Working principle of harmonic gear reducer
Release time:
2025-11-14 13:56
A harmonic gear reducer consists of a fixed internal gear, a flexible gear, and a wave generator that causes radial deformation of the flexible gear. It is a novel transmission structure within the gear reducer category. It utilizes the controllable elastic deformation wave generated by the flexible gear to induce relative tooth misalignment between the teeth of the gear and the flexible gear, thereby transmitting power and motion.
This transmission method differs fundamentally from conventional gear transmission, possessing unique characteristics in meshing theory, assembly calculations, and structural design.
Harmonic gear reducers offer advantages such as high precision and high load-bearing capacity. Compared to ordinary reducers, they use 50% less material, resulting in a reduction in volume and weight of at least one-third.
Composition and Structure
A harmonic gear reducer consists of three main components: a fixed rigid gear, a flexible gear, and a wave generator.
The fixed rigid gear is a rigid internal gear.
The flexible gear is a easily deformable thin-walled cylindrical external gear. Both have triangular (or involute) tooth profiles and equal peripheral pitch, but the rigid gear has a few more teeth (usually two) than the flexible gear.
The wave generator consists of an elliptical disk and a flexible ball bearing, or a rotating arm with rollers at both ends.
Typically, the wave generator is the driving element, one of the flexible or rigid gears is the driven element, and the other is a stationary component.
Before assembly, the flexible wheel and its inner bore are circular. When the wave generator is inserted into the flexible wheel's inner bore, because the length of the wave generator is slightly larger than the diameter of the flexible wheel's inner bore, the flexible wheel expands into an elliptical shape. This forces the flexible wheel to fully engage with the fixed rigid wheel along the major axis of the ellipse and completely disengage along the minor axis. The teeth at other points are either in an "engaged" or "disengaged" state depending on the flexible wheel's rotational position. Because the rigid wheel is fixed, when the wave generator rotates counterclockwise, the flexible wheel rotates clockwise. As the wave generator rotates continuously, the positions of the flexible wheel's major and minor axes, as well as its "engaged" and "disengaged" positions, constantly change. The flexible wheel teeth shift from engaged to disengaged, then back to engaged, and then back to disengaged, repeating this cycle of engagement, disengagement, engagement, and so on, forcing the flexible wheel to rotate continuously.
As the flex wheel rotates with the wave generator, when one of its teeth engages with a tooth on the rigid wheel and then engages with that tooth again, the flex wheel completes one revolution. During this time, the wave generator rotates many revolutions. The ratio of the number of revolutions of the wave generator to the number of revolutions of the flex wheel (one revolution) is the reduction ratio of the harmonic gear reducer, hence its high reduction ratio. Throughout the entire motion, the deformation of the flex wheel forms a continuous simple harmonic waveform on its circumference development diagram; therefore, this transmission is called a harmonic gear drive.
Harmonic gear reducers can be classified according to the number of mechanical waves: single-wave, double-wave, and triple-wave, with double-wave transmission being the most common. In harmonic drives, the difference in the number of teeth between the rigid wheel and the flex wheel should be an integer multiple of the number of mechanical waves, usually taken as equal to the number of waves.
Advantages:
1. High transmission ratio.
The speed ratio range of a single-stage harmonic gear transmission is 70~320, reaching 1000 in some devices, while multi-stage transmissions can achieve ratios exceeding 30000. It can be used not only for speed reduction but also for speed increase.
2. High load-bearing capacity.
This is because harmonic gear transmissions involve a large number of teeth meshing simultaneously. In dual-wave transmissions, the number of teeth meshing simultaneously can reach over 30% of the total number of teeth. Furthermore, the flexure uses high-strength materials, and the teeth make surface contact.
3. High transmission accuracy.
This is because the large number of teeth meshing simultaneously in harmonic gear transmissions averages out errors. The multi-tooth meshing provides mutual compensation for errors, resulting in high transmission accuracy. Under the same gear accuracy grade, the transmission error is only about 1/4 that of ordinary cylindrical gear transmissions. Additionally, the radius of the wave generator can be slightly altered to increase the deformation of the flexure, resulting in very small backlash, even achieving backlash-free meshing. Therefore, harmonic gear reducers have small transmission idle distances and are suitable for reverse rotation. 4. High transmission efficiency and smooth operation.
Because the flexspline teeth move radially and evenly during transmission, even at high input speeds, the relative slip velocity of the teeth remains extremely low (approximately one-hundredth of that of ordinary involute gear drives). Therefore, tooth wear is minimal, resulting in high efficiency (69%~96%). Furthermore, since both sides of the gear participate in engagement and disengagement, there is no impact, leading to smooth operation.
5. Simple structure, few parts, and easy installation.
With only three basic components and coaxial input and output shafts, the structure is simple and installation is convenient.
6. Small size and light weight.
Compared to general reducers, for the same output torque, the harmonic gear reducer can reduce its volume by 2/3 and its weight by 1/2.
7. Can transmit motion into enclosed spaces.
Utilizing the flexibility of the flexspline, this valuable advantage of gear drives is unmatched by other existing transmission methods.
Disadvantages
1. The flexspline deforms periodically, generating alternating stress, making it prone to fatigue failure.
2. High moment of inertia and starting torque, unsuitable for low-power tracking transmissions.
3. Cannot be used in applications with a transmission ratio less than 35.
4. Harmonic drives using roller wave generators (free-deformation waves) have non-constant instantaneous transmission ratios.
5. Poor heat dissipation.
Applications
Harmonic gear reducers are increasingly widely used in aviation, aerospace, energy, marine, shipbuilding, bionic machinery, general military equipment, machine tools, instruments, electronic equipment, mining and metallurgy, transportation, hoisting machinery, petrochemical machinery, textile machinery, agricultural machinery, and medical devices. They are particularly advantageous in high-dynamic-performance servo systems. The power transmitted ranges from tens of watts to tens of kilowatts, but high-power harmonic gear drives are mostly used for short-term applications.
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