Actuators and dc machines
- convert electromagnetic energy into kenetic energy - v(t)=N(dΦ/dt)=di/dt L - can be modelled as an RL circuit - p=LI^2/2 - as current increases more energy is stored in magnetic field in inductor - if L changes then conservation of energy states that the change in electrical energy stored equals work done moving the actuator rod in/out the coil - this is basis of electric solenoid - if the rod is high reluctance, it effects inductance greatly by its presence - if rod is attached to spring, the work done on it keeps it in circuit, else with circuit off it is pushed out - F=½ i^2 dL/dx - F is force, x is distance moved by actuator rod - B(g)= µ0 Ni/2g - air gap is g - Fx=Fspring at equilibrium - torque T=½ i^2 dL/dθ where θ is angle - DC generators work by moving a coil through magnetic flux lines - there are 2 main components, the stator and the rotor - stator is stationary and holds magnetic field in place - rotor spins, holding coils which pass through field lines - e=Blv - generated emf using flux density, length of coil and velocity - emf is only induced as coils pass through flux lines - thus as coils pass parallel to flux lines nothing is induced - time taken to turn from position 1 to 2 of rotation = θ2-θ1/ω =θ2-θ1/2πf - where f is revolutions per second - peak generated = epk= NΦmax*n/15 *α - where a is pole arc/pole pitch ~0.7 - e=CnΦ in general, where C is machine constant - electromagnetic torque T=BILR - where R is radius of armature - T = K(m)ΦI(a) where K(a) is machine constant - the reversibility of electric machines is the principle that a generator can be a motor and vice versa - In a motor, n motor speed = V-IR/CΦ - e= K(e)n for back emf - If is approximately constant determined by supply voltage - R(a) is always very small - because resistance is s small current surge is possible, so starts with low controlled current - increasing R(a) reduces speed - greater resistance in field windings increases
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