EDNE May 2012 - (Page 38)

AU I TO TIVE MO AERO SP A CE M N G CE Control Systems Digital Control Systems E D S IC S A L MECHATRONICS IN DESIGN ccording to novelist and physicist Charles P Snow in his influential 1959 lecture entitled “The two cultures,” not knowing the second law of thermodynamics is equivalent to having never read a work by Shakespeare. Two cultures also appear to exist in the engineering community, and the situation is worsening. At one extreme, engineers use the trial-and-error, plug-and-chug approach of just getting an answer. The other approach embraces a world of understanding through modeling and the application of the laws of nature through their language, mathematics. The mathematical statements of Maxwell’s equations specify the divergence and curl of E (electric)- and B (magnetic)-vector fields. They include the laws of Gauss, Ampère, and Faraday. Maxwell’s four equations simply state that E diverges outward from positive charges and inward to negative charges; E curls around changing B fields; B never diverges, always looping around; and B curls around currents and changing E fields. Magnetic-circuit analysis represents algebraic approximations to exact field-theory solutions. Mechanical motion must occur in all electromechanical devices; this motion changes flux linkages. In a linear electromagnetic system, inductances are functions of mechanical motion. The figure shows in cross-section the dynamics of motion for electromechanical systems. In a cylindrical solenoid magnet, the cylindrical plunger of mass, M, �0 moves vertically in brass guide rings of �1 SPRING COIL thickness, g, and mean diameter, d. a The permeability of x brass is the same as that of free space. A spring with a conh �� stant of K supports the plunger. Its unstretched length is ℓ0. The mechania g cal system that conCYLINDRICAL d GUIDE RING nects to the plunger STEEL SHELL applies a mechaniCYLINDRICAL STEEL PLUNGER cal load force, ft, to APPLIED FORCE the plunger. 38 EDN EUROPE | MAY 2012 M AT E R IALS PR O Control Electronics RAPHY ROG XE Software mechatronics Mechanical CAD Electromechanics Electronic Systems FRESH IDEAS ON INTEGRATING MECHANICAL SYSTEMS, ELECTRONICS, CONTROL SYSTEMS, AND SOFTWARE IN DESIGN T E Mechanical Systems M S M CO A S CT NSU MER PRODU Circuits without wires Understanding magnetic circuits illuminates electromechanical devices. A Assume that the frictional force is linearly proportional to the velocity and that the damping coefficient is B. The coil has N turns and exhibits resistance. Its terminal voltage is et, and its current is i. The effects of magnetic leakage and reluctance of the steel are negligible. The reluctance of the magnetic circuit is that Kevin C Craig, PhD, of the two guide rings in series, with is the Robert C Greenheck the flux directed radially through chairman in engineering them. Assume constant flux density design and a professor of in the guide rings with respect to the mechanical engineering at radial distance because the length of the College of Engineering the flux path in the direction of the at Marquette University. field is much less than the diameter. For more mechatronic The upper and lower areas of the flux news, visit mechatronics path are perpendicular to the field. zone.com. For the upper gap’s reluctance expression, assume that the field is concentrated in the area between the upper end of the plunger and the lower end of the upper guide ring. As the electrical resistance of a wire, ℓ/ σA, the reluctances of the upper and lower gaps are g/μ0πxd and g/μ0πad, respectively, which add together to give the total reluctance. The inductance, L(x), is equal to N2 divided by the total reluctance, and the magnetic force acting upward on the plunger is given by ½i2(dL/dx). The induced voltage in the coil is given by d(Li)/dt. Application of Newton’s second law and Kirchhoff’s voltage law results in the following two dynamic equations of motion for the system: 2 2 ft= –M d x –B dx –Mg–K(x–�1)+1/2L' ai 2 ; dt2 dt (a+x) and et=iR+L' where x di +iL' a 2 dx ; (a+x) dt a+x dt L'= µ0πadN2 . g These equations provide a better understanding of the concept of circuits without wires.EDN www.edn-europe.com U N FA C TU S NS FE DE RI NG E Y S http://mechatronicszone.com. http://mechatronicszone.com. http://www.edn-europe.com

Table of Contents for the Digital Edition of EDNE May 2012

Cover
Contents
International Rectifier
RS Components
Masthead
Comment
International Rectifier
Pulse
Analog Devices
Toshiba
Digi-key
Bergquist
Baker's best
Test & Measurement
Agilent Technologies
Digi-key
Audio-converter-subsystem design challenges in the 21st century
Coilcraft
Silicon Labs
Digi-key
Cover Story
Digi-key
Sensor & Test
Mechatronics in design
Vicor's insert
Understand and reduce dc/dc-switching-converter ground noise
Power MOSFETs continue to evolve
Design Idea
Product Roundup
Tales from the cube

EDNE May 2012