Over pin measurement of odd teeth helical gear 1

[asong]

Thanks gearcutter first for his introduction of this forum.

I've posted this title in some forums, but almost no respond.
Do you think the formula Mdp=2*rM*cos(pi/(2*z))+dp is right?
Mdp -Measure over pins or balls
rM -Distance from pin center to gear center.
rM can be caculated out by finding out the pressure
angle of pin center first, it can be found in some
books.
z -Number of teeth
dp -Diameter of measure pin or ball

This formula requires two pins or balls stayed in the same gear section plan, but it is not reasonable: if want the pin stably sit in gear space, the 3 points(1 measure point, 2 contact points with flanks) must stayed in the same pin transversal section (the ball also the same). If they say in the same transversal section of gear, the pins or balls will not be stable. So they are not in the same transversal section of gear. I have my own formula:

psi/sin(psi+pi/z)=(tan(beta_M))^2
beta_M -helical angle at pin center.
with known of pressure angle of pin center,

tan(beta_M)=TAN(beta)*COS(alphat)/COS(alphaMt1)
beta -helical angle
alphat -transveral pressure angle
alphaMt1 -transveral pressure angle of pin center.

z -number of teeth
psi -when pin moves along gear space, the angle at
transversal section of pin center movement.

M=rM*sqrt(psi*sin(psi+pi/z)+2*(1+cos(psi+pi/z)))+dp

I get psi from first equation by iterative calculation. (in Excel, there is a goal seek tool. But with VBA, I can have it calculated automaticly). then put psi in the next equation. psi is in radians.

The result is smaller than the classic when helical angle is somewhat smaller then 45 degrees. it can be bigger then classic when helical angle is somewhat bigger then 45 degrees.

Sorry for my poor English.

 

[Philrock]

The first formula is correct. It also true that the balls must be in the same transverse plane, and they will tend to move due to the helix angle and pressure from the caliper. You may have to come up with fixturing to hold the balls in place while taking measurements.

 

[asong]

If use pins instead, and they are balanced by pressure of caliper. Do you think that will be easier?

 

[smah]

Pins will give you an incorrect measurement because the contact point will not be through the spherical center (and consequently the tangent points of the profile). For convenience, measuring 'balls' are often made like dumbells - balls with a fixed length rod between. This helps to set them in a particular axial plane as well making them easy to hold during the measurement.

Steve
Eichenauer, Inc.

 

[asong]

If we put only one pin in between teeth with holding gear steady, do you think the contact points of pin with flanks will be on the same pin transversal section ?
It is definitly, yes. Because if they are not on the same plane, the pin will turn to keep two contact points on the same section.
And then let's see the press point of caliper. if the press point is not on the same section, the pin will turn to make these 3 points on the same section.
What will happen when 2 pins? that must be a position for 2 pins in a 3 dimension, where the distant between them (a line is right angle for both of them) is what we need. the line is through the caliper contact points.
both of ball and pin contact with tooth at a point. but the curvature of pin is flatter than ball at pin axile way, by my opinion, it will be more correct than ball.

 

[scarecrow55]

Use the base tangent measurement, far easier

 

[smah]

I did this for several years and unfortunately longer have the information readily available, but I am 100% confident that using pins or wires to measure a helical gear with odd numbers of teeth will give an inacurate measurement. It might be 'close' depending on pin diameter, pitch & pressure angle at the contact points, & helix angle; but it will not be quite right.

scarecrow55, I'm curious if I'm interpreting your comment correctly. Are you referring to a span measurement, tangent to the tooth profiles over some number of teeth?

Steve
Eichenauer, Inc.

 

[gearcutter]

As already noted; asong's equation is for measurment across 2 balls rather than pins. Equation for across pins would be very complicated as it would have to allow for factors already mentioned. Although if the helix is small enough and the pins used are short enough you might be able to get away with it.
Span measurment is certanly easier as long as the face width of the gear allows for it.
Gear tooth micrometers are available that use interchangble balls for the anvils.

 

[scarecrow55]

Smah, yes it's tangent to the base circle and the profiles over a calculated number of teeth and like the gearcutter says, you need to check the facewidth allows it. Most usual designs of standard face to dia. gears can be measured this way. Check a text book for a picture & better description.

 

[asong]

gearcutter, for outer helix gear, the pins and balls will get the same result as they are not at the same transversal section. if keep them at the same section, balls are required indeed.
for inner helix gear, both odd and even helix gear require balls to measure. and like you said, a kind of short enough pin and small enough helical angle are allowed.

