# Go beyond horsepower when sizing a servo motor

## When using a servo motor, one should consider torque, speed, and other applications for a specific motion control application.

02/14/2014

When attempting to correctly size a servo motor for a specific motion control application, using a measurement as broad as horsepower or kW rating is not sufficient. Horsepower determines how much work a motor can produce, but several factors must be taken into account to ensure that the correct motor is selected for a specific application.

Before making the calculations required to fill specific requirements, one must know what kind of job this motor will be used for. What’s the most critical aspect of the job? Is it the speed? The torque? Every situation is unique.

Perhaps in one scenario someone needs a motor that must be able to do X amount of cycles per minute, while another situation calls for a specific amount of torque required. After identifying the requirements that a particular job may need, getting into the math and selecting the correct motor becomes a critical task. The motor must be able to provide the required torque, speed, and accuracy if the system is to perform its job with the utmost efficiency.

All too often I see our industry classifying servo motors by horsepower or kW. This may be sufficient for induction motors, but for the applications that call for a servo motor, selecting one based on a specific horsepower doesn’t make much sense. In this situation, horsepower isn’t telling me everything I need to know. It’s telling me how much work the motor is capable of producing, but it’s not telling me exactly how that work is balanced. Is it working fast? Is it pulling a large load? All of these are critical pieces of information for a given job.

For an induction motor, providing me with how much horsepower is being produced is sufficient. This is because induction motors are sized and selected based on a horsepower curve. For example, if someone is sizing a motor for a pump that needs to pump out 1,000 gal of water per hour, he or she would select a motor by looking at the pump curve that specifies the required horsepower requirements for the pump to output that amount of water at a given head pressure.

As long as the horsepower of the motor selected is above this line and the motor can hit the speed requirements of the pump, the motor will not overheat. However, in applications where a motor must start and stop often, and when a motor must accelerate quickly to a speed, decelerate, and stop, a servo motor is generally required and horsepower is no longer a sufficient measurement. One must be able to understand the ability of the motor to control speed, position, and torque.

Horsepower is calculated by multiplying torque (in ft/lb f) by speed (in rpm) and dividing the product by a constant 5252. This means that there are many combinations of torque and speed that will in fact fall in line with a specific horsepower. Two servo motors can have relatively similar horsepower numbers but still operate differently. This means that every job must be understood by determining the outcome desired.

For example, both a rider lawn mower and a go-kart may have the same horsepower, but they differ in how they are geared and their motor's rated speed. One will have a higher speed, while the other will be capable of pulling more load (or cutting more grass)

Similarly, when selecting a servo motor for a specific job, one must make sure the job falls under the motor’s torque/speed curve.

A torque/speed curve shows how a motor’s torque production varies throughout the different phases of its operation. This curve is crucial in understanding the kinds of jobs that any particular motor is designed to handle. To be safe, a good rule of thumb when selecting a servo motor is to take the worst-case scenario of torque and speed a job will require and make sure that this falls inside the continuous operating region of the system’s torque/speed curve. This will ensure that the motor selected will be sufficient at any given time.

The other critical factor one must take into account when selecting a servo motor for a specific job is the inertia of the load, which has a direct impact on what kind of motor is required. To correctly choose a motor, taking into account inertia, a number known as the inertia mismatch ratio must be calculated for a job. This number reflects how much bigger the inertia of the load is in reference to the inertia of the motor.

I don’t recommend this number going too far beyond 10::1. That is, the inertia of the load shouldn’t be much more than 10 times the inertia of the rotor in the motor itself. I’ve seen this recommendation not followed closely, but as this number grows higher—the inertia of the load is more than 10 times the inertia of the rotor—it’s difficult to expect a very dynamic performance from the motor.

The final pieces of information to consider when selecting a servo motor are the physical limitations and constraints presented by the specific job. These rules to sizing a servo motor correctly can be applied to motors that come in all physical sizes. Servo motors can range in size from as small as a roll of quarters to a weight of 50 lb to 60 lb.

So depending on a project’s physical requirements and space considerations, a number of different physical size options are available. Thankfully, the requirements regarding speed, torque, and inertia remain the same.

John Brokaw is an application engineer for Valin Corporation.

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