Correctly sizing motors in a motion control application is more difficult than sizing an AC induction motor because not only must acceleration, deceleration and running torque be taken into account, but also the ability of the servo motor to tightly control the load’s speed, position or torque. This means the peak torque measurements must be calculated, usually during acceleration or deceleration, along with the running/normal torque. Also, the inertia of the system (the load’s resistance to change in speed) must be calculated to ensure that the motor/drive system will be able to control the load.

A motor’s continuous torque is its ability to produce the rated torque and speed without overheating. Intermittent torque indicates how much torque a motor can produce in a short period of time based on current limits of the drive and motor. The intermittent (or peak) torque of a motor can be much higher than its rated torque, and servo systems are usually designed to operate within that peak torque range when accelerating or decelerating the load.

Here’s a look at the key parameters to consider when sizing a servo motor.

**Load
**Correctly sizing a servo motor begins with knowing the load. This is also spoken of in terms of inertia. Generally speaking, the important figure is the inertia ratio, which is the ratio of the load inertia to the motor inertia, or Inertia Ratio = JL / JM where JL is the moment of inertia of the load and JM is the moment of inertia of the motor.

The motor’s moment of inertia can be found from the manufacturer data sheets. However, the moment of inertia of the load is a bit more complex. Basically, each component that is moved by the motor contributes to the total load inertia. This includes not only the load itself but any other mechanical components of the transmission system such as couplings, lead screws, rails, and so forth.

**Speed
**Another important factor is the speed or velocity. This involves knowing how far and how fast the load must travel. Knowing the inertia ratio can help with this as well as knowing the motion profile of the system. Figuring out what the motion profile is and knowing the system inertia helps determine the required speed, acceleration and torque.

**Torque
**Once the load and speed are known, calculate the required torque values. This can be determined from the motor’s torque-speed curve. Calculations need to be made to determine the required continuous torque, peak torque, and maximum motor speed. The required amount of continuous torque must fall inside the continuous operating region of the system torque-speed curve. The required amount of peak torque must also fall within the servo system’s intermittent operating region of the system torque-speed curve.

**Sizing Software
**The calculations involved with correctly sizing a servo motor are complex, but there are many different software programs available to make the selection process easier. For instance, there is free downloadable servo motor sizing software available at (http://www.sureservo.com/downloads_visualsizer.htm.) These programs calculate the torque, speed, and inertia requirements according to the user’s application specifications and are helpful for selecting the right size motor for the application.

Sizing software will ask for the system hardware that will be used (drive, motor, gearing, load), and will ask for a definition of the type of move the system will perform (i.e. the motion profile.) Providing the distance and time, or providing the distance and speed of the required move, will allow the software to determine the continuous torque and the peak torque required by the motor.

Sizing software can also help calculate the inertia mismatch of the load to the motor. A general rule of thumb is to keep the inertia mismatch to less than 10:1 (inertia of the load:inertia of the motor). While many servo systems can handle mismatches of much higher than 10:1, better system control and response will result with an inertia mismatch of 10:1 or less.

**A Word About Gearing
**The servo motor size directly affects other servo system components, so right-sizing the motor is critical. If a servo motor is oversized, it will need a larger amplifier than that required for a smaller motor. This means much higher hardware costs, and also increased energy requirements.

Servo motors generally run at speeds in the 3,000 to 5,000 RPM range, and in many applications the motor is paired with some type of gearing to increase output torque. Gearing increases the available torque by the gear ratio, so a 3:1 pulley system will increase available torque by a factor of 3 (neglecting efficiency losses). Gearing will also lower the inertia mismatch ratio by the square of the gear ratio, so a 10:1 gearbox will reduce the reflected load inertia by a factor of 100.

In many instances, gearing allows smaller motors to be used successfully, more than offsetting the cost of the gearing system. In many applications, adding a gearbox (or some type of gearing) can allow the use of not only a smaller motor, but also a smaller drive. Downsizing the motor and drive can sometimes pay for the increased cost of additional gearing, particularly when operational costs are considered.

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