A section of the system is shown in detail in the bottom figure. Assume that this...
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A section of the system is shown in detail in the bottom figure. Assume that this magnet is supporting about 5 metric tons, which implies about 50 kN of required lift force. Dimensions and other data are as follows: ] . . Note that the pole width is w and we assume the coil dimensions are w x w. The rail width is such that when the yoke is centered each side has an overlap of w. In the bottom figure, the system is sitting with x = 0. Nominal Support Force Required F 50,000 N Magnet Length L 0.5 m Pole width w 0.1 m Relative Motion Gap g 0.01 m I B B Section A-A 2 Moving Yoke Script Coil L View B-B a) With the yoke centered and providing the required support force, what is the required number of ampere-turns in the exciting coil? W b) How does the required current change with lateral position x? Calculate and plot the required current as a function of position x, ranging from x=-w/4 to +w/4. c) If the car moves laterally (direction x), this system provides a restoring force. Find that lateral force as a function of x and exciting current NI. d) Now combine these two parts and, assuming that current is controlled to maintain a 1 cm relative motion gap g, find and sketch restoring force as a function of lateral position x. N turns Fixed Rail u μ 1 2 W = 0.1; 3 4 MMF_a = []; 5 6 x = [-w/4: (w/4)/1000:w/4]; 7 8 MMF = []; 2 w W O W Note that g and x are variable. In the image above x = 0 A ∞ Direction of Motion 9 10 % You can uncomment the stuff below to see the plot 11 %figure (1); 12 %plot (x, MMF) 13. 14 Fx = []; 15 16 % You can uncomment the stuff below to see the plot 17 %figure (2); 18 %plot(x, Fx) 19 g A section of the system is shown in detail in the bottom figure. Assume that this magnet is supporting about 5 metric tons, which implies about 50 kN of required lift force. Dimensions and other data are as follows: ] . . Note that the pole width is w and we assume the coil dimensions are w x w. The rail width is such that when the yoke is centered each side has an overlap of w. In the bottom figure, the system is sitting with x = 0. Nominal Support Force Required F 50,000 N Magnet Length L 0.5 m Pole width w 0.1 m Relative Motion Gap g 0.01 m I B B Section A-A 2 Moving Yoke Script Coil L View B-B a) With the yoke centered and providing the required support force, what is the required number of ampere-turns in the exciting coil? W b) How does the required current change with lateral position x? Calculate and plot the required current as a function of position x, ranging from x=-w/4 to +w/4. c) If the car moves laterally (direction x), this system provides a restoring force. Find that lateral force as a function of x and exciting current NI. d) Now combine these two parts and, assuming that current is controlled to maintain a 1 cm relative motion gap g, find and sketch restoring force as a function of lateral position x. N turns Fixed Rail u μ 1 2 W = 0.1; 3 4 MMF_a = []; 5 6 x = [-w/4: (w/4)/1000:w/4]; 7 8 MMF = []; 2 w W O W Note that g and x are variable. In the image above x = 0 A ∞ Direction of Motion 9 10 % You can uncomment the stuff below to see the plot 11 %figure (1); 12 %plot (x, MMF) 13. 14 Fx = []; 15 16 % You can uncomment the stuff below to see the plot 17 %figure (2); 18 %plot(x, Fx) 19 g
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