1 Involute tooth profile harmonic gear research The tooth profile proposed by CWMusser, the inventor of the world's first harmonic gear reducer, is a linear tooth profile with a large pressure angle.
The use of such a tooth profile is based on two reasons, which not only meets the requirements of the fixed gear ratio, but also enables the tooth to achieve surface contact to improve its load carrying capacity. According to the analysis, if the working section of the neutral deformation curve of the flexible wheel is the Archimedes spiral, the linear tooth shape can ensure a nearly constant transmission ratio. However, since the model used by Musser does not consider the tangential displacement of the point on the center of the flexible wheel, and the rotation of the symmetry line of the flexible tooth caused by the change of curvature during the deformation of the midline, plus the diameter and spiral of the Archimedes spiral The angle between the normals of the corresponding points on the line is not constant, so there are some shortcomings in this tooth shape.
In view of the shortcomings of Musser's determination of the tooth profile model and some scholars' misconceptions, after 1964, domestic and foreign scholars have started to establish the harmonic gear transmission meshing theory. A series of theoretical studies have been carried out on its parameters. From the practical use, the following conclusions are drawn: Since there are flexible wheels that can produce controllable elastic deformation in the harmonic gear transmission, whether the two-wheel teeth are strictly conjugate, the influence on the transmission performance is not significant, and the tooth shape parameters The impact is very large, which prompted people to mainly explore the influence of the tooth profile of the harmonic gear transmission and its parameters on the meshing performance.
In the tooth profile of the existing harmonic gear, the development of the involute profile is relatively perfect. Let's take the involute profile as an example to discuss the influence of the tooth profile on the transmission performance. The initial proposal to replace the linear tooth profile with an involute is based on two considerations: First, when the number of teeth is large, the involute tooth profile is close to the linear tooth profile, and the involute tooth profile replaces the linear tooth profile. The error does not have an essential effect on the transmission performance. Secondly, the involute tooth profile is easy to process in the process, and the existing machining method of the conventional gear can be slightly modified to be used for the machining of the harmonic gear. Involute profiles can be divided into two categories:
(1) Involute narrow groove teeth (the groove width along the root circle is much smaller than the tooth thickness), which is widely used due to the advantages of the process; (2) Involute wide groove teeth (the groove width along the root circle is close to or larger than the tooth width) Thick) is a modification of the involute profile (reducing the tooth height) to reduce the root stress. Theoretical analysis and experimental research have shown that regardless of the involute narrow slot teeth or the wide slot teeth, in the no-load state, the gear teeth participating in the meshing are only a limited number of pairs. When the nominal torque is transmitted, the number of teeth that are simultaneously meshed can be greatly increased, but most of the teeth are in the edge meshing state. This edge contact is not conducive to the formation of oil film between the teeth. In order to improve the tooth contact state, the involute tooth should be handled. The profile is properly shaped. Therefore, before the 1990s, in the research and application of harmonic gears, it was highly praised for the involute profile or the involute profile after modification.
Although the involute profile does have many advantages in practical applications, the involute tooth profile is the ideal tooth profile for harmonic gear transmission and lacks rigorous proof and convincing basis.
The trajectory of the soft teeth and the characteristics of the involute tooth shape determine that the envelope of the flexible wheel is formed in a small range under no-load condition, so the correct meshing of the harmonic gear transmission is only possible in one Occurs in a small local area; in the loaded state, although multi-tooth engagement occurs due to elastic deformation, an edge contact or a tip is formed. It should be noted that in the above-mentioned tooth profile, the multi-pair of the teeth simultaneously participating in the meshing is mainly achieved by the cusp engagement in the harmonic gear load transmission.
Through the analysis of the 2S toothed harmonic gear, it can be noted that with the tooth shape research method described above, the obtained tooth profile is actually an approximate conjugate tooth profile.
The result of the approximate conjugate is that there is no guarantee that there will be an accurate motion law, and the instantaneous gear ratio will change. Based on the above understanding, Japanese scholars in the 1990s abandoned the traditional tooth form in the study of harmonic tooth shape and proposed a new tooth shape, which is called S tooth shape according to the shape of its working tooth profile.
