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  1. #21
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    According to the utility in Conrad Hoffman's site 32 / 37 x 28 / 29 gets you 0.835039 within 0.000003. If you have a 37 tooth gear. 29 is rare enough. Like poop in garden soil, prime numbered tooth counts in the lead gear rack provide lenghty irrational numbers. When selected and compounded in four gear combinations rthey esult in low error lead ratios impossible to acheive with rational parings.

    Small errors in the spindle index has the effect of turning a spur gear into a helical gear and altering the helix angle of a helical gear. Before the introduction of the differentisl in the gear hobber, helical gear were cut by employing a deliberate error in the index train combined tithe a carefully calculated feed rate. The hand of the hob, etc and a few other variables have to come together to generate accurate helix angles when cutting helical gears index over feed.

    When the pinoin and gear are meshed in their housings the teeth have to bear straight across when fully loaded. This rash statement has to bring raised eyebrows from power transmision engineers and old school gear cutter and experiences bench hands. Elasticity in the force loops in a transmission means the perfect gear pair in a perfect mesh in a well designed transmission may be plagued with end bearing under load - a real life shortener in the world of geared power transmission.

  2. #22
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    Quote Originally Posted by Macsbig View Post
    Sorry jbc, really don't understand what you'r trying to say there!
    Most ratios are not available. Only the ratios formed from integers. And in the case of a hobber, relatively small integers at that.

    The other half of my post was about tooth form. How does one estimate the lead angle and gearing for an unknown hob in order to cut a test blank?

  3. #23
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    Quote Originally Posted by <jbc> View Post
    How does one estimate the lead angle and gearing for an unknown hob in order to cut a test blank?
    By posting pictures of the ends of the hob some of us may be able to help decode the info.


    Forrest:
    It's the prime number gear mating with another gear with a 1 tooth difference that creates the long irrational numbers. 28/29 = 0.9655172413793

    32/37*28/29 = 0.835041940212

    and 91/71*43/66 = 0.835040509700 just a little closer.

    20/72 * 74/73 * 86/29 = 0.835039097687 Closer yet with 6 gears
    20/24 * 74/73 * 86/87 = 0.835039038767 even closer.

    25/39 * 25/82 * 94/22 = 0.835039000619 Good to 9 places.

    Bill
    Last edited by hitandmiss; 10-29-2013 at 03:11 AM.

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    Quote Originally Posted by hitandmiss View Post
    By posting pictures of the ends of the hob some of us may be able to help decode the info.
    The hobs in the photo are each etched with a single 4 digit number.

    Quote Originally Posted by <jbc> View Post
    What kind of hobs are these, and how can I work out a sensible tool/workpiece ratio to cut something that ends up with teeth, with only the hobs themselves and the diameter of the gear blank to calculate from?

    I am looking for copies of old tooling (8mm hobs) catalogs, that may have the factory part nos. therein. I am also looking for any documentation concerning the Mikron A90 hobber. When I get organized I'll start another thread for those subjects.

  5. #25
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    Quote Originally Posted by <jbc> View Post
    What kind of hobs are these, and how can I work out a sensible tool/workpiece ratio to cut something that ends up with teeth, with only the hobs themselves and the diameter of the gear blank to calculate from?



    Does there exists a textbook 'reverse engineering hobs'? Or maybe 'practical hob design'???

    The OPs question does not take into account that the hob itself is a gear and may generate more than one sensible workpiece.

    On edit: picking gear ratios from sets of gears is a type of problem in number theory known has Diophantine equations. There are some some (sub)optimal algorithms to speed and narrow the search.
    The middle one looks like a ratchet hob.
    Bill

  6. #26
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    Quote Originally Posted by Forrest Addy View Post
    According to the utility in Conrad Hoffman's site 32 / 37 x 28 / 29 gets you 0.835039 within 0.000003. If you have a 37 tooth gear. 29 is rare enough. Like poop in garden soil, prime numbered tooth counts in the lead gear rack provide lenghty irrational numbers. When selected and compounded in four gear combinations rthey esult in low error lead ratios impossible to acheive with rational parings.

