Hauppauge, NY-When engineers want to reduce the size, weight, and backlash in a motion control system, many opt for harmonic-drive gearing as the power transmission device. Until recently, however, the lowest practical gear ratio was 50:1. To open up high-speed automation applications for such gearing, HD Systems modified its patented "S" tooth profile to achieve 30:1 ratios. Now design engineers can increase output speeds in many applications, and benefit from the reduced size, weight, and backlash of harmonic-drive gearing.
Harmonic-drive operation depends upon multiple teeth being engaged at the major axes and then the disengagement at the minor axes. The challenge says Brian St. Denis, HD Systems senior engineer, was to come up with a design that minimizes tooth wear and flex spline fatigue. Because gear ratios fundamentally depend on the number and size of gear teeth, as a rule lower ratios use fewer, larger teeth. Generally, larger teeth require a wave generator with a more elliptical shape to provide sufficient clearance at the minor axis for the teeth to completely disengage. But increasing the wave generator's ellipticity elevates bending and torsional stresses in the flex spline's toothbed and diaphragm areas, causing fatigue as the flex spline conforms to the rotating ellipse. Hence the desire for small tooth height. "But for minimum flex stress in the flex spline, it's desirable to keep ellipticity to a minimum," explains St. Denis.
After modifying the design of these areas bringing stresses within acceptable limits, reducing the clearance requirement, and minimizing the degree of wave generator ellipticity, engineers conquered the geometrical limitations imposed by lower ratios. As a result, the design achieves 30:1 gear ratios without placing excessive stresses on the flex spline. Other benefits of the new tooth design include:
Double the torsional stiffness
To achieve lower ratios, engineers had to develop a complex three-dimensional simulation of tooth engagement so that parameters of the "S" tooth profile could be modified in such a way that would eliminate improper tooth engagement and reduce sliding friction, tooth wear, and flex stress. Moreover, the designers performed a new and far more detailed finite element analysis of the flex spline toothbed. Such analysis pinpointed critical high-stress areas. For example, the root filet area is a focus for stress concentration and fatigue due to bending. "When you increase the radius," explains St. Denis, "you make a stronger tooth that will resist higher bending (tension) loads, while maintaining a safe stress margin."
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| 1. Flex-spline teeth engage circular-spline teeth across the elliptical wave generator’s major axis |
2. Engaged teeth travel with the major axis as wave generator rotates |
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| 3. Every 180° of clockwise wave-generator motion moves the flex spline one tooth counterclockwise relative to the circular spline |
4. Each wave generator revolution moves the flex spline two teeth in the opposite direction from its previous position relative to the circular spline |
| Torque transmission results as the gearteeth along the major axis of the wave generator engage, and the gearteeth along the minor axis of the wave generator disengage and move relative to the unengaged circular-spline teeth. |
The increased root filet radius also has the effect of increasing the root thickness of the tooth. A greater root thickness means the tooth has a larger load capacity based on acceptable shear stress. "Together, both of these factors make a much stronger tooth that is more rigid and less likely to bend," says St. Denis. This stronger tooth and the increased engagement angle, he adds, is why the torsional stiffness of the "S" Series is now two times greater than the previous design. Plus, the torsional stiffness curve is practically a straight line, providing a linear stiffness relationship rather than the parabolic shape of conventional harmonic-drive gearing.
With the same rated load torque, explains St. Denis, the "S" Series has double the life of conventional units. The larger angle of engagement distributes the radial forces on the bearing over a larger surface, and increases bearing life by a factor of 2.3.
The modified "S" tooth profile uses a series of pure convex and concave arcs instead of the involute curve profile, common to most spur gears, used in the original toothform. The design closely matches the loci of engagement points dictated by theoretical and CAD analysis, and the corresponding kinematics of tooth engagement for the harmonic-drive gearing. This reduces the amount of clearance required for the non-engaged teeth, as it increases the number of teeth being engaged at any given time. Consequently, the torsional stiffness and life of the gear are doubled.
Torque specification for momentary and repeated torque is also doubled as a result of the new tooth profile. Nonetheless, even though by design more teeth are engaged, the rolling action of engagement maintains efficiency between 60 and 90% depending on the load, speed, and lubrication.
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Why flat teeth are better
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| Planing down the top of the flex-spline tooth profile reduces clearance requirements. |
The 30:1 ratio makes harmonic-drive gearing more appropriate for high-speed applications in semiconductor chip mounting, SCARA robots, and assembly equipment. Traditionally, such high-speed applications used planetary gears, and designers had to accept backlash of 6 arc-min in order to achieve high output speeds. "Designers can now achieve high output speeds while maintaining the zero-backlash and 1.5 arc-min positional- accuracy benefits of harmonic-drive gearing," says St. Denis.
Weight is another reason for replacing planetary gearing with high-speed harmonic drive gearing. The 30:1 gear ratio allows the designer to achieve the higher speeds while using low-weight gearing components.
Additional details...Contact Brian St. Denis, HD Systems, 89 Cabot Cte., Hauppauge, NY 11788; Tel: (516) 231-6630; Fax: (516) 231-6803.
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