Servo Expert

Servo Expert Helping people design new world class machinery.

02/04/2025

What is inertia match and why it is important to calculate?

As I mentioned in a previous post inertia is an object’s resistance to a change in velocity.

Thanks to Newton we know how to calculate the inertia of an object. See previous posts for details.

Inertia ratio is the ratio of the prime mover eg a servo motor verses the total reflected inertia of the load including any drive train between the motor and the load.

Therefore

the Inertia ratio = motor inertia / total reflected load inertia.

See previous post to see how to calculate the total reflected load inertia.

So why is this important?

Generally speaking, the drivetrain between the motor and load is rarely stiff enough. This causes a windup or deflection between the motor and load. This windup limits how quickly and how accurately the motor can control the load during acceleration and deceleration.

To help reduce this windup, if the motor to load inertia ratio is 1, then you can load highest PID gains otherwise you have to use lower gains which means your accuracy and control will not be as good as they can be.

Now with that said, you may be satisfied with the lower accuracy and control which is fine but as the inertia ratio gets larger (no matter if the load is larger than the motor or vice versa) the accuracy and controllability gets worse.

Therefore it makes performing this calculation before you build the machine a good decision point to see what are the machine goals.

Some of you will say use a bypass or notch filter!

Ok but realize a filter dampens the controllability which may not meet your machine goals.

So a better solution is to explore ways to lighten and stiffen the drive train before you build the machine.

I’ll talk about calculating the natural frequency in a future post.

There is another reason to get the inertia match as close to 1 as possible.

At an inertia ratio of 1, the amount of energy needed is the lowest. Anything else requires more input energy. Keeping input energy down is something the end user of the machine will appreciate for years to come.

So, with all this information above, there are some servo manufacturers that can provide good accuracy and control at higher ratio.

For example at Bosch Rexroth, they don’t rely on PID alone which PID loops require an error before they can provide correction.

Bosch Rexroth uses a proprietary combination of feedforward, vector control, very high resolution feedbacks, and state control which I never had to tune a servo in 25 years!

Bosch Rexroth offers a free engineering tool called Indrasiz.

Well there you have it. You know what inertia ratio is, how to calculate it, why it should be discussed, and what to do.

If you have any questions, please ask.

Played music with my son-in-law at Copper Muse last weekend. What a great time playing music James and his father’s 76 ...
08/15/2024

Played music with my son-in-law at Copper Muse last weekend. What a great time playing music James and his father’s 76 Les Paul. Green Eyed Lady and Hotel California were phenomenal!!!

06/12/2024

Playing live music at Inner Compass Brewing, 10316 Technology Terrace, Bradenton, Florida from 5-8 pm. Come enjoy some great food and beers and some live Acoustic Music by Monte!

03/30/2024

Alejandro Totsi rocks at Texas Children’s Houston Open! Keep it going.

10/26/2022

How does reducers affect inertia?

Answer, a reducer which takes a higher input speed and reduce the output speed, reduces the reflected inertia of the reducer’s output load by the ratio on the reducer squared.

A 2:1 reducer reduces the reflected output load of the reducer by 2^2 or 4 times - making the reflected load seem 1/4 of its real inertia.

Neat!

Now one has to add the inertia of the reducer to the new reduced load inertia but generally speaking a reducer helps reduce the amount of force or torque needed to accelerate or decelerate the load for relatively small increase increase in input speed.

This partially explains why your car quickly accelerates thru the first and second gear but accelerates slower thru 3 and 4 gear because first is the highest ratio and second gear is smaller ratio and so on.

Wind friction plays a role in how quickly a car can accelerate because the faster the car speed the input power needed goes up as a ratio cubed.

When the power of the car engine meets the wind resistance plus any gravity forces needed plus any rolling friction and any inertial resistance then the car won’t go any faster.

More about this when we look at free body diagrams later.

10/26/2022

So what is inertia? Answer inertia is a measure of an object’s resistance to a change in motion. To move an object which is sitting still to a velocity, one has to overcome the object’s inertia. Friction is not included in an object’s inertia. Friction and gravity are additional forces and not included in inertia.

Generally speaking the heavier and object the more inertia it has and the more resistance to a change in velocity it has.

The units are generally inch pound second square inlbs^2 or kgm^2. There are other units but they all have a reference to weight and time.

Again we had Sir Newton to thank for this discovery!

06/25/2020

I’ll create a posting showing how to use Newton’s laws to size a motor and drive next.

Who is the most influential person in regards to machine design? Love to hear your feedback.
06/10/2020

Who is the most influential person in regards to machine design? Love to hear your feedback.

Let’s talk about Newton’s second law Force equal Mass times Acceleration. F=maTo me it is the building block of industr...
06/09/2020

Let’s talk about Newton’s second law Force equal Mass times Acceleration. F=ma

To me it is the building block of industrial machinery. We owe everything to this. No products we use would exist if we didn’t have it.

Want to know how much force does it take to accelerate a box of goods so you can wrap it and ship it? Use Newton’s second law.

From this we get Torque = rotary inertia (mass) times angular acceleration. T=ja

We also get Weight = mass times gravity. W=mg

What to know how much Torque to bend a pipe? Well add laws of metal forming with Newton’s second law and you have the answer.

Unfortunately a lot of fellow engineers have forgotten Newton’s second law and they oversize their machines which makes them not competitive on the world stage.

I’ve travelled around the world and worked with engineers who haven’t forgotten Newton’s second law so their machines cost less.

So it’s time to stop using rules of thumb and time to start using real math to develop new competitive machines.

If you want some help, feel free to contact me. There is no charge.

Monte

05/01/2020

Why machines owe a lot to Sir Newton. Coming up next.

05/01/2020

Hello World! I created this page to offer anyone help with selecting the electric servos and motion controls. I’ll post short helpful hints periodically and welcome questions.
Wishing everyone the best!
Monte

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