Engineering Expert Witness Blog

      Last week we worked with a gear train equation and found that the gears under consideration were not sized properly to run a lathe.   Today we’ll increase the gear train torque and solve that problem.

      How do we manipulate things to obtain the 275 inch pounds of torque required to drive the lathe?   Last week we tried using a driven gear with a diameter of 8 inches and found that to be insufficient in size.   So today the first thing we’ll try is a bigger driven gear, one with a pitch diameter of 8.5 inches.   That’s 0.5 inches larger in diameter than the gear used in last week’s equation, and this just so happens to be the next size up in the gear manufacturer’s catalog.

      As we did last week, we’ll begin our calculations with the torque ratio equation:

T₁ ÷  T₂ = D₁ ÷  D₂

      We’ll use the same values as last week for T₁, and D₁, 200 inch pounds and 3 inches respectively, but we’ll increase the new value for D₂, the driven gear pitch radius, to 4.25 inches (the new pitch diameter divided by two).

      Inserting these values into the torque equation, the only variable remaining without a value is torque T₂.   Let’s determine that value now by using algebra to rearrange terms.

(200 inch pounds) ÷ T₂ = (3 inches)  ÷ (4.25 inches)

(200 inch pounds)  ÷  T₂ = 0.70

T₂ = (200 inch pounds) ÷ (0.70) = 283.33 inch pounds

      The value of T₂ is found to be 283.33 inch pounds, which meets the torque requirement required to run the lathe.   We were able to arrive at this torque by simply increasing the size of the driven gear relative to the size of the driving gear.

      In the world of Newtonian physics, this is a rather straightforward arrangement.   It all boils down to this simple dynamic:  When the motor’s force is acting upon a wider gear, the force is located a longer distance from the center of the driving gear shaft, which results in more torque on the shaft.

      As borne out by the example provided today, the larger the driven gear is in comparison to the driving gear, the more the gear train amplifies the torque that’s delivered by the motor.   The principle at play here is exactly the same as that presented in a previous blog article where, for a given force exerted upon a wrench, torque was increased by simply increasing the length of the wrench handle.

      Some of you may be wondering why we didn’t just use a bigger, more powerful motor to begin with, thereby eliminating the need for a gear train and all the calculations we’ve been running?   We’ll see why that’s not always possible or practical next time.

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