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# Modified Gear O.D. Calculation / Confusion(4)

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 changedsoul (Computer) 3 Jun 12 22:48
 A while back I was asking questions about calculating MOW from a given test radius. Thanks to "mfgenggear" I was able to put that into a nice TI89 calc prog that people at my shop use often. Now I am back wanting to add some more info to its output. I have hit a snag. Mostly because I am still learning about gears. Some Background. We have an old DOS program that spits some info out. Some of which I would like to duplicate to the TI calc. I can calculate everything this old DOS prog can with exception of a modified Gear I.D. or O.D.Example: 23T, 20DP, 20PA. Modified C.T.T = .06526.My calculation ( which is suspect ) for change in O.D. gives: 1.21351The DOS program gives a value of 1.21757And the Manufacturing Print actually calls out a O.D. of 1.219 +- .001.So I'm trying to See which value is correct and what formula was used.For mine I used the formula: C.T.T. = ( CP / 2 ) - ( 2 * O.D._Change * TAN(PA) ).I Solved for the change in OD, Multiplied that by 2 and Subtracted that from the STD OD ( 1.25 ).Am I on the right path? And I understand that the O.D. is not all the critical, but being math, I would like to know where there are three different answers for this.Thanks.
 (2)  tpederzani (Mechanical) 6 Jun 12 13:32
 I'm also trying to make a program (in Excel, which is awkward compared to an actual programming language). For 23T, 20DP, 20PA and CTT max = .06526, I get a profile shift coefficient (AKA addendum modification coefficient) of -0.365, which gives an OD of 1.2135. I use AGMA 913 to calculate the profile shift coefficient, and the OD from AGMA 917. The OD tolerance formula from AGMA 917 uses TCE.The profile shift formula is:((tooth thickness) * (diametral pitch) - Pi/2) / (2 * tan (pressure angle))The OD formula (for external gears) is:(standard pitch diameter) + 2 * (profile shift) / (diametral pitch) + 2 / (diametral pitch)The OD tolerance (external) on blanks from AGMA 917 is:+ 0.5 * (total composite error) + 0.1 / (diametral pitch)- 0I'd suggest looking at the specs and going from there -- that's what I do. You might arrive at the same answers, but if future generations of employees have to understand your work, working from the specs might make all the difference.
 changedsoul (Computer) 6 Jun 12 19:10
 Can you double check that formula you posted? I tried to use it and got nowhere close to what you stated. But it seems the first (Profile shift) formula you gave is very similar to what I had posted. Perhaps some parenthesis were omitted by mistake.It seems you have reached the same size O.D. as I have though. So the question still remains, which is correct?is it 1.2135, 1.2175, 1.219.Thanks again
 dinjin (Mechanical) 7 Jun 12 5:37
 At some point you have to know the amount of backlash that is assumed to be in the circular tooth thickness or is it a result simply of profile shift and is it a nomimal tooth thickness before backlash. There are two components to OD calculations one is the profile shift and the other is addendum shortening especially.
 Occupant (Mechanical) 7 Jun 12 6:53
 Using my old Machinery's Handbook - which predates DOS by 10 years at least - I've come to the same result that you both have O.D. = 1.2135. So what's the question?
 mfgenggear (Aerospace) 8 Jun 12 12:11
 tpederzanican you please redo the last equation.Let me say, very well done.changesoulyou did very well also.OccupantWhat can I say I tip my hat to you.All Please find attached which is freely available on the web.Mfgenggear http://files.engineering.com/getfile.aspx?folder=19669192-6cb9-4776-9b18-ee
 changedsoul (Computer) 10 Jun 12 11:02
 Im not sure I am fully understanding my problem. When looking over a bunch of specs, I cant seem to find a formula for the OD. So is the OD "ALWAYS" the distance from the working pitch plus the addendum? For all these formulas for change in addendum , can I just add that to the working pitch?
