Engine Vibration
The subject of engine vibration can be divided into two categories: vibration of the engine parts relative to each other, called internal vibration, and movement of the engine as a whole, called here external vibration.
Internal Engine Vibration. Within the engine structure, the forces created by the interia of the moving parts and by the varying gas pressure in the cylinders must result in deflections of the structural members of the engine, since these parts are elastic. Thus, vibrations of varying frequencies and amplitudes are set up throughout the engine structure.
In any machine in which the applied forces may vary with time, there is always vibratory motion. In practice, this motion must be controlled so as to avoid malfunction, mechanical failure, or excessive noise. Experience shows that the problems in this category most often include crankshaft vibration, both torsional and bending, and vibrations in the valve-operating mechanism.
Crankshaft Torsional Vibration. This subject is treated exhaustively in refs. 8.400 - 8.694. The scope of this volume allows only to summarize the important general relationships involved. It is assumed that thereader is familiar with the general characteristics of vibrating systems.
In general, any engine speed in which torsional vibration is markedly severe is called a critical speed. The order of this speed is the ratio of the observed vibratory frequency to the crankshaft rotational frequency. The torsional vibration characteristics of a crankshaft are of course heavily influenced by the connected equipment. Reduction gears, driveshafts, generators, propellers, couplings, etc., all become part of the torsional system and must be considered in connection therewith (8.06). Particularly complex is a vibration system consisting of an engine with an air propeller mounted on its output shaft, since the propller blades usually have important modes of vibration which tie in with crankshaft torsional vibration (see ref. 8.492).
In predicting critical speeds and other aspects of torsional vibration, the crankshaft-rod-piston system is usually considered to be equivalent to a shaft carrying a disc at each crank position: so chosen that its moment of interia is equal to the moment of interia of the rotating mass at the crank plus R2 times a mass equal to half the total reciprocating mass. The rotating and reciprocating masses are considered to include the concentrated connecting-rod masses indicated in fig. 8-3. The remaining system is simplified in a similar manner by assuming a system of shafts carrying discs whose moments of interia are equivalent to those of the flwheel, couplings, gears, propellers, etc., which form part of the torsional system. The sizes and lengths of the shafts between the various interia elements are chosen so as to be equivalent in stiffness to the actual shafts, as nearly as that can be estimated. Methods of estimating crankshaft stiffness are given in refs. 8.400-8.490 (see espcially 8.400).
In multicrank engines the problem of torsional-virbation analysis is complicated by the fact that the torsional impluses originate at different crank positions at different times. Thus, even if the indicator diagrams were exactly the same in all cylinders andthe firing impluses exactly evenly spaced in time, no torsional order would completely cancel out because of angular deflection of the crankshaft. In the actual case, where indicator diagrams are never exactly alike, it is apparent that all orders of the Fourier series reperesenting engine torque may cause some torsional vibration.
In many practical cases, engines are so connected to the load that their crankshafts behave essentially as isolated vibration system systems. A familiar example is tha conventional automobile engine, where the external system (consisting of gearbox, propeller shaft, rear axle and wheels) has great torsional flexibility compared to with that of the crankshaft and is excited in torsional vibration at very low engine speeds only. The use of a hydrualic clutch or a torque converter between load and flywheel is also an effective way of isolating the engine's torsional system. In such cases, crankshaft torsional vibration is essentially an internal engine problem, and critical speeds can be predicted with a good degree of approximation (8.400-8.490). Calculation of torsional amplitudes is more difficult because damping coefficients are not easy to predict. Some work on this problem (8.50-8.52) indicates that a typical figure for the engine torsional system is 0.02 times critical damping.
Modes of Crankshaft Vibration. Let is consider an isolated torsional system consisting of a crankshaft with a flywheel at one end that has a relatively large moment of interia. The first mode of vibration will be with a node at the flywheel and an antinode at the free end. The higher modes will have a node and antinode at these positions, plus intermediate noeds from 2 to n interger numbers. It is seldom that modes higher than the second are of practical importance, except in the case of in-line engines of more that 8 cylinders (8.400).
For exactly similar designs, frequency in any mode is proportional to I/L (see Volume 1 chapter 11). Figure 8-28 gives data on the first-mode torsional frequency of crankshafts torsionally isolated from the external driven system and carrying a heavy flywheel at one end. In spite of large differences in detail design, this natural frequency shows the paramount influence of shaft length on the torsional frequency. This figure can be used for a rough prediction of first-order critical speed.
