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As a component rotates it emits a response (acoustic and/or vibration) at a certain amplitude. As the speed of rotation changes, the response changes. Orders track the relationship between this response, the RPM, and the frequency of rotation.

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**Why do we care about orders? **

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Orders aid in the analysis of noise and vibration signals in rotating machinery. Each component of a system (gears, shafts, pistons, pumps, tires, etc.) contributes to the overall level of noise and vibration of the system. Order analysis helps to identify how an individual component contributes to the overall level.

**How orders are calculated?**

Orders essentially are related to the number of events per revolution.

Let’s first look at how an order is calculated for one rotating shaft.

*A rotating shaft: this represents one component of a machine. *

We begin by spinning the shaft at 600 RPM. What is the frequency of rotation?

The frequency of rotation is 10 Hz: the shaft completes 10 rotations in one second.

Below is a plot of the frequency and corresponding amplitude (whether it be pressure, acceleration, etc.). This amplitude might be measured at any location on the machine and can vary as a function of location. The amplitude of vibration on the steering wheel would be much less than the amplitude of vibration on the cylinder head cover.

Now the shaft spins at 3300 RPM. What is the frequency of rotation?

Now the shaft is rotating at 6000 RPM. The frequency of rotation is 100 Hz.

The frequency is plotted vs amplitude for this RPM.

If we take the points we have measured thus far and put them on a three dimensional (3D) plot with frequency, amplitude, and RPM, we will get the plot below.

We generated the order data at three points for one shaft.

Now, imagine instead we steadily increase the RPM from 600 to 6000 RPM and calculate the frequency and amplitude data at small RPM increments along the sweep.

The complete frequency vs amplitude vs RPM spectrum as shown below. This is the first order.

If the map is cut along the green line it is called an *order cut. *An order cut follows the RPM and amplitude of a particular order. See the figure below.

Now imagine the system consists of two shafts connected by a pulley. Shaft A is three times larger in diameter than Shaft B.

Again, Shaft A will complete an RPM sweep from 600 RPM to 6000 RPM, simultaneously rotating Shaft B.

If Shaft A is spinning at 600RPM. The frequency of rotation for Shaft A is 10Hz. Multiply this by the pulley ratio of 3 to get the frequency of rotation for Shaft B.

The amplitude of the response is added to the graph at 30Hz and 600RPM:

Shaft A now spins at 6000 RPM, which causes Shaft B to spin at 18000 RPM.

18000 RPM corresponds to 300Hz. Plot this on the graph as well.

Fill in the rest of the data from the sweep: the RPM / frequency data and the corresponding amplitude data. This will be the 3^{rd} order.

The order number is a ratio of the events per revolution relative to the first order.

In the example above, for every one revolution of Shaft A, there were three revolutions of Shaft B. This makes shaft two’s response third order.

First order is set as the reference shaft and all orders are determined subsequently according to the ratio of events per revolution relative to the first order.

The LMS Test.Lab software automatically sets the first order as whichever rotating component the tacho is tracking. If the tacho was reading on the crankshaft, the crankshaft would be set as first order. If the tacho was reading on the alternator, then the alternator would be set as first order and all orders would be relative to the events per revolution of the alternator.

So, what if Shaft B was first order instead? What would the order of Shaft A be?

For every one revolution of Shaft B, Shaft A completes 1/3 of a revolution. Therefore, if Shaft B was first order, Shaft A would be 1/3 order.

**What displays are commonly used for orders? **

Waterfalls and colormaps are commonly used for plotting order data.

These graphs are generated by creating autopowers at small RPM increments and stacking them together along the RPM axis.

Each one of the lines along the frequency axis is an individual autopower that was taken at a specific RPM increment. Stacked together they create the waterfall graph.

A more eye-friendly version of this graph is called a colormap. The colormap tilts the waterfall so that the amplitude axis is coming directly out of the page.

The amplitude is then represented by the color intensity. The darker/cooler colors are lower amplitude while the warmer/brighter colors are higher amplitude.

Key things to identify on the colormap/waterfall include resonant frequencies and order lines. The order lines are the diagonal lines coming from the origin on the map. The resonant frequencies are the high amplitude lines that extend vertically from the frequency axis.

In LMS Test.Lab there are lots of cool ways to interact with the color map including the interactive order cursor. Check it out!

**Order versus Frequency Relationship**

The frequency at which a rotating system is operating can be calculated from an order and the rotational speed (expressed in rpm) via the *Equation* below:

Frequency and orders are really both the same: a measure of events over an observation frame:

- Frequency – Number of events per unit of time
- Order – Number of events per revolution

If the time and revolutions can be related for a rotating system, then the same phenomenon can be expressed as either a frequency or an order. Thus knowing the revolutions per minute (rpm) of a rotating system allows frequency and order to be related to each other.

For example, if an engine has a 2^{nd} order vibration at 600 rpm, the frequency of vibration is 20 Hz. Take the 600 rpm, divide by 60 to get 10 Hz. Then multiply by two to get 20 Hz.

**PRACTICE PROBLEMS:**

**Fan:**

A fan with 6 blades is spinning at 6000 RPM.

What is the frequency of the main shaft?

What is the order of the blade pass?

Frequency of the main shaft is 100 Hz.

The frequency of the blade pass is 600Hz.

The order of the blade pass is 600Hz/100Hz = 6^{th} order.

Note that it is not necessary to calculate the frequencies. Simply knowing that for every one rotation of the main shaft there will be 6 blade passes allows us to figure out that the blade pass is 6^{th} order.

**Gear: **

An 86 tooth gear is on a shaft spinning at 600 RPM.

What is the shaft frequency?

What is the frequency of gear mesh?

What is the order of gear mesh?

The gear mesh order is 86^{th} order.

**Two Gears:**

The blue shaft rotates at 60RPM. What is the order of rotation of the green gear?

The green gear is a 1.625 order response.

Orders don’t have to be integers!

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**4 stroke engine: **

** **

Now try this slightly more complicated engine example:

A 4 stroke, 6 cylinder engine is in operation. What is the combustion order?

A 4 stroke engine has 1 combustion event every two revolutions of the crankshaft (see the graphic below).

Therefore, if we had one cylinder engine, the combustion order would be 1/2 as there is 1 combustion event for every 2 rotations of the crankshaft.

However, because we have 6 cylinders, the combustion order is 6(1/2) = 3.

So, the combustion order is 3^{rd} order.

The order is independent of the RPM.

Enjoy the power of order analysis!

Questions? Contact us!

**Related Rotating Machinery dynamics links:**

- Siemens LMS Test.Lab Solutions for Rotating Machinery dynamics
- What is torsional vibration?
- Calculate a VECTOR SUM to make understand
ing vibration data easy! - Zebra tape butt joint correction
- Balancing: Rotating Machinery Dynamics

**LMS Test.Lab Rotating Machinery Tips:**

- LMS Test.Lab Tips for measuring torsional vibration
- Harmonics and harmonic cursors
- Interactive order cursor
- Time Signal Calculator
- LMS Test.Lab throughput processing tips
- LMS Test.Lab Single Plane Balancing
- Shaft centerline plot using LMS Test.Lab XY display

**Digital Signal Processing Tips:**

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