Orders and Harmanic

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Orders and Harmanic

Postby Jabsam » Tue Mar 13, 2018 4:29 am

Hi All,

I have some confuse about the items. Could someone make some interpretation for me? Many thanks.

1. Orders

If we have very perfect balance shaft rotating, it should no vibration at all. If we attach a weight on it to make it imbalance, it will be a first order vibration (let's us E1 stand for it).

If we attach 2 weights on it to make the imbalance, so there will be ONLY a E1 (2 weights tegother make one point imbalance ), or there will be a E1 and E2 (the mainly vibration from the 2 weights, one rotation two vibration, the amplitude E2> E1) , right or not ?

If we attach 5 weights on it to make the imbalance, there will be show E1, E2,E3,E4,E5?

2. Harmanic

If a vibration, we named it E1, causing harmanic E2,E3, E4, E5......,
the amplitude is E1>E2>E3>E4>E5>....., or the amplitudes is random?

Hope can clear up th cloud over my head. Thank you all.

Best wished
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Re: Orders and Harmanic

Postby Steve Smith » Thu Mar 15, 2018 12:30 am

Hello Jab and thank you for the post.
I understand the “cloud over your head” as I wrestle with theories everyday
Let’s initially break this right down to speeds and frequencies

Speeds and frequencies are one and the same
but we incorrectly recognise them as different based on their respective measurement unit
As technicians we understand speed as RPM as (rev per minute)
However frequency is simply RPM / 60 = CPS (cycles per second) or Hz
So the next time a customer calls and claims he/she has a misfire at an engine frequency of 50 Hz you know that 50 Hz x 60 = 3000 rpm

Now Vibration orders and harmonics are essentially one and the same.
These terms are used to describe the number of disturbances per revolution of a component.

So using the engine as an example, the first order vibration is referred to as the fundamental vibration which occurs at the same speed/frequency as the engine rotation.

If we have an engine running at 3000 rpm / 60 = 50 Hz generating 1 shock or disturbance per revolution we have a possible imbalance occurring at the fundamental frequency of the engine

This is called a 1st order engine vibration (NVH identifies vibrations at these frequencies as E1)

We refer to Engine orders or harmonics of vibration when we describe multiples of the fundamental frequency.

So again using the engine as an example, a 4 cylinder 4 stroke engine generates 2 combustion events per engine revolution. This generates 2 disturbances or shocks into the crankshaft which ultimately generates a vibration

Vibrations or disturbances that occur twice per engine revolution are referred to as a 2nd harmonic /order engine vibration. (NVH identifies vibrations at these frequencies as E2) Twice the fundamental frequency (Engine speed)

The key to remember here is that the fundamental engine speed/frequency in the example above is 50 Hz where we look for peak vibrations creating 1 disturbance per engine revelation (E1)

Even though the engine fundamental speed/frequency is at 50 Hz we must also look for vibrations occurring at 100 Hz where we find 2nd order engine vibrations (E2) occurring at twice per engine revelation.

The fundamental engine speed/frequency (E1 50 Hz) has not increased to 100 Hz, the number of vibrations per engine revolutions has increased

2 disturbances per engine revolution x fundamental engine frequency (E1 50 Hz)
2 x E1 50 Hz = 100 Hz = E2 2nd order engine vibration

Moving onto your weight analogy you are correct.
A perfectly balanced shaft = no vibration

Add a single weight at the 12 O’ Clock position, we now have an imbalanced shaft with one disturbance per revolution of the shaft (First order vibration)

Now add another weight at the 3 O’ Clock position so we have a weight at the 12 and 3 O’ Clock

This does not generate two disturbances per revolution, only an increased imbalance due to the additional weight. Here we generate a single disturbance per revolution but in a different direction to the single weight.

This is where the term Vector Sum is used to denote the amplitude and direction of a vibration

Vector Sum

I recall aiming to balance wheels and tyres to 0 grams using a single weight on the inside and outside of the rims.

Often the wheel balancer would request the addition of 5 grams at a specified location opposite the weight I had already applied in order to obtain a true zero wheel balance

Not wishing to decorate the rims with weights, moving the newly applied single weight slight forward or rearward of its current position would balance the wheel to zero grams without applying the additional 5 grams.

