scholarly journals On the calculation of the coefficient of mutual induction of a circle and a coaxial helix, and of the electromagnetic force between a helical current and a uniform coaxial circular cylindrical current sheet

1898 ◽  
Vol 62 (379-387) ◽  
pp. 247-250
Keyword(s):  
Current Sheet ◽  
Electromagnetic Force ◽  
Extreme Points ◽  
Helical Angle ◽  
Helical Current ◽  
Mutual Induction

1. Let M Θ be the coefficient of mutual induction of a circle and a portion of a coaxial helix, beginning in the plane of the circle and of helical angle Θ. Then if M is the coefficient of mutual induction of the circle, and any portion of the helix for which the extreme points are determined by helical angles Θ 1 and Θ 2 , we have M=M Θ 2 –M Θ 1 . It will therefore be sufficient to show how to calculate M Θ for all values of Θ.

scholarly journals A new current weigher, and a determination of the electromotive force of the normal weston cadmium cell

1907 ◽  
Vol 80 (535) ◽  
pp. 12-18
Keyword(s):  
Current Sheet ◽  
Electromotive Force ◽  
Unit Length ◽  
Screw Thread ◽  
Late Professor ◽  
Convenient Formula ◽  
Association Meeting ◽  
Helical Current ◽  
Mutual Induction

The instrument described is the outcome of conversations between the late Professor J. Viriamu Jones, F. R. S., and one of the authors (W. E. A.), on their return from the British Association Meeting held in Toronto in 1897. Its object was to determine “ the ampere ” as defined in the C. G. S. system, to an accuracy comparable with that attained in the absolute determination of the ohm by Lorenz’s apparatus, an account of which was given by Professors Ayrton and Jones at the Toronto Meeting. Professor Jones had previously developed a convenient formula for calculating the electromagnetic force between a helical current and a coaxial current sheet, viz., F = γ h γ (M 2 -M 1 ),† where γ h is the current in the helix, the γ current per unit length of the current sheet, and M 1 , M 2 the coefficients of mutual induction of the helix and the two ends of the current sheet respectively. By using coaxial coils with single layers of wire wound in screw-thread grooves, advantage could be taken of the above formula.

scholarly journals On the calculation of the coefficient of mutual induction a circle and a coaxial helix, and of the electromagnet force between a helical current and a uniform coaxial circular cylindrical current sheet

1898 ◽  
Vol 63 (389-400) ◽  
pp. 192-205 ◽  
Keyword(s):  
General Solution ◽  
Current Sheet ◽  
Electrical Resistance ◽  
Circular Disc ◽  
Mcgill University ◽  
The Mean ◽  
Helical Current ◽  
Mutual Induction

1. In measuring electrical resistance by the method of Lorenz have to determine the coefficient of mutual induction of a helix wire and the circumference of a rotating circular disc placed coaxially with it, the mean planes of the helix and the disc being coincident. In a paper presented to the Physical Society November, 1888, I gave a method of calculating this coefficient; by subsequent consideration of the problem in connection with the Lorenz apparatus recently made for the McGill University, Montrea has led me both to a simplification of the method previously described, and also to a more general solution. 2. If M is the coefficient of mutual induction of any two curve we have M = ∫∫cos ϵ / r dsds' , where r = the distance between two elements ds, ds' ; and ϵ = the angle between these elements.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

Extreme Points and Majorization: Economic Applications

2020 ◽  
Author(s):  
Andreas Kleiner ◽  
Benny Moldovanu ◽  
Philipp Strack
Keyword(s):  
Extreme Points ◽  
Economic Applications

Analysis of Vibration Caused by Electromagnetic Force on Stator End-Winding of Large Dry Submersible Motor

2013 ◽  
Vol 416-417 ◽  
pp. 428-432
Author(s):  
Li Shan ◽  
Xiao Wei Cheng ◽  
Yong Fang ◽  
Xiao Hua Bao
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Transition State ◽  
Electromagnetic Force ◽  
Radial Displacement ◽  
Radial Direction ◽  
Axial Direction ◽  
Axial Displacement ◽  
Force Density ◽  
Submersible Motor

