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UDC 621.01
DEPENDENCE OF BENDING STRESSES ON THE MODULUS VALUE
Ishmuratov Khikmat Kakharovich Tashkent State Technical University PhD., Professor
Mamasalieva Muqaddas Ibadullaevna Tashkent State Technical University, Associate Professor
Anotation. The article presents the most common type of mechanical gears, providing along with high efficiency and ease of maintenance, reliability and durability in operation.
Аннотация. В статье представлен наиболее распространенный тип механических передач, обеспечивающий наряду с высокой производительностью и простотой обслуживания надежность и долговечность в эксплуатации.
Keywords: reliability, stability, wear resistance, hardness, durability, meshing modulus.
Ключевые слова: надежность, стабильность, износостойкость, твердость, долговечность, модуль зацепления.
The surfaces of gear teeth as a result of machining have roughness, i.e. protrusions and depressions, which are subjected to plastic deformation during gear meshing under the influence of load and as a result of slippage [1], due to which the roughness of the contacting surfaces changes and differs from the initial one, which is called equilibrium roughness. Profilograms of tooth surfaces with equilibrium roughness showed that their protrusions have approximately the same height and large radii of rounding [1], which causes a large contact area of mating friction surfaces of gear teeth.
The wear intensity of the friction pair depends largely on the normal load on the contact
areas.
If the contact stress does not exceed the yield strength of the tooth material, the friction surfaces wear without seizure, if the yield strength of the material is exceeded, seizure may occur.
The process of wear product separation during meshing operation is cyclic [2] and occurs after a certain number of repeated deformations.
Machine building is one of the developing branches of industry, and gears in modern machine building are the most common type of mechanical gears, providing along with high efficiency and ease of maintenance, reliability and durability in operation. The development of engineering and technology depends on quality, reliability, competitiveness, cost and improvement and other factors.
A special place in modern gears is occupied by open and closed gears. Practice shows that the gears of many machines, such as: High-performance grain combines, plowing and tilled tractors, cotton harvesters, etc., operating in conditions of increased environmental dustiness, are subject to abrasive wear, sharply reducing their service life. One of the ways to increase the durability of such gears is the selection of optimal meshing parameters (modulus and number of teeth).
The present paper is devoted to the investigation of the influence of the module value and, accordingly, the number of teeth at certain diameters of the initial circles of a spur gear installed in a coaxial reducer of a slow-speed stage of a working machine drive. [3]
The drive of the working machine is a three-stage drive with an open flat-belt transmission and a two-stage coaxial gearbox. The data of kinematic calculation of the drive are presented in Table 1.
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Table 1
№ Speed,rpm Torque, Nm Transfer attitude EFFICIENCY
1 2950 66 2 19 0 95
2 1374 137 3 55 0Q7
3 379 470 3,15 0,97
4 120 1435
As a result of design calculation of the most loaded low-speed stage of the coaxial gearbox from the condition of contact strength determined the center-to-center distance of the material of spur wheels, for better working out of the teeth, steel with hardness HB < 400 with allowable contact stresses wheel.
As is known, the value of the meshing modulus is usually set within the limits when designing gears. And for power transmissions, the module is not recommended less, and in the case of overloads or the possibility of wear of teeth is taken the highest value, ie. [4] In order to increase the serviceability, all machine elements must be of equal strength. The contact strength of the teeth is the main criterion for the serviceability of most gears. The highest contact stress in the meshing zone is determined by Hertz's formula. The contact strength of wheel teeth depends on the material and dimensions of the gear and does not depend on the modulus and number of teeth individually. But according to the conditions of contact strength at the accepted center distance, the module and number of teeth can have different values, but with observance of the conditions: and the gear ratio.
The second of the two main performance criteria for gears is the bending strength of the teeth. When designing, equal bending strength of gear and wheel is sought. Fig. 1 shows the dependence of
contact stresses on the modulus of gears.
360
unit
Figure 1: Dependence of contact stresses of the gear and wheel on the modulus value.
Fig. 2 shows the graph of change of bending stresses of the gear and wheel from the values of modulus
unit
Figure 2: Dependence of bending stresses of the gear and wheel on the modulus value.