    Small errors in the spindle index has the effect of turning a spur gear into a helical gear and altering the helix angle of a helical gear. Before the introduction of the differentisl in the gear hobber, helical gear were cut by employing a deliberate error in the index train combined tithe a carefully calculated feed rate. The hand of the hob, etc and a few other variables have to come together to generate accurate helix angles when cutting helical gears index over feed.

    When the pinoin and gear are meshed in their housings the teeth have to bear straight across when fully loaded. This rash statement has to bring raised eyebrows from power transmision engineers and old school gear cutter and experiences bench hands. Elasticity in the force loops in a transmission means the perfect gear pair in a perfect mesh in a well designed transmission may be plagued with end bearing under load - a real life shortener in the world of geared power transmission.


    Which is why I said any errors in the Spindle Index can possibly corrected by making the reverse error in the Differential gearing?

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    Quote Originally Posted by hitandmiss View Post
    25/39 * 25/82 * 94/22 = 0.835039000619 Good to 9 places.
    Check your math.

    I get (25*25*94)/(39*82*22) == 29375/35178 ~= 0.83503894479504235602 with an arbitrary precision calculator rounding to 20 places.

    Maybe you have a floating point rounding error?

    Limiting the search space to gears with less than 95 teeth I see different results. Here are the best 20 combinations:

    Code:
    echo -e 95\\n0.83503900 | time  ./abc-def-gears.pl 
    program to calculate gear ratios of the form (A/B)*(C/D)*(E/F).
    enter biggest gear ==> for 6 gears with 23 to 95 teeth ratios fall between 
    min(0.0141909899402245)
    and max(70.467247472672)
    enter the desired gear ratio ==> hash generated ... and sorted ... 389017 3*products found
    
     A/B  *  C/D  *  E/F  ::    ratio 
    71/55 * 62/65 * 59/87  ==  0.835038984004501
    59/55 * 62/65 * 71/87  ==  0.835038984004501
    71/55 * 59/65 * 62/87  ==  0.835038984004501
    62/55 * 71/65 * 59/87  ==  0.835038984004501
    59/55 * 71/65 * 62/87  ==  0.835038984004501
    62/55 * 59/65 * 71/87  ==  0.835038984004501
    61/81 * 73/54 * 73/89  ==  0.835039020154848
    73/81 * 61/54 * 73/89  ==  0.835039020154848
    73/81 * 73/54 * 61/89  ==  0.835039020154848
    94/55 * 51/95 * 81/89  ==  0.835038976399118
    81/55 * 51/95 * 94/89  ==  0.835038976399118
    81/55 * 94/95 * 51/89  ==  0.835038976399118
    51/55 * 94/95 * 81/89  ==  0.835038976399118
    51/55 * 81/95 * 94/89  ==  0.835038976399118
    94/55 * 81/95 * 51/89  ==  0.835038976399118
    67/75 * 61/66 * 89/88  ==  0.835039026629936
    67/75 * 89/66 * 61/88  ==  0.835039026629936
    89/75 * 67/66 * 61/88  ==  0.835039026629936
    61/75 * 67/66 * 89/88  ==  0.835039026629936
    61/75 * 89/66 * 67/88  ==  0.835039026629936
    3.49 user 
    0.02 system 
    0:03.52 elapsed
    Here is a little program that finds the best 20 (and all perfect) gearings for six gears A/B*C/D*E/F of arbitrary ratio. On my laptop the computation takes less that 4 seconds.

    Code:
    #!/usr/bin/perl
    
    $minteeth=23;
    $biggest=130;
    $tol=0.00001;
    
    print "program to calculate gear ratios of the form (A/B)*(C/D)*(E/F).\n";
    print "enter biggest gear ==> ";
    chomp($big = <>);
    if ($big > $biggest) { $maxteeth = $biggest } else { $maxteeth = $big }
    $minrat=$minteeth**3/$maxteeth**3;
    $maxrat=$maxteeth**3/$minteeth**3;
    print "for 6 gears with ",$minteeth," to ",$maxteeth," teeth ";
    print "ratios fall between \nmin(",$minrat,")\nand max(",$maxrat,")\n";
    print "enter the desired gear ratio ==> ";
    chomp($want = <>);
    
    for ($minteeth .. $maxteeth) { 
      $a=$_;
      for ($minteeth .. $maxteeth) { 
        $b=$_;
        for ($minteeth .. $maxteeth) { 
          $c=$_;
          $p=$a*$b*$c;
          $product{"$a $b $c"} = $p;
        }
      }
    }
    print "hash generated ... ";
    
