In Dc Machine The Number Of Slots Per Pole Usually Lies
N = number of turns per coil. Whereas in a 4 pole machine, 180 electrical degrees is equal to 90 mechanical degrees. Most DC machines are designed in such a. The other thing to be aware of is that the more poles (magnets) there are on a motor the more work the ESC has to do per revolution. ESCs have a max RPM (usually somewhere between 120kRPM and 240kRPM for a 2 pole motor) that they can support, so a low magnet count high RPM motor will be compatible with more ESCs. A four-pole, DC generator with lap winding has 48 slots and 4 elements per slot. How many coils does it have? Assume one conductor per coil side. ANS: 96 coils Note: One conductor per coil side means two conductor or elements per coil. A 4-pole DC generator with duplex lap winding has 48 slots and 4 elements per slot. The friction and windage and core loss of the machine is 400 W. Its armature copper loss on full load and shunt field loss is a. 2156.7 W, 200 W b. 2232.6 W, 200 W. Machine the number of brush arms is the number of poles. A) less than b) equal to c) greater than d) none of the above.
Magnetic circuit calculations
The different parts of the dc machine magnetic circuit / pole are yoke, pole, air gap, armature teeth and armature core. Therefore, the ampere magnetic circuit is the sum of the ampere That is,
AT / pole = ATy + ATp+ ATg
1. Yoke,
2. Pole,
3. Air gap,
4. Armature teeth,
5. Armature core,
6. Leakage flux ab: Mean length of the flux path corresponding to one pole
Magnetic circuit of a 4 pole DC machine
Note: Leakage factor or Leakage coefficient LC.
All the flux produced by the pole will not pass through the desired path i.e., air gap. Some of the flux produced by the pole will be leaking away from the air gap. The flux that passes through the air gap and cut by the armature conductors is the useful flux and that flux that leaks away from the desired path is the leakage flux
where LC is the Leakage factor or Leakage coefficient and lies between (1.15 to 1.25). Magnitude of flux in different parts of the magnetic circuit
a)Flux in the yoke
b)Flux in the pole
c)Flux in the air gap
d)Flux in the armature teeth
e)Flux in the armature core
Reluctance of the air gap
Where
lg = Length of air gap
t = Width (pole arc) over which the flux is passing in the air gap
L = Axial length of the armature core
y t L = Air gap area / pole over which the flux is passing in the air gap
PROBLEMS:
EX.1. Calculate the ampere turns required for the air gap of a DC machine given the followingdata. Gross core length = 40cm, air gap length = 0.5 cm, number of ducts = 5, width of each duct = 1.0cm, slot pitch = 6.5cm, average value of flux density in the air gap = 0.63T. Field form factor = 0.7, Carter’s coefficient = 0.82 for opening/gap length = 1.0 and Carter’s coefficient = 0.82 for opening/gap length = 1.0, and Carter’s coefficient = 0.72 for opening/gap length = 2.0.
EX.2. Find the ampere-turns/pole required for a dc machine from the following data. Radicallength of the air gap = 6.4mm, tooth width = 18.5 mm, slot width = 13.5mm, width of core packets = 50.8mm, width of ventilating ducts = 9.5mm, Carter’s coefficient for slots and ducts = 0.27 and 0.21, maximum gap density = 0.8T. Neglect the ampere turns for the iron parts.
EX.3. Find the ampere turns required for the air gap of a 6pole, lap connected dc machine withthe following data. No load voltage = 250V, air gap length = 0.8cm, pole pitch = 50cm, pole arc = 33cm, Carter’s coefficient for slots and ducts = 1.2, armature conductors = 2000, speed = 300RPM, armature core length = 30cm.
EX.4. Calculate the ampere turns for the air gap of a machine using the following data. Corelength = 32cm, number of ventilating ducts = 4, width of duct = 1.0cm, pole arc of ventilating ducts = 4, width of duct = 1.0cm, pole arc = 19cm. Slot pitch = 5.64 cm, semi-closed slots with slot opening = 0.5cm, air gap length = 0.5cm, flux/pole = 0.05Wb.
