Tham khảo tài liệu 'sustainable energy harvesting technologies past present and future part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modelling Theory and Applications of the Electromagnetic Vibrational Generator 69 If the magnetic field B is constant with the position x then Fm BlI where l is the coil mean length. In this chapter we will present the magnetic flux density B varies with the coil movement so that V dộ 1 dÉ 2 F __ V _ dộ dx dộ _dx__ịx_ em Rc Rl jaL dx Rc Rl jaL dx dt dx Rc Rl jaL dt where V is the generated voltage Rc is the coil resistance L is the coil inductance and Rl is the load resistance. For an N turn coil the total flux linkage gradient would be the summation of the individual turns flux linkage gradients. If the flux linkage gradient for each turn is equal then the electromagnetic force is given by Fm N A2 dx dx _ D dx_ Rc Rl JaL dt em dt Where the electromagnetic damping Dm em N 2 2 dx Rc JaL Rl 15 It can be seen from 15 that electromagnetic damping can be varied by changing the load resistance Rc the coil parameters N Rc and L magnet dimension and hence flux ộ and the generator structure which influence ỂẤ. Putting the electromagnetic force dx F _ D dx in equation 7 gives em em dt d2 x dx dx f r Demdĩ Ia F S nat 16 The solution of equation 9 defines the displacement under electrical load condition and is given by the following equation _ Fosm at -ff 17 xioad _ f ----------------------- T V I - m 2 Dp Dem a 2 Where ff tan-1 DJ- d111 k - ma1 The displacement at resonance under load is therefore given by 70 Sustainable Energy Harvesting Technologies - Past Present and Future _ - F0 cos at Xload Dp Dem a 18 Generated mechanical power The instantaneous mechanical power associated with the moving mass under the electrical load condition is Pmech t F t U t dx F0 sin at dxod-dt Fữ sin at using equation 18 Dp Dem Where F t and U t are the applied sinusoidal force and velocity of the moving mass respectively due to the sinusoidal movement. This corresponds to maximum mechanical power when Dem 0 . at no load. The average mechanical power .
