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Linear motors step out

Aug. 1, 2000
Engineers can choose from several types of linear motors. When the application calls for quick, precise linear motion, a linear step motor may be the choice.

Some applications that require a linear motor are best served with a linear step motor. One example is an application that requires moving a tray of radioactive fluid held in containers. The tray must move in small, precise, smooth motions to prevent tipping and spilling the fluid and the resulting contamination. After evaluating several solutions, engineers chose a linear step motor, mounting the tray on the motor. It smoothly moves the tray in small increments, 12,500 steps/in., meeting the application’s throughput requirements. The motor runs open-loop, which made this a low-cost solution as no feedback device is needed.

Another application involves welding, Figure 1. Parts constantly move on a conveyor belt that varies in speed. A weld head must adjust its position to spot weld parts at precise locations while the parts are in motion. A linear step motor can make the quick adjustments in position and velocity to compensate for the conveyor’s speed fluctuations sensed by an encoder.

Linear step motors generally operate to travel lengths of about 10 feet. Beyond that length, run-out error becomes significant and it is difficult for manufacturers to hold flatness tolerances.

A linear step motor, like a linear servo motor, provides quick, precise moves in short increments. With a linear step motor, though, once peak current is set, it does not require parameter tuning. Thus, system setup time is low.

As mentioned earlier, these motors can operate open-loop, eliminating the cost of encoder feedback. This makes it simpler to change the length of travel by simply changing the platen. A new feedback device is unnecessary.

Like rotary step motors, linear step motors:
• Have a high pole count. Industry standard is 25 poles per inch. With microstepping drives these motors can give 10,000 or more steps per in.
• Do not accumulate position error over time (because of the pole structure), enabling good repeatability.
• Offer brushless design.
• Can be repeatedly stalled without damaging the motor.
• Are easy to construct and are one of the least expensive types of linear motors.

Also like rotary step motors, linear step motors have a few constraints. These motors may experience position and velocity oscillations during movement. External damping can combat these disturbances, as can modifing the normal sinusoidal phase currents to actively control resonance, which is available on newer drives. When internal sensors sense the resonance, additional current is commanded to create a torque to mitigate the oscillation. One drive, for example, uses accelerometers mounted in the forcer to sense vibrations. The drive then closes an acceleration loop to create a smooth linear motion.

Friction, whether coulomb or viscous, is another constraint that can cause error in the final position as the motor comes to rest.

And, unlike rotary step motors, there are no commercial standards for linear step motors. Rotary motors have standard frame and shaft sizes. By contrast, each linear motor has a different mounting configuration, requiring custom interfacing. This can add cost and development time.


A Sawyer motor, Figure 2, helps illustrate the operation of a linear step motor. The Sawyer motor is one of the simpler linear step motor configurations; more complex motors build on the same physical characteristics. As with other linear motors, the stationary element (stator) is frequently called the platen. It is a series of equally spaced teeth machined from one piece of steel. In a rotary step motor, the stator teeth are used repeatedly during rotation. In a linear step motor, each platen tooth is used only during a portion of the move.

The moving element of a linear step motor, the forcer, contains the permanent magnet and the phase windings. For step motors, it is generally impractical (and expensive) to insert the windings in the platen, although it is done for other linear motor types. The length of the platen, less the forcer length, determines the maximum travel distance for the motor.

The platen provides a passive return path for the magnetic flux. With windings on the forcer, multiple units can operate from the same platen. Thus, engineers can design machines with linear motors to perform parallel operations. Since the forcers usually operate open-loop, the same drive can power multiple units.

Cabling is carried along during movement. It must be rugged enough to withstand constant flexing, and positioned so that it does not interfere with the machine operation.

In the forcer, the flux from the permanent magnet passes through Phase A, the platen, and then Phase B. The electromagnets steer the flux into the correct air gap, Figure 2. First, a positive current is applied to Phase A with Phase B unenergized. The electromagnets guide the flux to the A1 pole face, causing it to align (for an unloaded motor). The A2 pole face is 180 degrees out of phase from A1, so no flux crosses the air gap at that point. If Phase A is relaxed and Phase B energized, the flux is then guided to the B2 pole face. When this pole face aligns, the forcer has moved one-quarter of a tooth pitch to the left.

