Machine Design

Sorting out gearhead semantics

An understanding of backlash, lost motion, and repeatability is the key to selecting servo gearheads.

John Landry
alpha gear drives
Bartlett, Ill.

Edited by Kenneth Korane

Precision gearheads are essential components of many servosystems, letting small motors control large loads. The TP+ gear reducer family, for instance, features small units with nominal output torque from 133 to 354 lb-in. at 3,300 to 5,500 rpm, to larger ones rated at 53,100 lb-in. at 1,500 rpm.

Backlash is the amount by which the tooth space exceeds the thickness of an engaging tooth. Backlash clearance is necessary to accommodate manufacturing variations, provide space for lubrication, and allow for thermal expansion.

Manufacturers determine gearhead stiffness by rigidly mounting a unit, locking the input, applying a series of torque loads to the output and, for each value, measuring angular displacement at the output. Stiffness, or torsional rigidity Ct = T/ , shown as the slope of the line near gearhead's rated capacity. When testing is bidirectional, the difference between the data upon reversal indicates lost motion or torsional backlash as a function of applied torque. One component of lost motion is clearance backlash, which alpha gear measures at ±2% of maximum torque.

Precision gearheads are essential to many servosystems. They reduce speed and inertia while increasing torque, letting compact servomotors control large loads quickly and economically. Without a gearbox, direct-drive systems require larger motors, cables, drives, and amplifiers — not to mention more energy.

Designers must consider backlash, lost motion, repeatability, and precision to properly spec servo gearheads. The trouble is, there's no standard rating method or terminology, which can create a lot of confusion. For instance, backlash and lost motion are often erroneously believed to describe a gearhead's output motion relative to input. This article clarifies the difference.

Backlash is the amount by which the tooth space exceeds the thickness of an engaging tooth, as measured along the pitch circle of the gears. It is sometimes termed slop, lash, free play, or simply play.

Backlash is necessary to accommodate manufacturing variations, provide space for a lubricating film, and allow for thermal expansion. For this reason, it's often referred to as clearance backlash.

Manufacturers of servomechanical transmissions typically hold the input shaft rigid and measure backlash at the gear-head output shaft. However, because there is no standard test, ambiguity exists among published values from different manufacturers.

Reputable manufacturers apply torque when measuring backlash and call the result torsional backlash. Others call it lost motion because the output rotates but the input does not, but the terms are synonymous. Contributors to lost motion include gear-teeth deflection, bearing clearances, as well as friction and clearance backlash. Common sense tells us that the magnitude of applied force greatly affects the value of lost motion. Other factors include tooth shape and manufacturing quality. Manufacturing irregularities can produce uneven tooth load distribution and skewed tooth engagements, resulting in deflections that affect torsional backlash.

Some manufacturers claim their gearboxes have zero backlash, due to the negative connotation associated with backlash. They are actually referring to free play, which is much different than torsional backlash. And claims of mechanical transmissions with zero clearance or free play are dubious at best.

Lost motion is a principal cause of positional un-certainty in motion systems. Manufacturers typically do not publish values for lost motion, because it is a function of applied torque in a particular application. However, a useful alternative is gearhead stiffness, sometimes termed torsional rigidity or torsional stiffness. This parameter, in units of torque per angular displacement (Nm/arc-min or lb-in./degree), describes a gearhead's "spring effect" or stiffness.

To test for stiffness, manufacturers rigidly mount a unit, lock the input, apply a series of unidirectional torque loads to the output and, for each value, measure angular displacement at several positions around the output-shaft circumference. Results become linear when torque load nears the gearhead's rated capacity and the slope of the line defines torsional stiffness. For bidirectional testing, the difference between data on reversal indicates lost motion as a function of applied torque.

Backlash and lost motion are not issues when gears turn only in one direction. However, any motion reversal (and some cyclical axial motions with high inertia) requires that teeth first disengage then reengage on opposite tooth surfaces.

Fortunately, servocontrol systems easily compensate for backlash — if backlash values are known for the loads and operating conditions. Obtain control-feedback data at the critical point-of-motion rather than at the end of the motor shaft. Although a sensor may be needed for motor control, an additional transducer for positioning control bypasses the series of individual components and their lost-motion characteristics. Drive manufacturer's software can also compensate for backlash by commanding the system to over or undershoot calculated positions based on the amount of backlash.

Torsional stiffness is another critical factor. If the drivetrain is not rigid enough to resist deflections under dynamic load, the output shaft will lag the motor shaft. Attempts to increase performance will be frustrated by servo instability (position hunting) or unacceptable settling time. Longer duty cycles are needed to let the system stabilize, which compromises throughput. Otherwise, unacceptably large positioning variations will result.

No servocontroller program or adjustment can fully compensate for insufficient stiffness. Thus stiffness/rigidity characteristics of the motion components fundamentally limit a system's dynamic response. The types of couplings and shafts also have a large impact on system stiffness and dynamic response.

Planetary gearheads maximize stiffness and torque capacity when the ring gear is part of the housing rather than just fastened to it. Gearheads with built-in ring gears also have higher torque capacity for a given size. And even if a lack of stiffness and the resulting oscillations are tolerable, premature fatigue failure of gears, shafts, and couplings may result.

Repeatability. The goal for many motion systems is accurate indexing — consistently positioning to a desired location. This is termed repeatability. Backlash and lost motion play minor roles here. The largest impact on repeatability comes from the accuracy of gear teeth or cam profiles, as well as the accuracy of the servomotor's positional feedback devices.

Precision. Precision relates to repeatability, speed, and the ability to cycle at peak loads in opposite directions. Gear-teeth inaccuracies, system backlash, and large manufacturing tolerances will cause gearheads to overheat, misindex, and can lead to fatigue failure. Torsionally rigid gearboxes with minimal torsional backlash have the greatest precision.

Design limitations. Planetary gearhead manufacturers generally specify backlash and, sometimes, torsional backlash. Cycloidal or harmonic gearheads, on the other hand, use cams and rollers or flexible splines preloaded together that roll in relation to one another. Manufacturers of these devices often claim zero backlash, but state values of lost motion in the 1 to 3-arc-min range. Thus, they imply the designs are more accurate than planetary gearheads. This is un-true, because planetary gearhead suppliers generally apply higher torque when measuring backlash than is the case with cycloidal or harmonic gearboxes. As stated previously, the magnitude of torque applied during measurement has a large effect on torsional-backlash values.

Another important point with cycloidal and harmonic designs is that preloading extracts a significant penalty in efficiency. Preloading can generate frictional losses as high as 50% compared to 10% or less for conventional gear mechanisms of similar size and construction. Inefficiency causes problems during small incremental moves because the torque required to overcome friction exceeds the overall torque requirement of the load, resulting in over-shoot and jerky motion. It also generates heat, which limits speed in cyclical applications and operating time in unidirectional ones.

A further limitation of many antibacklash designs is that elastic preloading causes friction to vary as the gearbox shaft rotates. This can lead to velocity-dependent torque ripple, which poses significant control problems at constant speeds near the natural frequency of preloaded elements. Such designs are unsuitable for applications requiring smooth rotation, such as laser cutting, painting, gluing, and contouring.

It is essential to keep in mind the objectives of the motion system and the gearhead's influence on system performance. For instance, many people instinctively specify zero backlash even though 2 arc-min may be acceptable. Remember, zero backlash does not mean exact positioning. The rigidity, lost motion, and dynamics of the control system together determine how close the system will get to perfect positioning.

alpha gear drives Inc., (888) 534-1222,

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