This paper investigates the vibration which caused by electromagnetic on the stator end-winding of the large dry submersible motor. Firstly, the electromagnetic field which included transition state and steady state is researched by 3-D FEM. Secondly, the electromagnetic force which lead to vibrations of end-winding is calculated by numerical method, it can be obtained that where endured the largest force density along the slant part of end-winding. Finally, the radial displacement and the axial displacement of the slant part which caused by vibrations is studied, the analysis results show that the axial displacement is larger than the amplitude of radial displacement. It indicates that the slant part of end-winding will be more easily damaged at axial direction than radial direction.

scholarly journals Research on the Non-Magnetic Conductor of a PMSM Based on the Principle of Variable Exciting Magnetic Reluctance

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 318
Author(s):  
Chunyan Li ◽  
Fei Guo ◽  
Baoquan Kou ◽  
Tao Meng
Keyword(s):  
Permanent Magnet ◽  
Electromagnetic Force ◽  
Electromotive Force ◽  
Permanent Magnets ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Magnetic Conductor ◽  
Critical Speeds ◽  
Motor Structure ◽  
Test Result

A permanent magnet synchronous motor (PMSM) based on the principle of variable exciting magnetic reluctance (VMRPMSM) is presented. The motor is equipped with symmetrical non-magnetic conductors on both sides of the tangential magnetized permanent magnets (PMs). By placing the non-magnetic conductor (NMC), the magnetic reluctance in the exciting circuit is adjusted, and the flux weakening (FW) of the motor is realized. Hence, the NMC is studied comprehensively. On the basis of introducing the motor structure, the FW principle of this PMSM is described. The shape of the NMC is determined by analyzing and calculating the electromagnetic force (EF) acting on the PMs. We calculate the magnetic reluctance of the NMC and research on the effects of the NMC on electromagnetic force, d-axis and q-axis inductance and FW performance. The critical speeds from the test of the no-load back electromotive force (EMF) verify the correctness of the NMC design. The analysis is corresponding to the test result which lays the foundation of design for this kind of new PMSM.

scholarly journals Double Closed-Loop Compound Control Strategy for Magnetic Liquid Double Suspension Bearing

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1195
Author(s):  
Jianhua Zhao ◽  
Yongqiang Wang ◽  
Xuchao Ma ◽  
Sheng Li ◽  
Dianrong Gao ◽  
...  
Keyword(s):  
Control Strategy ◽  
Electromagnetic Force ◽  
Closed Loop ◽  
Static Characteristic ◽  
Magnetic Liquid ◽  
Initial Current ◽  
Electromagnetic System ◽  
Initial Flow ◽  
Hydrostatic Force ◽  
Position Feedback

As a new type of suspension bearing, the magnetic liquid double suspension bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic support. At present, the MLDSB adopts the regulation strategy of “electromagnetic-position feedback closed-loop, hydrostatic constant-flow supply” (referred to as CFC mode). In the equilibrium position, the external load is carried by the electromagnetic system, and the hydrostatic system produces no supporting force. Thus, the carrying capacity and supporting stiffness of the MLDSB can be reduced. To solve this problem, the double closed-loop control strategy of “electromagnetic system-force feedback inner loop and hydrostatic-position feedback outer loop” (referred to as DCL mode) was proposed to improve the bearing performance and operation stability of the MLDSB. First, the mathematical models of CFC mode and DCL mode of the single DOF supporting system were established. Second, the real-time variation laws of rotor displacement, flow/hydrostatic force, and regulating current/electromagnetic force in the two control modes were plotted, compared, and analyzed. Finally, the influence law of initial current, flow, and controller parameters on the dynamic and static characteristic index were analyzed in detail. The results show that compared with that in CFC mode, the displacement in DCL mode is smaller, and the adjustment time is shorter. The hydrostatic force is equal to the electromagnetic force in DCL mode when the rotor returns to the balance position. Moreover, the system in DCL mode has better robustness, and the initial flow has a more obvious influence on the dynamic and static characteristic indexes. This study provides a theoretical basis for stable suspension control and the safe and reliable operation of the MLDSB.

scholarly journals A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

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