Application of Four-Pole Parameters to Torsional Vibration Problems

Abstract

This paper deals with the application of the method of four-pole parameters to torsional vibrations. Results are developed from fundamental principles. The four-pole parameters for the basic rotational elements are derived. These include shafts (both lumped and distributed-parameter cases), disks, dampers, and gears. The equations which must be obeyed, when these elements are connected, are presented. The application to construction of equivalent electrical circuits is given and in particular a method for constructing the equivalent circuit of distributed-parameter systems is put forth. The torsional analogs of Thevenin’s and Norton’s theorems are given for rotational sources. The fundamentals mentioned above are then applied to the following problems: (a) The effect of substituting one four-pole for another in a torsional system. (b) The effect of opening a four-pole system and inserting a new four-pole between the separated four-poles. (c) Calculation of all the torques and angular velocities in a tandem system. (d) Calculation of natural frequencies of undamped four-pole systems.