As an essential component of a servo system, when selecting a precision planetary gearhead the designer needs to understand backlash, lost motion, repeatability and precision. Wittenstein explains.
Precision planetary servo gearheads are often an essential component of a servo system. But in order to select the correct servo gearhead, a designer must consider backlash, lost motion, repeatability and precision. There is, however, some confusion regarding these factors.
Backlash is the amount by which the width of a gear’s tooth space exceeds the thickness of an engaging tooth measured at the pitch circle of the gears. It is an angular quantity due to the gear’s circular geometry, and can be termed clearance backlash.
Backlash is necessary for clearance to accommodate manufacturing errors, provide space for lubrication and allow for thermal expansion of components.
In servo-mechanical transmissions, backlash is measured at the output shaft of the gearhead while holding the input shaft rigid. Quality manufacturers will apply some amount of torque when measuring backlash and call the result Torsional Backlash, others will call it lost motion because it involves rotating the output with no rotation at the input. The manufacturing quality of the gearhead and the shape of the teeth are the major determinants of torsional backlash.
Some manufacturers claim zero backlash in their gearboxes due to the negative connotation associated with backlash, but this claim is in regard to the actual free-play and much different than the torsional backlash.
Lost Motion describes the condition in which an input to a mechanism yields no corresponding displacement at the output, and is one of the principal causes of positional uncertainty in a motion system. Lost Motion is not typically specified as such, since it is a function of the torque applied in a particular application. However, a useful alternative is the stiffness of the gear-head, sometimes termed torsional rigidity or torsional stiffness. This characteristic, in units of torque over an angle (Nm/arcmin or in-lb/degree), denotes a gearhead’s ‘spring effect’ or stiffness.
Stiffness of the gearhead is determined by rigidly mounting the unit, locking the input, applying a series of unidirectional torque loads to the output and, for each value, measuring the angular displacement at a number of positions about the circumference of the output shaft. The resulting data series is linear when the torque load nears the capacity of the gearhead. The slope of the line in this area defines the torsional stiffness in units of force per angle increment. When this test is performed with bi-directional rotation and torque application, backlash contributes to the results. The difference between the data upon reversal indicates the lost motion or torsional backlash as a function of the applied torque.
Backlash, or lost motion, is not an issue in the case of continuous single direction motion. Here, the resistance of the load forces the meshing gear teeth into contact that is maintained by constant unidirectional gear rotation. However, any reversal of motion (and some cyclical horizontal motion with high inertia) requires that the teeth first dis-engage then re-engage on the opposite tooth surfaces. Unless programming of the servo control system compensates for backlash (and the values for backlash are correct), this will give rise to positioning errors in many applications. If you know what the backlash value is, and more importantly what it will be after many hours of operation under load, you can easily compensate for it in your servo system.
Backlash can be negated by obtaining position data for control feedback at the critical point-of-motion rather than at the end of the driving motor shaft. While a motor shaft-mounted sensor may be needed for control of the motor itself, locating an additional transducer for positioning control at the critical motion point bypasses the train of components along with their lost motion characteristics. Another method of compensating for backlash is in the drive manufacturer’s software.
For single direction motion systems, where backlash has been shown to be inconsequential, adequate torsional stiffness is critical to achieving duty cycle objectives. Consider a uni-directional rotary mechanism for cut-off applications. The intermittent cutting forces result in instantaneous high torque demands. These torque ‘spikes’ through the gearhead input cause the gear teeth to deflect or move, the output shaft to twist, etc., which may produce erroneous cuts.
The inertia of the knife is very important here as well, because the higher the inertia, the greater the effect the stiffness will have in the control of the system. In these dynamic applications, a gearhead is used because the gearhead ratio has an exponential effect on the control of the system. This allows a motor to use its energy to move the load quickly.
A controlled motion profile for this cut-off system entails accelerating and decelerating the knife. If the torsional rigidity of the drivetrain is not rigid enough to resist deflections due to the dynamic loads, the output shaft will lag the motor shaft and its feedback transducer (resolver or encoder).
Unlike backlash, no servo controller programming or adjustment can fully compensate for insufficient stiffness.
For a gearhead, maximum stiffness and torque capacity are achieved when the ring gear is manufactured integral to the largest torque capacity and internal component size for a given envelope size. The higher the stiffness, the easier it is to control a system’s accuracy of movement.
It is equally important to consider the torsional rigidity of all components between the output shaft of the gearhead and the load to get a true measurement of the lost motion in a system.
The objective for many motion systems is accuracy in indexing or moving and the desire for positioning to a location to be repeated consistently – called repeatability. The largest impact on repeatability is the accuracy of the gear teeth or cam profile, as well as the accuracy of the positional feedback device on the servomotor.
Precision relates to repeatability, speed and the ability to cycle at peak loads in opposite directions. If the inaccuracies of the gear teeth, backlash in the system or manufacturing tolerances are great, the gearhead will overheat, mis-index or fatigue to failure. A torsionally rigid gearbox with minimal torsional backlash will allow the precision.
Manufacturers of planetary gearheads generally specify backlash, sometimes offering a specification for torsional backlash, which is the same as lost motion. Cycloidal or harmonic gearhead designs use cams and rollers or flexible splines that are pre-loaded together and roll in relation to one another. These designs often claim zero backlash,
but state values of lost motion in the one to three arcmin range. Therefore the semantics give the impression that these designs are more accurate than a planetary gearhead. This is untrue, because many planetary gearhead suppliers apply a higher torque when measuring the backlash than cycloidal or harmonic gearbox manufacturers.
An important downside of the cycloidal and harmonic designs is that pre-loading extracts a significant penalty in efficiency. Frictional losses due to pre-loading can be as high as 50% compared to 10% or less for a conventional gear mechanism of similar size and construction. This lack of
efficiency causes problems in small incremental moves.
A further limitation of many anti-backlash designs is that the elastic pre-loading causes variable friction at the output as the gearbox input shaft is rotated, which can lead to a velocity-dependent torque ripple. This may pose significant control problems at constant speeds associated with the natural frequency of the pre-loaded elements. These designs are not suitable for those applications requiring smooth rotation, such as laser-cutting, painting, gluing or contouring applications.
It is essential to keep in mind the objectives of the motion system and the gearhead’s significant influence in determining system performance. While many people may think they need zero backlash, the reality may be that backlash readings not exceeding two arcmins may be acceptable.
Considering the design elements
Gearheads offer a mechanical advantage, plus the ability to control large loads quickly in an economical fashion. A combination of precision, position, repeatability or reliability will determine the most suitable gearbox for the application. The rigidity, lost motion and dynamics of the control system as a whole will determine how close the system can come to perfect positioning.
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