    $inc=0;
    foreach (sort {$product{$a} <=> $product{$b}} keys %product) {
      $sorted_triples[$inc++]=$_
      }
    print "and sorted ... ",$inc," 3*products found\n";
    
    $last=0;
    for (0 .. ($inc-1)) {
      $outer=$_;  #outer loop for gears B*D*F
      $bdf=$sorted_triples[$outer];
      $pbdf=$product{$sorted_triples[$outer]};
      $seen=0;
      for (($last-0) .. ($inc-1)) {
        $inner=$_;    #inner loop for gears A*C*E
        $ace=$sorted_triples[$inner];
        $pace=$product{$sorted_triples[$inner]};
        $rr=$pace/$pbdf;
        if ($rr>$want+$tol) { last }
        $last++;
        $fit=$rr-$want;
        if ( abs($fit) <= $tol ) {
          $gearings{"$ace $bdf : $rr"} = abs($fit);
          $seen++; }
        else {
         if ($seen) { last }
          }
        }
      }
    
    print "\n A/B  *  C/D  *  E/F   ::    ratio \n";
    $n=20;
    foreach (sort {$gearings{$a} <=> $gearings{$b}} keys %gearings) {
      if ($n) {
        $key=$_;
        @values=split;
        $A=$values[0];$C=$values[1];$E=$values[2];
        $B=$values[3];$D=$values[4];$F=$values[5];
        $ratio=$values[7];
        print $A,"/",$B," * ",$C,"/",$D," * ",$E,"/",$F,"  ==  ",$ratio,"\n";
        if ($gearings{$_} != 0) {$n--}
      }
    }

  8. #28
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    Take a look at some of the gear programs on my webpage,

    http://www.myvirtualnetwork.com/mklotz/

    GEARATIO will attempt to construct a gear set to match a desired ratio from a set of available gears that you specify in a data file.

    GEARFIND will attempt to match a ratio when free to choose gears from a range of tooth counts specified by the user.

    These programs output the gear sequence, the ratio it forms and the error relative to the desired ratio.

    All of my programs are free. However, they're built to run under DOS so you may need the free application DOSBOX to run them if you have a newer computer.

  9. #29
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    We bought a Pfauter P400 machine years ago in the U.K.. From memory, we also bought a book called (something like) 'Change gears are no longer calculated'. Maybe worth a search?
    Cheers
    Mike

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    Hello Mark,

    I may be able to help you with this if it is not too late. I have written a Microsoft Excel spreadsheet to work out combinations of index gears and feed gears for hobbing helical gears on a hobbing machine to a close accuracy and another for hobbing worm gears using tangential feed. Please e-mail me on [email protected] if I can help, you are welome to the speadsheets gratis. I am located in Lymington, Hampshire, UK.

    Happy New Year and regards,

    Chris

  11. #31
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    I apologize for dragging up this old thread. This is for anyone that might be interested.

    This is from a program that solves using 8 gears (located here, it's 64 bit for Windows Vista or newer: http://1drv.ms/1uBga45).

    Choosing from 1,677,721,600,000,000 ((100-20)^8) combinations is too many for the normal brute force method, so this uses a different approach.

    Using Mark’s 0.835039 and limits of 20 to 100, it returns: 58/97 * 59/81 * 83/73 * 86/51 that has an error of 0.000000000074218

  12. #32
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    Quote Originally Posted by Macsbig View Post
    Sometimes it appears you can't get the exact ratio.