 

[smah]

Yes, scarecrow55 that's where I was going - face width, helix angle, shaft shoulders & other physical limitations. I'm aware of what it is & how it's used, I just was making sure that's what we were talking about before pointing out some of the possible limitations to using it.

asong, for odd numbers of teeth on external helical gears, pins & balls will not get the same result.

Steve
Eichenauer, Inc.

 

[gearcutter]

asong, you are correct for external even number of teeth but not for external odd number of teeth, as many have already mentioned.
Example: 5 module, 20deg PA, 35deg HA, 31 teeth, 9mm balls/pins. Across balls = 202.454. Across pins = 202.702.
A significant difference. I have'nt time to dig up the math at the moment so this was calculated with software. I'll try to find the equations for you.

 

[asong]

smah and gearcutter
For odd teeth, pins and balls will not get the same result when they are measured on a fixture which trying to keep the measure gage right angle to gear axile, that is right.
gearcutter, my formula gives this result, 202.194 it is the same to both balls and pins, and this is the shortest distance we can measure. 202.454 is right for balls at transversal section of gear.
To measure over pins with fixture is nonsense. Having the fixture first, then acording to the fixure or the way we measure, to give the formula of pins. that direct to a wrong way, although the equations could be found.
You can get a shorter distance than 202.454 with 9mm pins, without use fixture, right? I hope all of you try it.

 

[EnglishMuffin]

We use neither pins nor balls - we use matching block sets consisting of one female and two male rack shapes instead. You can't really beat these in my view. Unfortunately, the outfit that made them long ago is no longer in business. The shop guys lost one of the very small ones inside a machine. Does anyone know who still makes them?

 

[gearcutter]

Found this on another forum. The guys name is Michael Ignat, hope he doesn't mind if I use it here. I think he pretty much sums up what we've all been trying to explain. The question asked was in relation to why there is a difference between measuring over pins and then balls.

"This is a very interesting question. I do not have a very accurate answer (yet), but I hope I can help to a certain extent.
If you consider the contact of a pin with the teeth of an external involute helical gear, you will easily find out that the two points of contact are the same as if using a ball; the axis of the pin makes with the gear axis an angle equal to the tooth helix angle at the diameter of contact (this diameter can be calculated without any iterations).
When the number of teeth is even, the two pins will have the centerlines in two parallel planes, so it is very easy to get a measurement with a micrometer. The dimension is identical to that over two balls; obviously, it is not very easy to persuade balls to stay nicely in a transverse plane and that is a good reason why a hob operator will always prefer to use pins. The line defined by the centers of the balls is perpendicular to both measuring faces of the micrometer. The same line will be in the same position if using pins.
When the number of teeth is odd, the two faces of the micrometer will get a dimension over two pins in a similar way, but their common perpendicular does not go through the axis of the gear; this line (which gives the dimensions over two pins) will not be in a transverse plane, but must go through the two centerlines of the pins. Because of the axial offset between the pins, if using the dimension calculated for balls, the teeth will be cut undersize and sometimes that will not be acceptable. My opinion is that this dimension can be calculated numerically as follows:
1) find the distance between the center of a ball (with the same diameter as the pin) and the axis of the gear (using the well known equations for balls);
2) consider two helixes at that diameter, through the centerlines of the spaces where the pins are located;
3) find the minimum value for the distance between 2 points on these helixes (numerical solution, using one parameter, which could be the axial distance between the two points);
4) add the diameter of the pin and this should be the dimension over two pins; this value must be larger than that calculated for two balls in a transverse plane.
I am not sure the above analysis is correct, but I hope it is; anyway, I expect to hear many different opinions.

Correction: the axis of the pin is tangent to the helix (with the same lead as the gear) going through the center of an equivalent ball; the angle of this helix is not equal to that of the helix through the contact points."

 

[asong]

gearcutter, the last correction is right, yes, "the angle of this helix is not equal to that of the helix through the contact points"
I agree with most of Michael Ignat's ideas, but his 4th opinion is not accurate, the value may not be always larger than that calculated for two balls in a transvers plane, it relays on the helix angle of pin center. For the normal helical angle we used, 15, 18 degrees, the value is smaller than that calculated for two balls in a transvers plane. If without the calculation with formulas, I am may also thinking it is larger.
I can not attach a drawing here, I have my idea in AutoCAD at 3 dimension. I hope you can see it.

 

[Spurs]

There is helical gear design software that can do all tis for you.

For external helical gers with odd numbers of teeth you can use radius over pin, or ball, dimension over 2 pins, dimension over 2 balls, dimension over 2 pins

All have slightly different calculating methods and results.

Not that for internal helical gears, you can only use balls accuratly.

http://www.webgearservices.com