Wave gears - Applied Mechanics

Wave transmissions

Wave transmission is based on the principle of converting the motion parameters due to wave deformation of one of the links. The most common transmission with a flexible cylindrical wheel.

Advantages : wave transfers, compared to other gears, have a small mass and overall dimensions, large gear ratios , high kinematic accuracy, low shaft loads , the ability to transfer motion to the sealed space and vice versa without additional seals.

Disadvantage: the complexity of the design and manufacture of a flexible flexible wheel.

The low weight, overall dimensions and high accuracy of the wave transmission are achieved due to the presence of several gearing zones and a large number of teeth (20-40% at load) transmitting the torque. Therefore, a smaller force acts on each tooth and its strength is ensured at small sizes. The coefficient of efficiency of the wave transmission (0.8-0.9) is close to the efficiency of planetary and multistage cylindrical transmissions.

Due to its advantages, wave transmission is widely used in chemical, atomic and space technology. For example, the American Lunokhod LRV successfully used a sealed wave transmission.

The wave transmission shown in Fig. 4.40, consists of three main links: the wave generator h, of the flexible wheel g and the rigid wheel . The spur gear of the flexible wheel is deformed by the wave generator and engages with the rigid wheel in the zones located at the points A and G. The flexible wheel in the hermetic wave gear is made in the form of a flanged cup . A toothed crown on a flexible wheel is cut from the outside in the middle of the glass. The wall of the glass has a small thickness, which allows it to easily deform when exposed to the inside of the wave generator. The two-wave wave generator consists of a profiled cam with a flexible bearing. The outside dimension of the generator along the AG axis (the larger axis of the generator) is greater than the inner diameter of the flexible wheel cylinder on . When installing the generator inside the flexible wheel, the pitch diameter of the flexible wheel is increased along the major axis by the value

Fig. 4.40

where - the dividing diameters of the rigid and flexible wheels.

Radial movement of the rigid wheel should be less than flexible, 20-50 times or more:

With a low stiffness of the generator and wheel, it is possible to skip and the motion is not transmitted to the driven wheel. When the wave generator rotates, the deformation wave moves along the circumference of the flexible wheel. Any point of the cylindrical surface of the flexible wheel moves and makes two oscillations in the two-wave transmission in one revolution of the wave generator. When the generator rotates, two waves run along the circumference of the flexible wheel, regardless of the speed of its rotation. At the points A and G , the teeth of the flexible wheel engage at the entire working height, and at the points B and E are on some distance from each other. In one revolution of the wave generator, the meshing zones of the teeth also make one revolution, resulting in a rotation of one wheel relative to the other by the number of angular steps equal to the difference of their tooth numbers.

If the three main links of a wave gear drive rotate, then it has two degrees of mobility and is called a differential. Wave transmissions are most often used, in which one of the links (a flexible or rigid wheel) is stopped; in this case the mechanism has one degree of mobility.

Kinematics of wave transfer. Wave transmission ratio

where - the number of teeth of the fixed wheel. With the immovable flexible wheel

(4.59)

and with a fixed rigid wheel

(4.60)

By setting the ratio and taking the number of waves equal to

(4.61)

determine the number of teeth of the flexible and rigid wheels.

At for one complete revolution of the generator there is a relative rotation of the wheels at two angular steps. With the directions of the rotation of the wave generator and the rigid wheel are the same, and at their rotation is opposite.

The geometry of the wave transfer. With the design calculation for fatigue strength, the diameter of the flexible wheel can be determined from the approximate formula with a fixed flexible wheel:

(4.62)

where - torque on the output shaft and wave generator, N ∙ mm; - Wave transmission efficiency; - endurance limit of wheel material, MPa; - the effective coefficient of stress concentration at the root of the tooth; - factor of safety; - coefficient of influence of the ring gear on the strength of the flexible wheel; coefficient of the thickness of the flexible wheel; - coefficient of the width of the ring gear.

If the rigid wheel is fixed, in formula (4.62), on

Having determined the diameter and the number of teeth of the flexible wheel, find the module and specify it in accordance with GOST. Geomet -

Fig. 4.41

The parameters are selected in accordance with the following recommendations (see Figure 4.4): radial deformation , displacement factor. , height of the teeth , depth of approach , wall thickness of the flexible wheel .

