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

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.