MOTION SYSTEM
HANDBOOK
GEARING ESSENTIALS
Strain-wave gearing Strain-wave
gearing is a special gear design for speed reduction. It uses the metal elasticity (deflection) of a gear to reduce speed. (Strain-wave gearing sets are also known as Harmonic Drives, a registered trademark term of Harmonic Drive Systems Inc.) Benefits of using strain-wave gearing include zero backlash, high torque, compact size and positional accuracy. A strain-wave gearset consists of three components: wave generator, flexspline and circular spline. The wave generator is an assembly of a bearing and steel disk called a wave generator plug. The outer surface of the wave generator plug has an elliptical shape machined to a precise specification. A specialty ball bearing goes around this plug to conform to the same elliptical shape of the wave generator plug. Designers typically use the wave generator as the input (attached to a servomotor). The flexspline— usually acting as the output—is a thin-walled steel cup. Its geometry makes the cup walls radially compliant but torsionally stiff (because the cup has a large diameter). Manufacturers machine the gear teeth into the outer surface near the open end of the cup (near the brim). The cup has a rigid boss at one end for mounting. The wave generator goes inside the flexspline so the bearing is at the same axial location as the flexspline teeth. The flexspline wall near the brim of the cup conforms to the same elliptical shape of the bearing. This Circular spline conforms the teeth on the outer surface of the flexspline to the elliptical shape. That way, the flexspline effectively has an elliptical gear-pitch diameter on its outer surface. The circular spline is a rigid circular steel ring with teeth on the inside diameter. It is usually attached to the housing and does not rotate. Its teeth mesh with those of the flexspline. The tooth pattern of the flexspline engages the tooth profile of the circular spline along the major axis of the ellipse. This engagement is like an ellipse inscribed concentrically within Flexspline a circle. Mathematically, an inscribed ellipse contacts a circle at two points. However, gear This is a progression of teeth have a finite height, flex-spline tooth engagement with so two regions (instead of circular-spline teeth. The profile of two points) engage. Harmonic Drive gear teeth lets up to 30% of the teeth engage ... for The pressure angle of higher stiffness and torque than the gear teeth transforms gearsets with involute teeth.
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gearing — Motion System Handbook 8-17 V2.LE.indd 94
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the output torque’s tangential force into a radial force acting on the wave-generator bearing. The teeth of the flexspline and circular spline engage near the ellipse’s major axis and disengage at the ellipse’s minor axis. The flexspline has two less teeth than the circular spline, so every time the wave generator rotates one revolution, the flexspline and circular spline shift by two teeth. The gear ratio is: number of flexspline teeth ÷ (number of flexspline teeth - number of circular spline teeth) The tooth engagement motion (kinematics) of the strain wave gear is different than that of planetary or spur gearing. The teeth engage in a manner that lets up to 30% of the teeth (60 for a 100:1 gear ratio) engage at all times. This contrasts with maybe six teeth for a planetary gear, and one or two teeth for a spur gear. In addition, the kinematics enable the gear teeth to engage on both sides of the tooth flank. Backlash is the difference between the tooth space and tooth width, and this difference is zero in strain-wave gearing. As part of the design, the manufacturer preloads the gear teeth of the flexspline against those of the circular spline at the ellipse’s major axis. The preload is such that the stresses are well below the material’s endurance limit. As the gear teeth wear, this elastic radial deformation acts like a stiff spring to compensate for space between teeth that would otherwise increase in backlash. This lets the performance remain constant over the life of the gear. Strain-wave gearing offers high torque-to-weight and torque-to-volume ratios. Lightweight construction and single-stage gear ratios (to 160:1) let engineers use the gears in applications requiring minimum weight or volume ... especially useful for designs with small motors. Another tooth profile for strain-wave gearing is the S tooth design. This design lets more gear teeth engage for a doubling of torsional stiffness and peak torque rating, as well as longer life. The S tooth form doesn’t use the involute tooth curve of a tooth. Instead, it uses a series of pure convex and concave circular arcs that match the loci of engagement points dictated by theoretical and CAD analysis. The increased root filet radius makes the S tooth much stronger than an involute curve gear tooth. It resists higher bending (tension) loads while maintaining a safe stress margin.
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