Question

9. The plunger with mass M shown in Fig. 2.10-5 is free to move within an electromagnet. Although the winding of the electromagnet consists of many turns, only one is shown. The mechanical damping varies directly as the surface area of the plunger within the electromagnet. (a) Write the voltage equation for the electric system. (b) Write the dynamic equation for the mechanical system. Include the force of gravity. (c) Express the mechanical damping D. (d) Express the electromagnetic 2.10. PROBLEMS 93 7777z77zzz777 Stop Figure 2.10-5: Cross section of plunger system. force . ifi-ar +ba(z-d). (e) Express the steady-state position r for a constant current flowing in the winding

Answer 1

"Given, a) the voltage of equation for the electric system Hear = E = Vertical-bar times phi times w x f Vertical-bar 10^t Hear 'E' is the induced EMF phi is the total number of turns in the winding of the electromagnetic 'f' is the frequency b) the dynamic equation for the mechanical system Hear different types of force involved in this system Electromagnetic force (F_e) gravitational force (F) Dynamic eq^n for mechanical system is obtained by balancing the two force F_e = F \r\n integral B^2 x d A/(2 times mu_0) = m times g Hear 'B' ids magnetic flux density 'x' is the stress vector on the surface defined by the normal 'n' is the intensity area of the pole pieces of the electromagnet ""mu_0"" is the permeability of force space B^2/(2 times mu_0) is the magnetic stress 'm' is the mass of the plunger and 'g' is the gravitational constant c) Express Mechanical damping"