Then calculate the coefficient of displacement of the rigid wheel , the diameter of the circles of the valleys and the tops of the flexible wheel , diameters circles of hollows and hard wheel tops (Figure 4.41, b); - the height factor of the tooth's head ( with ; with ). In the design calculation, we can approximately take (Figure 4.41, c) followed by a refinement of 15 J.

Wave transmission constructions. The fastening of the wave generator to the shaft can be movable or deaf. Movable connection is provided by elastic elements made of rubber or splined, hinged and other connections. In this design, the forces acting on the shaft of the wave generator are balanced and the loads on it are small. With a blind connection, the load on the shaft increases and high demands are placed on the accuracy of the manufacturing.

The wave generator transfers the torque to the flexible wheel by deforming it, which is done by rollers (Fig.4.42, a, b ), disks (Figure 4.42, c), cams (Figure 4.42, d). In the wave transmission, the shape and size of the deformation of the flexible wheel and its conservation under load are important. When the flex wheel is deformed incorrectly, the stresses in it are sharply increased. According to the nature of the deformation of the flexible wheel caused by the wave generator, free and forced deformation are distinguished. For forced deformation, its shape is determined by the profile of the cam or disk of the wave generator in the areas of their contact with the flexible wheel. Under the action of loads, the occurrence of

Fig. 4.42

casting in the meshing zone, the shape of the deformation in these sections varies little. Free deformation occurs in those areas where the movement of the flexible wheel is not limited. In cam generators, the given shape is stored under load, so they are used in power transmissions. Roller generators under load do not retain the original shape. They are used in low-loaded gears, for example, in friction wave gears that do not have teeth, and load transfer is performed by friction forces. In transmissions with a cam generator, flexible bearings with a smaller ring thickness and a special generator design are used. The designs of the disk generator of the will are simpler than the cam generator - there are no special bearings and cams with a complex profile, therefore, disk generators are preferable for individual and small-scale production. However, with specialized mass production, the cam generator is easier and cheaper to manufacture.

In Fig. 4.43. The non-hermetic wave reducers with cam wave generators are shown, where h is the wave generator; g and b - flexible and rigid wheels; p is a glass. It should be noted the compactness of the design of the wave reducer in question (Figure 4.43, a), which has small axial dimensions. In most wave reducers there is no glass p, and the flexible wheel is directly connected to the output shaft (Figure 4.43, b). Then the two bearing bearings are shifted to the right, and the overall dimension along the axis more -

Fig. 4.43

Steadily increases. The hermetic reducer is shown in Fig. 4.40. For non-hermetic gearboxes where there is no need to transfer to a sealed space, the flexible wheel does not have the right-hand side H. In this construction, the axial and radial deformations of the flexible wheel are limited to the edges on one side by a flange, and on the other, which affects the stress state. To reduce the effect of the edge effect and, accordingly, to reduce the stress level, increase the length of the sections l (recommended ) and reduce the stiffness of the transition sections from the cylinder to the flange and bottom. Usually they are made of the same thickness as the wall of the cylindrical part of the flexible wheel, and are provided with holes in the leaky gears.

The main reasons for the failure of wave transmissions associated with the strength of their elements are the fatigue fractures of flexible wheels and flexible bearings in the jaws of the wave generators.

When checking the strength of a flexible wheel, the normal stresses from its deformation and stretching from the circumferential forces, as well as the tangents from the torque, are taken into account.

Flexible and hard wheel materials . Heavily loaded flexible wheels are made of structural steels with increased viscosity 40Х НМ А, 38МЮА. They are less sensitive to stress concentration. Medium- and light-loaded flexible wheels of general purpose are made from cheaper steels 30ХГСА and 30ХМ A. Flexible wheels are subjected to heat treatment - improvement (НВ 280-320). To increase the strength of the surface, the crowning of the serrated crown or nitriding (surface hardness ) is used. The stresses of a rigid wheel are much lower than those of a flexible wheel. Therefore, the rigid wheel is made of structural steels 45A, 40X, 30HGSA with a hardness of 20-30 units. HB is lower than that of a flexible wheel.

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