Flatter reducer makes waves

The new CSD-type strain-wave speed reducer from HD Systems Inc., Happauge, N.Y., is less than half the width of the company's previous CSF design, yet retains 70% of the rated torque. It's also 20% lighter per rated torque and consumes 27% less volume. Developers say these attributes make CSDs attractive for next-generation satellite solar-array drives, antenna pointers, as well as precision robots arms.

For those not familiar with the technology, strain-wave speed reducers have three basic parts: a circular spline, a flexspline, and a wave generator. The circular spline is a solid cylindrical ring with internal teeth that also acts as a rigid mounting flange. Riding inside the cylindrical ring is a nonrigid flexspline with external teeth. A wave generator with a thin-raced ball bearing fitted to an elliptical-shaped plug inserts in the flexspline i.d. A motor drives the plug, causing a wavelike distortion of the flexspline and engagement of multiple gear teeth adjacent to the ellipse major axis. Because the flex spline has two less teeth than the circular spline, one complete revolution of the wave generator rotates the flexspline two teeth relative to the fixed circular spline. For example, a fixed circular spline with 202 teeth and an output flexspline with 200 teeth, gives the reduction ratio:

Ratios are negative because flexspline rotation is always in a direction opposite to wave generator rotation. It is by varying gear tooth counts that the reduction ratio changes.

NARROWING OPTIONS
Like CSF types, the CSD uses an S-tooth gear profile for both geared members, though the CSD flexspline and the teeth themselves are 50% narrower. The narrower teeth shrink overall width but also lower flexspline fatigue strength and torque rating. To increase tooth contact area and boost torque capacity, the CSD flexspline eliminates the tooth relief typically used to prevent tooth interference. Instead, a new elliptical shape for the wave generator adjusts the moving locus of flexspline teeth to prevent interference, says HD.

Still, a narrower flexspline has another downside: a larger coning angle. Coning angle is a measure of flexspline deflection caused by the wave generator shape and increases with decreasing flexspline width. Larger coning angles also raise diaphragm-bending stress, lower fatigue strength, increase tooth interference, and shrink the gap within the bearing raceway. This, in turn, boosts starting torque, an undesirable outcome.

The problem is overcome by opening up clearances between the flexspline inside surface and the outside of the wave generator bearing. In addition, the wave generator bearing has more radial clearance to accommodate the CSD gear shape. Applying torque to the reducer elastically deforms individual gear teeth and closes clearances. This improves torsional stiffness, especially at lower torque inputs.

HOLDING UP TO THE STRAIN
Durability is another important metric, defined here as an increase in lost motion with wave generator revolution count. Lost motion equals the torsional angle viewed from the low-speed shaft when a small torque (approximately 4% of the rated torque) is applied to it with the high-speed shaft fixed. Tests are performed in both the clockwise and counterclockwise directions and the results are added together. Results show essentially no increase in lost motion after 4 10⁸ wave-generator revolutions. Of course, gear wear life depends on operating condition and lubrication. Space applications, for example, use special lubricants so the above durability test results don't apply directly.

Thinning down is the first hurdle cleared by the CSD speed reducer. The next step boosts power density by replacing the steel wave generator plug and circular spline with lighter-weight materials. For example, the circular spline can be made entirely of an aluminum alloy or a composite of aluminum and cast iron. One prototype gear reducer (aluminum-alloy wave-generator plug and aluminum-alloy and cast-iron circular spline) has shown to have wear life on par with an equivalent all-steel production model. A version for space applications would use a composite circular spline of aluminum alloy and stainless steel, though technical challenges remain.