The S-tooth shape was first patented by Japanese scholar S. Ishikawa in 1989, and was not named for this new tooth shape. In this paper, the meshing discontinuity (in the meshing zone) of the traditional involute tooth profile during the meshing process is first analyzed, and it is pointed out that the conventional tooth profile relies on the deformation after loading to achieve continuous contact and multi-tooth meshing of the meshing zone. Since the load deformation greatly weakens the bearing capacity and service life of the gear, a new tooth profile based on curve mapping is proposed from the perspective of no need to deform and ensure continuous contact. The mapping reference curve is the relative of the soft tooth tip. The trajectory of the wheel. Then the paper introduces in detail the improvement and improvement of the meshing performance and bearing capacity of the harmonic gear after adopting this new tooth shape, and gives the reference tooth profile equation of this new tooth profile.
In 1995, Ishikawa and Yoshihide Kiyosawa improved on the existing flexible gear tooth profile. The improved flexible gear tooth profile is shown in Figure 1. It has a working tooth profile composed of arcs at both ends, which is large near the crest and root. Radius arc, but the ultimate goal is to achieve continuous contact in the meshing zone without the need for deformation after loading. Since then, many scholars (mostly Japanese scholars) have made some progress in the study of S-tooth shape, for example, in the literature [3] [4], respectively, in eliminating interference, increasing the depth of penetration, etc. This tooth shape has been further explored and improved.
It can be said that the appearance of S-tooth shape is a major breakthrough in the research of harmonic gear tooth shape. It has been proved theoretically and practically that it is superior to the traditional tooth shape in improving the meshing characteristics and increasing the rated load (for example, involute Tooth shape). But unfortunately, the inventor took the idea of ​​the motion of the harmonic gear transmission determined by the literature [1][7], and did not thoroughly analyze the motion law, and according to the soft wheel and The practical experience of a large number of teeth has abstracted the gears into racks with the same tooth shape. The study of the racking characteristics of the two gears has been studied, which greatly limits the application of this tooth shape. If the number of teeth of the toothed gear is small, the error will increase), so it is not solid enough on the theoretical basis, and it cannot be more powerfully stated that the tooth profile is the ideal tooth profile of the harmonic gear. Therefore, it is necessary to conduct more in-depth research.
3 Arc tooth profile harmonic gear research and involute tooth shape research at the same time is the study of arc tooth shape and its substitute tooth shape. Arc tooth profile harmonic gear transmission is a new application field of arc gear transmission. The arc tooth profile is used in the harmonic gear transmission, which is not only easy to implement in the process, but also can effectively improve the stress condition of the soft tooth root, reduce the stress concentration, and eliminate the flexible compensability of the flexible wheel due to the wide tooth groove. Edge contact and wedge-shaped backlash facilitate oil film formation, improve the meshing quality of the transmission, and improve load carrying capacity and torsional stiffness.
Beginning in the 1970s, the Soviet Union first appeared on the use of circular tooth profiles for harmonic gear transmissions. Hey. Γинзбург and В. Hey. Ромашин et al. first studied the application of the arc profile to the field of harmonic gear transmission. The former used the concept of the constant velocity curve proposed by him in 1966, and first studied the flexible wheel that meshed with the rigid wheel with a circular tooth profile. The tooth profile, due to the concept of the error, has not been adopted by people. When the transmission is working, in the case of the fixed wheel, the trajectory of the soft tooth is approximately a hypocycloid, which requires that the rigid tooth should be a convex tooth, and the tooth profile of the conjugate with the rigid tooth is For the tooth profile of the flexible wheel, the circular tooth is used as the tooth profile of the harmonic gear transmission, so the latter proposed a flexible tooth profile with a double arc profile and a convex shape in the work published in 1975. The tooth profile of the tooth profile, although not strictly conjugated, has been practically applied in countries such as Japan and the United States.
Since the mid-1980s, Japan has begun to produce harmonic gear transmission products with double arc profiles. Due to the large number of teeth meshed at the same time, the meshing side gap distribution between the teeth is relatively uniform. Therefore, the arc tooth profile can greatly improve the motion accuracy of the harmonic gear transmission and improve the fatigue strength of the flex wheel. The arc profile harmonic gear transmission manufactured in Japan has been used in the field of robots to improve the torsional stiffness of robot joints.
