Engine Order Excitation
Engine-order forcing in rotating machinery, including shaft-order harmonics, vane and blade passing, spatial circumferential content, operating-speed mapping and resonance relevance.
Definition
An engine order is a forcing frequency expressed as an integer or, in some systems, fractional multiple of shaft rotational frequency. A 1EO excitation occurs once per revolution, 2EO twice per revolution, and so on. Stationary vanes, inlet distortion, structural asymmetry, combustion pattern and other periodic features generate characteristic orders. Expressing forcing this way makes resonance screening across speed intuitive.
Frequency relation
For a shaft speed N in revolutions per minute, shaft frequency is N/60 hertz. An order k therefore produces excitation frequency kN/60. On a Campbell diagram these appear as straight lines through the origin. Their intersections with speed-dependent modal branches identify candidate resonances.
f_EO = k N / 60
Vane and blade passing
A blade row passing a stationary vane row experiences periodic wake and potential-field loading. The dominant forcing order is related to the number of upstream or downstream vanes and the relative rotation. Likewise stationary structures can be excited at blade-passing frequency. The exact spatial harmonic and temporal frequency should come from the aerodynamic architecture rather than being guessed from one count alone.
Spatial order and nodal diameter
Excitation has both frequency and circumferential shape. A mode couples strongly only when the forcing spatial pattern is compatible with its nodal-diameter content. This selection rule is fundamental in bladed-disc forced response. A frequency coincidence with poor spatial coupling can produce little response, while a compatible harmonic can be severe.
Distortion and low orders
Inlet distortion, casing ovality, gravity or support asymmetry can generate strong low-order excitation such as 1EO or 2EO. These may excite rotor or casing modes as well as blades. Distortion can also create multiple harmonics. Measured pressure or strain spectra are useful for identifying which orders are actually present in a machine.
Speed sweep
Because order frequency scales directly with rpm, excitation sweeps continuously through modal frequencies during acceleration and deceleration. A machine can therefore cross several resonances even if it does not dwell at them. The importance of each crossing depends on forcing amplitude, damping and acceleration rate. Operating schedules can sometimes avoid prolonged dwell near critical intersections.
Non-integer and asynchronous forcing
Not all forcing is synchronous with shaft order. Aerodynamic instabilities, bearing phenomena, rotating stall and other mechanisms can create sub-synchronous or super-synchronous content not represented by simple integer EO lines. Campbell diagrams should therefore include known non-order excitations or measured spectra where relevant.
Verification
Trace every excitation order to a physical source and confirm the frequency calculation at representative speeds. Check whether the forcing is stationary or rotating relative to the blade row and whether its circumferential harmonic matches the structural model. Avoid plotting numerous arbitrary EO lines without identifying which are physically present.
A Campbell intersection only matters if the corresponding engine order exists with sufficient amplitude and compatible spatial content.
Order content from measurement
Engine test or rig data can be transformed into order spectra, allowing measured forcing or response to be plotted against shaft order rather than absolute frequency. This is particularly useful during run-up because synchronous features remain at a constant order while unrelated frequencies move differently. Order tracking can confirm which physical source drives a resonance and can reveal harmonics that were not included in the original analytical screening.
Multiple shafts and geared systems
Multi-spool engines and geared turbomachinery can contain several rotational frequencies simultaneously. An excitation may be synchronous with one shaft but asynchronous with another component. Define each order relative to the correct reference shaft and account for gear-mesh or blade-passing relationships explicitly. A Campbell diagram using only one shaft speed can miss important cross-shaft excitations in coupled machinery.
Engineering judgement — governing sensitivities
For Engine Order Excitation, the most useful review question is not simply whether the solver has produced a plausible contour or scalar result, but whether the model preserves the operating-speed dependence of natural frequency, mode shape and excitation order. Rotation, temperature, attachment stiffness and aerodynamic forcing can move both the structural modes and the excitation lines, so separation margin should be assessed over the full operating envelope rather than at a single speed. This is where apparently small modelling choices can change the engineering conclusion. The analyst should identify the variables that can move the governing response, separate physical uncertainty from deliberate conservatism, and show that the selected modelling fidelity is proportionate to the decision being supported. Where the response is close to an acceptance boundary, sensitivity cases should bracket credible changes rather than apply arbitrary percentage perturbations.
Verification evidence for the engineering record
A defensible Engine Order Excitation assessment should leave an evidence trail that another engineer can independently interrogate. At minimum, review speed sweeps, prestressed modal states, mesh and attachment stiffness sensitivity, mode tracking, damping assumptions, excitation-order bookkeeping and correlation with spin, tip-timing or vibration-test data where available. Numerical convergence should be demonstrated on the response quantity that drives the decision, not only on generic mesh or solver metrics. The report should distinguish verified numerical behaviour from validation against test or service evidence, record any extrapolation beyond the supporting data, and state which assumption would most likely change the conclusion. This turns the analysis from a plausible calculation into an auditable engineering substantiation.