Mathematical modelling of transients in the electric drive of the turnout of the mono-sleeper type with switched-inductor motor

Introduction. The study is devoted to the development of the functionality of a railway track switch by introducing a switched-inductor electric drive. This solution justifies simplifying the mechanical part of the switches by changing the gearbox to a ball-screw and locating the all kinematic line of the switches on the mono-sleeper type. Goal. A study of the mono-sleeper turnout type behaviour to meet modern traffic safety requirements and improve operational reliability factors. Methodology. Based on electric drive theory, a kinematic line of a mono-switch turnout type with nonlinear friction characteristic is presented. Using differential equation theory and Laplace transformation, a mathematic description of a four-phase switched-inductor motor with ball-screw in a mechanical line of a single-mass electromechanical system has been made. A simulation mathematical model of the electric drive of mono-sleeper turnout type as the control system with a switched-inductor motor and nonlinear friction characteristic was built in MATLAB. Results. Simulation modelling of a mathematical model of a mono-sleeper turnout type with a switched-inductor motor and ball-screw gear has been developed and implemented. Studies of dynamics of turnout point movement have shown that, in contrast to the motors used today, the switched-inductor motor makes it possible to simplify the mechanical part of the drive, which leads to reduced time spent on laying and maintenance of turnout points, and therefore makes the design more reliable. The application of PID controller and fuzzy speed controller has shown improved dynamics of turnout point, while the fuzzy PID controller provides better performance of the set values and turnout point movements. Originality. First developed a mathematical model of the electric drive of the mono-sleeper turnout type, taking into account nonlinear friction characteristic, as an object of speed control of turnout point movement, is developed. Practical value. The developed mathematical model of a railway track turnout of the mono-sleeper type with a switched-inductor motor and ball-screw gear enables more efficient use of a microprocessor control system, creation of promising electric motor protection means and control of a turnout point.

Mathematical Model of the Tensioning in the Collet Clamping Mechanism with the Rotary Movable Input Link on Spindle Units

Increasing machining productivity causes the cutting forces acting on tools or workpieces to grow and requires extra clamping forces for their fixation reliably. In the research, a mathematical model of the operation of the clamping mechanism for fixating cylindrical objects on the spindle of machine tools at the stage of tension is presented. The presented design of the mechanism contains screw gear and provides self-braking. Based on the calculation model, mathematical dependencies are developed to describe the relationship among the movements of the parts of the mechanism when clamping forces are growing. The presented analytical dependencies allow considering the stage of growing clamping forces separately when the conservative type of forces are prevailing in the mechanism’s operation. That stage of work when both types of forces of dissipative and potential characters exist is considered. The developed dependencies describe the position of parts of the clamping mechanism depending on the generalized coordinate. The angle of rotation of the input rotating link is used as the generalized coordinate. This fact allows calculating the position of the elements of the clamping mechanism of this type depending on time. Results of the research enhance understanding the pattern of the change in the interaction of the elements and forces that act in the mechanism during the final stage of clamping. The obtained mathematical dependencies are a precondition for the development of design methodology for mechanisms of this type.