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

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.

A General Framework for Crankshaft Balancing and Counterweight Design

In the automotive field, the requirements in terms of carbon emissions and improved efficiency are shifting the focus of designers towards reduced engine size. As a result, the dynamic balancing of an engine with strict limitations on the number of cylinders, the weight and the available space becomes a challenging task. The present contribution aims at providing the designer with a tool capable of selecting fundamental parameters needed to correctly balance an internal combustion engine, including the masses and geometry of the elements to be added directly onto the crankshaft and onto the balancing shafts. The relevant elements that distinguish the tool from others already proposed are two. The first is the comprehensive matrix formulation which makes the tool fit for a wide variety of engine configurations. The second is an optimisation procedure that selects not only the position of the mass and centre of gravity of the counterweight but also its complete geometric configuration, thus instantaneously identifying the overall dimensions and weight of the crankshaft.

Mathematical modeling of imbalance and dynamics of a disc-shaped rotor

It is shown, that the existing methods and means for modeling the dynamics of a rotor on a balancing machine are unsuitable for the implementation of dynamic balancing of disk-shaped rotors, which ensures their highest quality balance. New models of imbalance and dynamics are proposed, which provide reliable and accurate identification of the characteristics of the imbalance of such rotors using a developed and practically tested technique. These models serve as a theoretical basis for the creation of a new computer technology for dynamic balancing of disk-shaped rotors. Keywords: disc-shaped rotor, imbalance, dynamics, modeling, dynamic balancing. [email protected]

A Dynamic-Balancing Testing System Designed for Flexible Rotor

In this paper, a dynamic-balancing testing system is designed. The innovative feature of the testing system is the dynamic balancing of the rotor system with robustness and high balance efficiency which meets the requirements of engineering application. The transient characteristic-based balancing method (TCBM) interface and the influence coefficient method (ICM) interface are designed in the testing system. The TCBM calculates the unbalance by the transient vibration responses while accelerating rotor operating without trail-weight. The ICM calculates the unbalance by the steady-state vibration responses while the rotor system operates with trail-weight and constant speed. The testing system has the functions of monitoring operations synchronously, measuring and recording the required vibration responses, analyzing the dynamic characteristics, and identifying the unbalance parameters. Experiments of the single disc rotor system are carried out, and the maximum deflection of the measuring point has decreased by 73.11% after balancing by the TCBM interface. The maximum amplitude of the measuring point at 2914 r/min has decreased by 77.74% after balancing by ICM interface, while the maximum deflection during the whole operation has decreased by 70.00%. The experiments prove the effectiveness of the testing system, while the testing system has advantages of convenient and intuitive operation, high balance efficiency, and security.

Critical Hydraulic Eccentricity Estimation in Vertical Turbine Pump Impeller to Control Vibration

In many applications, pumps are tested against standard specifications to define the maximum allowable vibration amplitude limits of a pump. It is essential to identify the causes of vibration and methods to attenuate the same to ensure the safe and satisfactory operation of a pump. Causes of vibration can be classified mainly into mechanical and hydraulic nature. Respective unbalance masses are the two major factors which cause dynamic effects and excitation forces leading to undesirable vibrations. In this paper, the procedure of vibration magnitude measurement of a vertical turbine pump at site and the process of dynamic balancing to measure mechanical unbalance of an impeller are explained. After that, the impact of hydraulic eccentricity on the vibration displacement of a vertical turbine pump has been explained using numerical simulation procedure based on “One-way Fluid Structure Interaction (FSI).” The experimental results from a pump at site are used to compare the numerical results. After the solver validation, the one-way FSI approach is used to find the critical hydraulic eccentricity magnitude of a vertical turbine pump impeller to limit the vibration magnitudes on motor component to less than 100 μm. From the numerical simulations, it is deduced that the critical hydraulic eccentricity should be limited to 400 μm in X and Y direction. The process can be used as a guideline procedure for limiting the hydraulic unbalance in vertical turbine pumps by limiting the hydraulic eccentricity.