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Working Principle of Harmonic Reducer



The harmonic gear reducer is composed of a fixed internal gear rigid wheel, a flexible wheel, and a wave generator for radially deforming the flexible wheel. The harmonic gear reducer is a novel transmission structure in the gear reducer. It uses a flexible gear to generate a controllable elastic deformation wave, which causes the teeth of the rigid wheel and the flexible wheel to be relatively misaligned to transmit power and motion. This type of transmission is fundamentally different from general gear transmission and is unique in terms of meshing theory, set calculation and structural design. Harmonic gear reducer has the advantages of high precision, high bearing capacity, etc. Compared with ordinary reducer, it uses at least 50% less material, and its volume and weight are reduced by at least 1/3.

The harmonic reducer is a kind of harmonic transmission device, and the harmonic transmission device includes a harmonic accelerator and a harmonic reducer.

Composition and structure

The harmonic gear reducer is mainly composed of four main components: a rigid wheel, a flexible wheel, a flexible bearing and a wave generator. Harmonic transmission reducer, English: harmonic gear drive, is a gear transmission reduction device that is equipped with a flexible bearing to make the flexible gear produce controllable elastic deformation and mesh with the rigid gear to transmit motion and power.

Among them, the wave generator is an active member, and one of the rigid wheel and the flexible wheel is a driven member. The fixed rigid wheel is a rigid internal gear. The flexible wheel is a thin-walled cylindrical external gear that is easily deformed. They have a triangular (or involute) tooth shape, and the circumferences of the two are equal, but the rigid wheel is softer than the flexible wheel. A few more teeth (usually two teeth). The wave generator consists of an elliptical disk and a flexible ball bearing, or a rotating arm with rollers on both ends. Usually, the wave generator is a motive body, one of the flexible wheel and the steel wheel is a driven body, and the other is a fixed part.

working principle:

Before the assembly, the flexible wheel and its inner hole are round. When the wave generator is inserted into the inner hole of the flexible wheel, since the length of the wave generator is slightly larger than the diameter of the inner diameter of the flexible wheel, the flexible wheel is oval, forcing the soft The wheel is completely meshed with the fixed rigid wheel in the long axis direction of the ellipse, completely separated in the short axis direction, and the rest of the teeth are different in the rotation position of the flex wheel, or in the "biting" state, or in the "engaged" state. . Since the rigid wheel is fixed and the wave generator rotates counterclockwise, the flex wheel rotates clockwise. When the wave generator continuously rotates, the long axis and the short axis of the flexible wheel and the position of "biting" and "engaging" change continuously, and the flexible teeth are engaged by the meshing and turning, and the meshing and steering are engaged. The steering is disengaged, thus, engaging, engaging, engaging, disengaging, engaging, engaging, and reciprocating cycles force the flexible wheel to rotate continuously.

When the soft wheel is engaged with the wave generator, one of the teeth meshes with one tooth of the rigid wheel to engage the tooth on the rigid wheel again, the soft wheel rotates exactly one time, and the wave generator has rotated A lot of circles. The ratio of the number of revolutions of the wave generator to the number of revolutions of the flexible wheel (one turn) is the reduction ratio of the harmonic gear reducer, so the reduction ratio is large. During the entire movement, the deformation of the flexible wheel is a continuous simple harmonic shape on the developed view of the circumference of the flexible wheel. Therefore, this transmission is called a harmonic gear transmission.

Harmonic gear reducers can be divided into single wave, double wave and three wave according to the number of mechanical waves. The most common one 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 integral multiple of the mechanical wave number, which is usually equal to the wave number.


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

2. High carrying capacity. This is because the number of teeth engaged in the harmonic gear transmission is large at the same time, and the number of teeth of the double-wave transmission simultaneously meshes to more than 30% of the total number of teeth, and the flexible wheel adopts a high-strength material, and the teeth are in surface contact with the teeth.

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, the multi-tooth meshing has mutual compensation effect on the error, so the transmission precision is high. In the case of the same gear accuracy grade, the transmission error is only about 1/4 of the ordinary spur gear transmission. At the same time, the radius of the wave changing machine can be used to increase the deformation of the flexible wheel so that the backlash is small, and even the backlash can be meshed. Therefore, the harmonic gear reducer has a small free motion and is suitable for reverse rotation.

4. High transmission efficiency and stable movement. Since the flex wheel teeth make a uniform radial movement during the transmission process, even if the input speed is high, the relative slip speed of the gear teeth is extremely low, so the gear teeth wear is small and the efficiency is high. Moreover, due to the engagement and the biting, both sides of the gear participate in the work, so there is no impact phenomenon and the movement is stable.

5. Simple structure, few parts and easy installation. There are only three basic components, and the input and output shafts are coaxial, so the structure is simple and easy to install.

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 pass the movement to the confined space. Taking advantage of the flexible nature of the flexible wheel, this valuable advantage of the wheel drive is unmatched by other existing drives.


1. The flexible wheel periodically deforms, thus generating alternating stress, which makes it easy to cause fatigue damage.

2. The moment of inertia and starting torque are large, which is not suitable for low power tracking drive.

3, can not be used in the case of transmission speed ratio less than 35.

4. The harmonic drive of the roller wave generator is not constant.

5, poor heat dissipation conditions.


Harmonic gear reducers in aviation, aerospace, energy, marine, shipbuilding, bionic machinery, common ordnance, machine tools, instruments, electronic equipment, mining and metallurgy, transportation, lifting machinery, petrochemical machinery, textile machinery, agricultural machinery and medical Mechanical and other aspects have been widely used, especially in high dynamic performance servo systems, the use of harmonic gear transmission shows its superiority. It delivers power from tens of watts to tens of kilowatts, but high-power harmonic gear drives are often used in short-term applications.


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