TRANSIENTS IN ROTOR-FED SHUNT COMMUTATOR MOTOR OF THE SCHRAGE TYPE

Abstract

The thesis gives a detailed study of the transients in Schrage Motor consequent to various types of switching operations and loading etc. The treatment makes use of the 'quadrature-components approach' for the analysis. Starting with a primitive machine with 4 coils on the stator and 2 coils on the rotor, a circuit representation of the Schrage motor for transient conditions has been obtained. Through the use of appropriate connection matrices, the circuit equations have been so simplified that the electrical char acteristics can be represented by a set of four simultaneous differential equations of the first order. .An equation link ing the electrical and mechanical quantities and the mech anical equation of motion completes the set of system equa tions used in the study. The system equations as finally derived can be reduced to a form identical to those obtained for a three phase induction machine, when the effects of additional tertiary winding are eliminated. The circuit equations are differential equations with constant coefficients if the rotor speed is assumed to remain constant, an assumption which is valid if the study is confined to small intervals of time. This assumption is widely made in the study of transient phenomena in induction machines. Analytical solutions of system equations for currents and electromagnetic torque are obtained for diff erent modes of switching-in operation e.g. starting from standstill but with a definite phase shift introduced in

the injected voltage, and the most general case of switching- in from any initial speed of rotor, with arbitrary brush-separation and brush-axis shift. The transient currents predicted from this analysis are compared with those actually recorded experimentally for varying operational conditions, and it is shown that the agreement between predicted values and actual values is very close. For more complicated cases of switching-in process, with non-quiescent initial condi tions, but with rotor speed still assumed constant, it is difficult to arrive at the analytical solutions, because of the lengthy nature of the expressions involved; however, the methods of such solution have been indicated herein. For such cases the method of numerical integration can be used more conveniently, to obtain a numerical solution with the help of a digital computer. The results of direct numerical integration and analytical solutions are shown to be in agreement. The influence of various machine parameters and switching conditions on the current and torque transients has been investigated. For studies where the speed cannot be assumed to remain constant, e.g. in study of dynamic torque-speed characteristics, acceleration process and effects of sudden loading etc., the system equations become differential equations with variable coefficients. Such equations are not amenable to analytical methods of solution and can only be solved either by analogue methods or, by numerical methods using digital computers. Methods for solution using digital, computers are given in this thesis. The computer flow chart and the source programme have been given. Application of the programme for the study of dynamic response for a few typical cases is given. An important, but hitherto unknown, operational feat ure of the Schrage motor has been brought out. It has been shown that a Schrage motor may be started from stand still even across a single-phase supply. Requisite condit ions have been deduced. The response of the machine when connected to a single-phase supply, or only two of the phases of a three-phase supply, has been investigated. Necessary circuit equations have been developed. Analytical solutions have been obtained on the assumption of constant rotor speed. For evaluation of dynamic response, treating speed as a variable, the method of direct numerical solut ion has been applied. The necessary computer flow chart and source programme developed are given. The influence of various parameters on winding currents and torque are inves tigated. The effects of opening of one of the supply phases, on the response of a running machine are discussed. Results recorded experimentally are compared with those predicted from the analysis given in this thesis. A record of experimental determination of machine para meters used in this analysis is also given. In brief, a mathematical analysis has been given for the study of transient phenomena of different types. The validity of this analysis has been checked at various stages by comparison with experimental records. The analysis has then been used to obtain further new information regarding •IVthe transient behvaiour of the machine under different operational conditions, which it is difficult to obtain by experimental methods.