ArticlePractical Implementation of Torsional Analysis and Field Measurements
by Malcolm E. Leader, P.E. and Ray Kelm, P.E.
This paper provides an overview of torsional vibrations including modeling, calculation of forced torsional vibration response for varied machines, and field measurement and analysis techniques illustrated with case studies. The complexities of modeling for calculation are related along with the correlation of theoretical studies to field measurements. Various methods of calculating torsional frequencies and amplitudes are discussed along with torsional damping.
While a minimum of two inertias connected by a spring (e.g. a motor driving a fan through a flexible coupling) are required, torsional analysis of rotating equipment is less complicated than lateral analysis. Torsionally it is easier to simplify the mechanical parts of a machine train into stiffnesses and inertias. Bearings and damping have little effect on the calculations. For simple systems, closed form equations often suffice to yield accurate torsional resonant frequency values. It can be difficult to obtain accurate inertia values of complex geometries like centrifugal impellers but these can also be measured experimentally. The torsional stiffness values of flexible couplings are available from the manufacturers. Elastomeric couplings are sometimes applied and introduce non-linear elements into the analysis. Gears may have backlash that can introduce additional non-linear effects.
Many different mechanisms can excite torsional resonances in rotating equipment trains. Some examples of prime movers that produce torque pulsations are synchronous motors, variable frequency drives and reciprocating engines. Speed changing gears also can produce torque pulsations. The driven equipment may also be a torsional exciter as with positive displacement pumps and compressors or blade-pass frequencies in centrifugal equipment. This paper uses English units and includes a unit conversion chart.
Basic Torsional Information: In order to begin torsional modeling of a rotating equipment train, the system geometry must be known. It is possible to do a lumped parameter analysis where the total inertia of the main components are connected by single-value stiffness springs. However, this approach is often inaccurate as it relies on the calculations of others and should only be done as a last resort. It is much better if the analyst has access to the complete system geometry and simplifies judiciously. Improper modeling is very difficult to detect without access to raw data and the assumptions of the analyst.
The most basic data required for the analysis is the polar moment of inertia, J. Figure 1 shows a simple circular disk that would be mounted to a shaft. If the disk is not a solid object, but rather something like an impeller, calculating the polar moment of inertia can be difficult. There are a number of ways to determine the correct values. Sometimes the manufacturer will provide the data. A previous lateral or torsional analysis may be available, or it can be determined experimentally. A good estimate for the density, ρ in Eq. 1, for closed centrifugal impellers is 21 to 25 percent of the actual material density.”
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