Question 18.6: Torque Equation of Step Motor Calculate the torque generated...
Torque Equation of Step Motor
Calculate the torque generated by a step motor.
Known Quantities: t = number of teeth per phase; L= axial length of rotor; g= rotor-to-stator radial air gap; r= rotor radius; \mathcal{F}= mmf developed across the two air gaps (in series) through which a line of flux must pass in one phase. Expression for the motor torque.
Find: Torque developed by the motor.
Schematics, Diagrams, Circuits, and Given Data: t=16 (48 steps, 3-phase excitation); L=6.35 \times 10^{-3} \mathrm{~m} ; g=6.35 \times 10^{-5} \mathrm{~m} ; r=1.29 \times 10^{-2} \mathrm{~m} ; \mathcal{F}=720 A-t.
T=0.314 \times 10^{-6} \frac{t L(r+g / 2) \mathcal{F}^{2}}{g} \quad \text { N-m }
Analysis: Using the expression given above gives
\begin{aligned}T &=0.314 \times 10^{-6} \frac{t L(r+g / 2) \mathcal{F}^{2}}{g} \\&=0.314 \times 10^{-6} \frac{16 \times 6.35 \times 10^{-3}\left(1.29 \times 10^{-2}+3.175 \times 10^{-5}\right) 720^{2}}{6.35 \times 10^{-5}} \\&=3.37 \mathrm{~N}-\mathrm{m}\end{aligned}