Stepper Variable Reluctance - MapleSim Help

Stepper Variable Reluctance

Variable reluctance stepper motor

 Description The Stepper Variable Reluctance Motor (or Stepper Motor VR) component models a two-phase variable reluctance stepper machine. The winding resistances and inductances of the two phase windings are identical. The losses in the winding resistances only are taken into account; saturation is not modeled.
 Equations $\mathrm{\theta }={\mathrm{\phi }}_{\mathrm{rflange}}$ $\mathrm{\tau }={\mathrm{\tau }}_{\mathrm{rflange}}$ $\mathrm{\omega }=\stackrel{.}{\mathrm{\theta }}$ ${i}_{a}={i}_{{\mathrm{pos}}_{1}}=-{i}_{{\mathrm{neg}}_{1}}\phantom{\rule[-0.0ex]{1.5ex}{0.0ex}}{i}_{b}={i}_{{\mathrm{pos}}_{2}}=-{i}_{{\mathrm{neg}}_{2}}\phantom{\rule[-0.0ex]{1.5ex}{0.0ex}}{i}_{c}={i}_{{\mathrm{pos}}_{3}}=-{i}_{{\mathrm{neg}}_{3}}$ ${v}_{{a}_{p}}={v}_{{\mathrm{pos}}_{1}}\phantom{\rule[-0.0ex]{1.0ex}{0.0ex}}{v}_{{a}_{n}}={v}_{{\mathrm{neg}}_{1}}\phantom{\rule[-0.0ex]{1.0ex}{0.0ex}}{v}_{{b}_{p}}={v}_{{\mathrm{pos}}_{2}}\phantom{\rule[-0.0ex]{0.5ex}{0.0ex}}{v}_{{b}_{n}}={v}_{{\mathrm{neg}}_{2}}\phantom{\rule[-0.0ex]{0.5ex}{0.0ex}}{v}_{{c}_{p}}={v}_{{\mathrm{pos}}_{3}}\phantom{\rule[-0.0ex]{0.5ex}{0.0ex}}{v}_{{c}_{n}}={v}_{{\mathrm{neg}}_{3}}$ $J\stackrel{.}{\mathrm{\omega }}+B\mathrm{\omega }=\frac{-1}{2}{i}_{a}^{2}\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{sin}\left({N}_{r}\mathrm{\theta }\right){N}_{r}+\frac{1}{2}{i}_{b}^{2}\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{sin}\left({N}_{r}\mathrm{\theta }+\frac{1}{3}\mathrm{\pi }\right){N}_{r}-\frac{1}{2}{i}_{c}^{2}\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{cos}\left({N}_{r}\mathrm{\theta }+\frac{1}{6}\mathrm{\pi }\right){N}_{r}-\mathrm{\tau }$ $\left(\frac{1}{2}{L}_{\mathrm{max}}+\frac{1}{2}{L}_{\mathrm{min}}+\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{cos}\left({N}_{r}\mathrm{\theta }\right)\right){\stackrel{.}{i}}_{a}+R{i}_{a}={v}_{{a}_{p}}-{v}_{{a}_{n}}+{i}_{a}\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{sin}\left({N}_{r}\mathrm{\theta }\right){N}_{r}\stackrel{.}{\mathrm{\theta }}$ $\left(\frac{1}{2}{L}_{\mathrm{max}}+\frac{1}{2}{L}_{\mathrm{min}}-\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{cos}\left({N}_{r}\mathrm{\theta }+\frac{1}{3}\mathrm{\pi }\right)\right){\stackrel{.}{i}}_{b}+R{i}_{b}={v}_{{b}_{p}}-{v}_{{b}_{n}}-{i}_{b}\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{sin}\left({N}_{r}\mathrm{\theta }+\frac{1}{3}\mathrm{\pi }\right){N}_{r}\stackrel{.}{\mathrm{\theta }}$ $\left(\frac{1}{2}{L}_{\mathrm{max}}+\frac{1}{2}{L}_{\mathrm{min}}-\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{sin}\left({N}_{r}\mathrm{\theta }+\frac{1}{6}\mathrm{\pi }\right)\right){\stackrel{.}{i}}_{c}+R{i}_{c}={v}_{{c}_{p}}-{v}_{{c}_{n}}+{i}_{c}\left(\frac{1}{2}{L}_{\mathrm{max}}-\frac{1}{2}{L}_{\mathrm{min}}\right)\mathrm{cos}\left({N}_{r}\mathrm{\theta }+\frac{1}{6}\mathrm{\pi }\right){N}_{r}\stackrel{.}{\mathrm{\theta }}$

Connections

 Name Description Modelica ID ${\mathrm{plug}}_{\mathrm{neg}}$ Negative pin plug_neg ${\mathrm{plug}}_{\mathrm{pos}}$ Positive pin winding a plug_pos $\mathrm{rflange}$ Shaft end rflange

Parameters

 Name Default Units Description Modelica ID $J$ $0.005$ $\mathrm{kg}{m}^{2}$ Rotor moment of inertia J $B$ $0.008$ $\frac{Nms}{\mathrm{rad}}$ Rotor damping B $R$ $1$ $\mathrm{\Omega }$ Winding resistance R ${L}_{\mathrm{max}}$ $0.007$ $H$ Maximum winding inductance Lmax ${L}_{\mathrm{min}}$ $0.002$ $H$ Minimum winding inductance Lmin ${N}_{r}$ $20$ $1$ Number of rotor teeth Nr