Gear test radius question? 1

[changedsoul]

I work at a gear manufacturing shop. Based on some formulas the gear cutters gave me, I was able to write up a program for them for their calculator that would calculate the MOW for given gear specs including backlash and or tooth thinning. One Gear cutter however asked if it were possible to calculate MOW based on a given test radius. And thats why I am here. The problem lies in that some of the prints they get do not specify a MOW, but only test radius and only for the gear being cut. They do not specify the mating gear.

So my question, is it possible to determine the MOW based on one gears data and a given test radius?

 

[israelkk]

Yes you can, but MOW testing is inferior to test radius. Test radius testing requires a double flank rolling test against a master gear and it gives you at the same time the Tooth to Tooth Error and the Total Composite Error. When AGMA, ISO or other spec classes are mentioned in the drawing and a minimum and maximum testing radiuses are specified in the drawing the MOW testing is not appropriate.

 

[mfgenggear]

I concur with israelkk he is the gear design guru.
however for manufacturing purposes it is OK to measure the parts in the machine with an MOW check then when the approximate target MOW is achieved then use the master gear to finish check the parts.
the MOW can then be adjusted to the corrected test radii.

in addition to what israelkk said the test radius test is an inclusive of the Total composite error test, tooth to tooth error test, pitch diameter runout, & tooth thickness.
so yes you can calculate circular tooth thickness but
it does not encompass all of the above.

I am not in the office so bear with me on this if i give not exact information.

The test radius is based on the ctt(circular tooth thickness of the part & of the master gear. change the master gear with a different ctt then the test radius changes.

now if the tooth thickness is given on the print then that is best to calculate the mow. you need the formulas from ctt to mow.

now if the ctt is not on the print then based on test radius of the gear it is possible to calculate to
MOW. based on a standard pitch diameter subtract the difference. +/- difference now if I remember the formula is like this
delta T = absolute(tan (std pitch radii - modified pitch radius))
delta T * 2 = total circular tooth change.

modified pitch radii = the test radius of the part.

if not given do this
take the center distance from the master gear & the part
sutract the pitch diameter of the master gear from center distance.

add or subtract the difference to the the standard circular tooth thickness.

if the test radii is smaller subtract.
if the test radii is larger add.

then calculate the MOW from CTT
this is a close approximation but it's close enough
to then adjust the mow on the machine to get the correct test radius.
there is more precise formulas. but the above works on a pinch

HTH
Mfgenggear

 

[changedsoul]

"it is OK to measure the parts in the machine with an MOW check then when the approximate target MOW is achieved then use the master gear to finish check the parts.
the MOW can then be adjusted to the corrected test radii."

This is exactly what they are trying to achieve, but since the prints only show test radius, they dont know how to come up with MOW. What they do now is cut a gear close to what they think, then check against master and go from there. They wanted an easier way to take the Test radius and calculate MOW so they dont have to do the trial and error and or waste parts and time. The prints they have dont give Center Distance or tooth thickness, if they gave tooth thickness, that would be great because the program I gave them can give them MOW from tooth thickness.

"it is possible to calculate to
MOW. based on a standard pitch diameter subtract the difference. +/- difference now if I remember the formula is like this
delta T = absolute(tan (std pitch radii - modified pitch radius))
delta T * 2 = total circular tooth change.

modified pitch radii = the test radius of the part."

Im not 100% familiar to some of these terms so I will review
them and see what i come up with. If what was given indeed gets me to a number I can use to calculate the MOW I thank you ever so much.

And thank you both for such quick responses.

 

[israelkk]

Years ago I encountered the opposite case. I had old drawings with the MOW on them and I transfered them to Minimum and Maximum testing radius and Tooth to Tooth Error and Total Composite Error to fit AGMA 2000-A88 accuracy number system.

 

[israelkk]

As mfgenggear mentioned the Testing Radius is Master gear dependent. Therefore, when someone puts a testing radius requirement in the drawing he has to give the master gear diameter (or number of teeth too) for absolute accuracy. I you check the gear with your master gear and then someone else checks it with a larger or smaller master gear the minimum and maximum testing radius he will receive will be slightly different.

 

[changedsoul]

I will try and get more info from them at work tomorrow about what is and is not on the print. The more I mess with this, the more I learn and the more able I am to understand their exact problems. Thanks for the help, Ill keep you informed.

 

[changedsoul]

Hello again. I tried the above formula without success. I did however find a formula that got me much much closer but it involved using the base circle if I remember correctly. It went something like this:

deltaT = (delta_base_circle) * tan(pressure_angle)

I substituted the base circle for the Std Pitch Diam, and subtracted it from the Test Diam. This actually got me, for the particular print i was looking at, within .0004 of a MOW reading. This may have been fluke with this particular part, Im not sure. But the method you gave mfgenggear set me of almost .01 for the MOW. Perhaps you missed something in the formula?

