# lect5 - Lecture 5 EE743 Lecture 5 EE743 Electromagnetic...

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Unformatted text preview: Lecture 5 - EE743 Lecture 5 - EE743 Electromagnetic Force and Torque Professor: Ali Keyhani Professor: Ali Keyhani 2 Electromagnetic Force and Torque ■ Review: Review: dx d f dx d N i f dx d N i f Ni N N i L dx dL i x W f N x L i x L W W em em em c e f c ℜ Φ- = ℜ ℜ- = ℜ = ℜ = Φ Φ = ℜ = = = ∂ ∂ = ℜ = = = 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 1 2 1 ) ( ) ( 2 1 λ λ 3 ■ Consider the electromechanical system given below, k f D φ φ m g x d Electromagnetic Force and Torque 4 ■ Assumptions such as: – The area of the center leg is twice the area of the outer legs – The reluctance of the materials of the electromagnet and the plunger is neglected. ■ Applying Ampere’s Law to solve the previous electromechanical system, Electromagnetic Force and Torque 5 Electromagnetic Force and Torque d x Ni H B H B d H x H Ni d d x x d x d x d d x x "d" length of airgap the in intensity Magnetic x" " length of airgap the in intensity Magnetic B B B H B H μ μ μ μ μ μ + = = → = = → = + = 6 Electromagnetic Force and Torque ■ Let – A: area of the center leg – A/2: area of the outer leg for Solving 2 2 2 2 d x NiA d A x A Ni B B A B A B BA d x d x + = Φ Φ Φ + Φ = = = Φ = Φ = Φ μ μ μ 7 Electromagnetic Force and Torque d x A N i N L i d x A N N + = Φ = + = Φ = 2 2 μ μ λ λ ■ The equation for the electrical system is, [ ] dt dx dx x dL i dt di x L Ri V i x L dt d Ri V ) ( ) ( ) ( + + = + = 8 ■ The mechanical system can be described by, where , g: the value of x at which the spring is relaxed. Electromagnetic Force and Torque ) ( 2 2 x x k dt dx D dt x d m f e- + + = 9 ■ The dynamic performance of the electromagnetic system is described by two-nonlinear equations, as shown previously....
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lect5 - Lecture 5 EE743 Lecture 5 EE743 Electromagnetic...

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