Article Review: Gearmotor Impact of Reflected Mass Inertia From Load?

As originally printed in MotionControlTips.com January 10, 2019, by Miles Budimir with updated March 1, 2019 content.

In any drive system (that is, a motor driving a load), there is going to be inertia. Specifically, the motor will have inertia as will the load. For a direct drive system (a direct motor-to-load connection) the individual inertias can just be added together in a straightforward way. However, for any other type of setup involving some additional mechanical drive components such as couplings or gears, the relationship changes.

 

The inertia of the gear train, as well as any elements of the motor connection system itself, will also need to be considered. Leaving these inertia values out of the overall calculation produces an incorrect value for overall inertia and can lead to under-sizing input torque requirements.

What’s missing from the total system inertia is the inertia of the gears themselves and any other components of the connection system such as couplings. Another factor to keep in mind is that even with the same ratio different types of speed reduction and couplings may have different inertia values.

The key point is this: If the gear reducer is added separately, then the inertia value of the gears (usually provided by the manufacturer) needs to be added into the total system inertia. However, when purchasing a complete gearmotor, check with the manufacturer to determine if the published gearmotor inertia value includes the inertia of the internal gear reducer.

The bottom line is when calculating the total inertia for any motion system, the final value must include the inertia of all rotating parts, including the drive (such as a belt and pulley system, screw, or rack and pinion, etc.), the load being moved, the motor, the gearbox (if used in the system) and the coupling between the load and the motor.

When looking at how gears impact a drive system’s inertia, there are some basic ways to look at it. The basics; any gear will reduce the load inertia reflected to the motor by a factor of the square of the gear ratio. When looking at a gearmotor, this is basically just a motor with an embedded gearset in it, so the calculations and formulas for calculating inertia are the same.

In high-performance motion control applications, it’s ideal for the reflected load inertia to equal the motor inertia. If inertia matching is the only concern, then the gear ratio can be calculated as:

N = √ (JLoad/ J Motor)

where N is the gear ratio, JLoad is the inertia of the driven load, and JMotor is the inertia of the motor.

Note: Another way to calculate gear ratio is by reference to the individual gears. For instance, if NIn is the number of gear teeth on the input gear and NOut is the number of gear teeth on the output gear, the gear ratio is then:

N = NOut / NIn

As for reflected inertia itself, this is best understood as the inertia of the load that is translated back to the motor through various drive components, in this case, the gearing of the gearmotor.

So in a simple direct-drive system, the total inertia would be calculated like this:

JTotal = JLoad + JMotor

However, for a geared drive system such as a gearmotor, the total inertia is calculated using the equation:

JTotal = ( JLoad / N2 ) + JMotor

This is because, as stated earlier, the reflected load inertia is equal to the load inertia divided by the square of the gear ratio.

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Choosing a Gearbox Drive and Electric Motor Supplier

When choosing manufacturing partners during a machine build, remember that there are two methods for choosing a gearbox and electric motor supplier. One is selecting a pre-engineered unit and the other is choosing a gearbox-motor combination and integrating them into the equipment.

Pre-engineered gearmotor solutions are suitable if a design engineer doesn’t have the time or engineering resources to build a gearmotor in-house — or if the design needs a quick setup. New modular approaches to support OEMs (and enable new machine tools, automation, and design software) now let engineers get reasonably priced gearmotors even in modest volumes.

It’s true that one benefit to selecting a separate motor and gearbox and then combining them can less expensive than choosing a pre-engineered gearmotor. Another benefit to this approach is that one may be able to design the most optimized gearmotor for the application at hand … because this approach also gives the design engineer the most control over the final configuration and cost.

No matter the approach to gearmotor selection, be sure to continually improve the design by comparing predictions of performance with measurements. Then use the result of the analysis to improve next gearmotor iteration.

Contact: Gabriel Venzin, President, ABM DRIVES INC, +1-513-576-1300, [email protected].