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Maintaining air gap

A bearing system maintains the air gap between the forcer and platen. Two types of bearing systems are commonly used on linear step motors: roller and air. A roller bearing places the forcer on wheels, keeping a constant air gap at all times. An air bearing uses a constant-pressure pneumatic source to float the forcer over the platen. However, the gap varies slightly as a function of position and load.

For both bearing types, the magnetic attraction between the forcer and platen is much larger than the weight of the forcer. This allows the motor to be oriented in any direction, even upsidedown. Air bearings have the lower friction coefficient, which results in better system dynamic performance.

Because there is no mechanical contact, there is no wear, so maintenance is minimal. However, engineers must weigh this against the complexity and cost of adding a pressurized air source to the system.

Engineers should consider two other factors when specifying air bearings because the actual gap varies as a function of load and position. First, the force ripple is more pronounced than the torque ripple in an equivalent rotary system. Studies have shown variations of over 20% between the maximum and minimum available force as a function of position. Second, because the forcer floats, it can move in all three dimensions. An improperly balanced load can induce a roll and a yaw on the unit. High acceleration and deceleration rates can cause the forcer to pitch. The magnetic force between the forcer and platen will serve to keep the teeth aligned. If the load applies significant external forces, though, engineers may have to use mechanical guides to keep the forcer properly oriented, or choose another motor. In most cases, if a pressurized air source is available, air bearings will outperform mechanical ones.

Calculating positional accuracy

An open-loop linear step motor can have lower positional accuracy than a closed-loop linear servomotor. Several independent factors contribute to the overall forcer positioning accuracy of a linear step motor and are calculated by the following equation. The values in parenthesis are for a commercially available product, the L20 linear step motor.

Etotal = Ec + Ed + Eh + Ep + Er + ET


Ec = Cyclic error (±37.5 μm)
Ed = Unidirectional repeatability (±2.5 μm)
Eh = Hysteresis (12.5 μm)
Ep = Cumulative platen error (0.1 μm/mm)
Er = Random platen error (637.5 μm)
ET = Thermal expansion error (11.4 μm/m per degree C)

The cyclic error is the repetitive error of every pole pitch and is attributed to the motor magnetics. Unidirectional repeatability refers to the motor’s ability to return to the identical position on the platen from the same direction and with the same velocity. Hysteresis includes both the magnetic nonlinearities and the mechanical friction. Cumulative platen error is the linear error of the platen as measured on the body of the motor. Random platen error includes all sources not covered by one of the other terms. Finally, since the platen is a single piece of steel, a thermal expansion term must be included. Adding all the numbers for the L20 motor, for example, it has a worsecase accuracy of 90 mm, plus the cumulative platen error, plus the thermal expansion error. The last two values are platen-length dependent and cannot be calculated as a single number.

The mechanical calculations for linear systems are identical to rotary ones. Consider the following example, again using the L20, a 10 lb load must move 40 in. in 1 second. Assume the trapezoidal move profile shown in Figure 3, where the total move time is split into quarters. The maximum velocity required is 53.2 in./sec. Thus, the minimum acceleration rate required is:

Figure 4 shows the maximum available force as a function of speed for the L20. At the maximum velocity of 53.2 in./sec, this linear step motor can provide 14 lb of force. Since its forcer weighs 2 lb, the peak acceleration rate is:

The desired move requires 47.5% of the available force. A rule of thumb for designing undamped step motor systems is to keep the required force under 50% of that available to have a 100% safety margin to account for possible resonance problems. Thus, the L20 would work in this application.


1. Nasar, S., “Linear Electric Motors - Past, Present and Future,” 16th Annual Symposium on Incremental Motion Control Systems and Devices, Champaign, IL, June, 1987, pp. 1-6.

2. Goodnick, S., “Active Damping Keeps Steppers Spinning,” Machine Design, November 9, 1995, pp. 76-80.

3. Hinds, W. and Nocito, B., “The Sawyer Linear Motor,” from Theory and Applications of Step Motors, B.C. Kuo, Ed., West Publishing, St. Paul, MN, 1974, pp. 327-340.

4. Ellerthorpe, S. and Blaney, J., “Force Estimation for Linear Step Motor with Variable Air Gap,” 25th Annual symposium on Incremental Motion Control Systems and Devices, San Jose, CA, June, 1996, pp. 327-335.

Scott Ellerthorpe is senior engineer, Power Products Group, Compumotor Div., Parker Hannifin Corp., Rohnert Park, Calif.

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