Engineering Expert Witness Blog

      In this blog series we’ve been examining gear train usefulness, specifically in terms of increasing torque.   Equations presented last week began us on the final leg of our journey, and we’ve arrived at the point where the closing combination of equations will demonstrate the loss of speed that takes place when torque is increased within a gear train.

     To that end, the two main equations under consideration as presented last week, are:

where R is the gear ratio of the gear train, N is the number of gear teeth, n is the gear rotational speed in revolutions per minute (RPM), T is the torque, and D is the gear pitch radius.

      We were able to link these two equations by working through five key design equations applicable to simplified gear trains.   For the full step-by-step progression see last week’s blog.

      After working through the equations presented last time we were able to arrive at an equation which links equations (1) and (2).   Here it is:

      If you follow the color coding, you’ll see the elements of equations (1) and (2) which come together in equation (7).   Because equation (7) links the gear speed ratios (red) with the gear pitch radii ratios (green), we can set the ratios in equation (1) equal to those in equation (2).   Doing so, we get:

      In order to see the tradeoff between speed and torque, we need only consider the parts of the equation which concern themselves with factors relating to speed and torque.   Removing the other unnecessary factors, we arrive at:

      Next week we’ll plug numbers into equation (8) and disclose the tradeoff of speed for torque.

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