 

[mfgenggear]

changedsol

sorry was out for the day

Test Radius = xxxx xxxxx
standard PD = xxxx xxxxx
subtract __________

delta M = XXXX XXXX (absolute)
2*(tan PA * delta m) = delta T

Delta T (subtract or add) from std T = actual tooth thickness of part. calc MOW from this.



if test radius is larger than std Pitch Dia. (ADD delta T to std tooth thickness)

if test radius is smaller than std Pitch Dia. (subtract delta from std Tooth thickness)


standard T = (Pi/DP)/2 (standard tooth thickness)
standard PD = N/DP (standard pitch dia.)
delta M = diff of std Pitch Dia & Test Radii. (take absolute)
PA=pressure angle of gear
delta T = tooth thickness change

see AGMA example for calc test radius from CTT, attached on the link below

post an example of a gear # T, DP, PA & test radius
and I will manually calc. it, it's very simple.

I will post the more accurate formula later

HTH

Mfgenggear

 

[mfgenggear]

changedsol

Test Radius = xxxx xxxxx
standard PD Radius = xxxx xxxxx
subtract __________
delta M = XXXX XXXX (absolute)
2*(tan PA * delta m) = delta T

the error is subtract the radius of the pitch dia.

Mfgenggear

 

[mfgenggear]

see link below for updated calc's

my apologies for error above

Mfgenggear

 

[changedsoul]

Awsome, thank you so much. I will check it out this weekend when I get more free time.

 

[changedsoul]

If I remember tomorrow, i will get some gear data and post for you.

 

[changedsoul]

Ok, so here is one we have at work.

Test radius = .2123/.2109
Wire Size = .02
AGMA Class = 9
Pressure Angle = 20
Number Of Teeth = 42
Diametral Pitch = 96
Pitch Diameter = .4375

Based on the calcs, i came up with a MOW = .4581/.4553
Is that correct?

 

[mfgenggear]

changesol

my other formula was in complete, it's a senior thing I guess. any way here are my results.

using the Tan PA formula

circular tooth thickness= .01166246 .011116246
Meas. over .020 wires = .4581043 .4567285

the second formula require this additional equation

(Dx * pi)/#Teeth - Tx =t

circular tooth thickness = .01189506 .011113563
Measure over 020 wires =.4587335 .4566538

your MOW =.4581 .4553
ctt= .0116611 .0106563

MfgEngGear

 

[changedsoul]

I guess I'm a bit at a lose. I tried the formulas given in that post you gave:

http://files.engineering.com/getfil...510-4101d33f70f1&file=TestRadiusToCttCalc.pdf

But I cant seem to reproduce your results. I dont know where my error is.

Tangent PA Formula:

TTstd = PI/96/2 = .016362
test rad = .2123 / .2109
dr = 42/96/2 = .21875
DeltaM_high = .21875 - .2123 = .00645
DeltaM_low = .21875 - .2109 = .00785

DeltaT_high = ( tan(20)*.00645)*2 ) = .004695216
DeltaT_low = ( tan(20)*.00785)*2 ) = .005714332

CTT_high = .016362 - .004695216 = .0116672457
CTT_low = .016362 - .005714332 = .0106481297

Does this look correct, because its different than what you have.
Also, the second sheet formulas, I seem to be getting even more erratic numbers.
I noticed part of the formula has acos(pressureA_x) = pressureA_x, and then has tan(pressureA_x) - pressureA_x( but with a curved line above). Does this curved line have special meaning?

Sorry if I dont seem to be getting this, but the TanPA formula seems to straight forward yet I seem to get different results than you.

 

[mfgenggear]

changedsoul

your numbers are correct
I transposed delta low .00517 instead of .00571= .0106481297

the second equation
the line over the pressure angle is the pressure angle in radians. which (Pi*PA)/180
pi*20deg/180=.34906585

pi*0x/180=
pi*14.47840060/180=.25269576=INVspecial

so for a std inv= tanPA-PA in radians

I will review my second equation & get back to you on monday.

Take care
Mfgenggear

 

[changedsoul]

Thanks for the info on the radians. I know the tan(a)-a formula well, just wasnt sure what that curved line symbol was. Thanks. I must have been doing something wrong in my calculation with the Second formulas that use the involute function. Even after you gave the rest of what was needed, I still got the wrong answer. However, this weekend I sat down and went through them again and got the correct answers. SO it looks like what you gave me is what I was looking for. Ill test it out some more at work and see how accurate it is.

Thanks for all your help.