• Welcome to engineeringclicks.com
  • Please help me with "Decimal Gearing"...

    Discussion in 'The main mechanical design forum' started by B:S, Feb 11, 2012.

    1. B:S

      B:S Member

      Joined:
      Feb 2012
      Posts:
      5
      Likes Received:
      0
      First, this seems like a great site and I hope to use it often.

      There is a bicycle company that is offering sprockets that they refer to as "decimal gearing". What the designer has dome is to slightly alter the Pitch Diameter (PD) and to then re-profile the sprocket teeth to prevent the chain rollers from interfering with the teeth. He claims that this decimal gear alters the 'effective' tooth count by up to .3 teeth.

      http://www.rennendesigngroup.com/Decimal.html

      We're talking about standard bicycle roller chain with a 1/2" pitch. 2 sprockets, one front, one rear. Nothing fancy.

      My belief is that a timed drivetrain is a timed drivetrain and that the ratio will always be determined by the number of teeth on the two sprockets. A 10t/10t combo yields a 1:1 ratio, regardless of any small variation in the PD.

      And in a sprocket with an under or over-sized PD, the chain rollers will have to alter their position relative to teeth throughout their engagement with the sprocket. This will cause loaded rollers to rotate, adding friction. Also, fewer teeth will carry the entire load, also increasing friction and wear.

      I simply cannot see how such a system could yield a ratio of anything other than that actual tooth count. If someone can confirm or rebut, I'd really appreciate it.
       
    2.  
    3. B:S

      B:S Member

      Joined:
      Feb 2012
      Posts:
      5
      Likes Received:
      0
      Is my question too dopey?

      Be honest.
       
    4. Ramana Rao

      Ramana Rao Well-Known Member

      Joined:
      Jan 2012
      Posts:
      47
      Likes Received:
      0
      You are spot on regarding the gear ratio. Modification of the tooth profile does not change this.
       
    5. B:S

      B:S Member

      Joined:
      Feb 2012
      Posts:
      5
      Likes Received:
      0
      Thanks for the reply!
       
    6. vic.blackall

      vic.blackall Well-Known Member

      Joined:
      Feb 2012
      Posts:
      45
      Likes Received:
      0
      The ratio of a drive is P.C.D of driver over P.C.D. of driven, the teeth provide the traction. For very small increases in the P.C.D. of the drive sprocket gives this fractional (decimal) increase in ratio. With a conventional sprocket the chain roller diameter is coaxial with the tooth sprocket profile and is therefore fully constrained. In order to run with a larger P.C.D. i.e. changing a 40t sprocket to 40.2t decimal sprocket would need an increase in P.C.D.of approx. 0.031", this has the effect of changing the circular pitch, to accommodate this change, additional clearance around the chain roller is required. This is not too much of a problem as the chain wrap around the drive sprocket is not much more than 180 degrees also the chain wheel only drives in one direction, so backlash is not important on reversal.
       
    7. Dana

      Dana Well-Known Member

      Joined:
      Sep 2010
      Posts:
      342
      Likes Received:
      3
      The gear ratio is the ratio of the number of teeth; nothing you do with fancy tooth shapes can change this. However, a chain drive is not perfect gearing; the instantaneous mechanical advantage (or disadvantage) you have varies according to the position of the chain roller. Think of a polygon where the corners correspond to the roller centers; the radius to the corner (roller) is greater than the radius to the flat (the point between the rollers). The instantaneous torque is greatest when the corner is at the tangent point and least when the flat is at the tangent point. Modifying the sprocket tooth shape might alter the way this variation goes and thus the "feel" that the rider perceives but it won't alter the overall (average) ratio. I have my doubts that a rider could feel the difference in torque but he might be able to feel the difference in smoothness and perceive it as a ratio change.
       
    8. vic.blackall

      vic.blackall Well-Known Member

      Joined:
      Feb 2012
      Posts:
      45
      Likes Received:
      0
      Dana, I think we will have to agree to disagree. I understand what you mean about the chain average radius, this is most prevalent in a smaller tooth sprocket, but this is not the theory of the drive in this instance the actual P.C.D. changes.
       
      Last edited: Feb 24, 2012
    9. B:S

      B:S Member

      Joined:
      Feb 2012
      Posts:
      5
      Likes Received:
      0
      Thanks for the input! I'm grasping to hang onto your explanations, but I think I understand. (In my best layman's terms:)

      In a free body diagram, I could understand how one would believe that any small increase or decrease in P.D. would change the lever, altering the ratio. It SEEMS totally clear, until we consider that it's a timed system. 5 rotations of a 40.2T gear would have to move 201 links of chain. Unfortunately, for Decimal gearing, that means that, at some point, the chain would have to 'jump' the sprocket in order to gain that tooth. Since a 40.2 sprocket only has 40 actual teeth, we can expect that it will move 40 links of chain per revolution.

      A flat, untimed belt can take full advantage of small changes in P.D., but I can't fathom how a timed system ever could.

      I made a sketch, and to the best of my understanding, on a decimal gear that is larger than the full-tooth size, the chain roller engages the sprocket in an advanced position, relative to that of a standard-pitch sprocket. Half-way through it's engagement, it is in an average (normal)position, and by the time it disengaged, it is in a retarded position. Average position during its engagement with the sprocket: average. And since the chain's position relative to the sprocket had to change during their mating, I would expect that wear and friction are increased. Net result should be increased friction and wear, with no change to the ratio.
       

    Share This Page