Economical motor sizing for peak loads
MTS Systems Automation Division
New Ulm, Minn.
Edited by Miles Budimir
Until a few years ago, designers looking to power a linear-motion-control application faced three imperfect options: traditional electric motors or hydraulic or pneumatic cylinders. Hydraulic actuators have many inherent problems, such as high cost, leakage, and inefficiency. Pneumatics are less expensive but require a fair amount of maintenance, and have accuracy and stiffness limitations.
That leaves rotary-to-linear conversion as the preferred means for most linear applications.
There are several ways to convert rotary motion to linear travel. Belts and pulleys provide fairly inexpensive linear motion when coupled with a rotary motor. However, belt elasticity makes control difficult when moving large masses. Over time, accuracy further diminishes as the belt stretches and pulleys wear. Ball screws provide stable motion and are easy to control, but have limited velocity, particularly over long traverses. Backlash is also a real concern with ball-screw systems, and changes as the system ages. They can be fairly inexpensive if high accuracy isn't required. High-accuracy, low-backlash ball screws are costly and require a great deal of maintenance.
Linear motors now offer a better option, particularly in applications where speed and accuracy are key design targets. Two basic types of linear motors are iron core and ironless. Iron core motors provide higher forces for their size, but exhibit large force variations due to the magnetic attraction between the coil and magnet track. They also require heavy bearing systems to withstand the high preload caused by the attraction of the iron core to the magnets. Also, the higher mass limits its acceleration and velocity.
Ironless linear motors are not as powerful given their size, but provide extremely high acceleration and velocity, faster settling times, and exhibit uniform force over the entire range of motion. Smaller guidance systems can be used because there is no magnetic preload between the coil and the magnets. Currently, only the physical limits of the guidance and positioning systems limit motor performance. The accuracy of the ironless motor is as good as the associated positioning device, because lack of cogging and ultrafast control systems allow virtually unlimited opportunity to improve positioning accuracy and optimize motion profiles.
Ironless linear motors are sometimes the only solution available for critical requirements, and can be very price competitive with precision ball screws. Neither belts, rack-and-pinion systems, nor ball screws perform at the level of linear motors if long travel lengths, accuracy, and speed are important system requirements.
The capabilities of the linear motor have opened up new opportunities in many existing markets, and spawned new advancements in automation technology. As linear motor use increases, the cost of these motors and their associated linear systems is decreasing. Price advantages attributed to other approaches to linear motion have decreased dramatically in the last couple of years. As direct-drive linear motors become more competitive from a cost standpoint, the uniform motion, high-velocity capabilities, and low maintenance features of ironless linear motors make them a clear choice in many applications where high throughput and maximum performance are required.
Consider these variables when sizing a linear motor.
Analyze the motion profile: The motion profile dictates the required force and duty cycle. From this profile, determine peak velocity of the motor and the maximum acceleration needed for the application. Combining the worst-case acceleration and peak velocity gives the worst-case force needed as well as the highest back EMF.
Calculate the motor force: To calculate the required motor force, use F = ma. Consider mass of the load, including the motor and heat sink. For simplicity, change the acceleration to a g force. Use either 64.4 ft/sec2 or 19.6 m/sec2 to determine the g force. For example, a 10-lb load accelerated at 2 g's will need 20 lb of force. The acceleration will have already been calculated from the motion profile. Remember to add in the force needed to overcome friction.
Calculate the duty cycle from the motion profile: Given the duty cycle, determine the RMS force required in the application. The RMS force requirement must fall within the continuous rating of the motor.
Calculate voltage requirements: Determine the voltage needed to overcome back-EMF by multiplying peak velocity by the back-EMF of the motor. Add this value to the voltage drop across the motor coil. Calculate voltage drop by multiplying the current required by the hot resistance of the motor. When these are added together, they must be less than the available bus voltage. Most systems require that the available bus voltage be at least 20% higher than the motor requirements.
Recalculate the system requirements: This is an iterative process. As the motor size increases, the force will go up. So it sometimes takes a few passes at the whole process to be sure that the motor is sized correctly.
This is a simplified description of the linear motor sizing process. There are many variables that need to be investigated to ensure that the application is thermally, electrically, and mechanically compatible with the selected motor. For instance, some applications need to minimize radiated heat. This may require a greatly oversized motor to reduce the generated heat. Applications that require extremely smooth motion may also require special considerations.