    For instance the Ratio I'm currently working with is 0.835039 - can't get it exactly with four gears (try your program), so I error correct with the Diff ratio - unless I'm missing something?
    I think what Conrad is saying (and if so, I agree with him) is that if you are cutting a gear with a whole number of teeth that are evenly spaced (say X), and you have a hob that generates one tooth/revolution (or I guess, a multiple thereof? Let's say one for now), then the gear blank has to rotate 1/X of a revolution for every revolution of the hob. Not 1.00001/X (which is 1 part error in 100,000). Because if its 1.00001/X, when you cut round to the first tooth cut, the last tooth is X times 0.00001 times 360° off. For a 20 tooth gear, that's 4.3 arc minutes. For a 100mm diameter blank, that's 0.06mm or >0.002 inch displacement between the first and last tooth cut. Maybe your application will tolerate that little "thump" every revolution, and ultrafast wear, but it doesn't have to. Because since you have change gears that have integral numbers of teeth, you should be able to get an exact ratio. Even if you have a metric gear hob and an inch-system leadscrew. If so (or if vice versa), you could end up using a 127 tooth gear somewhere in the train, and then you can use other gears to get exact.

    Or am I missing somthing?

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    Quote Originally Posted by bosleyjr View Post
    I think what Conrad is saying (and if so, I agree with him) is that if you are cutting a gear with a whole number of teeth that are evenly spaced (say X), and you have a hob that generates one tooth/revolution (or I guess, a multiple thereof? Let's say one for now), then the gear blank has to rotate 1/X of a revolution for every revolution of the hob. Not 1.00001/X (which is 1 part error in 100,000). Because if its 1.00001/X, when you cut round to the first tooth cut, the last tooth is X times 0.00001 times 360° off. For a 20 tooth gear, that's 4.3 arc minutes.
    The error’s multiplier is the hobber’s index constant (k factor) not the number of teeth. (0.00001 * k * 360 * 60^2) / hob’s lead-count equals a rotational error of 0⁰2’9.6” assuming an index constant of 10 and a single-lead hob. This is why you strive for an error that is 100 times more accurate: 0.000000x or better. The error from .0000001 = 0⁰0’12.96”


    For a 100mm diameter blank, that's 0.06mm or >0.002 inch displacement between the first and last tooth cut. Maybe your application will tolerate that little "thump" every revolution, and ultrafast wear, but it doesn't have to.
    Don’t forget that with rotation you are feeding, so instead of a thump, you get a very slight spiral (angle varies with the feed rate; it is a vector of rotation and translation). With a feed rate of fifty-thousandths and a face-width of 2 inches the hob is *fully* engaged for 40 turns. 40 * 0⁰0’12.96 equals 0.0015 difference side to side in the flank height of a tooth with a 6-inch pitch diameter and 2-inch face width. This is much better than a ‘thump’, but it is still not good enough. The differential allows you to add a counter-acting ‘error’ to remove this spiral.

    Because since you have change gears that have integral numbers of teeth, you should be able to get an exact ratio.
    That is if prime factorization of the ratio results in numbers that you can duplicate with the change-gears. When you calculate a ratio to cut a 101-tooth gear and have change-gears from 20 to 100 it will not work out exactly, but 97 would.

    Even if you have a metric gear hob and an inch-system leadscrew. If so (or if vice versa), you could end up using a 127 tooth gear somewhere in the train, and then you can use other gears to get exact.
    That works for a lathe, but a 127-tooth gear is not a magic bullet (unless you are cutting a 127-tooth gear) in the case of a hobber, unfortunately.

    Or am I missing somthing?
    Last edited by David_M; 11-02-2014 at 12:01 PM.

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    Default Hello There

    I recently brought pfauter rs1/2. But i can't be under stand about my machine helical ratio.,

    My additional machine have 0.2299.

    I mean i want make gear than i calculate example.. 16dp sin15° × 0.2299 = my older machine ratio is 0.2299

    But rs1/2 what have i don't know. If anybody know plz help thanks

  15. #35
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    My first bit of advice: please start a NEW thread rather than reviving a 4 year old thread.

    Second bit of advice: It may be that I just don't know enough about gear hobbers, but I did not understand your question. Any way you could clarify? Add pictures? (And again - do this in a NEW thread?)


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