/2 deg PA, Circ Tooth Thickness 2.745 mmm, OD  28.504mm  Root Dia 21.754mm  Tip Rad .2 mm

Spur Gear
40 teeth   1.5454218 module 20 deg PA, Circ Tooth Thickness 1.988 mmm, OD  653.7mm  Root Dia 56.745mm  Tip Rad .2 mm

Operating Center Distance  42.908 mm

I am not saying that these designs represent a totally optimised approach, but these can run with action just as good as a 20 degree PA pair or a 14 1/2 degree PA pair.

You will also notice that since the modules are non-standard, this may not be a desirable approach if off the shelf cutting tools are needed.

Where I have seen this a approach used is for companies that have quite a large seletion of plastic gears in their inventory, and they mix and match in order to achieve certain ratios without having to double up on 14 1/2 and 20 degree pressure angle versions for for each tooth count.

Bear in mind that the beauty of the involute is that conjugate action can be maintianed with differences in center distance.

Gearmolds posting on March 17th is correct.

In my posting of Dec 21/06, I want to point out that it is not the pressure angles that define conjugate action, but that the normal base pitches of the two gears match.  This is the premis of the formula that I gave in that earlier posting.

Notice that this same formula for normal base pitch

(Pi x Cos (Pressure Angle) x Normal Module)

would explain why two gears at 20 degree pressure angles would not mesh with conjugate action if they have different normal modules.


RE: 20deg. Vs 14.5deg.

I find it interesting that you could accomplish the same gear with a 14.5 degree pressure angle and cut it on a
.26082 long addendum (ie hold the cutter .26082) and achieve the same basic gear.  The tooth thickness at the 20 degree pitch line of this gear would give you the 1.988
tooth thickness at the 20 degree pressure angle of this
same gear.  What is the advantage of defining it other
than a 14.5 degree pressure angle gear?
It would give you an od of 63.522 and id of 63.522
which is close enough to what you have specified as to parameters and would use standard tooling to cut it.

RE: 20deg. Vs 14.5deg.

Reading some of this discussion, I'd like to note that we apparently have two distinct viewpoints on this topic, since Spurs and gearguru seem to agree with my approach, while dimjim, israelkk, and gearcutter do not.  First, it's important that we can all hope to learn something from disagreements like this, and second, to be sure that noone takes this personally!  On that note, I'd like to respond to dimjim, israelkk, and gearcutter, who seem to disagree.

I have expressed ideas which are based purely on involute geometry, not on any specific standard, of which AGMA publishes several.  The original question did not include any reference to standard gearing, so it is my opinion that references to particular AGMA systems are inherently limiting the scope of the question.  I am in the plastic gearing business.  We can easily cut a cavity and produce millions of gears to non-standard parameters.  I have to assume from his handle that gearcutter is a bit more restricted in what he experiences in production, and israelkk must adhere very strictly to established standards (from the fact that he's in aerospace).  

I believe gearguru is precisely correct in pointing out that gearcutter's rack examples are confusing the generating method with the actual gear geometry.  If gearcutter is used to, in fact, cutting gears to a standard, that is entirely understandable.

Israelkk seems strictly adherent to standards.  I would only ask that you further consider the mathematics BEHIND those standards.  It is not "cheating" and in no way less "accurate" to test with a master which does not precisely match your test gear, so long as you can mathematically adjust for the difference.  I understand it may be more professionally risky, in your business, to do this, but there are many other industries in which we have to come up with really creative and sometimes, unusual, solutions to gearing problems.

dimjim, It doesn't matter which "circle" the involute is based upon.  Both the circle and involute are geometric forms with a single eccentricity!  There is only one shape to a circle and only one shape to the involute of a circle (unlike an ellipse or hyperbola).  Only the "size" of these curves can be changed.  You seem to also be used to using gear standards.  I would ask that you look beyond the standards.  If you've got a copy of Buckingham volume 2, or Khiralla is even better, you can get a better feeling of the geometry behind the standards.  

As I said:
1.  The original question did not reference any particular standard gearing system and
2.  The ideas offered here refer to pure involute geometry rather than being limited by any standard system of gearing.

I hope this helps to clear things up.

RE: 20deg. Vs 14.5deg.


Spur didn't cut it he is probably referring to injected plastic gears where the mold is machined using EDM wire machine. The whole issue as I understand started with plastic gears. In the injected gear business they do all kind of odd thing forgetting one major issue. Sometimes they manufacture gears without the option to test then against STANDARD master gears because the design is not standard (is not equivalent to hobbed gear). Most of the time they can get away with that because plastic materials has very low module of elasticity so they locally deform and compensate for inaccuracies.

I am currently consulting a company that is manufacturing measuring devices. For years they worked this way and now when they tried to develop more accurate and sensitive devices the production yield is very low because the friction between the gears is too high. They can not check the gears after production with STANDARD master gears and a check under magnification is impractical and is not economical.

Now they are shifting to design for plastic gears that will be designed as though they were machined ny a hob but will be injected. This way they will be able to do a double and single flank rolling tests against STANDARD master gears even when the gears are corrected (profile shifted).

RE: 20deg. Vs 14.5deg.


I suspect that the reason why some people mesh gears with different pressure angles is that they are already designed and built - initially to mesh with like pressure angle mates.  Then at some point they realize that they already have a part tooled up that gives them the number of teeth they want, but at a different pressure angle, but since they have the same normal base pitch as another part that is tooled up - they can use it.

I still believe that the most interesting lesson in this whole discussion has to do with gear noise.  As long as two gears that mesh have the same normal base pitch, they will run with conjugate action.  Both gears can be off spec, but if they are off spec by the same amount, they will run well.  This is the  the most important thing to remember when trying to figure out why gears are noisy running agianst eachother.


The cases where I have seen this are in fact plastic gears as I mentioned in my previous post.

I am not sure what you mean by the issue started with plastic gears.  The ability to mesh gears with two different pressure angles is all based on involute geometry, and is not just a plastic gear phenomenon.

I really dont understand what you mean by your comment that the injected gear business forgets the major issue of measurment against a standard master.  Regardless of what material the gear is made in, the master gear must properly measure the test gear.  Sometimes this can be accomplised with standard off the shelf masters, and sometimes it cannot.  It is extremely important regardless of what material or manufacturing process is used to have a suitably designed master.  As an example, I recently completed an automotive transmission project for a client that used 18 normal pressure angle and 18.37 degree helix angle paralell axis helical gears - hobbed and shaved.  The tooth proportions did not fall within any off the shelf basic rack geometry, but it was the right thing to do for that appllication.  The masters had to be specially made.

The bottom line is, regardless of the manufacturing technique, gears need to be designed to do the right job.  If standard rack profiles can accomplish this - great, it certainly is the way to go.

The notion that plastic gears deforming under the test load with a master to compensate for inaccuracies is absurd - its not Jello!  To prove my point - try measuring a plastic gear with featherlike parting line flash that can be easily flexed with your fingernail - you see every defect on the test result.  It doesnt come out good.

RE: 20deg. Vs 14.5deg.


I meant that under work conditions (not testing) the gears deform.

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