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Calculations were carried out on the computer in the program Autodesk Inventor. Analysis of the obtained dependencies showed that the gear and wheel have the same contact and bending stresses, i.e. equal strength, with underloading on contact stresses, respectively, 14.4% and 18% [5].
Reducing the modulus and the corresponding increase in the number of teeth contributes to a decrease in specific slip, which increases the efficiency and reliability of the transmission against seizure, but increases the degree of unevenness of load distribution between neighboring teeth and reduces the reserve of bending strength of the transmission.
In the given study of the low-speed stage of the coaxial gearbox, it was assumed that the wear of the teeth will not reach the limit value, limited by the margin of tooth strength on bending stresses, so the modulus was taken as the design one for the gears. Table 2 shows the geometric parameters of the gear pair.
Table 2.
Geometric parameters.
Model type Gear Wheel
Number of teeth 34 106
dividing diameter 136 mm. 424 mm.
Outer diameter 144 mm. 432 mm.
Diameter of depressions 126 mm. 414 mm.
Diameter of the main circle 127.798 mm. 398.430 mm.
Diameter of the initial circle 136 mm. 424 mm.
Wheel width 118 mm. 114 mm.
The Autodesk Inventor program allowed us to determine the mass of the gearbox at different values of design and allowable contact stresses. In our case there is an increase in the mass of the gearbox by compared to if. By varying the tooth widths it is possible to achieve equality, which is optimal for reducing the metal intensity of the gearbox. [6].
The optimum values of the modulus and, accordingly, the number of teeth, which provide the greatest durability of spur gears subjected to abrasive wear according to the criterion "bending strength", can be selected by calculation at the design stage.
Conclusion
1. The largest size of abrasive particles retained on the friction surface of the teeth of the teeth of open gears according to the obtained expression increases with the increase of the meshing modulus, the number of teeth of the driven gear and the coefficient of friction between the abrasive particle and the tooth surface of the driven gear, decreases with the increase of the radius of curvature of the contact point of the teeth on the profile.
2. In open gears, in order to reduce the size of abrasive particles involved in the wear process and increase the wear resistance of the idler gear teeth in the presence of abrasive particles in the environment, it is necessary to use a gear with a smaller gear ratio.
3. When slippage occurs between the head and foot of the gear teeth in the meshing gear, the wear rate increases with the increase of environmental dustiness, abrasive particle size, meshing modulus, abrasive particle strength, relative slippage degree and gear speed; decreases with the increase of the hardness of the gear material, the number of deformation cycles of the wearing surface, the length of the gear teeth, the total number of teeth and the gear ratio of the meshing gear.
4. In the pole meshing due to the lack of slippage between the teeth of gears, wear of teeth
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occurs as a result of the formation of crater-shaped holes, while the rate of wear of teeth increases with increasing strength and size of abrasive particles and the speed of rotation of gears. The hardness of the gear material has the greatest influence on the reduction of the wear rate of gear teeth, relatively less influence is exerted by the number of deformation cycles of the wearing surface, the length of gear teeth and the gear ratio of the meshing.
REFERENCES
1. Dunayev P.F., Lemikov O.P. Design of units and machine parts: textbook for technical specialties of higher educational institutions. 9 - e ed. M.: Publishing Center "Academy", 2006, 496 pp.
2. Irgashev A. Assessment of wear resistance of rolling friction units working in abrasive environment. -Tashkent: TashGTU, 1996. -131с.
3. Ishmuratov H.K. Theoretical substantiation of the resource of gears of cotton harvesting machines on the criterion of wear. Dissertation of the degree of Doctor of Philosophy on technical sciences (PhD). Tashkent, 2019.- 156 p.
4. Ishmuratov H.K. Wear resistance of gear teeth, when rolling without participation in the wear process of abrasive particles // International Scientific and Practical Conference Automobile and Tractor Engineering".-Minsk, 2019. С. 16-20
5. Лемеков О.П. Основы расчета и проектирования деталей и узлов машин. Конспект лекций по курсу «Детали машин»: 3 - е изд. переб. и доп. - М.: Машиностроение, 2007. -464с.; ил.
6. М. Mamasalieva. The influence of the tread pattern on the performance of a tractor engine. E3S Web of Conferences, 2024, Tom 471, Номер статьи 01007.
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