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

Gear ration

  1. Jul 24, 2016 #1
    I am using two motor which are coupled with the mechanical coupling. The coupling has moment of inertia. The gear ratio of both motors is same 26:1.
    I want to know i also need to divide the coupling moment of inertia with the gear ratio?
  2. jcsd
  3. Jul 24, 2016 #2

    jack action

    User Avatar
    Science Advisor
    Gold Member

    I'm not sure what you mean by «coupling», so I will show you how to find the equivalent moment of inertia of a simple system with gear ratio.

    Imagine you have a gear set with gear 1 and 2. They have a gear ratio ##GR##, and each gear has inertia ##I## and angular acceleration ##\alpha##. We know the input torque ##T_{1\ in}## and angular acceleration ##\alpha_1## of gear 1. Doing the sum of moments on each gear:
    [tex]T_{1\ in} - T_{1\ out} = I_1\alpha_1[/tex]
    [tex]T_{2\ in} - T_{2\ out} = I_2\alpha_2[/tex]
    And we also know that:
    [tex]T_{1\ out} = GR T_{2\ in}[/tex]
    [tex]\alpha_2 = GR \alpha_1[/tex]
    We now have 4 equations, 4 unknowns (##T_{1\ out}, T_{2\ in}, T_{2\ out}, \alpha_2##). Finding ##T_{2\ out}## starting with the first equation:
    [tex]T_{1\ in} - T_{1\ out} = I_1\alpha_1[/tex]
    [tex]T_{1\ in} - GR T_{2\ in} = I_1\alpha_1[/tex]
    [tex]T_{1\ in} - GR \left(T_{2\ out} + I_2\alpha_2\right) = I_1\alpha_1[/tex]
    [tex]T_{1\ in} - GR \left(T_{2\ out} + I_2 GR \alpha_1\right) = I_1\alpha_1[/tex]
    [tex]T_{1\ in} - GR T_{2\ out} = \left(I_1 + GR^2 I_2\right)\alpha_1[/tex]
    We now have an equation of the form ##T_{in} - T_{out} = I\alpha## (sum of moments), but for the complete gear set, based on the input torque and acceleration. Note that the inertia of the second gear is multiplied by the square of the gear ratio.
  4. Nov 6, 2016 #3
    Please sketch what you mean by "coupling two motors which are coupled with mechanical coupling".
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted