Engineering Expert Witness Blog

      Last time we developed torque equations for the driving and driven gears within a simple gear train.  They are,

T₁ = D₁ × F

T₂ = D₂ × F

where, T₁ and T₂ are the driving and driven gear torques, D₁ and D₂ are the driving and driven gear pitch radii, and F is the resultant Force vector, the common factor between the two equations.

      Now we’ll combine these two equations relative to F to arrive at a single equation which equates the torques and pitch circle radii of the driving and driven gears in the gear train.   This type of computation is commonly used to design gear trains to ensure they perform at a given level.

      As a first step we’ll use algebra to rearrange terms and place the two equations equal to F.    First we’ll do it for the driving gear, dividing both sides of the equation by the pitch circle radius, D₁.

T₁ ÷  D₁ = D₁ ÷ D₁ × F

T₁ ÷ D₁= 1 × F

F = T₁ ÷ D₁

      In a similar fashion, we’ll do it for the driven gear by dividing both sides of the equation by the pitch circle radius, D₂.

T₂ = D₂ × F   →   F = T₂ ÷ D₂

      Since F is the common term between the two equations, we can set them up as equal to each other,

F = T₁ ÷ D₁ = T₂ ÷ D₂