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Guidelines to Engine Dynamics and Vibration

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Guidelines to Engine Dynamics and Vibration The Ship Power Supplier Guidelines to engine dynamics and vibration by Hannu Tienhaara Technology Wärtsilä Corporation In recent years shipyards and shipowners have increasingly Vibration response tuned in to the negative consequences of engine vibrations. As this article will make clear, there are three important factors contributing The pressure on engine manufacturers to improve vibration to the vibration levels and behaviour of an engine and its components. behaviour has increased, which has also driven the development and use of advanced vibration analysis and 1. A rigid body motion of the engine on its flexible mounting simulation methods. The challenge is to keep vibrations on an The engine is moving as a solid part, sometimes causing problems with acceptable level while output power increases and structures connections. become lighter. A piston engine is, by its nature, a vibrating 2. Deformation of the engine block (global vibrations) machine. To keep vibrations under control it is essential to When in resonance, this causes high stresses that might lead to failures. understand the basics and the main sources of engine 3. Local vibrations of a component vibrations. Vibrations of a component with respect to its mounting. Structural vibration is generally a result of the exciting force and dynamic It is not always easy to distinguish the global and local vibrations based on properties of the structure (Figure 1). The same analogy can be used for any simple overall measurements. The contribution of the flexible mounting is vibrating system. easy to detect, but rigid body modes are of minor importance for most In modern engine development work all these different components - constructions because they cause only small deformations and stresses. excitation, structure and vibration response - can be analyzed and taken Rigid body modes, however, might cause problems with flexible mounts or into account at the design phase itself, as has been done in the case of the pipe connections. Wärtsilä 46F engine, using advanced numerical calculation and simulation When traditional vibration measurements are performed, only the techniques. Excitation forces with all possible firing orders can be vibration response is measured. This is the quickest way to get an compared and analyzed, structural properties like the stiffness of the engine impression of the vibration behaviour of an engine or generating set. But can be optimized, and finally a dynamic simulation of the vibration response vibration response alone, without knowing anything about the engine’s can be performed. excitation and structural properties, doesn’t actually tell us very much about Mathematically the schematic diagram in Figure 1 is often described the actual reason for the vibration. with the general equation of motion: The vibration amplitude is the first thing to give an indication of possible excessive vibration of an engine or component. Normally vibration is Mx&&() t++= Cx&() t Kx () t f () t (1) measured as the Root Mean Square (RMS) velocity value, which is proportional to the energy content of the vibration. Sometimes where M, C and K are matrices of mass, damping and stiffness, x(t) is the displacement or acceleration are measured as well. vector of displacement (response), and f(t) is the vector of applied force (excitation). Harmonic orders Excitation 5.0 Frequency, Amplitude, 1.5 Direction, Location,… Vibration response Amplitude, Frequency, Mode Structure properties 1.0 2.0 Natural frequencies, Natural mode shapes Amplitude (mm/s Rms) (mass, stiffness,damping) Frequency (Hz) Fig. 1 Schematic diagram of the relationship between Fig. 2 A typical vibration spectrum measured from a running excitation, structure and vibration response. 4-stroke diesel engine. 20 - Wärtsilä 2-2004 To see the frequency content of the vibration curvature a Fast Fourier numerically, or by means of experimental modal analysis where a known Transformation (FFT) must be applied to the vibration time signal. The result excitation force - e.g. a hammer blow - is given to the structure and the is called frequency spectrum, and it shows the vibration amplitude as a response is measured. This way it is possible to see how a big force is function of frequency. needed to get the structure to vibrate at a certain level. The measurement FFT is often performed automatically by modern vibration measurement gives the natural frequencies, often called resonance frequencies, as well as tools. A typical vibration spectrum recorded on a running diesel engine is the damping properties of the measured structure, and if the measurement shown in Figure 2. In this spectrum several peaks, called ‘harmonic orders’, is performed at several locations, the natural mode shapes can be can be seen. Harmonic order number 1 represents the vibration amplitude composed. of the engine running frequency. In this case (Wärtsilä 6L46F) the running An