# How to calculate the inertia of gearbox?

• Automotive
• Sri_Vars
In summary, the Gearbox Inertia Procedure is as follows:1) Calculate the inertia of each rotating assembly.2) Calculate gear ratios.3) Define the starting point. It's normally the output shaft.4) The output shaft is geared to the input shaft with a gear ratio. The inertia of the input shaft reflected to the output shaft is the inertia of the input shaft multiplied by the square of the gear ratio between the two shafts.5) Proceed to the next shaft. The inertia of the next shaft reflected to the output shaft is the inertia of the next shaft multiplied by the square of the gear ratio between the output and next shafts. 6) The inertia

#### Sri_Vars

Do I have to sum the inertia of all the gears and shafts? If so, how to do that?

Welcome to PF.
That depends on what type of gearbox it is.
The traditional automotive gearbox uses an input shaft that drives the lay (or counter) shaft. The output shaft is, in effect, a single unit. The ratio of the input shaft to the output shaft is gear dependent.

The moment of inertia of three subsystems must be measured or calculated.
1. The engine and flywheel should include the clutch pressure plate.
2. The gearbox input shaft and lay shaft should be grouped with the clutch friction disc.
3. The gearbox output shaft should be grouped with the drive shaft, differential, drive axles and all wheels.

We are currently using the traditional gearbox only. But I am not sure how to calculate the inertia of the subsystems. It would be so helpful if you could brief it with formula.

You will need to dismantle the gearbox, then weigh and measure every component. Take a look at a gearbox parts diagram to see how many items are held on the main shaft.

The pitch diameter of a gear will be misleading due to the radius squared. You will have to approximate gear wheels as polygons, or find some other way.

A ball bearing race will probably have the inner race moving, the outer race static, and the balls spinning, somewhere in between.

https://en.wikipedia.org/wiki/Second_moment_of_area#Examples
https://en.wikipedia.org/wiki/List_of_moments_of_inertia

Sri_Vars
Thank you so much for your help!

Sri_Vars said:
Do I have to sum the inertia of all the gears and shafts? If so, how to do that?
No, because all gears and shafts don't necessarily have the same angular velocity. You can do a free body diagram for each rotating component which will give you a set of equations to solve (1 equation for 1 unknown).

This post shows how to do it with the equivalent kinetic energy method.

Sri_Vars said:
Do I have to sum the inertia of all the gears and shafts?
Yes. And you have to calculate the inertia of each component reflected to a common point in order to include the effects of gear ratios. Having done this calculation more than a few times, here's the procedure that I use. It's the same as the procedure in the post linked in Post #6 by @jack action above, just stated differently.

1) Calculate the inertia of each rotating assembly.
2) Calculate all gear ratios.
3) Define the starting point. It's normally the input shaft.
4) The input shaft is geared to the second shaft with a gear ratio. The inertia of the second shaft reflected to the input shaft is the inertia of the second shaft multiplied by the square of the gear ratio between the two shafts.
5) Proceed to the third shaft. The inertia of the third shaft reflected to the input shaft is the inertia of the third shaft multiplied by the square of the gear ratio between the input and third shafts.
6) The inertia of each shaft is the total inertia of the rotating components attached to that shaft.
7) When you have the inertia of all rotating components reflected to the input, then sum them. That's the inertia of the gearbox at the input shaft.

If you want the inertia at the output shaft, the procedure is similar, except that you start at the output shaft and work back to the input shaft.

## 1. What is inertia and why is it important to calculate for gearboxes?

Inertia is the resistance an object has to changes in its motion. In the context of gearboxes, it refers to the resistance of the gearbox components to changes in speed or direction. It is important to calculate inertia in gearboxes in order to understand the forces and stresses that the gearbox may experience during operation, and to ensure the gearbox is properly designed and able to function effectively.

## 2. How is inertia calculated for a gearbox?

Inertia can be calculated by multiplying the mass of each component of the gearbox by its respective distance from the axis of rotation, and then summing these values for all components. This calculation can be simplified by using the moment of inertia equation, which takes into account the shape and distribution of mass for each component.

## 3. What factors can affect the inertia of a gearbox?

The inertia of a gearbox can be affected by various factors, such as the mass and distribution of components, the type and design of the gear teeth, and the speed and direction of rotation. Additionally, any added components or modifications to the gearbox can also impact its inertia.

## 4. How does inertia impact the performance of a gearbox?

Inertia can impact the performance of a gearbox in several ways. A higher inertia can result in slower acceleration and deceleration, as well as increased wear and stress on the components. It can also affect the response time and accuracy of the gearbox in controlling speed and direction changes. Therefore, it is important to properly calculate and consider inertia in the design and operation of gearboxes.

## 5. Are there any tools or software available to assist with calculating the inertia of a gearbox?

Yes, there are various tools and software available that can assist with calculating the inertia of a gearbox. These include CAD software, which can generate 3D models and calculate inertia based on component dimensions and materials, and specialized software specifically designed for gearbox design and analysis. It is important to use reliable and accurate tools for calculating inertia to ensure the gearbox is properly designed and functional.