Advantages

When this condition was studied, the natural question was, " Can we design a gear system where by design we have increased tooth engagement?"

The CAD graphic of Figure 1 shows the results of the mathematical and kinematic studies that were conducted. In the graphic, which is like a multiple exposure photograph, the progression of engagement can be seen for three gear teeth. Engagement starts at the tip of a tooth and continues until there is full tooth engagement. Further studies have shown that the total angle of engaging teeth for the new "S" series toothform is about double the conventional tooth form designs.

Figure 3

The original toothform has an involute curve profile that is common to most spur gears.

The new "S" Series toothform does not use the involute curve, instead it uses a series of pure convex and concave circular arcs created to match the loci of engagement points dictated by theoretical and CAD analysis.

The tooth profile below shows a picture of the geometry. (For a more complete explanation of this geometry you can ask us for a copy of the ASME conference proceedings paper referenced at the end of this article.)

Figure 4

Notice a very important design change with this new "S" tooth profile. See how substantial the root fillet radius is? This increased root fillet radius makes the "S" Series tooth much stronger than an involute curve gear tooth.

The root fillet radius is a focus for stress concentration and fatigue due to bending. By increasing the radius, a stronger tooth is created, a tooth that will resist higher bending (tension) loads, while maintaining a safe stress margin.

The increased root fillet radius also has the effect of increasing the root thickness of the tooth. With a greater root thickness 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. From this design result comes the nearly doubled momentary peak torque ratings of the "S" Series products.

This stronger tooth and the increased engagement angle is why the torsional stiffness of the "S" Series is now twice as large as conventional gearing. You can see this in the curve for "S" Series torsional stiffness (Figure 2 ). In addition to having double the stiffness, the curve is practically a straight line, providing a linear stiffness relationship rather than the parabolic shape of conventional strain wave gearing.

With the same rated load torques, the "S" Series life has double the life of conventional units. The larger angle of engagement distributes the radial forces on the bearing over this larger surface area. This results in an increase in the life of the bearing by a factor of 2.3!

We have torque specifications for momentary and repeated peak torques. Because of the new tooth profile in the "S" Series, both of these torque specifications have been doubled. This provides a compact package with an even higher packaging ratio of torque per cubic inch, and with lower weight for those applications where space and weight are at a premium.

With all of this improvement in load capacity, the efficiency of the "S" Series drive units has been maintained at the same levels of previous Harmonic Drive® gears. Even though by design more teeth are engaged, the rolling action of engagement maintains a high efficiency, in the range of 60% to 90% depending upon the load, speed and lubrication.

We think our new "S" Series products with our new tooth profile brings a quantum improvement to Harmonic Drive® gears. If you would like to discuss this further, please give us a call or send us an email message. We enjoy talking about this technology and would be glad to answer any questions that you may have.

Reference:

Y. Kiyosawa and S. Ishikawa, "Performance of Strain Wave Gearing Using a New Tooth Profile", ASME International Power Transmission and Gearing Conference, Vol. 11, Book No. 10288B1989.