Motion control systems usually operate under rotary power, but as many as half are employed in linear applications. For many designers, this means selecting and specifying a rotary-to-linear converter, the details of which also play a role in the selection of the motor itself. Here we consider the most common linear transmission devices, including ball and lead screws, belt drives, and rack-and-pinion gearing.

Ball and lead screws

Many precision motion systems employ screw drives to convert rotary motion into linear motion. The two types we will focus on here are lead screws and ball screws.

Lead screws are great for moving heavy loads at a fairly low price. However, the friction coefficient between the nut and screw tends to be higher than with ball screws, so more torque is required to move them. Usually a plastic or metal nut rides on the shaft with a certain pitch or thread count.

Ball screws, on the other hand, employ a nut that holds a series of small ball bearings in place that ride on a special screw. The balls create a much lower frictional coefficient, and if lubricated, will exhibit rolling hydrodynamic friction. Ultimately what this means is a slightly lower torque will be required to move the load. This comes at the expense of a higher initial cost than with lead screws.

Screw drives can move heavy loads with ease thanks to the mechanical advantage inherent in the threads, but the nature of thread count and pitch means these linear motion devices have a tough time moving loads quickly. As a result, steppers acting on screws usually have to run faster to get loads moving at an acceptable rate. This has both positive and negative consequences.

First the positive. Since the stepper has to run faster, it will most likely be running outside of its resonance range. This helps overcome annoying and sometimes harmful vibrations that occur at lower speeds. This is especially important in rigid systems, which tend to translate and sometimes amplify structure-borne noise and vibration generated by the stepper.

The negative impact of running the stepper faster is that it puts the motor outside of its high-torque range. Steppers typically generate high torque at low speeds and drop off quickly as pulse rates increase. For this reason, designers need to pay careful attention to motion ramp profiles to avoid losing synchronism when pushing the envelope.

Another concern when using steppers with screws is the basic quality of the component. A lesser-quality screw may have more dramatic runout, which in extreme cases can cause binding, or at the very least, higher constant (frictional) torque. Although this can be overcome, it does require more from the motor. If this torque required is higher than what the stepper can produce at speed, it raises the risk of losing synchronism. The importance of sizing the stepper in conjunction with the drive component cannot be understated.

As with any motion system, inertia is critical with screws. Although the inertia of the actual load may be minimal, the screw’s own inertia often makes up for it. Screw inertia is determined by the following equation:

J=(πLρr4)

where ρ is the density of the screw, L is the length, r is the radius, and g is the gravitational constant. As the equation shows, the radius of the screw has the most influence on inertia. When driving lightly loaded screws, the greatest challenge facing steppers may be simply moving the screw itself.

Belt drives

Belts and pulleys are another common method for converting rotary motion to linear motion. Belts can range from narrow, edge-belt configurations to wide, flat-belt conveyor systems. In contrast to screw-based systems, steppers on belt drives can move loads very quickly. A larger diameter drive pulley translates to a faster linear speed. However, the load must be much lighter and have much lower inertia. Using a reduction stage can compensate for this at the expense of speed. The inertia of a belt drive system is given in the following formula:

J = Jd + (W1 + Wb)r2g

where J is the total inertia of the system (minus rotor), Jd is the inertia of the drive pulley, and Js is the inertia of the slave or driven pulley. W1 and Wb are the weights of the load and belt. The radius of the drive pulley is defined by r, and the gravitational constant is defined by g.

Steppers have a unique advantage compared to other motors when coupled with belt systems. Since steppers run open-loop and do not require feedback for positioning, they can move a beltdriven load quickly and have a very short settling time. Belt-driven systems are high compliance; they are “springy.” Since closed-loop servomotors (brush or brushless) require feedback for positioning, they inevitably receive (and act on) signals contaminated by oscillations produced from the “spring” in the system. This can be tuned out, but it may be at the expense of longer settling times. Thus, when it comes to belt drives, steppers offer a distinct advantage if the objective is to produce short, quick moves.

Another beneficial interplay between belts and steppers stems from the dynamic nature of the components themselves. Steppers consist of a toothed rotor and stator, the dynamics of which produce a cogging effect. This cogging, in part, causes stepper vibration, which is effectively damped by belt compliance, culminating in a quieter, less “buzzy” system.

Not everything takes care of itself, however. One concern with belt-driven systems is belt tension. Tighter belt tensions translate to higher overhung loads on the stepper motor shaft. If these loads become excessive, they are likely to cause premature bearing wear.

Rack-and-pinion gearing

Rack-and-pinion systems are simple and fairly cost effective. As with belt-and-pulley configurations, step motors can move loads very quickly through a rack-andpinion drive. Moving a very heavy load is not so easy, however. A rack-and-pinion differs from a true gearbox in that there is no reduction. Thus, reflected inertia goes directly into the motor without being decreased at all. The inertia of a rack-and-pinion system is given by the same equation for that of a belt and pulley. However, in this case “r” is the radius of the pinion gear, and the weight of the rack replaces the weight of the belt.

As with screws, rack and pinions are rigid systems, and thus have a tendency to transmit vibrations produced by the stepper. The remedy here is to use a smaller diameter pinion gear and run the motor faster to get out of its resonance range. The smaller pinion gear will also help when moving heavier loads, if required to do so.

Backlash is also a concern when using a rack and pinion. Today’s high-torque hybrid steppers are typically accurate to 3 to 5 arc minutes. This high accuracy can be swallowed up by backlash in lower quality gears, and must be accounted for when positioning. Still another concern is noise; the meshing of gear teeth sometimes creates undesirable acoustics.