ME-503-B Dynamics of Machine - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aExplain the terms coefficient of fluctuation of energy and coefficient of fluctuation of speed.
   How to answer

   • Define coefficient of fluctuation of energy as ratio of max fluctuation to mean work per cycle
   • Define coefficient of fluctuation of speed as (N1-N2)/N mean
   • Give formulas: Ce = delta E / Wmean, Cs = 2(N1-N2)/(N1+N2)
   • Explain role in flywheel design
2. 7 Marks
   bThe turning moment diagram for a petrol engine is drawn to a vertical scale of $1\text{ mm} = 500\text{ Nm}$ and a horizontal scale of $1\text{ mm} = 3^\circ$. The turning moment diagram repeats itself after every half revolution of the crank shaft. The areas above and below the mean torque line are $260$, $-580$, $80$, $-380$, $870$ and $-250\text{ mm}^2$. The rotating parts have a mass of $55\text{ kg}$ and radius of gyration of $2.1\text{ m}$. If the engine speed is $1600\text{ r.p.m.}$, determine the coefficient of fluctuation of speed.
   How to answer

   • Compute energy scale from vertical and horizontal scales
   • Find max fluctuation of energy from areas above/below mean torque line
   • Compute mass moment of inertia $I = m k^2$
   • Use $\Delta E = I \omega^2 C_s$ to find $C_s$
3. 7 Marks
   aDerive an expression for the height of Watt governor and prove that the height of the governor is inversely proportional to the square of the speed of governor.
   How to answer

   • Draw Watt governor with arms, balls and sleeve
   • Resolve forces: centrifugal force, weight, tension
   • Take moment equilibrium to get $h = g/\omega^2$
   • Show $h \propto 1/N^2$
4. 7 Marks
   bThe lengths of the upper and lower arms of a Porter governor are $200\text{ mm}$ and $250\text{ mm}$ respectively. Both the arms are pivoted on the axis of the rotation. The central load is $150\text{ N}$, the weight of each wall is $20\text{ N}$ and the friction of the sleeve together with the resistance of the operating gear is equivalent to a force of $30\text{ N}$ at the sleeve. If the limiting inclinations of the upper arms to the vertical are $30^\circ$ and $40^\circ$, determine the range of the speed of the governor.
   How to answer

   • Calculate geometry: radius of rotation from arm lengths and angles
   • Apply Porter governor speed formula with central load and friction
   • Compute Nmin at 30° and Nmax at 40° including ± friction
   • Range = Nmax - Nmin
5. 7 Marks
   aWhat is meant by the term 'stability of a governor'? Derive the necessary condition of stability for a centrifugal governor.
   How to answer

   • Define stability: speed increases with radius, sleeve returns to equilibrium
   • Derive condition dM/dr or dN/dr relation for centrifugal governor
   • State necessary condition: F/r vs r slope criterion
   • Give example of stable vs unstable
6. 7 Marks
   bA Hartnell governor having a central sleeve spring and two right-angled bell crank levers operates between $290\text{ r.p.m.}$ and $310\text{ r.p.m.}$ for a sleeve lift of $15\text{ mm}$. The sleeve arms and the ball arms are $80\text{ mm}$ and $120\text{ mm}$ respectively. The levers are pivoted at $120\text{ mm}$ from the governor axis mass of each ball is $2.5\text{ kg}$. The ball arms are parallel to the governor axis at the lowest equilibrium speed. Determine :

   1. i)Loads on the spring at the lowest and the highest equilibrium speeds
   2. ii)Stiffness of the spring
   How to answer

   • Compute centrifugal force at min and max speeds from ball mass and radius
   • Use Hartnell lever moment equilibrium to get spring loads S1, S2
   • Compute stiffness = (S2-S1)/sleeve lift
   • State units in N/mm
7. 7 Marks
   aDefine and explain the term 'Balancing of Rotating Masses'. What will be the harm if the rotating parts of a high speed engine are not properly balanced?
   How to answer

   • Define balancing of rotating masses: resultant force and couple zero
   • Explain centrifugal force, bearing reactions, vibration
   • List harms: vibration, noise, bearing failure, fatigue
   • Need for balancing in high speed engines
8. 7 Marks
   bFour masses A, B, C and D carried by a rotating shaft at radii $80\text{ mm}$, $100\text{ mm}$, $160\text{ mm}$ and $120\text{ mm}$ respectively are completely balanced. Masses B, C and D are $8\text{ kg}$, $4\text{ kg}$ and $3\text{ kg}$ respectively. Determine the mass A and the relative angular positions of the four masses if the planes are spaced $500\text{ mm}$ apart.
   How to answer

