Eddy-current losses in solid and laminated iron

Agarwal, Paul D.

doi:10.1109/tce.1959.6372977

Cited by 147 publications

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“…For currents up to 10 A, the power operational 10 Litz wire of an appropriate gauge was used to construct the cables that connect the power amplifiers to the coils, so that the increase in resistance attendant with AC operation would not be significant. Section 5.3.6 provides a discussion on the underlying mechanism for increased AC resistance and Litz wire.…”

Section: Voltage Budget and Power Dissipated In The Amplifiermentioning

confidence: 99%

“…Agarwal [10] describes a method of calculating eddy current losses in saturating iron. Although this more accurately represents the case for the actuator in the 10 kHz FTS than full penetration does, that refinement is not pursued here.…”

Section: Eddy Current Lossmentioning

confidence: 99%

“…Jiles [85] devotes three chapters to discussing magnetic domains, domain walls, and domain processes. 10 The three typical shapes for hysteresis loops are round loop ("Form R"), rectangular loop ("Form Z"), and flat loop ("Form F") [24].…”

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confidence: 99%

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High Bandwidth Rotary Fast Tool Servos and a Hybrid Rotary/Linear Electromagnetic Actuator

Montesanti

2005

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This thesis describes the development of two high bandwidth short-stroke rotary fast tool servos and the hybrid rotary/linear electromagnetic actuator developed for one of them. Design insights, trade-off methodologies, and analytical tools are developed for precision mechanical systems, power and signal electronic systems, control systems, normal-stress electromagnetic actuators, and the dynamics of the combined systems.A fast tool servo (FTS) is a high-speed auxiliary servo axis that is added to a diamond turning machine (ultra-precision lathe) to allow generating free-form nonaxisymmetric or textured surfaces on a workpiece. A rotary fast tool servo produces an in-and-out motion of the tool relative to a workpiece by swinging the tool along an arc having a fixed radius. The rotary fast tool servos developed in this project were designed for diamond turning prescription textured surfaces on small spherical workpieces (diameters in the range of 10 mm or less), and are suitable for generating free-form non-axisymmetric surfaces on similar-sized workpieces. Straightforward modifications would allow them to be used on larger workpieces. These rotary fast tool servos set new benchmarks for demonstrated closed-loop bandwidth (2 kHz and 10 kHz) and tool tip acceleration (400 g).The first machine, referred to as the 2 kHz rotary fast tool servo, uses a commercially available moving-magnet galvanometer as the actuator (Lorentz force), and provides proof-of-principles for a flexure bearing, small diamond tool and mounting method, circuit topology for a high bandwidth current-mode amplifier, and control system design. The following closed-loop performance is demonstrated for the 2 kHz rotary fast tool servo: -3dB bandwidth of 2 kHz, 20 g tool tip acceleration at 2 kHz, maximum tool travel of 50 µm PP, and tool position noise level of 10 nm PP. The 2 kHz FTS is integrated with a diamond turning machine and used to produce optical quality textured surfaces on the face and outside diameter of aluminum workpieces while operating at 2 kHz. The machining tests validate that a rotary-type fast tool servo can be used to produce optical quality surfaces on a spherical workpiece from its pole to its equator.The second machine, referred to as the 10 kHz rotary fast tool servo, incorporates 5 the proof-of-principles from the first machine and is the vehicle for developing the hybrid rotary/linear electromagnetic actuator used in it. The actuator is a normalstress variable reluctance machine with a demonstrated order of magnitude increase in the peak torque and in the ratio of peak torque divided by the electrical power at its terminals, when compared to the actuator used in the 2 kHz FTS. By integrating the tool holder directly to the moving mass of the actuator to form a single rigid body, the overall torque-to-inertia ratio for the system and the frequency of the first uncoupled-mass resonance are both increased. The following closed-loop performance is demonstrated for the 10 kHz rotary fast tool servo: -3dB bandwidth of ...

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Section: Voltage Budget and Power Dissipated In The Amplifiermentioning

confidence: 99%

Section: Eddy Current Lossmentioning

confidence: 99%

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High Bandwidth Rotary Fast Tool Servos and a Hybrid Rotary/Linear Electromagnetic Actuator

Montesanti

2005

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“…1 For this reason, the subscript A has been used to distinguish the parameters derived by this method. A comparison with the linear theory of Section 3.1 is very interesting.…”

Section: 2mentioning

confidence: 99%

“…The field strength within the sheet is given by the expression cosh (1 + j)x/8 H= 1 cosh (1 + j)d/8 (1) where x is measured from the centre of the lamination, and 8 = ^/(2/CO/ACT) is called the penetration or skin depth. The power loss per unit area of sheet is given by p _Hl sinh 2dj8 -sin 2dj8 08 cosh 2d/8 + cos 2d/8 (2) If this power is supplied by an exciting current of r.m.s.…”

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Universal loss chart for the calculation of eddy-current losses in thick steel plates

Lim

Hammond

1970

Proc. Inst. Electr. Eng. UK

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Eddy-current effects in thick steel plates are investigated with particular reference to saturation. The BjH characteristic is represented by the Frohlich equation B = H\(a + bH). The field equations are expressed in nondimensional form, and the losses are computed using a numerical finite-difference scheme. The information is presented in the form of a loss chart which embodies the effects of thickness, conductivity, frequency, shape of the saturation curve and magnetic-field strength. Information is also given in the paper about the penetration depth and power factor. The calculations are compared with measurements on steel blocks. List of symbolsB, B A , B s = magnetic-flux density, equivalent step-function flux density, saturation flux density H, HQ = magnetic-field strength, applied-magnetic-field strength /, 7 0 = electric current, applied electric current P, P A = power loss per unit area, Agarwal power loss per unit area Z, Z A = equivalent impedance, Agarwal impedance a, b = constants in Frohlich curve {b -1IB S ) d = halfthickness of sheet / = frequency h, h Q = standardised magnetic field strength, standardised applied magnetic field strength P n = standardised power loss / = time x, x = distance, standardised distance 8, 8 A , 8 F = penetration or skin depth, penetration depth based on Agarwal's theory, penetration depth based on Frohlich curve 7) = nondimensional parameter (afB s d 2 l£) A, X s , X b -nondimensional flux parameter (Ocuo-J/2^), parameter for infinite sheet, parameter for iron block JU, == permeability a = conductivity T = standardised time O, O 0 = magnetic flux, applied magnetic flux , A = power-factor angle, Agarwal-power-factor angle £ = Frohlich-curve shape factor (a/b) a> = Angular frequency 1 IntroductionThe difficulties associated with the calculation of eddy currents in steel plates are well known. They arise chiefly from the complicated relationship between the flux density and the magnetic-field strength. The simple linear theory which assumes constant permeability, as shown in Fig. 1, is unsatisfactory where there is appreciable saturation. An alternative simple theory is based on a step-function B\H curve, as shown in Fig. 2. Better results are achieved using this theory, but an empirical factor has to be introduced, and the flux penetration is not predicted correctly. Recent advances have been made using actual B\H curves and employing numerical calculation. So far, this work has lacked generality and has

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2023

Eddy Currents

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Eddy-current losses in solid and laminated iron

Cited by 147 publications

References 0 publications

High Bandwidth Rotary Fast Tool Servos and a Hybrid Rotary/Linear Electromagnetic Actuator

High Bandwidth Rotary Fast Tool Servos and a Hybrid Rotary/Linear Electromagnetic Actuator

Universal loss chart for the calculation of eddy-current losses in thick steel plates

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