The Ernest Kempton Adams Fund for Physical Research of Columbia University Reprint Series

The calculation of torsional oscillations in crankshaft-propeller systems is carried out by a new method which reduces considerably the numerical work in the case of in-line engines. The theory is briefly outlined and the reader is referred to another publication of the author for further details. Three applications follow. In the first, all six natural frequencies and the corresponding modes are calculated for a V-12 engine. In the second ‘example the method is adapted to the direct determination of the fundamental frequency. The third example deals with a la-cylinder flat opposed engine coupled to a blower and through gears to a propeller; all eight natural frequencies are determined. The natural frequencies are determined by plotting a simple curve generally close to a straight line and the corresponding modes of oscillation in the crank are expressed in terms of a sine function. The amount of numerical work involved in the procedure is independent of the number of cylinders of the engine. INTRODUCTION s REGARDS torsional oscillations, an internal A combustion engine with a long crankshaft is generally considered to be equivalent to a uniform shaft carrying equidistant identical discs. The procedures for deriving this equivalent system are familiar to vibration technicians. It is easy to calculate the discs; the moment of inertia of each is proportional to the average rotational inertia of each crank with the attached alternating masses. There will be as many discs as there are cranks. The calculation of the torsional rigidity of the equivalent shaft is not as straightforward. The crankshaft being a rather complicated elastic structure, it is generally difficult to evaluate exactly its average torsional rigidity. Moreover, it will depend on the bearing clearances. A practical rule is to adopt a shaft of the same length and diameter as the crankshaft, and, depending on one’s judgment and experience, to vary this length slightly in accordance with bearing clearances, web rigidity,’ etc. The system is thus reduced to a shaft carrying a certain number of discs. The various numerical methods devised to calculate the torsional oscillation of such a system become extremely tedious if the number of cranks exceed four. The object of the present paper is to show that it is possible to introduce considerable simplification in this numerical work.