SM_Simulator

Stepper motor simulator. Program simulates moving of hybrid stepper motor.

• Program solves system of ODE for stepper motor: $$\ \frac{d\varphi(t)}{dt} = \omega(t)$$ $$\ \frac{d\omega(t)}{dt} = (T_{e}(t) + T_{d}(t) - T_{f}(t))/J$$ $$\ \frac{dI_{1}(t)}{dt} = \frac{V_{1}(t) + V_{emf1}(t) - I_{1}(t)R}{L}$$ $$\ \frac{dI_{2}(t)}{dt} = \frac{V_{2}(t) + V_{emf2}(t) - I_{2}(t)R}{L}$$ where: $$\ N $$ - number of poles of stepper motor $$\ T_{e}(t) = -K(I_{1}(t)sin(N/2\varphi(t)) - I_{2}(t)cos(N/2\varphi(t)))$$ - electrical torque, Nm $$\ T_{d}(t) = -T_{d max} sin(4*N/2\varphi(t))$$ - detent torque of magnetic of stepper motor, Nm $$\ T_{f}(t) = \sqrt{2e}(T_{brk} - T_{c}){e}^{-(\frac{\omega(t)}{\omega_{brk} \sqrt{2}})^{2}}\frac{\omega(t)}{\omega_{brk} \sqrt{2}} + T_{c} tanh(\frac{\omega(t)}{\omega_{brk}/10})$$ - friction torque, Nm $$\ J$$ - moment of inertia, kg m^2 $$\ V_{1}(t)$$ - voltage on first phase of stepper motor, V $$\ V_{2}(t)$$ - voltage on second phase of stepper motor, V $$\ V_{emf1}(t) = -N/2 F_{max}\omega(t)sin(N/2\varphi(t))$$ - back EMF voltage of first phase of stepper motor, V $$\ V_{emf2}(t) = N/2 F_{max}\omega(t)cos(N/2\varphi(t))$$ - back EMF voltage of second phase of stepper motor, V $$\ F_{max} = \frac{T_{d} L}{K} $$ - maximum magnetic flow of poles $$\ \varphi(t)$$ - mechanical angle of rotor, radian $$\ \omega(t)$$ - angular velocity of rotor, rad/sec $$\ I_{1}$$ - current of first phase of stepper motor, A $$\ I_{2}$$ - current of second phase of stepper motor, A

• Scheme of directions of vectors:

1. Python model

• Requires: python3, numpy, scipy, matplotlib
• Run Python model: cd ./Pyhton python3 SM_simulator.py
• Parameters are inside SM_simulator.py file

2. LTSpice model Schemes:

• MotorControlStepping.asc - movement simulation of stepper motor with electro-thermal scheme of stepper motor driver
• MotorControlSteppingSimplfied.asc - simplified scheme of movement simulation of stepper motor without electro-thermal scheme of stepper motor driver
• MotorControlFreeRotation.asc - free rotation simulation of stepper motor until stopping by friction force

Subcircuits:

• StepMotor.asc - electro-mechanical scheme of stepper motor.
• HalfBridge.asc - scheme of half bridge for current stabilization and control in step motor. Dependent of subcircuit: IRFB4615PBF_therm.asc, feedback.asc
• Radiator.asc - thermal scheme of heat sink Wakefield OMNI-UNI-30-50-D
• IRFB4615PBF_therm.asc - electro-thermal model of transistor IRFB4615PBF Dependent of subcircuit: irfb4615pbf.asy
• feedback.asc - logical block of current stabilization
• irfb4615pbf.asy - symbol for spice model irfb4615pbf.spi

Quick start: cd ./LTSpice

• Download Infineon spice-model file of transistor irfb4615pbf.spi. Link: https://www.infineon.com/dgdl/irfb4615pbf.spi?fileId=5546d462533600a4015357128143396c
• Change next parameters for .MODEL MM: .MODEL MM NMOS LEVEL=3 IS=1e-32 +VTO=Vth NFS=1.988288E+12 KP=74.89621574661534 THETA=0.31480607500134106 KAPPA=42.67943561393658 VMAX = 4E+3 +NSUB=1E+15 PHI=0.576 GAMMA=0.5276 TOX=1E-07 XJ = 0 DELTA=0
• Change RS: RS 8 3 0.0001
• Change RD: RD 9 1 {Rds_val}
• Open asc-file in LTSpice and press Run button
• Run