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Using eąuations (1.3) to (1.5), the incremental mechanical energy is derived as: aw_m = aw_e - aw_f - area (OBC 0),    (1.6)

and that is the area between the two curves for given magnetomotive force. In the case of a rotating machinę, the incremental mechanical energy in terms of the electromagnetic torąue and change in rotor position is written as:

aW_m=T_cS0,    (1.7)

where: T_e is the electromagnetic torąue and 60 is the incremental rotor angle. Hence the electromagnetic torąue is given by:

T_e

dW„,

d0

(1.8)

For the case of constant excitation (mmf is constant), the incremental mechanical work done is eąual to the ratę of change of coenergy W'f, which is nothing but the complement of the field energy. Hence the incremental mechanical work done is written as:

dW_m=dW'_f,    (1.9)

where: W'_t=J<MF = J<M(Ni) = jN<Mi = J(K0,i)di = Jl(0,i)idi,    (1.10)

and the inductance L and flux linkages i//are functions of rotor position and current. This change in coenergy occurs between two rotor positions O2 (x2) and 0\ (xl). Hence, the air gap torąue in terms of coenergy represented as a function of rotor position and current is:

T_e

dW_m

~d0

dW’_f ćW'_f (0,i)

-=-1 i = constant .

dG dO

cni)

If the inductance is linearly varying with rotor position for given current, which in generał is not the case in practice, then the torąue can be derived as:

where:

_{T =} dL(6»,i) i²

^e Ae 2 ’

dL(fl,i) _ L(^₂,i)-L(<9,,i)

ó>e ~ e₂-e_x

i = constant ,

(1.12)

(1.13)

and this differential inductance can be considered to be the torąue constant expressed in Nm/A². In fact it is not constant and it varies continuously. This has the implication that the SRM will not have a steady-state equivalent Circuit in the sense that the DC and AC motors have. Eąuation (1.12) has the following implications:

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