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Консультация № 138127
27.05.2008, 17:49
0.00 руб.
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Жёсткость пружины рессора вагона 481кН/м. Масса вагона с грузом 64т. Вагон имеет 4 рессора. При какой скорости вагон начнёт сильно раскачиваться вследствие толчков на стыках рельс, если длина рельса 12,8м?
Помогите, пожалуйста...
Помогите, пожалуйста...
Обсуждение
Неизвестный
28.05.2008, 09:03
общий
это ответ
Здравствуйте, Korablestroitel!
Вагон начнет сильно раскачиваться, когда собственная частота ω колебаний системы, состоящей из четырех рессоров, станет равна частоте Ω внешнего воздействия, каким являются толчки при прохождении стыков рельс. Частота Ω внешнего воздействия равна:
Ω=2*pi/T=2*pi/(L/V)=2*pi*V/L (1)
где L=12,8 - длина рельса, V - искомая критическая скорость движения вагона
Систему пружин рессоров рассматриваем как пружинный маятник, состоящий из четырех пружин, соединенных параллельно; формула для собственной частоты ω пружинного маятника выглядит как:
ω=√(k<sup>*</sup>/m) (2)
где m=64 т=64*10<sup>3</sup> кг - масса вагона, k<sup>*</sup> - общая жесткость четырех пружин, соединенных параллельно; при параллельном соединении жесткость пружин складывается, т.е. k<sup>*</sup>=4*k, где к=481 кН/м=481*10<sup>3</sup> Н/м. Приравнивая правые части (1) и (2) с учетом, что k<sup>*</sup>=4*k, выражаем V:
V=L*√(4*k/m)/(2*pi)=12,8*√(4*481*10<sup>3</sup>/64*10<sup>3</sup>)/(2*3,14)=11,2 м/с=40,3 км/ч
Вагон начнет сильно раскачиваться, когда собственная частота ω колебаний системы, состоящей из четырех рессоров, станет равна частоте Ω внешнего воздействия, каким являются толчки при прохождении стыков рельс. Частота Ω внешнего воздействия равна:
Ω=2*pi/T=2*pi/(L/V)=2*pi*V/L (1)
где L=12,8 - длина рельса, V - искомая критическая скорость движения вагона
Систему пружин рессоров рассматриваем как пружинный маятник, состоящий из четырех пружин, соединенных параллельно; формула для собственной частоты ω пружинного маятника выглядит как:
ω=√(k<sup>*</sup>/m) (2)
где m=64 т=64*10<sup>3</sup> кг - масса вагона, k<sup>*</sup> - общая жесткость четырех пружин, соединенных параллельно; при параллельном соединении жесткость пружин складывается, т.е. k<sup>*</sup>=4*k, где к=481 кН/м=481*10<sup>3</sup> Н/м. Приравнивая правые части (1) и (2) с учетом, что k<sup>*</sup>=4*k, выражаем V:
V=L*√(4*k/m)/(2*pi)=12,8*√(4*481*10<sup>3</sup>/64*10<sup>3</sup>)/(2*3,14)=11,2 м/с=40,3 км/ч
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