Contents
The impedance of a rectangular conductor of the starting cage of a double-cage motor is calculated by using the Babnow-Galerkin method. The working cage is assumed to consist of cylindrical conductors. Graphs of the resistance and inner reactance are given.
Übersicht
Die Impedanz eines Leiters mit rechteckförmigem Querschnitt im Anlaufkäfig wird mit Hilfe der Bubnow-Galerkin-Methode berechnet. Dabei wird angenommen, daß der Arbeitskäfig zylindrische Leiter aufweist. Es werden Diagramme des Widerstandes und der inneren Reaktanz angegeben.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A :
-
z-component of the vector potential (complex r.m.s. value)
- B x ,B y :
-
components of the magnetic induction (complex r.m.s. values)
- h :
-
length of slot between conductors
- I, I J ,I 2 :
-
currents (complex r.m.s. values)
- \(\begin{gathered} j = \sqrt { - 1} \hfill \\ k = \sqrt {\omega \mu \gamma } \hfill \\ q = R_{2.0} /R_{1.0} \hfill \\ \end{gathered} \) :
-
imaginary unit
- r 1 :
-
radius of conductor
- R 1,R 2 :
-
resistances
- R 1.0,R 2.0 :
-
ohmic resistances
- X 1,X 2 :
-
reactances
- Z,Z 1,Z 2 :
-
impedances
- z * :
-
conjugate complex number ofz
- Rez, Imz, |z|:
-
real part, imaginary part and modulus of complex numberz
- ∂/∂n :
-
derivative in the normal external direction
- ∇2 :
-
scalar Laplacian
- α:
-
half of the angle corresponding to slot width
- μ:
-
permeability
- γ:
-
conductivity
- ω:
-
pulsation
- δn :
-
Kronecker symbol
References
Annell, H.: The alternating current impedance of a solid conductor of circular cross-section placed in a semi-closed circular slot. Transactions of the Royal Institute of Technology (Electrical Eng.) No. 200, Stockholm 1963
Bahr, K.: Die Stromverdrängung in einer Rechtecknut als Grenzfall der Stromverdrängung in einer Trapeznut. Arch. f. Elektrotech. 51 (1966) 52–57
Buchholz, H.: Die zweidimensionale Stromverdrängung in einer wechselstromdurchflossenen, trapezförmigen Nut. Arch. f. Elektrotech. 49 (1965) 291–298
Sikora, R.; Lipiński, W.: Twodimensional displacement of current in slots of electric engines. Archiwum Elektrotechniki 20 (1971) 467–478 (in Polis)
Sikora, R., Rolicz, P.: Impedance of a cylindrical conductor placed in a slot of an electric machine. Archiwum Elektrotechniki 21 (1972) 401–405 (in Polish)
Swann, S. A.; Salmon, I. W.: Effective resistance and reactance of a solid cylindrical conductor placed in a semiclosed slot. Proceedings of IEE 109 (1962) 611–615
Swann, S. A., Salmon, I. W.: Effective resistance and reactance of a rectangular conductor placed in a semiclosed slot. Proceedings of IEE 110 (1963) 1656–1660
Swann, S. A.; Noton, R. M.: Effective resistance and reactance of a conductor of trapezoidal cross-section placed in a semi-closed slot. Proceedings of IEE 117 (1970) 401–408
Rolicz, P.: Calculation of conductor impedance by direct methods of functional analysis. Doctoral Thesis, Polytechnic of Szczecin, 1973 (in Polish)
Purczyński, J.; Rolicz, P.; Sikora, R.: Use of Ritz and Bubnow-Galerkin methods for calculation of inductance and impedance of conductors. Arch. f. Elektrotech. 57 (1975) 119–126
Rolicz, P.: Application of Bubnow-Galerkin method to computation of conductors impedance. Archiwum Elektrotechniki 24 (1975) 89–102 (in Polish)
Rolicz, P.: Transient skin effect in a cylindrical conductor placed in a semi-closed slot. Arch. f. Elektrotech. 58 (1976) 273–281
Rolicz, P.: Impedances of rotor-conductors with circular cross-section of a double-cage motor. Arch. f. Elektrotech. 62 (1980) 13–18
Alexiewicz, A.: Functional analysis. Warsaw: PWN, 1969 (in Polish)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rolicz, P. Impedance of a rectangular conductor of the starting cage of a double-cage motor. Archiv f. Elektrotechnik 63, 303–307 (1981). https://doi.org/10.1007/BF01574888
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01574888