In today’s article we will go over inertia, sometimes called moment of inertia or mass moment of inertia, and why it is important when designing a system that contains our gearbox.
What is inertia?
Inertia is the resistance of an object to a change in its state of motion. Basically, this means how hard it is to accelerate or decelerate an object. All solid objects have an inertia based on their weight and geometry, and the payload, servo motor, gearbox and other moving components in a system are no different.
Inertia is calculated differently depending on the geometry of an object, but is mainly affected by the mass and distance away from the rotational axis. A heavier payload will increase the inertia, as will having more of the mass further away from the rotational axis.
This means that even if the weight of the object is exactly the same, the size will have a significant effect on the inertia (for example, a large diameter cylinder will have a larger inertia compared to a smaller diameter cylinder with the same mass).
Let’s look at an example. Think of an ice skater, who pull their arms and legs in closer to their body in order to rotate faster. What they are doing is pulling mass closer to the axis of rotation and decreasing their inertia which makes it easier to accelerate.
Why this matters
Inside of a moving system, all parts have different inertias (such as the motor, gearbox, coupling connecting the two, and the load on the other end of the gearbox). And as with the ice skater, the larger the inertia is the harder these will be to accelerate.
A larger inertia will need a larger motor to provide sufficient torque. The different inertias in the system interact with each other as well, and not properly considering the effect of each can cause complications.
Inertia Mismatch
When sizing a motor for an application, the required speed and torque are the main criteria that will be used for preliminary selections. However, the inertia mismatch between the motor and what the motor is driving (gearbox, payload, etc..) is arguably just as important.
Inertia mismatch is often overlooked when sizing a gearbox, but Nabtesco considers this vital information and we always include it when assisting a customer with sizing a gearbox. Mathematically, the inertia ratio is the load inertia (what the motor is driving), divided by the inertia of the motor.
For an application with a Nabtesco gearbox,
where I is the inertia of the payload (on the output side of the gearbox), RR is the reduction ratio of the gearbox, and Igear is the inertia of the gearbox and input pinion/coupling.
While there are many other things that need to be considered when sizing and programming a motor for a new application, most motor manufacturers suggest an inertia ratio of 10:1 or lower as a general rule of thumb. A mismatch that is too large will increase motor instability, with the motor either moving erratically or not moving at all.
The Inertia Mismatch is too big, what can I do?
First of all, the motor manufacturer should be consulted with to decide if the inertia ratio for the application will possibly lead to an issue.
If the inertia mismatch is indeed too large, there are usually two options.
1) Move to a larger motor that has a larger inertia, although this comes with the downside of increasing costs.
2) Reduce the inertia of the load. This can be achieved by doing things like lowering the overall load, decreasing the COG offset by adding a counterweight (if the load is not centered), adding a prestage between the motor and gearbox, or by adjusting the reduction ratio of the gearbox. As can be seen from the equation above for JM, the reduction ratio has a huge effect on the inertia, and an increased reduction ratio will cause a huge decrease in the inertia.
All of our gearboxes have several different ratios that can be changed without changing the size of the gearbox, and we also have developed several high ratio solutions for many gearboxes that are not in our catalog. Moving to a high ratio solution can allow you to use a smaller, more cost-effective motor while keeping everything else the same.
Final Thoughts
Need help with the inertia or inertia mismatch for your application using one of our products? Please contact us for engineering assistance.
