Working principle of harmonic gear reducer

Update:24 Nov 2020

The harmonic gear reducer consists of a fixed internal tooth rigid wheel, a flexible wheel, and a wave generator that deforms the flexible wheel radially. The harmonic gear reducer is a new type of transmission structure in the gear reducer, which uses The flexible gear generates a controllable elastic deformation wave, causing the teeth of the rigid wheel and the flexible wheel to be relatively staggered to transmit power and motion.

This kind of transmission is essentially different from general gear transmission, and has particularity in meshing theory, collective calculation and structural design.

Harmonic gear reducer has the advantages of high precision and high bearing capacity. Compared with ordinary reducer, because it uses 50% less materials, its volume and weight are reduced by at least 1/3.

Composition and structure

Harmonic gear reducer is composed of three main components: rigid wheel, flexible wheel, and wave generator.

The fixed rigid wheel is a rigid internal gear

The flexspline is a thin-walled cylindrical external gear that is easy to deform. They have a triangular (or involute) tooth shape and the pitches of the two are equal, but the rigid gear has a few more teeth (usually two teeth) than the flexspline.

The wave generator consists of an elliptical disk and a flexible ball bearing, or a rotating arm with rollers at both ends.

Usually the wave generator is the motive body, one of the flexible wheel and the rigid wheel is the driven body, and the other is the fixed part.

Before assembling, the flexspline and its inner hole are circular. When the wave generator is installed in the inner hole of the flexspline, the length of the wave generator is slightly larger than the diameter of the inner hole of the flexspline. The wheel is fully meshed with the fixed rigid wheel in the direction of the long axis of the ellipse, and completely separated in the direction of the short axis. The rest of the teeth are either in the "engaged" state or "engaged out" state depending on the rotation position of the flexible wheel. . Because the rigid wheel is fixed, when the wave generator rotates counterclockwise, the flexible wheel rotates clockwise. When the wave generator rotates continuously, the positions of the long and short shafts of the flexspline and the "engaging in" and "engaging out" will continue to change. The teeth of the flexspline change from engagement to engagement, and then engagement to engagement. The outgoing steering is disengaged, so that the reciprocating cycle forces the flexspline to continuously rotate.

When the flexspline rotates with the wave generator, when one of the teeth meshes with one tooth of the rigid wheel to mesh with this tooth on the rigid wheel again, the flexspline rotates exactly once, and the wave generator rotates For many turns, the ratio of the number of turns of the wave generator to the number of turns (1 turn) of the flexspline is the reduction ratio of the harmonic gear reducer, so the reduction ratio is very large. During the whole movement process, the deformation of the flexspline is a continuous simple harmonic shape on the expanded view of the flexspline circumference. Therefore, this transmission is called a harmonic gear transmission.
Harmonic gear reducers can be divided into single wave, double wave and triple wave according to the number of their mechanical waves. The most commonly used is double wave transmission. In harmonic drive, the difference between the number of teeth of the rigid wheel and the flexible wheel should be equal to an integer multiple of the mechanical wave number, which is usually equal to the wave number.


1. Large transmission speed ratio.

The single-stage harmonic gear transmission speed ratio ranges from 70 to 320, in some devices it can reach 1000, and the multi-stage transmission speed ratio can reach more than 30,000. It can be used not only for speed reduction, but also for speed increase occasions.

2. High carrying capacity.

This is because the number of teeth meshing simultaneously in the harmonic gear transmission is large, and the number of teeth meshing simultaneously in the double-wave transmission can reach more than 30% of the total number of teeth. Moreover, the flexspline uses high-strength materials, and the teeth and teeth are in surface contact.

3. High transmission accuracy.

This is because the number of teeth meshed at the same time in the harmonic gear transmission is large, and the error is averaged, that is, multi-tooth meshing has a mutual compensation effect on the error, so the transmission accuracy is high. In the case of the same gear accuracy grade, the transmission error is only about 1/4 of that of ordinary cylindrical gear transmission. At the same time, the radius of the wave generator can be changed slightly to increase the deformation of the flexspline so that the backlash is small, and even the backlash-free meshing can be achieved, so the harmonic gear reducer has a small idle stroke and is suitable for reverse rotation.

4. High transmission efficiency and smooth movement.

Due to the uniform radial movement of the flexspline gear teeth during the transmission process, even if the input speed is very high, the relative slip speed of the gear teeth is still extremely low (so it is one percent of the ordinary involute gear transmission) Therefore, the gear teeth are less worn and the efficiency is high (up to 69%-96%). Also, because both sides of the gear are engaged in work when engaging in and out, there is no impact phenomenon and the movement is stable.

5. Simple structure, few parts and convenient installation.

There are only three basic components, and the input and output shafts are coaxial, so the structure is simple and the installation is convenient.

6. Small size and light weight.

Compared with the general reducer, when the output torque is the same, the volume of the harmonic gear reducer can be reduced by 2/3, and the weight can be reduced by 1/2.

7. Can transmit motion to confined space.

Utilizing the flexibility of the flexspline, this valuable advantage of the wheel drive is unmatched by other existing drives.


1. The flexspline is deformed periodically, thus generating alternating stress, making it prone to fatigue damage.

2. The moment of inertia and starting moment are large, so it is not suitable for low-power tracking transmission.

3. It cannot be used in occasions where the transmission ratio is less than 35.

4. Harmonic transmission using roller wave generator (free deformation wave), its instantaneous transmission ratio is not constant.

5. Poor heat dissipation conditions.

Application occasion

Harmonic gear reducers are used in aviation, aerospace, energy, navigation, shipbuilding, bionic machinery, commonly used ordnance, machine tools, instruments, electronic equipment, mining and metallurgy, transportation, cranes, petrochemical machinery, textile machinery, agricultural machinery and medical treatment Apparatus and other aspects are increasingly widely used, especially in the servo system with high dynamic performance, the use of harmonic gear transmission shows its superiority. It transmits power from tens of watts to tens of kilowatts, but high-power harmonic gear drives are mostly used in short-term work situations.

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