## Definition

An **electrical order** is the ratio between a frequency with the fundamental **electrical frequency** :

Similarly, the **mechanical order** is the ratio between a frequency f with the rotational **mechanical frequency** :

For synchronous machines, the shaft mechanical speed is given by so we have

where is the pole pair number.

## Application to e-NVH

The frequency of magentic noise and vibrations is the same as the exciting electromagnetic force. Besides, most of Maxwell force harmonics are proportional to speed in synchronous machines. **A magnetic excitation or acoustic line can therefore be characterized by its electrical or mechanical order**, rather than being characterized by its frequency in Hz.

A 48 stator slot, 8-pole permanent synchronous machine produces force harmonics of wavenumber r=0 at twelve times the electrical frequency in open circuit. These pulsating forces have an** electrical order 12**, or a **mechanical order 48 **(p=4). The mechanical order is sometimes noted as H48 like “mechanical harmonic of order 48”. More generally in EV/HEV NVH, pulsating forces are dominant and for **distributed winding PMSM magnetic noise due to slotting effects occurs at multiples of stator slot passing frequencies** (HZs). On the contrary, **induction motors e-NVH due to slotting effects occurs around multiples of rotor slot passing frequencies** (HZr).

In induction machines, the concept of orders still holds in no-load conditions (null slip). However in load conditions some of the magnetic excitations are proportional to the rotational frequency, and some others are not.

## Application to Manatee

Manatee e-NVH software post processing allow to plot all quantities (permeance, flux, force, vibration, noise) as a function of electrical order or mechanical order.