Using Mode Shapes for Real Time ODS Animation

Abstract

In a rotating machine, the dominant forces are applied at multiples of the machine running speed, called orders. An order-tracked ODS is assembled from the peaks at one of the order frequencies in a set of response frequency spectra of a machine. An order-tracked ODS is a convenient way to visualize and monitor the health of the machine.In this paper, it is shown how modes participate in an order-tracked ODS of a rotating machine, and how they participate differently at different operating speeds. It is also shown how the modal participation can be used to expand an order-tracked ODS so that it is suitable for display on a model of the machine. With an animated ODS display, changing vibration levels and vibration hot spots can be observed while the machine is running. IntroductionIt is well known that most rotating machines will exhibit different vibration levels under different loads and speeds. A convenient way to troubleshoot these problems is to visualize the operating deflection shapes (ODSs) of the machine in "real time". This is conveniently done by attaching multiple accelerometers to the machine surfaces, and acquiring vibration data from the machine while it is running. In addition to visualizing the deflection of the machine in real time, an ODS can be used to diagnose machine faults by numerically comparing its current values with previously archived values.All machines and mechanical structures have resonances, also called modes of vibration. Each resonance has a unique natural frequency, damping value, and mode shape. It is well known that if a resonance is excited, the response of the machine or structure can be excessive. In this sense, modes are referred to a "mechanical amplifiers". Over time, sustained excessive vibration levels will cause a variety of failures.When excited, modes participate in or contribute to the overall vibration response of a machine. In an ideal sense, a mechanical structure has an infinite number of modes, but in a practical sense only a few modes participate significantly in its response.In this paper, it is first shown how modal participation in an ODS is calculated. Once the modal participation is known, mode shapes with many components in them can be used to expand the ODS, thus providing a more accurate and realistic description of the machine's vibration. When displayed in animation, an expanded ODS is useful for observing overall vibration levels and for quickly spotting areas of excessive vibration (hot spots) under different operating conditions.

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

“…Due to this feature, a steady-state vibration shape of the structure under sinusoidal excitation can be measured in a point-by-point, but automatic and rapid, manner. In this measurement, the excitation signal given to the speaker was used for a reference signal, with which a vibration shape with a correct phase at each measurement point can be obtained [27].…”

Predicting System Response at Unmeasured Locations

“…and 15 singular vectors from U were retained corresponding to the largest 15 singular values from S. These became the U matrix for that band that were used in eq. (11)(12)(13)(14)(15). (The authors considered cases with just the real part of the FRFs, just the imaginary part of the FRFs and both real and imaginary parts.…”

“…Chen [12] expanded 3 laser velocity measurements to strain utilizing three modes on an aluminum plate mounted to a block in both air and water environments. Using the notation of "modal participation factor" for the coefficients of the mode shapes, very similar concepts were presented to reconstruct unmeasured operating deflection shapes as well as associated strain at a particular frequency by Schwarz and Richardson [13][14][15].…”