# Analytical solution of the problem of dynamic synthesis of a six-link straight-line converting mechanism of the sucker-rod pumping drive

## Authors

• Ayaulym Rakhmatulina Institute of Mechanics and Engineering Science named after academician U. A. Dzholdasbekov KN MES RK; Almaty Technological University, Kazakhstan
• Nurbibi Imanbayeva Institute of Mechanics and Engineering Science named after academician U. A. Dzholdasbekov KN MES RK, Kazakhstan
• Sayat Ibrayev Institute of Mechanics and Engineering Science named after academician U. A. Dzholdasbekov KN MES RK , Kazakhstan
• Assemgul Uderbayeva Almaty Technological University, Kazakhstan
• Aiman Nurmaganbetova Kazakh Leading Academy of Architecture and Civil Engineering, Kazakhstan

## Keywords:

sucker-rod pump drive, converting mechanism, balancer, optimal balancing, dynamic synthesis

## Abstract

The paper presents an analytical solution to the problem of optimal dynamic balancing of the six-link converting mechanism of the sucker-rod pumping unit. This problem is solved numerically using a computer model of dynamics, namely by selecting the value of the correction factor k. Here we will consider an analytical method for solving this problem, that is, we find the location of the counterweight on the third link of the six-link converting mechanism for balancing. To solve the problem, we use the principle of possible displacement and write an equation where we express the torque through the unknown parameter of the counterweight. Further, such a value of the unknown parameter is found, at which the minimum of the root-mean-square value of torque M is reached. From the condition of the minimum of the function, we obtain an equation for determining the location of the counterweight. Thus, we obtain an analytical solution to the problem of optimal dynamic balancing of the six-link converting mechanism of the sucker-rod pumping drive in various settings.

According to the results, it was found that with the combined balancing method, the value of the maximum torque M and the value of the maximum power are reduced by 20 % than when the counterweight is placed on the third link of the converting mechanism, as well as when the value of the maximum torque is determined through the correction factor k.

In practice, balancing is carried out empirically by comparing two peaks of torque M on the crank shaft per cycle of the mechanism movement. Solving the analytical problem, we determine the exact location of the counterweight.

## Supporting Agency

• This research has been funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08052127).

## Author Biographies

### Ayaulym Rakhmatulina, Institute of Mechanics and Engineering Science named after academician U. A. Dzholdasbekov KN MES RK; Almaty Technological University

PhD, Associate Professor

Department of Mechanical Engineering and Robotics

Department of Automation and Robotics

### Nurbibi Imanbayeva, Institute of Mechanics and Engineering Science named after academician U. A. Dzholdasbekov KN MES RK

PhD, Associate Professor

Department of Mechanical Engineering and Robotics

### Sayat Ibrayev, Institute of Mechanics and Engineering Science named after academician U. A. Dzholdasbekov KN MES RK

Doctor of Technical Sciences, Professor

Department of Mechanical Engineering and Robotics

### Assemgul Uderbayeva, Almaty Technological University

PhD, Associate Professor

Department of Department Automation and Robotics

PhD, Associate Professor

Department of General Construction

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2021-12-21

## How to Cite

Rakhmatulina, A., Imanbayeva, N., Ibrayev, S., Uderbayeva, A., & Nurmaganbetova, A. (2021). Analytical solution of the problem of dynamic synthesis of a six-link straight-line converting mechanism of the sucker-rod pumping drive . Eastern-European Journal of Enterprise Technologies, 6(7 (114), 21–28. https://doi.org/10.15587/1729-4061.2021.245591

## Section

Applied mechanics