Review and complement of methods for changing the movement speed of mechanisms and machines elements
Authors:   Department of Analytical Mechanics, Engineering Drawing and Mechanical Engineering, National University of Water and Environmental Engineering, Strilets Oleh , Malashchenko Volodymyr ,   Department of Technical Mechanics and Dynamics of Machines, Lviv Polytechnic National University, Kłysz Sylwester ,   Airworthiness Division, Air Force Institute of Technology
Published: March 2022

In mechanical drives of machines there is a need to control changes in the speed of their actuators. Stepped and stepless gearboxes are used for this purpose. Known speed control devices have many disadvantages that adversely affect the durability and reliability of drive components and machines in general. These include the design complexity, high material consumption, automation complexity, dynamic loads during transitions from one speed to another, intensive wear of parts due to the friction connections use. The purpose of the work is to develop an algorithm for determining the kinematic, power parameters and dimensions when designing speed change devices through the ring gear of a gear differential with a rotary stopper in the form of a closed-loop hydraulic system based on authors’ previous computer-theoretical research and classical scientific advices. To solve these problems analytical expressions and graphs have been obtained for the relationship between speeds of gear differential links, the efficiency has been determined by the method of potential power – based on friction losses in each gearing. With the help of computer modeling of analytical expressions, using the MATLAB software, graphical dependences of efficiency have been obtained, which made it possible to evaluate the accomplishment of the gear differential in terms of energy consumption and possible self-braking. Based on Lagrange's theory, a dynamic model of a speed change device with a ring gear control has been constructed and a solution of the obtained system of equations has been proposed. The 3D modeling of the device has been executed and at the final choice of the optimum variant of model, after some specifications, development of technical documentation can be started. The results obtained have practical application at the stage of development and design of new speed control devices through the ring gear, allow to evaluate the operation of gear differentials in terms of energy consumption and self-braking and are the basis for further research. The graphical dependences obtained for the efficiency of the gear differentials clearly allow us to trace the change in the value of the efficiency depending on the angular velocity of the ring gear and the gear ratio. For the first time, analytical expressions were obtained to determine the efficiency of the gear differential of a speed-changing device with a driving sun gear, driven carrier, or vice versa, more accurately. The resulting graphical dependences for efficiency visually allow to trace change of efficiency value depending on angular speed of a ring gear, as a control link, and the gear ratio. Results are recommended for introduction into design and engineering practice at development of designs of speed change devices through differential gears of drives of various equipment and in educational process of higher technical educational institutions in discipline of mechanical engineering. Areas of further research – improvement of speed change devices through gear differentials in the design, manufacture, operation and repair.