The fundamentals of machine design is done before desgn a machine and it is important part. Also It need to be consider all considerations about all factors.
Symbols – Fundamentals of machine design
n = speed in revolution per second(rps)
ns = synchronous speed(rps)
p = number of poles
a = number of parallel paths in the windings
z = total number of conductors in the winding
Tph = total number of series turns per phase
Kw = winding factor
Ƭ = pole pitcg(m)
Ia = armature current(A)
and Iz = current in each conductor(A)
Iph = current per phase(A)
E = induced emf(V)
Eph = induced emf per phase(V)
W = Power developed by armature
Ø = average flux per pole (Wb)
Principle Dimensions
Two magnetically active members stator(fixed) and rotor(armature), capable of rotating and they are separated by a narrow annular air gap.
Principle Dimensions
- The stator bore diameter(D)
- Stator core length(L)
Active materials in an electric machine are iron and copper
Total magnetic loading – fundamentals of machine design
Total flux that leaves or enter the airgap around its entire periphery.
Btot = P Ø
p = number of poles of the machine
Ø = average flux per pole
Specific magnetic loading
Average flux density over the air gap of an electric machine. Indicates extent to which the magnetic material iron is utilized in the machine (there is magnetic loss)
Bsp = Total flux/Total area = P Ø/2π(D/2) L
Bsp = P Ø/πDL
Design Criteria
Use highest possible Bsp within around the permissible range of iron loss
Total electric loading
Total no of ampere conductors around the entire periphery of stator (or the armature) winding.
Atotal = IzZ
Specific electric loading
Number of armature conductors per meter length of the armature (or stator) periphery.
Specific electric loading (Asp) = Total armature ampere conductors/Armature periphery at the airgap
Asp = IzZ/ πD
Directly related to the mmf produced by the armature winding choice of its value also depends on the permissible I2R (i.e. Temperature rise) and the amount of cooling provided
Design Criteria – Fundamentals of machine design
Use highest possible Aspwithin permissible range of copper loss
Temperature rises
Breakdown of insulation
Output if DC machines
Power developed by the armature of the dc machines (Internal power)
Wa = generated emf X Armature current
Wa = E. Ia
But E = Ø.Z.(P/a). n. Ia Ia/a = Iz (current in each conductor)
Wa = (P. Ø). (Iz.Z.n)
Wa = Total magnetic loading X Total electric loading X speed(rps)
Output of the DC machine
Wa = (P. Ø). (Iz.Z).n
Wa = (πD.L.Bsp). (πD. Asp). n
Wa = π2. Bsp..Asp. D2.L.n = C0. D2L.n
Where the output coefficient C0 = π2. Bsp.Asp
Note – Fundamentals of machine design
D2L is proportional to the machine
Therefore, output of the machine is directly proportional to its volume for given values of electric and magnetic loadings.
Also from equation of Wa , high speed motor is smaller than a low speed motor for same power rating.
We should not confuse the power Wa developed by the armature with the rated output W of the machine. The relation between Wa and W depends on whether the machine is running as a motor or a generator.
Example, consider a DC shunt machine running in the generator mode
Power developed by armature in a generator in a generator: Wa
Wa = W + total copper loss
Also, Wa = input power – friction and windage loss
Wa = W/n – (friction + windage losses)
n is the generator efficiency
If the same machine running in the motor mode
Wa = output power +friction and windage losses
and
Wa = W + (friction + windage losses) Wa = W/n –(copper loss)