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Gearbox design calculations

  1. Feb 13, 2009 #1

    Thanks for you help, I have to design a gearbox which will be connected to an electrical motor with a 11 Kw, 960 rpm, 42 mm shaft diameter, I want the gearbox to rotate a sprocket with a diameter of 337 mm in a speed of 40 rpm, I don't know how the gearbox is to be designed for the pinion and the gear diameter and ratio, and also I don't know what's the output shaft diameters, it's length it should be and which materials I should choose for the gears and for the shaft,if any one can help please tell how can I do that gearbox calculations.

    Thanks for your help
  2. jcsd
  3. Feb 23, 2009 #2
    For starters, you might want to consider the size of the shafts that are going to be required for the torques that will be on each one. Do you know anything about shaft design? You might want to consult a design textbook such as Shigley and Mishkey (sp?) for this and for a lot of the details about gear design as well.

    You know what the input and output shaft speeds are supposed to be, so this should enable you to set the tooth numbers, if all works out simply. It does not always work that way. You may, or may not be able to accomplish all of the speed change in a single stage, and you need to be careful to pick tooth numbers that are relatively prime in each gear mesh. You may have to make some compromise on the gear ratio; it may not be possible to hit the exact output speed requirement, although in a two stage change you might be surprised at how close you can come to any requirement.

    You have a very big project here, with many parts. Good luck!
  4. Feb 25, 2009 #3
    There is a massive reduction required, 24:1, so for starters this should set you to look at doube helical gears and doube stage reduction.

    Its best to use Prime numbers for gear teeth numbers, or numbers with little or no common factors with the other meshing gear.

    That said, i have also read that its best to avoid integer values for ratio's as this can add to wear too.

    Remember that gears are only around 98% efficient too.

    If using gears from catalouge, then most are around 20mm for facewidth, which can mean that you need to use higher tooth numbers so that the bending stress on teeth is not to high.

    You also need to make sure the pitch line velocity is no too great, but if your using double helical which i would say you should with such a large ratio step, then 150 m/s is the max pitch line velocity, which is very fast.

    Here is what i got, doube reduction

    Gear 1 = 19, Gear 2 = 97, Gear 3= 19, Gear 4 = 89

    Giving 40.144 rpm

    Using all prime number teeth.

    You then need to pick a tooth module to calculate the stress and loads of other variables.

    You also should be aware that the torque will increased by a factor of 24?

    Output torque = input * ratio

    I got another 10 combinations within 1rpm, and used a range of 19 - 127 gears.

    However, i am guessing that with a module of 2, you will need around 50 teeth in order to get a face width of around 20mm and keep the stress under around 300mpa.
  5. Feb 25, 2009 #4
    A ratio change of 24:1 is hardly a massive speed change in a double reduction gear, but whatever ...

    Herpamad's tooth number choices will probably be OK, but there is no need to be restricted to prime numbers for the tooth numbers. The only requirement is that the tooth numbers in each mesh be relatively prime.

    Note that herpamad did all his work with the tooth numbers that he indicated, but then eventually concluded that you need a higher number of teeth for the face width he was using. Thus you cannot use all of his work blindly, but have to consider the trade off of going to a wider face width or greater tooth numbers.

    You will probably need to make these calcs many times, so it is worthwhile to write some computer code to make them for you over and over as you vary the parameter until you get a workable combination for your case.
  6. Feb 25, 2009 #5
    I took 24 to be a big change as data books i have been reading say that typical you should not go above 15:1 for double helical gears. Maybe wrong, you know more, way more than I do, or i wouldnt be asking so many questions.

    Stupid to post a solution and then bust it as it goes above the face width when stress is accounted for.

    So how about.

    Starting with 53, is prime, and is within limits for a module of 2.

    You could use 53, 157, 19, 153, and this gives the desired output.

    153 is not prime, but the rest are.

    However, please put me right about the ratio, i have obviously read something wrong, or understood it wrong.

    Ratio using double reduction, and my values would be more like 2 and 8 right? even though the total reduction in one go would be 24?

    If thats right, would the output torque be input torque * (2+8) or * 24?

    Trying to learn more, so put me right where i have gone wrong please, its most welcome.
  7. Feb 25, 2009 #6
    What ratios are workable depends to some extent on what type of gearing (what purpose) it is. A power transmission train is different from an instrumentation gear train, etc.

    That said, I think your tooth numbers are generally pretty high for most purposes. Typically tooth numbers are in the range 15 to 110, so in a single mesh you can change by a ratio of about 7:1, just speaking roughly. In a two stage train, that same reasoning would indicate that you could get 49:1. All of this is using simple stationary shaft spur gearing, not epicyclic gearing.

