What is an electrical order (or mechanical order)?


An electrical order k_e is the ratio between a frequency f with the fundamental electrical frequency f_e:

    \begin{equation*} k_{e} = f / f_{e} \end{equation*}

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

    \begin{equation*} k_{m} = f / f_{m} \end{equation*}

For synchronous machines, the shaft mechanical speed is given by f_{m}=f_{e} / p so we have

    \begin{equation*} k_{m} = p k_{e} \end{equation*}

where p 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.