# Contact Problem for Crank-Planetary Reduction Gear

## Authors

• Igor V. Yanchevskyi Igor Sikorsky Kyiv Polytechnic Institute, Ukraine
• Pawel Komada Lublin University of Technology, Poland
• Nataliia V. Stelmakh Igor Sikorsky Kyiv Polytechnic Institute, Ukraine
• Denys M. Lytvynenko Igor Sikorsky Kyiv Polytechnic Institute, Ukraine

## Keywords:

Crank-planetary reducer, Contact problem, Design contact force

## Abstract

Background. The problem of calculating the contact force in the parallelogram mechanism for taking the rotary motion from satellites in the crank-planetary gearbox, depending on the angle of rotation of the eccentric shaft of the gearbox, is considered.

Objective. The aim of the paper is to develop a method for calculating the contact force in the parallelogram mechanism, depending on the rotation angle of the gear unit eccentric shaft and determination of its maximum value. The maximum force value determines the maximum stresses of the mechanism parts, and, consequently, the strength of the gear unit as a whole.

Methods. In the first stage, on the basis of formulas of analytical geometry, the contact pairs of the parallelogram mechanism are classified on leading (active) and passive. In the second stage, the method of calculating the contact force in active contact pairs is given. This method is based on the principle of possible displacements in the framework of the assumption about the quasi-static operation mode of the crank-planetary reducer. When calculating the maximum stresses in contact pairs the classical formula for cylindrical surfaces can be applied.

Results. A formula is derived that allows you to set the numbers of leading contact pairs at a given position of the crank-planetary reducer's eccentric shaft. The resulting graph of the contact force in each contact pair is obtained. The formula for determining the approximate maximum value of the contact force in contact pairs is presented, which is valid for reducers with the number of such pairs from 3 to 10.

Conclusions. The results of the developed method of calculation of reducers with the parallelogram mechanism for taking the rotary motion from the satellites are presented. It was found out that when designing gears with a parallelogram mechanism for taking the rotary motion from satellites, the issues of ensuring the dynamic strength of its parts are relevant. When checking the contact strength or ben­ding strength in the toothed engagement classical calculation methods can be applied. At the same time, when evaluating the strength of the satellite in the place of contact with the trickles of the reducer output link, Hertz’s formula can be applied, in which, as the design contact force, it should be taken to its maximum value, which is approximately equal to  X×(4F/KN), where X = (0.8 + 0.05N)2 – KF0 = T/LT – torque at the output of the gear unit; KN – total number of contact pairs; L – The distance between the of the trickle axles and the gearbox axle. It should be noted that the above formula is obtained for reducers with K = 1; 2 and .

## Author Biographies

### Igor V. Yanchevskyi, Igor Sikorsky Kyiv Polytechnic Institute

Ігор Владиславович Янчевський

Павел Комада

### Nataliia V. Stelmakh, Igor Sikorsky Kyiv Polytechnic Institute

Наталія Володимирівна Стельмах

### Denys M. Lytvynenko, Igor Sikorsky Kyiv Polytechnic Institute

Денис Миколайович Литвиненко

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