GEARING
Using gears to change the inertia ratio of a
motor-driven system LOAD
Adding a gear set or gearbox between the motor and the load can improve the load-motor inertia ratio.
GEARS
MOTOR
ANY
system using a motor to drive a load with precise positioning, velocity, or torque
requires consideration of inertia. That’s because the ratio of load inertia to motor inertia significantly impacts a motor’s ability to effectively and efficiently control attached loads. That’s especially true during the acceleration and deceleration portions of the motion profile. In this context, the inertia to which we’re referring is mass moment of inertia, sometimes called rotational inertia — an object’s resistance to change in rotational speed. An object’s mass moment of inertia depends on its mass and geometry … usually the radius defined by the object’s center of mass and the point around which the object rotates. If the load’s inertia significantly exceeds the motor’s inertia, that load will essentially “try” to “drive” the motor … and the motor will struggle to get the load to its target position, speed, or torque. That in turn will prompt the motor to draw higher current … which decreases efficiency and increases wear on the motor and electrical components. On the other hand, if the motor’s inertia significantly exceeds the load’s inertia, it’s likely that the motor is oversized.
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That in turn has negative implications throughout the system — including higher initial cost, higher operating cost, larger footprint, and the need to oversize other components such as mounting hardware, couplings, and cables. If the inertia ratio is too high, the load inertia is much higher than the motor inertia and will cause problems with positioning accuracy, settling time, or control of velocity or torque. If this is the situation at hand, load inertia that is seen by (reflected to) the motor can be decreased by adding a gearset or gearbox between the motor and the load:
Where JL = Inertia of the load reflected to motor and JM = Inertia of the motor Adding a gearset or a gearbox to a motor-driven system reduces the load inertia by the inverse square of the gear ratio, meaning that even a relatively low gear ratio can have a significant effect on the inertia ratio.
5 • 2020
DESIGN WORLD — MOTION
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