ELECTROMAGNETS WITH EXTERNAL TURNING ARMATURE

 

During realization of preliminary calculation of electromagnets of the indicated type (fig. 1.1) next assumption is accepted:

1. That part of critical force is taken into account only, which created in a basic working gap. This force of F₀ in future behaves to the axis of core.

2. At the calculation of conductivity of this gap accept, that an armature is located in parallel to the butt end of core, on distance, equal to length of axis piece of core between the plane of its butt end and adjoining to its plane of armature (length of critical gap δ₀, corresponds to the critical angle of armature turn α₀)

3. Actual conductivity of this gap, determined by a Fig. 1.1 presence in it of the heterogeneous field, is replaced (in supposition of presences of the homogeneous field) by equivalent conductivity of cylinder with a height, to equal length of gap δ₀ and diameter of d₀ = ε∙d_p, where a coefficient ε as though takes into account "goggling" of flux at the butt end of core. For simplicity of exposition the indicated equivalent conductivity and corresponding to it equivalent basic working gap is called a basic gap and basic conductivity, and an index "0" is appropriated characterizing them values, for example: diameter of d₀, induction of B₀ and so on.

For a preliminary calculation, as comparison showed results of analysis and experiment, done in пп. 1-3 assumptions itself are justified practically.

In future electromagnetic force in accordance with Makswell’s formula, shown in kilograms, ie determined so:

F₀ = 5,1∙B₀²s₀ / μ₀,[kg], (1.1)

where B₀ − induction in a basic gap, Wb/cm²; s₀ − equivalent cross-section of basic gap, sm²; μ₀ = 4π∙10^-9 [Wb/A∙cm] ≈ 1,25∙10^-8, Wb/A∙cm.

We will express a value В₀ and s₀ through the qualificatory size of electromagnet core − d_с (diameter of core) and row of correction coefficients.

Because s₀ = π∙d₀/4, then, entering denotations of d₀/d_p = ε and d_p/d_c = τwe will define d₀ = ε∙τ∙d_c and, so, s₀ = ε²∙τ²∙d_c², (1.2)

where d_c − diameter of pole tip, cm; ε, τ − dimensionless coefficients of proportion, (in default of pole tip τ = 1); d₀ and d_c − accordingly equivalent diameter of basic gap and diameter of electromagnet core.

At position of armature, determined by a gap δ₀, a basic part of complete MMF (wI)₀, created at the set terms of coil operation, is spent on a basic working gap. We will designate a relation

(wI₀ / wI_f) = φ(1.2,a)

At this MMF (wI)₀, spent on a basic gap, as is generally known, is determined at the homogeneous magnetic field by field strength Н₀ and gap length δ₀, i.е.(wI)₀ = Н₀∙ δ₀, where (wI)₀ is determined taking into account possible lowering of nominal MMF of coils (wI) in the process of service and gets out with some reserve, i.е.

(wI)_f = χ∙(wI), (1.2,b)

where χ ≤ 1

Comparing (wI)₀ and (wI)_f, we will get: φ = Н₀∙ δ₀ / χ∙(wI)

or, because Н₀ = B₀/μ₀, then φ = Н₀∙δ₀ / χ∙μ₀∙(wI), from where

В₀ = χ∙μ₀∙φ∙(wI) / δ₀ (1.3)

Substituted (1.2) and (1.3) in (1.1), we will get:

F₀ = 4∙χ²∙τ²∙ε²∙μ₀∙φ²∙d_c²∙ (wI)² / δ₀² (1.4)

It is possible to reduce the expression of force to the similar formula, got of power balance of electromagnet :

F₀ = 5,1∙(wI)₀²∙|dG₀ / dδ₀|

In this case follows in (1.4) to replace ε² by the new coefficient ε_eq² = δ₀²∙|d(ε² / δ₀) / dδ|, the value of which it easily to get from (1.4) and (1.2,а), substituded value of MMF from (1.2,а), (1.2,b) and derivative conductivity

dG₀ / dδ = d(μ_0∙ s₀ / δ₀) / dδ = 0,25∙π∙τ²∙d_c²∙d(ε² / δ₀) / dδ

In these formulas φ, ε, ε_eq, τ, χ − dimensionless factors; wI − coil MMF, the value of which also can be expressed through the qualificatory size of electromagnet and row of dimensionless coefficients depending on the electromagnet operation mode and possible exceeding of temperature of heating of its coil Θ_per.

Here and in future they understand under Θ_per an average value along coil windows cross section a permissible exceeding of temperature, related to the environment temperature ϑ_env = 35⁰С, and chosen with some reserve, i.е. on 10 ÷15°C less than a maximum permissible value, indicated in ГОСТ for this class of isolation, compose the coil construction (table. 1).

In general cases, based on production experience, for the coils of electromagnets it is possible to recommend the following types of winding wire :

ПЭЛ and ПЭВ − for the devices of direct-current at the diameter of wire by a metal no more than 1,56 mm; for devices of alternating current at the diameter of wire no more than 0,55 mm.

ПЭЛШО − for the devices of alternating current at the diameter of wire from 0,55 to 0,7.

ПЭЛБО − in the devices of alternating current at a diameter from 0,56 to 1,00 mm and devices of direct-current with the diameter of wire higher 1,56 mm.

ПБД − in the coils of alternating current at the diameter of wire higher a 1,0 mm and direct − at the diameter more 1,56 mm.

ПСД − in the coils of especially responsible devices at the diameter of wire 0,56 and higher, operating in conditions, where the large increases of surrounding temperature are possible.

ПШКД − in those cases, when it is required to provide independence of resistance of coils from a temperature or application of copper thin wires not technological.

Table. 1

#	Isolation of wire, fabrication and treatment of coil	Rated values (°С)	Reserve on most heated point and production error, °C	Rated excess over tempe rature Θper, °C
Tempe rature	Excess over 350С
	Wire with a cotton or silk isolation (class of − Y). Coil is not impregnated with			5-10	45-50
	Wire enamel-insulated, there are paper gaskets between layers. Coil is not impregnated with			5-10	45-50
	Wire with cotton, silk or enamel isolation with paper gaskets (class of А). A coil is impregnated with or dipped in oily or oilmodified varnish			5-10	60-65
	Wire enamel-insulated or of the isolation of class A. Coil, compounded or saturated with compositions, attributed to the higher classes of thermiance			10-15	70-75
	A wire with glass-fibre isolation, coil, saturated with compositions on the basis of shellac or synthetic resins (class of В)			10-15	80-85
	A wire with glass-fibre isolation. Coil, saturated with compositions of enhanceable thermiance (class of F)			15-20	100-105
	A wire with glass-fibre isolation. Coil, saturated with organic-silicon resins (class of − Н)			15-25	120-135
	Naked wire - limited only in case of necessity to prevent some damage of nearby details.

 

We will consider determination of nominal MMF for the most often occuring electromagnets operation modes: