Last time we developed torque equations for the driving and driven gears within a simple gear train. They are,
× F
Fwhere, T are the driving and driven gear torques, _{2}D and _{1}D are the driving and driven gear pitch radii, and _{2}F is the resultant Force vector, the common factor between the two equations. Now we’ll combine these two equations relative to As a first step we’ll use algebra to rearrange terms and place the two equations equal to
In a similar fashion, we’ll do it for the driven gear by dividing both sides of the equation by the pitch circle radius,
Since
which means that,
Next time we’ll see how to use this equation to manipulate our gear train so that it acts as a torque converter by increasing T and the ratio of _{1}D to _{1}D, thus providing a mechanical advantage to the electric motor the gear train is attached to._{2}_______________________________________ |

## Posts Tagged ‘machinery design expert’

### Equating Torques and Pitch Circle Radii Within a Gear Train

Thursday, May 29th, 2014### Distance and Force Vectors of a Simple Gear Train

Monday, May 5th, 2014
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, D. 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 _{2}F and _{1}F are aligned._{2} As we learned last time, the Force vector, F 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 _{1}F, a resisting force, which extends along the same line of action, but in a direction opposite to that of _{2}F. These two Force vectors butt heads, pushing back against one another._{1} F must be greater than _{1}F, in other words, it must be great enough to overcome the resistance presented by _{2}F._{2} With the two Force vectors pushing against each other along the line of action, the angle D, is the same as the angle _{2}ϴ between F. Next time we’ll use the angular relationship between these four vectors to develop torque calculations for both gears in the gear train._{1} and D_{1}_______________________________________ |