EX.5. A DC machine has an armature diameter of 25cm, core length of 12cm, 31 parallel slots 1.0cm wide and 3.0cm deep. Insulation on the lamination is 8.0%. The air gap is 0.4cm long and there is one radial duct 1cm wide in the core. Carter’s coefficient for the slots and the duct is 0.68.
Determine the ampere turns required for the gap and teeth if the flux density in the gap is 0.7T.
The magnetization curve for the iron is:
EX.6. Find the ampere turns/pole required to drive the flux through the teeth using Simpson’s rule with the following data: flux/pole = 0.07Wb, core-length = 35cm, number of ducts = 4, width of each duct = 1.0cm, slot pitch at the gap surface = 2.5cm, slot pitch at the root of the tooth = 2.3cm, dimensions of the slot = 1.2cm x 5cm, slots/pole-pitch = 12
EX.7. Find the ampere turns required to drive the flux through the teeth with the following datausing graphical method. Minimum tooth width = 1.1cm, maximum tooth width = 1.5cm, slot depth = 4.0cm, maximum value of flux density at the minimum tooth section = 2.0T. Material used for the armature is Stalloy.
EX.8. Calculate the apparent flux density at a section of the tooth of the armature of a DCmachine with the following data at that section. Slot pitch = 2.4cm, slot width = 1.2 cm, armature core length including 5 ducts each 1.0cm wide = 38cm, stacking factor = 0.92, true flux density in the teeth at the section is 2.2T for which the ampere turns/m is 70000.
EX.9. Calculate the apparent flux-density at a particular section of a tooth from the followingdata. Tooth width = 12mm, slot width = 10mm, gross core length = 0.32mm, number of ventilating ducts = 4, width of the duct each = 10mm, real flux density = 2.2T, permeability of teeth corresponding to real flux density = 31.4x10-6H/m. Stacking factor = 0.9.
EX.10. The armature core of a DC machine has a gross length of 33cm including 3 ducts each10mm wide, and the iron space factor is 0.9.If the slot pitch at a particular section is 25 mm and the slot width 14mm, estimate the true flux density and the MMF/m for the teeth at this section corresponding to an apparent flux/density of 23T. The magnetization curve data for the armature stamping is,
Choice of specific electric and magnetic loadings in DC machine
Effect of higher value of q
Note: Since armature current Ia and number of parallel paths A are constants and armature diameter D must be as less as possible or D must be a fixed minimum value, the number of armature conductors increases as q = Ia Z / A π D increases.
(a) As q increases, number of conductors increases, resistance increases, I2R loss increases and therefore the temperature of the machine increases. Temperature is a limiting factor of any equipment or machine.
(b) As q increases, number of conductors increases, conductors/slot increases, quantity of insulation in the slot increases, heat dissipation reduces, temperature increases, losses increases and efficiency of the machine reduces.
(c) As q increases, number of conductors increases, armature ampere-turns per pole ATa / pole = (Ia Z / 2 A P) increases, flux produced by the armature increases, and therefore the effect of armature reaction increases. In order to overcome the effect of armature reaction, field mmf has to be increased. This calls for additional copper and increases the cost and size of the machine.
(d) As q increases, number of conductors and turns increases, reactance voltage proportional to (turns)2 increases. This leads to sparking commutation.
Effect of higher value of Bav
(a) As Bav increases, core loss increases, efficiency reduces.
(b) As Bav increases, degree of saturation increases, mmf required for the magnetic circuit increases. This calls for additional copper and increases the cost of the machine.
It is clear that there is no advantage gained by selecting higher values of q and Bav. If the values selected are less, then D2L will be large or the size of the machine will unnecessarily be high. Hence optimum value of q and Bav must be selected.
- In general q lies between 15000 and 50000 ampere-conductors/m.
- Lesser values are used in low capacity, low speed and high voltage machines.
In Dc Machine The Number Of Slots Per Pole Usually Lies Within
- In general Bav lies between 0.45 and 0.75 T.