Over pin measurement of odd teeth helical gear
Over pin measurement of odd teeth helical gear
(OP)
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.
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.





RE: Over pin measurement of odd teeth helical gear
RE: Over pin measurement of odd teeth helical gear
RE: Over pin measurement of odd teeth helical gear
Steve
Eichenauer, Inc.
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
asong, for odd numbers of teeth on external helical gears, pins & balls will not get the same result.
Steve
Eichenauer, Inc.
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
RE: Over pin measurement of odd teeth helical gear
"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."
RE: Over pin measurement of odd teeth helical gear
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.
RE: Over pin measurement of odd teeth helical gear
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.
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