Experimental Study of the Kinematics of a Double-Row Planetary Mechanism Using Two Elliptical External Gears

Introduction . Mechanisms with non-circular gears are of wide interest to researchers and inventors due to their compactness and the implementation of a wide range of transfer functions. The development of this area is stimulated by the advancements and reduction in cost of mechanical processing and additive manufacturing technologies, as well as the use of applied mathematical modeling packages for the analysis and synthesis of non-circular gears. Traditionally, noncircular gears are used to transmit rotational motion between parallel axes with a variable ratio of angular velocities. However, their use in planetary gear schemes provides implementing various types of output link motion. The analysis of the papers on the research area shows that gears with movable rotation axes have not been sufficiently studied from the point of view of kinematics and dynamics. Most research papers reveal the theory of such mechanisms without verifying the results obtained in practice. This work is aimed at the experimental verification of the kinematics of a planetary mechanism with two external engagements, which contains elliptical gears. Materials and Methods . The kinematic model of the mechanism under study is built on the basis of the velocity diagram of its links, which made it possible to obtain expressions for finding an analogue of the angular velocity and the position function of the output shaft. The experimental study of kinematics was performed on a laboratory stand containing a model of a planetary mechanism with a set of replaceable gear wheels, absolute encoders on the input and output shafts of the mechanism, a controller, and a PC for recording and processing the signal. The analysis of the obtained results was performed on a computer using statistical analysis methods. Results . As a result of kinematic analysis, position functions were constructed for three alternative planetary mechanisms, which had different geometric parameters of the gears and made it possible to implement various types of motion of the output shaft: swinging motion, discontinuous motion, and unilateral uneven rotation. Discussion and Conclusion . The analysis of the experimental results showed the adequacy of the constructed mathematical model of kinematics to real mechanisms. The confidence interval of measuring errors at a reliability level of 95% was 0.16±0.08° for the first version of the mechanism, 0.57±0.22° — for the second version, and 0.08±0.26° — for the third. The proposed planetary mechanism with elliptical gears for implementing various types of motion can be used in drives of process equipment in numerous industries: chemical and food (mixers), oil refining (pumping units for crude production), mechanical engineering (compressors, pumps, automated machines), and others. The conducted kinematic studies of the planetary mechanism and their experimental analysis are needed for further dynamic and force investigations, as well as for the design of drives based on the proposed transmission.