### Definition

An **electrical order** ke is the ratio between an excitation frequency f with the fundamental stator winding **electrical frequency** fs:

`k_{e}=f/f_{s}`

Similarly, the **mechanical order** km is the ratio between an excitation frequency f with the rotational **mechanical frequency** fR:

`k_{m}=f/f_{R}`

For synchronous machines we therefore have

`k_{m}=p k_{e}`

where p is the pole pair number.

### Application to e-NVH

The frequency of electromagnetically-excited acoustic noise frequency is the same as the exciting 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.

A 48 stator slot 8-pole permanent synchronous machine has radial force harmonics of wavenumber r=0 occuring at LCM(Zs,2p)fR=12fs. These pulsating forces have an** electrical order 12**, or a **mechanical order 48**. 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 EV HEV NVH due to slotting effects occurs around multiples of rotor slot passing frequencies** (HZr).

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