Torsional Analysis Of Reciprocating Machinery: Damping And Forced Response

Early analysis and treatment help prevent catastrophic failure

This article was originally published in the October issue of COMPRESSORtech2. We only publish a fraction of our magazine content online, so for more great content, get every issue in your inbox/mailbox and access to our digital archives with a free subscription.

By Justin Hollingsworth

Torsional problems with machinery trains have been compared to high blood pressure in humans — both issues often go undetected using common observation methods, and can eventually be catastrophic if left untreated. Once finally detected, the extra measures necessary to diagnose and remedy the situation are usually more dramatic than methods that could have been used at an earlier stage. In the case of reciprocating machinery, the best cure involves a thorough torsional analysis undertaken early in the design stage, to avoid failures such as the example shown in Figure 1. This approach can help eliminate the need for retrofit solutions or repairs in the field, which can be costly and time consuming.

Unfortunately, conducting a torsional analysis does require that some judgment calls be made in order to provide an effective outcome while avoiding excessive cost. Consumers of this information also need to ensure that they understand and agree with the assumptions made to perform the analysis in order to minimize the risks involved.

A torsional analysis fundamentally seeks to minimize interaction between the torsional critical speeds of a machinery train and excitation energy produced by the driver and load. This is normally accomplished by preparing a mass-elastic model, determining the torsional frequencies and mode shapes, comparing them with potential excitation sources and determining the forced response stress and/ or torque levels expected in the rotating components for the anticipated operating conditions. Such an analysis may also need to include additional work to ensure that the train can accommodate transients or off-design conditions, such as startup or engine misfire events.

Figures 2a and 2b (top, bottom). Excitation of a torsional critical speed and representative amplification factor (Q) calculation.

The intent of this article is not to provide a listing of requirements for a complete torsional analysis, as several notable resources are available that outline such information (for example, see the Gas Machinery Research Council publication “Guideline and Recommended Practice for Control of Torsional Vibrations in Direct-Driven Separable Reciprocating Compressors,” and API 684, among others). Rather, this article is intended to review two common issues requiring decisions that can significantly impact the results of a torsional analysis involving reciprocating machinery: damping assumptions, and the scope of forced response calculations.

Damping assumptions

Damping occurs when the amplitude of an oscillation decreases as energy is removed from a system to overcome resistive forces. Torsional damping is normally accounted for during an analysis as either an inherent system dynamic amplification factor (Q), or discrete component damping. For reciprocating machines, inherent system damping can be provided by a number of sources, including friction, material hysteresis and bearing oil films. The assumed Q value can have a profound impact on the analysis results, as the dynamic torque and stress levels developed in the shafting are proportional to this parameter. Assumptions for Q are normally guided by torsional testing experience with similar configurations and can vary greatly depending on the systems involved. Some trains (such as reciprocating compressors directly driven by electric motors through rigid couplings) have been known to exhibit Q values of 80 or more, while other types of reciprocating machinery might be subject to values of 35 or lower, depending on the specific equipment involved.

One method of experimentally determining an appropriate Q value involves capturing a waterfall plot of torsional oscillation during a startup event (Figure 2), and calculating Q by utilizing the half-power point method (described in API 684 and elsewhere) to examine the response peaks that occur as various orders of running speed traverse the torsional modes.

Discrete damping is generated in specific components, such as viscous dampers attached to engines. These devices produce torsional damping by shearing a viscous fluid between an external housing and internal flywheel. This shearing action also produces heat, which can be- come elevated while the machine operates on a torsional critical speed. Over time, the heat can break down the viscous fluid, resulting in a loss of the damping mechanism. Manufacturers of these devices normally provide a damping value for the torsional analyst to utilize. However, it is important to realize that this damping can degrade (or completely disappear) if the device is not maintained. Therefore, it is prudent for the analyst to consider how the stress levels in the machine can be influenced if the viscous damper fails. Failure of the viscous fluid can also cause the internal flywheel and housing of the damper to seize, inducing a shift in the torsional critical speeds. These factors have the potential to result in shaft or coupling failures if not properly accounted for in the torsional analysis.

chart
Figure 3. Representative allowable stress and strength reduction factors (ASME B106M method).

Another common source of discrete damping is an elastomeric coupling. The torsional stiffness from these devices is nonlinear and can vary over a wide range, depending on the durometer of the elastomer utilized, and operating parameters such as mean torque and temperature. These factors must also be taken into account during the torsional analysis. Parameter studies or other special techniques may be necessary to properly characterize the behavior over the range of anticipated operating conditions.

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