At present, the arc tooth shape used in production is mainly a single arc tooth profile, a common tangent double arc profile and a stepped double arc profile. According to the motion characteristics of the harmonic gear transmission, it is determined that the flexible wheel and the rigid wheel can only adopt a single circular tooth profile or a common tangential double circular tooth profile, and can not adopt the helical gear transmission, and the common tangential double circular tooth profile. The tooth shape is as shown in 2. Because the arc length of the single arc profile drive is shorter, and the arc profile tool of the flexible wheel and the rigid wheel is different, a small modulus double arc profile harmonic gear drive should be developed. Before developing the arc profile harmonic gear drive reference profile, the form of the wave generator and the radial deformation coefficient of the flex wheel must be determined. For the current state of the art in China, the wave generator form generally adopts an elliptical cam. Considering the motion accuracy, transmission efficiency and flex wheel life, the radial deformation coefficient of the flex wheel should be determined from the perspective of mainly improving the transmission performance.
Although the arc tooth profile harmonic gear transmission has many advantages with respect to the involute profile, special tools are required for machining, and the shape of the cutter is complicated, so the cost is high and it is not easy to promote, and a circle is proposed in use. The alternative tooth shape of the arc tooth (someone is called the cycloidal tooth profile) has the advantage of being able to be machined with a straight edge cutting edge, inheriting the advantages of the circular tooth profile, but the manufacturing of the cutting tool is more general. The involute cutting tool is complicated. It can be seen from the application of foreign countries that the arc tooth harmonic gear transmission developed by Russia is mainly for the four-roller wave generator. Because the force is different from the long axis angle φ of the deformation, the corresponding gear cutter is also different, so it Developed a flexible wheel cutter and a rigid wheel cutter corresponding to φ≈25° and φ≈35°, and a large-scale arc-tooth harmonic gear transmission of a single elliptical wave generator is produced in Japan, which has the advantage that it can be adopted. The minimum number of tools.
Therefore, for our technicians, the development of harmonic gear cutters with circular tooth profile is also an important part of future research.
At present, China is working on the development of arc tooth profile harmonic gear transmission technology that can improve the meshing stiffness, load carrying capacity and transmission life of harmonic gear transmission, and has achieved many theoretical research results.
The new toothed short tube flexible wheel harmonic transmission technology successfully developed by Beijing Feida Kemei Harmonic Transmission Technology Innovation Co., Ltd. is actually changing the involute tooth profile used in the past to the new tooth shape of double arc, which not only improves Load capacity and transmission accuracy, and shorten the axial dimension of the flexible wheel, reduce the volume and weight of the product, save a lot of steel and energy, and improve the rigidity, can better meet the space technology and industrial robot to drive device The performance requirements replace the traditional products and similar products imported from abroad; at the same time, due to the low manufacturing cost of China's harmonic transmission products, it is conducive to the competition of Chinese products in the international market. The main technical performance indicators of this product:
1 Transmission accuracy, empty return ≤ 2', transmission error ≤ 2'; 2 transmission efficiency ≥ 80% (under rated input speed, rated output torque); 3 load capacity, stiffness, structure, volume, weight and other indicators have reached abroad The level of similar products.
As the new toothed short tube flexible wheel harmonic drive technology is an innovative product of harmonic drive technology, it has more advantages than conventional harmonic drive, thus expanding the application coverage of this technical achievement.
4 Conclusions With the development of China's aerospace technology, military industry, and mechatronics technology, there are urgent needs in many domestic fields to apply new tooth-shaped harmonic gear transmission technologies, such as domestic robot manufacturing, various space vehicles, such as satellite antennas. Deployment, drive mechanism, solar cell windsurfing deployment, drive mechanism, spacecraft antenna, solar array deployment drive mechanism, space laboratory to be developed, moon landing vehicle, etc. Therefore, for the research and technical personnel in China, the research and exploration of the new toothed harmonic gear transmission technology has far-reaching significance.
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