Engineering Expert Witness Blog

      In our last blog we mathematically linked the driving and driven gear Force vectors to arrive at a single common vector F, known as the resultant Force vector.   This simplification allows us to achieve common ground between F and the two Distance vectors of our driving and driven gears, represented as D₁ and D₂.   We can then use this commonality to develop individual torque equations for both gears in the train.

      In this illustration we clearly see that the Force vector, F, is at a 90º angle to the two Distance vectors, D₁ and D₂.   Let’s see why this angular relationship between them is crucial to the development of torque calculations.

      First a review of the basic torque formula, presented in a previous blog,

Torque = Distance × Force × sin(ϴ)

      By inserting D₁, F, and ϴ = 90º into this formula we arrive at the torque calculation, T₁ , for the driving gear in our gear train:

T₁ = D₁ × F × sin(90º)

      From a previous blog in this series we know that sin(90º) = 1, so it becomes,

T₁ = D₁ × F

      By inserting D₂, F, and ϴ = 90º into the torque formula, we arrive at the torque calculation, T₂ , for the driven gear:

T₂ = D₂ × F × sin(90º)

T₂ = D₂ × F × 1

T₂ = D₂ × F

      Next week we’ll combine these two equations relative to F, the common link between them, and obtain a single equation equating the torques and pitch circle radii of the driving and driven gears in the gear train.

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