# Linear Shaft Motor 50 Percent More Efficient than Coreless Linear Servos

## Jeramé Chamberlain, Sales Manager, Nippon Pulse America

Dr. Harry C. Powell, University of Virginia

Linear motors have gained a name for themselves as being a high-precision and power-efficient alternative to conventional rotary-to-linear transmission systems. How is this possible?

Well, let’s look at the Ball Screw, which also can be considered, in its own right, a high precision rotary-to-linear transmission system. The Ball Screw is typically only 90 percent efficient[1]. When we add the efficiency of the servo motor (range from 75 to 80 percent[2]) and losses that will be introduced by the coupling (and if using a gear box), it is possible that only 55 percent of the power we are supplying is going towards work. When we compare the typical linear motor, where the motor is driving the load linearly, we can quickly see why the linear motor has gained a name as being more power-efficient.

Linear motors have been described as cutting a rotary motor open and rolling it out flat; in fact, some of the first linear motor designs were just that. The Iron Core “flat” linear motor came on the market and earned market share as a powerful and efficient alternative to other forms of linear transmission systems. Though the design was not very efficient, due to the many losses caused by eddy currents, cogging, etc., it was better than other forms of linear transmission systems from an efficiency standpoint. These losses also worked against the high precision nature of the linear motor.

The Coreless (U-shaped) linear motor was intended to address many of the issues of the Iron Core linear motor. While this new design addressed the issue raised by losses from eddy currents and cogging, it also had new issues that limited its use in the ultra high-precision market: namely, lower motor stiffness and greater heating issues.

For the ultra high-precision market, the linear motors were a godsend, offering the promise of being infinitely positionable and high efficiency. Reality set in when heat from the inefficiency of the linear motor was channeled directly to the work point. While it did increase the amount of work the linear motor was able to do, the thermal growth caused by generated heat from the inefficiency made positioning in the submicron world very difficult, if not impossible.

To increase the efficiency of the linear motor, it was required to go back to the very basics of its design to optimize every aspect to have the most power-efficient linear transmission systems possible, while having the highest level of stiffness possible.

The basic law behind motor design is Lorentz force law[3]. Lorentz law simply states: the amount of force (F) a motor can generate, is equal to the current (I) in the winding, times the magnetic field strength (B), times the vector cross product (X), times the Length of wire in the wire (L). So to develop a more efficient linear motor, the amount of current must be reduced. In order to do this and keep the same force output, the other three parts of Lorentz force law must be increased and optimized. The designer of the Linear Shaft Motor, along with a number of ultra high-precision machine tool manufacturers, did just this. In fact, in a recent study, the University of Virginia (UVA) found that the Linear Shaft Motor uses about 50 percent less power input to achieve the same work output of a comparably rated coreless linear motor[4]. Let’s look at each aspect of Lorentz force law and see how they were able to achieve this increase in the efficiency of the Linear Shaft Motor.

## The vector cross product (X)

Fleming’s law (often called the left-hand rule) helps us to understand that the optimal crossing vector for current to cross the magnetic field to create linear motion is 90 degrees. The design of a typical linear motor is for the coil to have between 30 to 80 percent of its length at a 90-degree angle to the magnetic field. The rest of the coil is basically a return path, adding losses due to added resistance. Even worse, this return path can generate forces that oppose the intended forces. The cylindrical design of the Linear Shaft Motor, on the other hand, allows for 100 percent of the coil to be at the optimal 90-degree crossing vector, and thus there are no forces generated outside of the intended linear force.

## The Length of wire in the wire (L)

This is where the design gets tricky. Adding too much length will increase losses due to added resistance. The Linear Shaft Motor finds the optimal balance between length of wire and losses due to added resistance. For example, in the linear motors tested by UVA, the length of the coil for the Linear Shaft Motor was about 1.5 times the length of the coreless linear motor.

## The magnetic field strength (B)

Where most linear motors use back iron to redirect the magnetic field, the Linear Shaft motor features a patented magnetic pattern which uses the natural repelling nature of the like magnetic field to optimize the magnetic field strength. This is achieved by kinking and redirecting the magnetic field so the maximum field strength is located at the current crossing point.

The amount of force that may be developed in a given magnetic structure is a function of the flux density at the air gap between the components that move relative to the stationary segment. As the reluctance of air is roughly 1000 times greater than that of steel and is directly proportional to the air gap length, minimizing it will reduce the magnetomotive force (MMF) required to generate a given field strength. Since MMF is also a direct function of the amount of current supplied, reducing this parameter will reduce power losses, and this has a profound effect since such losses are proportional to the square of the current.

As we can see, thought was given to every aspect of the design of the Linear Shaft Motor to make it the most efficient motor possible. But how is this useful and practical in general automation? Higher efficiency in a linear motor is extremely useful. Let us look at only two areas: heating and life-time cost.

All linear motors will heat up, due to wasted energy. When this heat is generated it must go somewhere. The first major side effect of heat is the thermal growth of the load the coil is attached to; also, you are heating the bearings, grease, and any sensors attached in the general area. Over time, the heating and cooling cycles can have negative effects on both mechanical and electronic components. Thermal growth is likely to cause issues with binding and increased friction. In the same test conducted by UVA, it was observed that, even though both motors are attached to identical plates[5] and had equal temperature rise within the coil, the heat transferred from the Linear Shaft Motor was about 33 percent less[6] than that of the comparably rated coreless linear motor.

By using less energy, of course the cost of operating the system will also decrease. Using the U.S. average cost per KwH of 12.17 cents, the annual operating cost of a coreless linear motor would be $540.91, while the operational cost of the Linear Shaft Motor would be only $279.54[7].

There are many options to select from when considering a linear transmission system for your application. While designed with the needs of the ultra high-precision machine tool manufacturers in mind, the power-efficient Linear Shaft Motor can offer many advantages to your application.

- [1] Wikipedia http://en.wikipedia.org/wiki/Ball_screw Subheading "Advantages"

The Number Factory https://www.numberfactory.com/Lead Screw Ball Screw Formulas.htm Box at bottom of page showing typical efficiency.

Nook Industries http://www.nookindustries.com/ball/BallGlossary.cfm#Efficiency under definition for "Efficiency" - [2] Motion System Design "How efficient is your servomotor" Sep 1, 2002 by John Mazurkiewicz

Energy Efficiency & Technology "Efficiency in Coreless Servomotors" September 1, 2009 by Paul McGrath - [3] Wikipedia http://en.wikipedia.org/wiki/Lorentz_force Subheading "Force on a current-carrying wire"
- [4] S250T from Nippon Pulse America to a 210-2-B-NC-WD1-S from Parker, both generating 10 pounds of force for 24 hours.
- [5] Plates 100mm x 150mm x 10mm
- [6] Both motors operating at 10 lbs of force for 24 hours. Temperature rise @ coil 41.3°C, @ coreless linear motor plate 30.8°C, @ Linear Shaft Motor plate 23.1°C.
- [7] Measured at AC supply to servo drive.