 tpederzani (Mechanical) 12 Jun 12 11:14
 Let's try this way of showing the formulas instead:Profile Shift, from AGMA 913 Eq B.1http://latex.codecogs.com/gif.latex?x_E%20=%20%5Cf..." border="0" alt="" />Nominal gear OD, from AGMA 917 Eq 21ahttp://latex.codecogs.com/gif.latex?D_%7BoP%7D%20=..." border="0" alt="" />Outside diameter tolerance, from AGMA 917 Eq 62http://latex.codecogs.com/gif.latex?%5Cbegin%7Bali..." border="0" alt="" />
 tpederzani (Mechanical) 12 Jun 12 11:17
 Sorry about that, guys. The preview was broken, but I assumed that was a flaw in the previewer.I've put the equations into a PDF instead (generated with www.codecogs.com online LaTex Equation Editor). http://files.engineering.com/getfile.aspx?folder=e006a286-ee40-4618-a1df-5e
 tpederzani (Mechanical) 12 Jun 12 11:26
 Sorry about the multiple posts, too. AGMA 917 is the "Design Manual for Parallel Shaft Fine-Pitched Gearing" (and successor to AGMA 370.01), and it has the OD formula in it. (That's about the only thing I've cherry picked out of the spec -- I've been mostly looking for equations, not all the other good stuff.)I haven't found anything covering runout of the blank, which my company's gear drawings typically have. If you find anything on that, I'd love to hear it.
 israelkk (Aerospace) 12 Jun 12 17:07
 For a full depth gear according to AGMA there is no importance to the OD run out as long as the OD is within the OD tolerance. The gear should correctly mesh with the mating gear in the designed center distance (and with a Master Gear on the testing machine).
 mfgenggear (Aerospace) 12 Jun 12 17:30
 Changesoul dinjin basically answered your question. To my opinion both are viable calculations. which I have not confirm if it is exact. another calculation would be to verify at tight mesh & at the specified center distance to verify there is no tooth tip interference with the tip (major dia) & the mating gear root radii. I would suggest to get in more depth about gears, to to purchase design gear hand books and read all you can stand. israelkk I believe tpederzani is inquiring about the pitch diameter runout, & not the major diameter. tpederzani can you be more specific on you question israelkk is correct about the major dia runout. it can generally be what the designer requires, .001-.005" runout. the pitch diameter depends on the function of the gears, The AGMA 2000-A88 class will general dictate that. Mfgenggear
 changedsoul (Computer) 12 Jun 12 20:51
 Thank you all for your work in helping me get through this. Based on all the responses it seems my original calculation of 1.213 was closest. I'm not sure why the program we use would give a value so high, and I'm not the designer so I cant say why they would want the O.D. to be even higher. But at least I can be fairly confident that based on AGMA specs, I know what the Diam Should be. Whether the customer wants that or not is a different question. I wish I knew more about the mating gear and center distance. It would probably shed some light on some of this confusion. But with all these responses, i believe my question has been answered. Thanks to you all for your help.
 changedsoul (Computer) 30 Jun 12 11:14
 Ok, I think I am on the verge of understanding some of this. Please let me know if I am dead on, close, or not even in the same state. So im reading more on differences between backlash and tooth thickness, and I think I had one of them headaches with pictures.....you know, an thought. So for example, using the same part specs I started this thread with. I have this part, specs are: Pitch Diam = 1.120 ( .03 smaller from standard) Number Of Teeth = 23 DP = 20 PA = 20 MOW = 1.23405 ( .0864 wires ) So here is my thinking, and please tell me if I am starting to grasp this. 1: They call out a pitch diameter smaller than standard which tells me the gear has been reduced. 2: I should not assume, but for the sake of this I will. Ill assume half the pitch diam of 1.120 is the Gears portion of the Gear / Pinion Operating Center Distance 3: chugging out calculations, to thin the teeth enough to obtain a working pitch diam of 1.120, the teeth need to be thinned by .01092". 4: So this reduction in gear tooth is probably the same increase in pinion to allow the pinion to mesh at this 1.120 pitch diameter with the gear( tight mesh ) 5: More chugging calculations show that with a tooth thinned by .01092" with .0864 wires my MOW is 1.240388, not the 1.23405 they ask for. 6: Now leaving the tooth thinned at .01092 putting me at a 1.12 Pitch diam, I add a bit of backlash into the mix, dropping my MOW down to what the print calls for. .01092 Tooth reduction, with .002405 backlash, I get the proper MOW. Can I say that this gear has been reduced to operate at 1.120 pitch diam, with .0024 backlash?

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