Engineering Expert Witness Blog

      Today we’ll analyze the relationship between the sizes of the gears within a gear train, as well as their torques, and get an understanding of how gear trains act as torque converters.

      Last time we developed a single torque equation for a simple gear train:

T₁ ÷  D₁ = T₂ ÷  D₂           (1)

where T₁ and T₂ are the driving and driven gear torques, and D₁ and D₂ are the driving and driven gear pitch circle radii.

      The first thing to be done in order to arrive at a torque conversion analysis is group together like terms in equation (1) so that we end up with terms relating to torque on one side of the equation and terms relating to gear size on the other.   We’ll use algebra to divide both sides of the equation by T₂ , then multiply both sides by D₁.     After doing so we get,

T₁  ÷ T₂ = D₁  ÷ D₂            (2)

      In equation (2), T₁ ÷ T₂ is a torque ratio.  Ratio means we’re dividing one of the torques by the other.   Likewise, D_{1 ÷} D₂ is a gear pitch radius ratio, that is to say, it’s the ratio of one gear’s physical size relative to the physical size of the other.   What equation (2) tells us is that the individual gears on the gear train will produce torque values which are dependent upon the physical sizes of the two gears with respect to one another.

      So what’s the practical significance of this?   When gear trains are used in industrial applications, they always act as torque converters.   One such example would be when a low-torque-producing electric motor is used to power a steel cutting lathe.   If the motor isn’t tough enough to power the lathe, it itself won’t be modified, but the torque it produces will be.   This modification is accomplished by converting the motor’s low torque value, T₁, to a higher torque value, T₂ , and it’s equation (2) that’s used to do it.

      Next time we’ll delve deeper into the methodology behind gear train torque conversions.

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