engine or generating set with its flexible mounting is a good example speed is 600 rpm; thus the first order is 10 Hz. The other harmonics are of this kind of vibration system. In the dynamic analysis of such a system multiples of this frequency, i.e. orders 0.5, 1.5, 2.0, 2.5,... In a 4-stroke the engine itself is normally treated as a rigid body, i.e. a mass point with engine also half orders are present unlike in 2-stroke engines. mass moments of inertia. The flexible elements are treated as springs Analyzing vibrations this way in frequency domain, it is much easier for where the stiffness and damping are located. Altogether six eigenmodes of an analyst to determine the origins of the vibration. rigid body motion can then be calculated, three translational and three When it is necessary to go even further in the analysis, vibration spectra rotational modes. Since the mathematical models are very small in these can be measured from several locations in the structure and they can be cases, the FE method is not needed but special dedicated software is used. combined with special software to build up a vibration mode shape. The The FE method is normally used for larger problems like calculating natural vibration mode shapes that appear during engine operation are called frequencies and elastic mode shapes of whole engines and generating sets. Operational Deflection Shapes (ODS). Animated mode shapes are a In these calculation models the mass and stiffness are uniformly distributed powerful tool normally used in problem solving to localize weak points or over the whole structure, but the same equations apply. identify failure mechanisms. In addition to these so-called global natural frequencies, where the whole engine or generating set is taking part in the vibration mode, Dynamic properties sometimes the reason for a component vibration can be found in a local The dynamic properties of a structure essentially mean its natural resonance. In such cases a local part of the construction, e.g. a plate or a frequencies and mode shapes, which depend on the mass and stiffness pipe, may vibrate heavily at a frequency where the engine itself is not properties. Mathematically this means the solutions of the eigenvalue vibrating too much. In some cases when the vibrating part, like a problem of an undampened system: turbocharger, is relatively heavy compared to the engine, its resonance can have a considerable influence on the vibration behaviour of the whole - []MK1 yly= (2) system. Normally these problems can be handled by stiffening the local part with an additional support or by adding extra mass to it. The aim of both of where l is a diagonal matrix of eigenvalues and y is a matrix of these methods is to prevent resonance by moving the natural frequency of eigenvectors. Together with damping they define how the structure the component away from the harmful excitation frequency. Adding behaves under a certain dynamic loading. stiffness moves the natural frequency higher, and adding mass moves it A natural frequency is the frequency at which the structure ‘likes’ to lower. vibrate. There it can be excited to vibrate very easily - even with a very small force. And when it is excited, it starts to vibrate in its natural mode shape, Excitation forces such as a bending or twisting mode. The structure is said to be ‘in In a combustion engine the dynamic forces are created by various things resonance’ when a dynamic excitation force happens to influence at the like the crank mechanism, pressure pulses from gas, fuel or air flow, valves, same frequency as the structure’s natural frequency. Most vibration gearwheels, an unbalanced turbocharger, etc. Practically all these forces problems are due to resonance phenomena and most of today’s vibration are also ‘periodic’, i.e. they contain harmonic components, so the control is about avoiding resonances. frequency domain analysis is normally well applicable. However, since gear The dynamic properties can be determined by using the Finite Element hammering is a non-linear phenomenon, it is necessary to simulate the Method (FEM) when the above mentioned eigenvalue problem is solved camshaft and gear vibrations using direct integration in a time domain. Torsion mode calculated using Torsion mode measured using Rigid body pitching mode the Finite Element Method. Experimental Modal Analysis. calculated with special software. Fig. 3 Some global natural mode shapes of a Wärtsilä 20 generating set. 2-2004 Marine News - 21 The Ship Power Supplier Main excitations of a combustion engine Excitation type Mass forces Gas forces Rotating masses Oscillating Cylinder Excitation source (unbalance) masses pressure Appearance Vibration at the first Vibration at lowest full orders, All harmonic orders, including harmonic order mainly orders 1 and 2 half orders in a multicylinder Rigid body vibration Rigid body, bending and Causes mainly torsion based deflections and vibrations on engine block and bending some torsion the engine Simple Complex Fig. 4 Categories of main dynamic excitations.
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