At the time I did not understand why but now using the image above I do. (I hope that makes sense)

Adding even more weight at different locations about the circumference of the shaft in the example above will result in multiple vibrations that will no doubt increase and decrease in amplitude as they combine and cancel each other out.

I dare not contemplate the math involved here but the more imbalance that occurs the greater the forces become and so the more harmonics/orders are generated

The amplitudes of orders/harmonics
I hope I have interpreted your final question correctly and please forgive me if not………

Generally speaking orders/harmonics diminish in size starting with the greater vibration level first.

Let’s look at a tyre imbalance generating 1 disturbance per revolution (T1)
No doubt this will induce other vibrations from the tyre at twice and 3 times the fundamental speed/frequency (especially if the vibration/imbalance is exceptionally bad)
The NVH software identifies vibrations at these frequencies as T2 and T3
There may even be a T4 and T5 but generally we discard orders/harmonics after the third order.

Now, an egg shaped tyre will generate 2 disturbances per revolution.
Here T1 (fundamental tyre frequency) will be low but T2 high, followed by T4 and then T6 diminishing in amplitude respectively

An engine is another typical example where E1 will be low but E2 will be high as we have 2 disturbances per engine revolution thanks to combustion (4 stroke 4 cylinder engine) followed by E4 and E6 diminishing in amplitude respectively.

The image below should help.

Engine orders

I hope this helps and please feedback for any clarification, take care……Steve
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Re: Orders and Harmanic

Postby Technician » Thu Mar 15, 2018 11:19 pm

I do like reading your posts Steve, they are very interesting. In this thread you reminded me of an experience I had about eleven years ago when a customer arrived for some work on a car, one of the jobs was changing a tyre and part of that job was balancing the wheel, but (and I like your explanation of the fore/after position of the mass) based on where the wheel balancer advises to fit the mass, the electricity for some reason went off (power cut) right in the middle of balancing the wheel!

The customer is sat in reception waiting for the car, what does one do now!

Well, remembering back to my University study days I vaguely remembered about what I had learned regarding Triangle of Forces, this is what I think you are referring to when you talk about vectors. Using this method I was able to mathematically work out where to position the remaining masses on the wheel rim, unfortunately I was not afforded the opportunity to check my work on the balancer afterwards, but our very old spirit level balancer seemed OK with the results :)
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Re: Orders and Harmanic

Postby Jabsam » Mon Mar 19, 2018 10:57 am

Hi Steve,

You have asked my questions, orders=Harmanic, amplitudes disminishing, the for the weights adding. Thank you.

Could I ask one more question? You made an egg shaped tyre for example, it will generate 2 disturbances per revolution. And I understand the T2>T1, our NVH software will show T1,T2,T3,T4,.....(T2>T4>T6...amplitudes disminshing as you said above).

My question is, if it's perfect egg shapled tyre why it won't just generate 2 vibration, T1 and T2? Can you explain this in some words? Sorry, I know this question may come into the "science topic", maybe difficult say in few words.

Thank you, Steve.
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Re: Orders and Harmanic

Postby Steve Smith » Fri Mar 23, 2018 5:38 pm

Hello and thank you for the feedback.

The image below should help when it comes to the number of disturbances per revolution of a tyre with Radial Run out.
(Perhaps an "Egg Shaped Tyre" was not the best analogy)


You are correct, this will generate two vibrations but for every revolution of the tyre

T1 refers to one disturbance per revolution of the tyre at the same frequency/speed of the tyre

T2 refers to two disturbances per revolution of the tyre.
These vibrations occur at twice the frequency/speed of the tyre (T1)

Keep in mind that the fundamental frequency/speed (T1) has not changed, the oval tyre is generating 2 disturbances per revolution (T2)


Tyre frequency 10 Hz (Tyre Speed 10 Hz x 60 = 600 rpm)

Imbalanced tyre generating one disturbance per revolution. High vibration amplitude recorded at 10 Hz (T1)

The same tyre but now "oval" at 10 Hz (Tyre Speed 10 Hz x 60 = 600 rpm)

Oval tyre now generating two disturbances per revolution. High vibration amplitude recorded at 20 Hz (T2)
The tyre frequency/speed has not changed, the frequency at which the vibration occurs has changed.

I hope this helps, take care.......Steve
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