   • Tabulate m*r for B,C,D and unknown A
   • Apply force polygon closure and couple polygon closure for 500 mm spaced planes
   • Solve for magnitude of mass A
   • Solve for angular positions of all masses
9. 7 Marks
   aExplain the method of direct and reverse cranks to determine the unbalance forces in radial engines.
   How to answer

   • Explain direct crank (rotating with crank) and reverse crank (opposite rotation)
   • Show primary force from direct+reverse, secondary effects
   • Give vector equations for radial engine unbalance
   • Mention application to multi-cylinder radial engines
10. 7 Marks
    bA shaft is rotating at a uniform angular speed. Four masses $m_1$, $m_2$, $m_3$ and $m_4$ of magnitudes $300\text{ kg}$, $450\text{ kg}$, $360\text{ kg}$ and $390\text{ kg}$ respectively are attached rigidly to the shaft. The masses are rotating in the same plane. The corresponding radii of rotation are $200\text{ mm}$, $150\text{ mm}$, $250\text{ mm}$ and $300\text{ mm}$ respectively. The angle made by these masses with horizontal is $0^\circ$, $45^\circ$, $120^\circ$ and $255^\circ$ respectively. Determine the magnitude of the balancing mass and the position of the balancing mass if the radius of rotation is $200\text{ mm}$.
    How to answer

    • Resolve each m*r into horizontal and vertical components
    • Sum components to get resultant unbalanced m*r
    • Equate to balancing mass radius product
    • Find angle of balancing mass by tan inverse
11. 7 Marks
    aWhat is meant by the expression friction circle? Deduce an expression for the radius of friction circle in terms of radius of the journal and angle of friction.
    How to answer

    • Define friction circle: circle of radius r*sin phi
    • Explain journal bearing friction moment
    • Derive radius rf = r*sin phi ≈ r*mu for small phi
    • State use in bearing analysis
12. 7 Marks
    bDescribe with a neat sketch the working of a single plate friction clutch.
    How to answer

    • Show construction: flywheel, friction plate, pressure plate, springs
    • Explain engagement/disengagement axial movement
    • Mention torque transmission by friction
    • Include neat labelled sketch
13. 7 Marks
    aCalculate the power transmitted by a single plate clutch at a speed of $2000\text{ r.p.m.}$, if the outer and inner radii of friction surfaces are $150\text{ mm}$ and $100\text{ mm}$ respectively. The maximum intensity of pressure at any point of contact surface should not exceed $0.8 \times 10^5\text{ N/m}^2$. Take both sides of the plate as effective and co-efficient of friction $= 0.3$. Assume uniform wear.
    How to answer

    • Determine axial force W from max pressure under uniform wear
    • Compute mean radius R = (R+r)/2 for uniform wear
    • Compute torque T = n*mu*W*R with n=2
    • Compute power P = 2*pi*N*T/60
14. 7 Marks
    bEstablish a formula for the maximum torque transmitted by a single plate clutch of external and internal radii $r_1$ and $r_2$, if the limiting coefficient of friction is $\mu$ and the axial spring load is W. Assume that the pressure intensity on the contact faces is uniform.
    How to answer

    • Consider elemental ring radius r thickness dr with uniform pressure p
    • Integrate friction moment dT = 2*pi*mu*p*r^2 dr
    • Relate axial load W = pi*p*(r1^2-r2^2)
    • Get T = (2/3)*mu*W*(r1^3-r2^3)/(r1^2-r2^2)
15. 7 Marks
    aWith a neat sketch, describe a single shoe brake. What is the advantage of double shoe brake over single shoe brake?
    How to answer

    • Sketch lever, drum, shoe, pivot and actuating force
    • Explain braking torque from normal and friction forces
    • Discuss self-energizing and pivot effects
    • State advantage of double shoe: balanced side thrust, higher torque
16. 7 Marks
    bWrite short notes on followings:

    1. i)Absorption dynamometer and transmission dynamometer
    2. ii)Dynamic analysis of cams
    How to answer

    • Define absorption vs transmission dynamometer with examples
    • Explain working of Prony brake / rope brake vs belt / epicyclic type
    • Define cam dynamic analysis: follower forces, jump, spring
    • Mention critical speed and vibration