Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to obtain the force acting on a gear teeth

  1. Jun 8, 2009 #1
    Hi everyone.
    I wonder how to obtain ,
    let say a 20T gear connect to a 40T gear compare to a 40T connect to 60T gear. (teeth size is the same)

    Suppose the transmitted force (at the outer of the gear) is the same, is there any different froce on the teethes in each pair (larger no. of gear teeth will suffer lower value due to sharing with neibour teethes)?

    Thanks for your kind help.
  2. jcsd
  3. Jun 8, 2009 #2


    User Avatar
    Science Advisor

    This is a hard question to quantify without real numbers. If the gear teeth are the same size, and you increase the number of them, then this will increase the size of the gear. For the same operating conditions, this will typically result in lower pitch line velocity and lower forces.

    The contact ratio (the average number of teeth in contact) is a function of more than what you provided.

    Aside from the standard bending stresses, there are also frictional stresses which are very dependednt on the pressure angle among other things.
  4. Jun 8, 2009 #3
    Sorry but ur question seems vague...bcoz
    For gear teeth we look at the stress induced and not the force acting on the teeth[I mean finally to conclude sumthing]

    Analysis of gear stresses can b done using diff theories...lets take the oldest 1:-
    Lewis theory...

    the main (i/p)s' to Lewis eqn r torque,No of teeth,module..then u get the Max stress induced ... from which u can conclude...

    Offcourse u need to get the forces acting on gear teeth[by P-torque*(Angular velocity) ;and F=M/d]
    But only forces just can help us to conclude anything related specifically to gear[u need them for bearings,shaft design]

    I hope this helped u...

    really soory if ur askin sumthing like stress distribution within a single teeth and then compare 2 diff teeth...
    I've approached ur question the Theoretical way...
    Practically there r mny softwares specially designed to analyse the same[Which I dont know!]
  5. Jun 8, 2009 #4


    User Avatar
    Science Advisor

    Right, fighting my way though lividv's post, I'd have to agree. To find the "force" you simply take your applied torque and multiply it by a distance. For maximum stress, that force is typically applied at what is called the highest point of single tooth contact (HPSTC). That generates the highest bending moment on that tooth.

    The force applied is easy, the stress calculation on the other hand...
  6. Jun 8, 2009 #5
    If you are very serious about machine design, or determining analytical data on gears, I'd suggest this book:


    It has a great example in the back on how to design a gear box as well. It addresses bending and contact stresses, shaft stresses, bearing selection, stress concentrations, keys, and almost anything imaginable. ( also has numerous tables for materials )

  7. Jun 8, 2009 #6
  8. Jun 12, 2009 #7
    Shorely once the max moment of the tooth has been determined, you simply divide by the section modulus (Z) of the gear tooth at the point of application of the load to determine the shear stress?
  9. Jun 12, 2009 #8


    User Avatar
    Science Advisor

    Not so. It will greatly depend on the radius at the root of the teeth.
  10. Jun 12, 2009 #9


    User Avatar
    Science Advisor

    Its actually bending stress that is the failure driver in gear fillets. As Fred said, MUCH of the stresses depend not only on the fillet radius, but even how the fillet was formed (hobbed, ground, etc).

    Gears are quite a complex little part, both geometrically and the dynamic loading that they see. You'll notice when you go through the standards that you are in fact NOT calculating stresses; you are calculating stress numbers. AGMA specifically does this to ensure that you do not compare these to material strengths. They are purely semi-arbitrary numbers that should only be compared to equivalent strength-numbers.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook