- •V.S. Martynjuk, I.I. Popovska
- •Study of the electromechanics energy converters design Aim of work
- •Theoretical positions
- •Design of direct current electromechanics converters
- •Design of synchronous electromechanic converters
- •Designs of asynchronous electromechanics converters
- •Order of work performance
- •Contents of a report
- •Control questions
- •Research of single-phase transformer Aim of work
- •Order of work implementation
- •Table of report contents
- •Control questions
- •Research of dc generator of parallel excitation Aim of work
- •Order of work implementation
- •Control questions
- •Research of direct current мотоrs Aim of work
- •Report content
- •Control questions
- •Research of three-phase asynchronous motor with squirrel-cage rotor Aim of work
- •Order of work performance
- •Table of report contents
- •Control questions
- •Calculation of electromagnets of direct-current а. Preliminary calculation of electromagnet. Calculation of key size of core
- •1.1. Electromagnets with external turning armature
- •B) Recursive short-time mode
- •C) Short-time duty
- •1.2. Electromagnets with external forward armature travel
- •B) Recursive short-time mode
- •C) Short-time duty
- •Design of asynchronous machines
- •Features of asynchronous generators operation
- •2. Determination of main sizes and calculation of asynchronous machine
- •Choice of number of stator and rotor slots
- •4. Active and inductive resistances of stator and rotor winding
- •5. Choice of excitation capacitor
- •6. A calculation of magnetic circuit and determination of o.C. Current of asynchronous machine in traction mode
- •7. Calculation and plotting of magnetic characteristic (b-h curve) of asynchronous machine
- •8. Plotting of operating characteristics of asynchronous motor
- •9. Losses of energy and efficiency of asynchronous machine
- •Home work (by discipline “Aviation electric machines and devices”)
C) Short-time duty
At this mode the electromagnet coil can endure considerably a greater current load, than at continuous running duty. It enables to decrease its sizes, and so, key size of electromagnet core.
At determination in the preliminary calculation of coil heating, switched on during the small interval of time (turn-on time ton), about a few
seconds, it is possible to consider that all heat, radiated in a coil, is expended on heating of its active material (for example, copper), i.е. to ignore heat emission in an external environment and heating of insulants, included in its construction.
Equation of coil heating in this case will be:
R∙I2∙ton = с∙G∙ Θper, (1.29)
where c − specific heat capacity of active material of wire, J/g∙0C;
G − weight of active material of wire, g;
I − current of this short-time duty, A.
Weight of active wire material can be determined in such way:
where γm is a specific gravity, g/сm3; lav is a length of middle loop of coil, cm; Sm – cross-section of wire metal, сm2; w − number of coil loops.
Substitution of value G from (1.30) and R from (1.8) in equation (1.29) gives: (I / Sm)2 = 104∙c∙γm∙ Θper / ρ∙ton.
A current density j, [A/cm2] in the coil section equals to:
j = I / Sm = √[104∙c∙γm∙Θper / ρ∙ton] (1.31)
At load duration in one second (ton = 1s, onesecond current), a current density is determined by a formula:
j = √[c∙γm∙Θper / 10-4ρ] and, so, j = j1 / √ton.
For coils of a copper wire, if to accept: γm = 8,9 g/сm3, c = 0,39 J/g∙0C, the permissible current density at the onesecond load practically can be accepted in accordance to a table. 1.2, where the values of temperatures ϑm.per and corresponding to it values of j1 are brought accepted by ГОСТ.
Table 4
-
Class of isolation
Y
A
Compounded coils
ϑm.per (0C)
90
105
120
Θm.per = ϑper − 35 (0C)
55
70
85
j1 (A/сm2)
10∙103
10,8∙103
11,7∙103
As follows from a table. 4, at a preliminary calculation it is possible on the average to accept j1 = 11000 A/сm2 = 110 A/mm2, or with some reserve on heating j1 = 100 A/mm2: j = 104 / √ton.
On the other hand, because by a formula (1.10)
Sm = fap∙m∙n∙dc2 / w, then j = I / Sm = w∙I / fap∙n∙m∙dc2, from where
w∙I = j∙ fap∙n∙m∙dc2 (1.33) and, so, by (1.3)
В0 = χ∙μ0∙φ∙(wI) / δ0 = χ∙μ0∙φ∙j∙fap∙n∙m∙dc2 / δ0 (1.34)
Substituted a value S0 (1.2) and В0 (1.34), we will define the size of electromagnetic force by (1.1) :
F0 = 4∙ χ2∙μ0∙φ2∙j2∙fap2∙n2∙m2∙dc6∙ε2∙τ2 / δ02 (1.35)
from where with a glance of (1.31) it is possible to find a key size of electromagnet core for short-time duty with the set turn-on time:
dc = 6√[2∙103∙ρ∙ton∙δ02∙F0 / (χ2∙φ2∙c∙γm∙fap2∙n2∙m2∙ε2∙τ2∙Θper)] or, if to take on a close value of j =104 / √ton,
dc = 6√[0,2∙ton∙δ02∙F0 / (χ2∙φ2∙fap2∙n2∙m2∙ε2∙τ2)] (1.36)
In general case we have:
dc = 3√[(C3∙ δ0/ε)√ F0∙ ton] (1.37)
where C3 = √[2∙103∙ρ / χ2∙φ2∙c∙γm∙fap2∙n2∙m2∙τ2∙Θper] = √{[C1∙h∙(1 + 2n + α) / [n∙(1 + n)∙fap∙c∙γm]} (1.38)
at the close value of j = 104 / √ton
С3 = 0,14/ (χ∙φ∙fap∙n∙m∙τ) (1.38,а)
Because ε, in turn, depends on dс, then, as well as before, for determination of dс can be recommended the following methodology.
We will transform a formula (1.37) so: (dс / δ0)2 = С3∙(√ F0∙ ton) / (δ02∙ε). From here
(√F0) / δ02 = χ3∙ε / (С3√ton) (1-39)
Set by values χ, it is possible to define (√F0) / δ02 and then, as well as before, to build graphic dependence (√F0) / δ02 in a function of χ.
At solution of reverse task by the known values of F0 and δ02 determine (√F0) / δ02 and find χ = dс / δ0 by a chart. By value χ and given δ0 find the key size of electromagnet core dc = χ∙δ0,
and so, coil sizes and cross-section of wire metal:
Sm = π∙ρ∙(1 + n)∙j∙fap∙n∙m∙dc3 / 104∙U, (1 -40)
or at the close value of j = 104 / √ton
Sm = π∙ρ∙(1 + n)∙fap∙n∙m∙dc3 / U∙√ton. . (1.40,а)
Because w∙Sm = НА∙fap, then a number of coil loops of electromagnet, operating in the short-time duty, is equal to: w = 104∙U / π∙ρ∙(1 + n)∙j∙dc or at the close value of j
w = U∙√ton / π∙ρ∙(1 + n)∙dc.
We will designate C4 = 102 / [π∙(1 + n)∙√(ρ∙c∙γm∙Θper)], or at a close value j: C4 = 1 / [π∙ρ∙(1 + n)].
Then the number of electromagnet coil loops, operating in the short-time duty, can be expressed so:
w = (U∙C4∙√ton) / dc (1.41)
Induction in a working air-gap δ0 can be defined by found value of dс, χ and ε from a formula (1.1) and (1.2), or before determination of dс approximately by a formula:
B0 = [4,8∙10-5 / (τ∙3√ С3)]∙3√[F0 / (δ0∙√ton)].