Consider the motor discussed in class, modeled in terms of the output load angular velocity ωl(t) and an input motor voltage Vm(t):
Jeq * ωl'(t) + Beq * ωl(t) = Aeq * Vm(t)
where:
Jeq = Jl + ηg*Kg²*Jm
Beq = Bl + ηg*Kg²*Bm + Rm*ηg*Kg²*ηm*kt*km
Aeq = Rm*ηg*ηm*Kg*kt
Using the given values, calculate Jeq, Beq, and Aeq. Most of this is simple plug-and-chug; you will need to calculate the total load moment of inertia. The load moment of inertia consists of contributions from the external load (disc with mass md and radius rd), a 24-tooth gear, two 72-tooth gears, and one 120-tooth gear. Treat each gear as a uniform disc with a constant radius; the associated masses and radii are m24, m72, m120, r24, r72, and r120.
Given values:
rd = 50 mm
md = 40 g
r24 = 6.35 mm, m24 = 5 g
r72 = 19 mm, m72 = 30 g
r120 = 32 mm, m120 = 83 g
ηg = 90%
ηm = 69%
Kg = 70
Rm = 2.6 Ω
Jm = 7.68E-3 N-m/A
kt = 7.68E-3 V/(rad/s)
Bl + ηg*Kg²*Bm = 0.015 N-m/(rad/s)
Calculate Jeq, Beq, and Aeq using the provided formulae and values.