The principle of action of wave transmissions is based on change of parameters of movement owing to wave deformation of one of links of the mechanism [1].
Wave transmission consists of three main links: wave generator h, flexible wheel g and rigid wheel b. The gear ring of the flexible wheel is deformed by the wave generator and engages with the central rigid wheel. The flexible wheel is made in the form of a glass with a flange. The ring gear on the flexible wheel is cut on the outside; its wall has a small thickness, which allows it to easily deform under the action of a wave generator inserted inside. The two-wave generator consists of a carrier with two rollers [1, 2].
When calculating the wave transmission are determined, as in the differential transmission, with input and output links, they can be two of the three main links of the wave transmission.
Consider an example of calculating the basic parameters of a sealed wave transmission with a disk wave generator, in which the flexible wheel remains stationary.
Initial data for the calculation are determined from the parameters of the motor: its power and shaft speed at the motor output. Also set the value of the required speed of the output shaft of the wave transmission to solve a practical problem.
The gear ratio in gears is determined by the ratio of the rotational speeds of the input and output shafts [2].
For a wave transmission with a fixed flexible wheel g, the rotational motion will be transmitted from the wave generator h to the rigid wheel b, therefore:
nh - speed of rotation of the drive shaft and wave generator, rpm;
nb - speed of rotation of the driven shaft and rigid wheel, rpm.
For a two-wave generator V = 2, at k = 1 we find the number of teeth of rigid b and flexible g wheels:
According to the initial data, calculate the torque on the output shaft of the motor, which will be the drive shaft for wave transmission, Nm:
Wh - power on the drive shaft, W.
Calculate the moment on the driven shaft of the wave transmission, Nm
Kd - coefficient of dynamics of external load - takes into account the occurrence of gear engagement of additional dynamic loads. Its value depends on the errors of the teeth of the wheels, the circumferential speed, the attached masses and other reasons. It is recommended to choose Kd in the range of 1 - 1.25.
The diameter of the dividing circle of the gear ring of the flexible wheel 𝑑𝑔 is determined from the condition of ensuring the strength of the working surfaces of the teeth for crushing, mm:
[σ_см ] - permissible bending stress on the working surfaces of the teeth; it is recommended to choose:
- [σсм]= 10... 30 MPa for steel gears (with a hardness of about 300 HB) for high-speed and medium-speed transmissions;
- [σсм]=60... 100 MPa for modes with short-term overloads and low-speed transmissions.
ψ_а=b_g/d_g - the ratio of the width of the toothed crown, it is recommended to take
𝜓а=0,1...0,3 (lower values are chosen for lightly loaded gears).
According to (6) determine the smallest allowable diameter).
Define the module:
Select the nearest value of the standard module m (it is recommended to choose the nearest higher value) according to the series:
1 row: 0.2; 0.25; 0.3; 0.4; 0.5; 0.6; 0.8.
2 row: 0.22; 0.28; 0.35; 0.45; 0.55; 0.7; 0.9.
The first row is more recommended.
Choose the basic geometric parameters of the gear when cutting teeth with a standard tool α = 20°, x0 = 0.3. Set the value of γ for the disk generator: γ = 20 ... 40° (larger values for larger i.)
We calculate other geometric parameters in accordance with the recommendations:
• ω0 = (1.05 ... 1.2)m (smaller values for smaller i),
• displacement coefficient xg - 3 ... 4;
• tooth height hg = (1.5 ... l, 8)m;
• depth of sunset hd = (1,3 ... 1,5)m,
it is recommended to choose higher values of hg and hd, because smaller ones are more likely to jump teeth under load.
Find the geometric parameters of the flexible wheel, cut by a worm cutter.
Determine the diameter of the circle of the depressions of the flexible wheel (Fig. 1, a):
Determine the inner diameter of the flexible wheel:
recommended h1= (0,005 ... 0,015) dg.
Determine the diameter of the circle of the tops of the teeth of the flexible wheel (Fig. 1, в):
Fig. 1. The geometry of the gears of the wave transmission:
a) flexible wheel, b) rigid wheel, в) height of the teeth of flexible and rigid wheels
We find the parameters of the gear ring of a rigid wheel, which is cut with a notch.
Hard wheel displacement coefficient
Determine the wheelbase in the machine gear with the dolbyak:
Find the diameter of the circumference of the depressions of the rigid wheel (Fig. 1, b)
da0 — the diameter of the circle of the protrusions of the dolbyak;
Find the diameter of the circle of vertices of the rigid wheel:
We calculate the geometric parameters of the design of the wave transmission:
- width of the gear ring of the flexible wheel:
- the width of the gear ring of the rigid wheel:
Find the width of the flexible wheel:
References:
[1] Konovaliuk D.M. Detali mashyn: pidruchnyk dlia studentiv vyshchykh navchalnykh zakladiv mashynobudivnoho profiliu / D.M. Konovaliuk, R.M. Kovalchuk // Kyiv: Kondor, 2021. – 582 p.: fig. i tabl. ISBN 966798222X.
[2] Malashchenko V.O. Praktychne proektuvannia i konstruiuvannia detalei mashyn : navchalnyi posibnyk / V.O. Malashchenko, V.M. Strilets, M.M. Koziar, O.R. Strilets; Ministerstvo osvity i nauky Ukrainy, Natsionalnyi universytet vodnoho hospodarstva ta pryrodokorystuvannia // Rivne NUVHP, 2020. – 145 p.: fig. i tabl. ISBN 9789663274614.
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