# Modelling and Analysis of Single-Phase Induction Motor with External Rotor Uma. R Edited By Sarath S Nair www.technologyfuturae.com 1.

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Modelling and Analysis of Single-Phase Induction Motor with External Rotor Uma. R Edited By Sarath S Nair www.technologyfuturae.com 1

Presentation Outline Introduction Why an external rotor? Equivalent circuit of rotor Lumped parameter equivalent circuit Mathematical model Role of conducting shell Steady state and dynamic analysis Summary References 2www.technologyfuturae.com

Introduction Many domestic appliances require low-power motors operating at constant speed that must start under load(compressors, pumps etc) Because of the reliability in operation the single- phase induction motor is one of the most widely used types of AC machines SPIM with external rotor is more advantageous for low power application Constant speed at different load can be easily achieved by increasing the motor inertia, by using an external rotor 3www.technologyfuturae.com

Why an external rotor? Allows a higher stability in operation at different loads due to higher inertia The fan blades can be attached directly to the outside of the rotor, making the motor more compact Heat generated within the rotor, is on the outside and can be dissipated easily The start-up and operating characteristics of single- phase induction motors with external rotor can be improved by covering the rotor with a conducting shell joining the two end rings 4www.technologyfuturae.com

External rotor of an Induction motor Fig1. axial half cross-section Fig2. Fluxes in longitudinal section L – laminations Φ σbx - leakage fluxes of bar B - rotor cage bars Φ δx - airgap flux R - end rings Φ ex - leakage flux of shell S - conducting shell 5www.technologyfuturae.com

Magnetic fluxes and Induced voltages Φ σbx= L σb I bx Φ σrx= L σr I rk Σ I rk= k r I bx k r =1/(2sin 2 (Πp/Z)) Φ σrx= k r L σr I bx The induced voltage by these fluxes equals the resistive voltage drops on the path г b jω(Φ δx + 2 Φ σbx + 2Σ Φ σrx )= 2R b I bx +2R r Σ I rk On the path г e- (a closed path, consisting from two "external bars“) -jω(Φ ex + 2Σ Φ σrx )= 2R e I ex +2R r Σ I rk 6www.technologyfuturae.com

Equivalent circuit of the Rotor U 1, U 2 etc -the bar e.m.f.s Each bar is represented by its complex impedance Each ring by its ring-segment complex impedance 7www.technologyfuturae.com

Contd… External shell Due to the symmetry of the bar and ring segment currents, a star equivalent of impedance & for the ring segments can be established equivalent impedance of a bar circuit is: without external conducting shell with external conducting shell 8www.technologyfuturae.com

Lumped parameter Equivalent Circuit Assumptions 1. Only the fundamental space-harmonic component of the air-gap flux distribution is considered. 2. A nonlinear resistor that is associated with the total stator flux linkage models core loss in d and q axis. 3. Stray losses, temperature effects and rotational losses are neglected 9www.technologyfuturae.com

Mathematical Model Mathematical model is described by the following state-variable matrix equations: 10www.technologyfuturae.com

Contd… Where the inductance terms are calculated using the notations: The induced voltages in the magnetising branch are readily determined with: 11www.technologyfuturae.com

Contd… Where Torque equation is: 12www.technologyfuturae.com

Role of conducting shell The ring impedance is especially high in small external rotor motors, because of the increased ring mean diameter The external conducting shell  ensures a parallel way for the ring currents  diminishes the equivalent ring impedance  decreases the rotor resistance and the leakage reactance  increases the cooling surface area 13www.technologyfuturae.com

Steady state and Dynamic analysis A split phase induction motor with following parameters are considered for analysis o Rated output power: 60 W o Rated frequency: 50 Hz o Rated speed: 2850 rpm o Rated voltage: 220 V o Stator main winding resistance:37.57 ohm o Stator auxiliary winding resistance: 56.83 ohm o Rotor resistance: 76.23 ohm 14www.technologyfuturae.com

Contd… 1) steady-state torque versus speed 2) steady-state torque versus for starting period speed for rated operating period 15www.technologyfuturae.com

Contd… Fig(1)Fig(2) 1) instantaneous torque versus speed for motor with extemal rotor and without conducting shell 2) instantaneous torque versus speed for motor with extemal rotor with conducting shell 16www.technologyfuturae.com

Contd… Fig(1)Fig(2) 1)Start-up speed response for motor with external rotor and without conducting shell 2)Start-up speed response for motor with external rotor with conducting shell 17www.technologyfuturae.com

Summary This paper focused on a new construction of SPIM with external rotor and conducting shell An equivalent circuit for analysis and modelling of the single-phase induction motor with external rotor is derived. The torque and speed characteristics of the motor with and without the conducting shell is compared A SPIM with external rotor and conducting shell finds its application in compressors, pumps, air conditioners etc 18www.technologyfuturae.com

References [l] M. Popescu, “Analysis and Modelling of Single-Phase Induction Motor with External Rotor for Domestic Applications”, IEEE Trans. Ind. Appl.,2000,pp463-470 [2]P.C. Krause, 0. Waszynchuk, S.D. Sudhoff: Analysis of Electrical Machinery, IEEE Press, New York, 1995 [3] S. D. Umans, “Steady-state, lumped-parameter model for capacitor-run, single-phase induction motors”, IEEE Trans. Ind. Appl., Vo1.32, no. 1, Jan/Feb 1996, pp.169-179 [4] E. Levi: “A unified approach to main flux saturation modelling in D-Q axis models of induction machines”, IEEE Trans. Energy Conv., Vol. 10, no.3, Sept. 1995,pp 455-461 19www.technologyfuturae.com

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