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