Engineering Expert Witness Blog

      Inertia.   It’s the force that keeps us in bed after the alarm has rung.   It seems to have a life of its own, and today we’ll see how it comes into play in keeping other stationary objects at rest.

      Last time we identified a specific point of contact between spur gear teeth in a gear train and introduced the opposing forces, F₁ and F ₂, generated there.   Today we’ll see what these forces represent, identifying one of them as inertia.

      So where do these forces come from?   They’re forces generated by different means that converge at the same point of contact, the point at which gear teeth mesh.   They follow a very specific geometric path to meet there, an imaginary straight line referred to as the line of action.

      F₁ is always generated by a source of mechanical energy.   In our locomotive example introduced earlier in this blog series that source is an electric traction motor, upon which a driving gear is mounted.   When the motor is energized, a driving force F₁ is generated, which causes gear teeth on the driving gear to push against gear teeth of the driven gear.

      Force F₂ is not as straightforward to understand, because it’s not generated by a motor.   Instead, it’s the resisting force that the weight of a stationary object poses against its being moved from an at-rest position, known as inertia.   The heavier the object, the more inertia it presents with.   Trains, of course, are extremely heavy, and to get them to move a great deal of inertia must be overcome.   Inertia is also a factor in attempting to stop objects already in motion.

      To get a stationary locomotive to move, mechanical energy must be transmitted from the driving gear that’s attached to its traction motor, then on to the driven gear attached to its axle.    At their point of contact, the driving force of the motor, F_1, is met by the resisting force of inertia, F_2. In order for the train to move, F₁ must be greater than F₂.   If F₁ is less than or equal to F₂, then the train won’t leave the station.

      Next week we’ll animate our static image and watch the interplay between gear teeth, taking note of the line of action during their movement.

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