DC Motors 26.1 How does DC Motor work? Crosssection section of DC motor Mgnetic field vector, B oft Iron Core (otor) Wire length vector, dl Force vector, df Current, i Permnent Mgnet (ttor) Crosssection section of DC motor otor supported on erings (free to rotte) Crosssection section of DC motor ottion pst 90 degrees Generting torque ow generting torque! Crosssection section of DC motor witch direction of current flow fter 90 degrees (the current switching process is clled ) ow generting torque! Two segment commuttion on rotor 2 Commuttor Brs %Torque vs. 100 Angulr 50 Position 0 Torque DC 0 90 180 270 360 Angulr Position
DC Motors 26.2 4 Commuttor Brs DC 24 Commuttor Brs DC Four segment commuttion on rotor ixteen segment commuttion on rotor %Torque vs. Angulr Position Torque 100 50 0 0 90 180 270 360 Angulr Position %Torque vs. Angulr Position Torque 100 50 0 0 90 180 270 360 Angulr Position How does DC Genertor work? Mgnetic field vector, B Assuming B, v, nd dl re mutully perpendiculr, Wire length vector, dl elocity vector, v Induced EMF, d (voltge) ote tht n induced EMF lwys gives rise to current whose mgnetic field opposes the originl chnge in mgnetic flux Lenz s Lw DC Motors & Genertor ote tht DC motor lwys egins to ct like genertor once the rotor wires strt to move through the mgnetic field the induced ck EMF is proportionl to ck EMF genertes which opposes the pplied current, the force (torque) output of the motor ME 372 Circuit Model for Permnent Mgnet DC Motor ME 360 Circuit Model for Permnent Mgnet DC Motor i = pplied rmture voltge = rmture resistnce L = rmture inductnce L = ck EMF i = rmture current i = pplied rmture voltge = rmture resistnce = ck EMF i = rmture current
DC Motors 26.3 i τ = PMDC Motor tedytte tte Equtions = = 1 ( ) from circuit from d= B v dl nd v = rω from df = i dl B nd τ = rf PMDC Motor tedytte tte Equtions For given motor,, K, nd K re Armture voltge, speed ω,, nd output torque τ re relted y the 3 equtions If we know 2 of these, cn solve for 3rd one InClss Exercise #1 A smll DC motor hs these prmeter constnts = 48 volts K = 0.17 m/mp K = 0.17 volt/rd/s = 0.9 ohms Determine the output torque, τ, for the speed ssigned to your group 1) find ckemf, for your speed 2) find current, i for your speed 3) find torque, τ for your speed Torque, m Plot for InClss Exercise #1 10 9 8 7 6 5 4 3 2 1 0 0 500 1000 1500 2000 2500 3000 peed, PM Mnufcturer s Dt 2nd InClss Exercise A smll DC motor hs these prmeter constnts =? volts K = 3.60 ozin/mp K = 2.67 volt/kpm = 50 ohms On single grph, we will plot the torque vs. speed reltionship for different input voltges 24, 18, 12, 6 DC
DC Motors 26.4 Torque, ozin 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 InClss Exercise #2 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 peed, PM DC Tchometer Equtions Mechnicl construction of DC tchometer is essentilly identicl to DC motor 1 i = ( ) = 0 High impednce lod, o current = k ω = τ = k i = 0 Output voltge proportionl to ngulr velocity, ω o current Unit Conversions m 1 = 1 1 = A s PMDC Motor Eqution Prt #2 = i = k ω τ = k i ustitute into units for the ckemf constnt, k, k m : = rd / s rd A s Conclusion: Multiply oth sides y i = i kω k = k τ = k i Electricl Power = Power Dissipted Mechnicl Power (Input) (s het) (useful output) PMDC Motor Eqution Prt #2 = i = k ω τ = k i PMDC Motor Eqution Prt #2 i = i τω 2 Multiply oth sides y i = i kω k = k τ = k i Electricl Power = Power Dissipted Mechnicl Power (Input) (s het) (useful output) Electricl Power = Power Dissipted Mechnicl Power (Input) (s het) (useful output) Efficiency = Power Out Power In
DC Motors 26.5 Circuit Model for Permnent Mgnet DC Genertor gen i externl DC Motor/Genertor gen = generted rmture voltge = ck EMF = rmture resistnce i = rmture current gen PMDC Genertor Equtions i = = ω k externli i = kω Multiply oth sides y i τ = k i k = k τ = k i Electricl Power Power Dissipted = Mechnicl Power (useful output) (s het) (Input) PMDC Motor Eqution Prt #3 τstll ω = 0 = i,stll τstll = k Torque, τ constnt peed, ω At ny point on lod curve, k ω = i ω L = nolod speed (i =0) = k ω L DC Motor Commuttion DC motors require periodic switching of currents to mintin rottion ( commuttion ) conventionl DC motors use to provide commuttion, ut "rushless" DC motors which use commuttion hve een developed.
DC Motors 26.6 DC Brushed Motor Advntges, requiring only voltge source, power op mp, nd nlog control input for vrile speed opertion. through design vritions without dditionl power input DC Brushed Motor Disdvntges,, the wer producing smll prticles which cn ffect the clenliness of surrounding opertions. High current through the rushes cn cuse them to urn out rpidly which is primrily conducted wy through the rotor shft re generted t the rush/rotor interfce DC Brushless Motor The mgnetic field in the rotor is provided y permnent mgnets on the Hll effect sensors (or resolver output) re used to signl motor driver when to switch the current in the windings Motor driver depends on the controller to set desired torque output DC Brushless Motor Permnent Mgnet otor Wound Wire ttor DC Brushless Motor Advntges nd hence the het conducted to the shft is minimized. Due to the lck of rushes, motors cn e operted t high torque nd zero rpm indefinitely s long s the winding temperture does not exceed the limit. or contminte the surroundings DC Brushless Motor Disdvntges Torque ripple y design Motor opertion requires the purchse of n otor mgnets cn ecome demgnetized in high current or temperture environments Most motor drivers rke DC rushless motors y pplying reverse current, in which lmost s much power is expended to stop the motor s ws required to strt it moving