Understanding Order Analysis for Variable-Speed Machines

Definition: What is Order Analysis?

Order analysis is a specialized vibration analysis technique used for machines that operate at varying speeds. Instead of plotting vibration amplitude against a fixed frequency axis (in Hz or CPM), it plots amplitude against “orders.” An order is a multiple of the machine’s primary rotational speed. For example, the 1st order is the vibration that occurs at exactly the running speed (1x), the 2nd order is at twice the running speed (2x), and so on.

Why is Standard FFT a Problem for Variable-Speed Machines?

A standard Fast Fourier Transform (FFT) analysis works by sampling data over a fixed period of time. This works perfectly for constant-speed machines. However, if the machine’s speed changes during the data acquisition period, the resulting FFT spectrum becomes “smeared.” A vibration component that is directly tied to the running speed (like unbalance at 1x) will have its energy spread across multiple frequency bins as the speed changes, resulting in a broad, low-amplitude peak that is difficult to read and trend accurately. Order analysis was developed to solve this specific problem.

The Solution: Order Tracking

Order analysis relies on a technique called order tracking. This requires a second sensor, a tachometer (or “tacho”), which provides a once-per-revolution pulse from the rotating shaft. The vibration analyzer uses this tacho signal as a dynamic time base. Instead of sampling data based on a fixed internal clock (e.g., every millisecond), it samples data based on the shaft’s angle of rotation (e.g., every degree of rotation). This process is also known as resampling in the angle domain.

By synchronizing the data acquisition to the shaft’s actual movement, the resulting spectrum is in terms of orders, not frequency. Now, if the machine speeds up or slows down, the 1x unbalance peak will remain a sharp, clear peak in the 1st order bin, eliminating the smearing effect completely.

Key Applications of Order Analysis

Order analysis is essential for any machine that does not operate at a single, constant speed. Common applications include:

• Vehicle and Engine Testing: Analyzing engine, transmission, and driveline vibrations across the full range of RPMs.
• Wind Turbines: The rotor speed varies constantly with wind speed, making order analysis essential.

– Machine Run-up and Coast-down Analysis: Analyzing vibration data as a machine starts up or shuts down is a powerful way to identify critical speeds and resonances. Order analysis makes these plots (like Bode and Waterfall plots) clear and easy to read.

• Reciprocating Machinery: Analyzing compressors and engines where instantaneous speed can fluctuate.
• Heavy Machinery: Earth-moving equipment, mining vehicles, and other machinery with variable-speed drives.

How is Order Analysis Data Displayed?

The results of order analysis are typically viewed in several ways:

• Order Spectrum: A plot of amplitude vs. orders, similar to a standard FFT but with orders on the x-axis.
• Waterfall or Cascade Plot: A 3D plot showing a series of order spectra stacked on top of each other as the machine’s speed changes. This clearly shows how the amplitude of each order changes with RPM.
• Bode Plot: A plot used in run-up/coast-down tests that shows the amplitude and phase of a specific order (usually 1x and 2x) as a function of machine speed.
• Campbell Diagram: A specialized plot that overlays the order lines on top of the system’s natural frequencies to clearly identify potential resonance points (where an order line crosses a natural frequency line).

Order analysis is a powerful and indispensable tool for accurately diagnosing the health of any machine that operates across a range of speeds.

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