Engineering Expert Witness Blog

      Last time we examined how torque and force are created upon the driving gear within a simple gear train.   Today we’ll see how they affect the driven gear.

      Looking at the gear train illustration above, we see that each gear has both distance and force vectors.   We’ll call the driving gear Distance vector, D₁, and the driven gear Distance vector, D₂.   Each of these Distance vectors extend from pivot points located at the centers of their respective gear shafts.   From there they extend in opposite directions until they meet at the line of action, the imaginary line which represents the geometric path along which Force vectors F₁ and F₂ are aligned.

      As we learned last time, the Force vector, F₁, results from the torque that’s created at the pivot point located at the center of the driving gear.   This driving gear is mounted on a shaft that’s attached to an electric motor, the ultimate powering source behind the torque.  F₁ follows a path along the line of action until it meets with the driven gear teeth, where it then exerts its pushing force upon them.   It’s met by Force vector F₂, a resisting force, which extends along the same line of action, but in a direction opposite to that of F₁.   These two Force vectors butt heads, pushing back against one another.

      F₂ is essentially a negative force manifested by the dead weight of the mechanical load of the machinery components resting upon the shaft of the driving gear.   Its unmoving inertia resists being put into motion.   In order for the gears in the gear train to turn, F₁ must be greater than F₂, in other words, it must be great enough to overcome the resistance presented by F₂.

      With the two Force vectors pushing against each other along the line of action, the angle ϴ between vectors F₂ and D₂, is the same as the angle ϴ between F₁ and D₁.   Next time we’ll use the angular relationship between these four vectors to develop torque calculations for both gears in the gear train.

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