    Tooth numbers as high as 157, for example, usually mean very expensive gears.

    I have no idea where you got the statement, "ratio using double reduction, and my values would be more like 2 and 8 right?" and then you foll this with the calculation
    torque * (2+8) or 24? Why did you add here?
  8. Feb 25, 2009 #7
    Stage 1 is about 2, and stage 2 is about 8 (2+8)?

    So, if you want to buy off shelf, then what do you do?

    If you take 20mm as the face width, you would need 53, 260, 53. 260 which is way to big.

    So do you up the module? or add another reduction stage?

    19, 93, 19, 93 gives 40ish rpm out, but 19 gives a fw needed to be around 40mm and module 2.

    So do you change the module, or just go for customer gears and get large face width?

    If you up the module, you tend to get a bigger face width right?

    The off shelf cat i am using only goes to 120 teeth, and thats £140, so your right about cost.

    So if you use 18, 87, 18, 89 then you get 40rpm, but would need to have a face width of 36 to be within stress with hard gears using a module of 2.

    So i tried a module of 3 and using 18, 87, 18, 89 everything was within limits, so i guess i have answered my question that to up the module can reduce the need for more teeth.

    But again, these four gears come to £440, so been very expensive.

    18 is the least number of teeth you'd want to use right, well if spur gears?

    And then to get half of the ratio for doube reduction you take the squareroot of the ratio (24)? Thus 4.899 in each reduction.

    18 * 4.899 gives 89 rounded up.
  9. Feb 25, 2009 #8
    Herpamad, I just suggested that gear tooth numbers in my experience typically run 15 to 110. Now you come back and say 18 is a minimum. What do you want to do, fight about it? I have seen trains with as few as 13 teeth on the pinion, (actually less than that on some watch trains), but why are we going back and forth like this?

    Your cost figures seem awfully high to me, but I really don't have much experience with buying gears off the shelf. Every place I have ever done gear work, gears were cut in-house, so costs were minimal.

    You are evidently in the UK, since I see you quote prices in pounds (I don't even have the symbol on my US keyboard) and you talk in terms of the module. I am in the US and we still work in inches and talk about the diametral pitch which is essentially the inverse of the module, although expressed in inches.

    Using your tooth number choices of 53, 157, 19, 153, I presume that you are saying that the first mesh ratio is 157/53 and the second is 153/19. These are (just very roughly) 3:1 and 8:1. Then the over all train ratio is the product (not the sum)
    TR = 3 * 8 = 24 all very roughly.
    Now, where did you get (2+8)? Where did the 2 come from, and why do you add?
  10. Feb 26, 2009 #9
    I used 18 as the book i was reading says 18 is the minimum you should use for spur gears.

    I used 2+8 as i didnt read the calc right, it should be 3+8, but now you have put me right that its 3*8.

    Gears prices are just off shelf, but if you order over 10 units you get 50% discount. It was just the cat i had, and i am sure there are cheaper in the uk.

    I realise you use DP and not MOD, i however dont know the conversion.

    http://www.hpcgears.com/products/spur_gears.htm [Broken] // url for where i got my gears from.

    I didnt mean to undermime you, i did it by mistake, using 18 was just because that was just what i read, i also read that anything over 12 is acceptable too.

    The gear stockist does them down to 9 teeth, so i guess people use them or they woudlnt make them.

    I quoted 18, as it said this is advisable to avoid backlash?

    Problem is, one book says one thing, and another another thing, and then some one with experience will say another.

    I would rather go with the person with experience, like yourself, as practical is always better than theory in my book.
    Last edited by a moderator: May 4, 2017
  11. Feb 26, 2009 #10
    The problem with the minimum number of teeth on a pinion in not backlash but undercutting. If the tooth is undercut, you get a noninvolute profile segment that comes into engagement. Undercutting is somewhat a function of the method by which the gear teeth are formed.

    Just how much undercutting matters in a particular application depends on the application. It always weakens the tooth, but that may not (or may) matter in a particular case.

    Your gear prices indicate that they will be custom made, and that the price drop is because of the reduced setup time for the greater quantity. Somebody is still making a killing on them!
  12. Feb 26, 2009 #11
    Thanks for that, will look into backlash and undercutting more.

    Well a few other companies are selling them at a similar price, so a fair few are making a killing here. Found a few companies in the US, and they are way cheaper, just UK over inflated prices.
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