# Inertia issues

Need some wisdom regarding reflected inertia. I’ve got a lead-screw electric
actuator, stoke length = 30". Lead = 0.1", vertical load = 1000lb’s. 5 sec move time.

Question: Is calculating the reflected inertia the same proceedure as that for

What do you mean by reflected inertia?

– Len

I didn’t know what it was either, but I learned a lot about it there. I still don’t know enough to answer your question, but maybe someone else here can. I’ve never done one of these calculations with one of our robots before, but after reading this I may start for chain/cable driven mechanisms that require precise motor control. So I guess it wasn’t the programmers’ fault all along?

Layman’s terms/“TL;DR”: the amount of inertia the motor shaft sees transmitted from the load. Modeled ideally by Load Moment of Inertia/[Mechanical Advantage]^2. Useful when precise motor control (i.e. speed or position control) is necessary and the motor is not rigidly coupled to its load. A large difference between the reflected inertia and the motor shaft inertia can explain why some arms or other mechanisms always seem to oscillate rather than behave as controlled. Not exactly Layman’s terms, but I think most people on ChiefDelphi would understand most of that.

Good find!

Inertia comes into play when something experiences acceleration or a change in velocity. Usually the effects of inertia are noticed when starting or stopping movement. In the initial post, there is inertia of the original 1,000 lb. mass, and a rotational inertia of the screw and the motor. Reflection implies bouncing off of something, which has little to do with inertia.

With a linear rate of 6" per second vertical, the inertia is no match for the force of gravity, if the actuator was required to start or stop. Elasticity in the system will play a much greater role, and here is where inertia will have an effect.

Assuming no friction between the worm and the rack, the shaft needs a torque of approximately 510 oz.-in. to oppose gravity and only a little more at 60 rpm to lift the load. There are a few 2012 KoP motors/gearboxes that theoretically can supply this torque at those speeds. In the real world, there is friction, and elastic deformation of all components, which both increase the torque required. All of the real world drags likely dwarf the inertia of the motors, in this application.

– Len

“Reflected inertia” is a term of art used in mechanical engineering.

In the present context, it means the effective inertia of a load as seen at the motor.

Sort of like an ‘effective inertia’, which is different because of the mechanism in-between?

So as you gear the load down (motor turns faster than load moves), the reflected inertia would be lower at the motor (because the mechanical advantage is greater than unity) right?

Right.