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A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken massless as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 x 1011 Pa. What is the critical speed of rotation of the shaft (in Hz)?
(Rounded off to the nearest integer)
    Correct answer is '90'. Can you explain this answer?
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    A flexible rotor-shaft system comprises of a 10 kg rotor disc placed ...
    Calculation of Critical Speed of the Shaft

    Given:

    • Mass of the rotor disc (m) = 10 kg

    • Diameter of the shaft (d) = 30 mm

    • Length of the shaft between bearings (L) = 500 mm

    • Modulus of elasticity of steel (E) = 2.1 x 10^11 Pa



    Calculations:

    1. Moment of Inertia of the Shaft (I)

    2. The moment of inertia of the shaft can be calculated using the formula:
      I = πd^4/32
      I = 3.14 x (0.03)^4/32
      I = 1.41 x 10^-8 m^4

    3. Stiffness of the Shaft (k)

    4. The stiffness of the shaft can be calculated using the formula:
      k = 3EI/L^3
      k = 3 x 2.1 x 10^11 x 1.41 x 10^-8/ (0.5)^3
      k = 1.51 x 10^6 N/m

    5. Critical Speed of the Shaft (N)

    6. The critical speed of the shaft can be calculated using the formula:
      N = (1/2π) √(k/m)
      N = (1/2 x 3.14) √(1.51 x 10^6/10)
      N = 90 Hz (rounded off to the nearest integer)


    Answer: The critical speed of rotation of the shaft is 90 Hz.
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    Community Answer
    A flexible rotor-shaft system comprises of a 10 kg rotor disc placed ...
    Given m = 10 kg, d = 30 mm = 0.03 m, l = 500 mm = 0.5 m, Eshaft = 2.1 x 1011 Pa
    We know that, static deflection due to 10 kg of Mass at the centre is given by,
    .............(i)
    The moment of inertia of the shaft,
    .......(ii)
    Substitute value in equation(i), we get
    If ωc is the critical or whirling speed in r.p.s then,
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    A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken massless as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 x 1011 Pa. What is the critical speed of rotation of the shaft (in Hz)?(Rounded off to the nearest integer)Correct answer is '90'. Can you explain this answer?
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    A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken massless as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 x 1011 Pa. What is the critical speed of rotation of the shaft (in Hz)?(Rounded off to the nearest integer)Correct answer is '90'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken massless as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 x 1011 Pa. What is the critical speed of rotation of the shaft (in Hz)?(Rounded off to the nearest integer)Correct answer is '90'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearings (shaft is being taken massless as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 x 1011 Pa. What is the critical speed of rotation of the shaft (in Hz)?(Rounded off to the nearest integer)Correct answer is '90'. Can you explain this answer?.
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