ME-503-B Dynamics of Machine - Nov 2023 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
   aIn a pin jointed four bar mechanism ABCD, the lengths of various links are as follows: $AB = 25\ mm$; $BC = 87.5\ mm$; $CD = 50\ mm$ and $AD = 80\ mm$. The link AD is fixed and the angle $BAD = 135^{\circ}$. If the velocity of B is $1.8\ m/s$ in the clockwise direction, find:

   1. i)Velocity and acceleration of the mid point of BC
   2. ii)Angular velocity and angular acceleration of link CB and CD.
   How to answer

   • State given link lengths AB, BC, CD, AD and configuration angle BAD = 135 deg with AD fixed.
   • Draw space diagram and velocity diagram to get velocity of mid-point of BC and angular velocities.
   • Draw acceleration diagram including tangential and centripetal components.
   • Report magnitude and direction of mid-point velocity/acceleration and angular velocity/acceleration of CB and CD.
2. 7 Marks
   bDerive the following expressions, for an uncoupled two cylinder locomotive engine:

   1. i)Swaying couple
   2. ii)Hammer blow
   How to answer

   • Define uncoupled two-cylinder locomotive with cranks at 90 deg and reciprocating masses.
   • Derive unbalanced primary force along and across stroke leading to swaying couple expression.
   • Derive vertical unbalanced force variation leading to hammer blow expression.
   • State formulas with $m, r, \omega, a$ (distance between cylinders) and angle $\theta$.
3. 10 Marks
   aIn a turning moment diagram, the areas above and below the mean torque line taken in order are $4400$, $1150$, $1300$ and $4550\ mm^2$ respectively. The scales of the turning moment diagram are: Turning moment, $1\ mm = 100\ N\text{-}m$; Crank angle, $1\ mm = 1^{\circ}$ Find the mass of the flywheel required to keep the speed between $297$ and $303\ r.p.m.$, if the radius of gyration is $0.525\ m$.
   How to answer

   • Compute energy from areas above/below mean torque line using given scales.
   • Find maximum fluctuation of energy $\Delta E$.
   • Use $\Delta E = I\omega^2 C_s$ with speed range 297-303 r.p.m. and $k=0.525 m$.
   • Solve for flywheel mass $m = I/k^2$.
4. 4 Marks
   bExplain the terms 'fluctuation of energy' and 'fluctuation of speed' as applied to flywheels.
   How to answer

   • Define fluctuation of energy as maximum variation from mean during cycle.
   • Define fluctuation of speed / coefficient $C_s = (N1-N2)/N$.
   • Explain role of flywheel in storing/releasing energy.
5. 14 Marks
   A Porter governor has links $150\ mm$ long and are attached to pivots at a radial distance of $30\ mm$ from the vertical axis of the governor. The mass of each ball is $1.75\ kg$ and the mass of the sleeve is $25\ kg$. The governor sleeve begins to rise at $300\ r.p.m.$ when the links are at $30^{\circ}$ to the vertical. Assuming the friction force to be constant, find the minimum and maximum speed of rotation when the inclination of the links is $45^{\circ}$ to the vertical.
   How to answer

   • Write Porter governor height and speed relation with sleeve mass and friction.
   • Find friction force from condition that sleeve begins to rise at 300 r.p.m. at 30 deg.
   • Apply $N^2 = (m+M)/m \times 895/h$ with +/- friction to get min and max speeds at 45 deg.
   • Calculate heights $h = l\cos\alpha$ with pivot offset correction.
6. 14 Marks
   A single cylinder engine runs at $250\ r.p.m.$ and has a stroke of $180\ mm$. The reciprocating parts has a mass of $120\ kg$ and the revolving parts are equivalent to a mass of $70\ kg$ at a radius of $90\ mm$. A mass is placed opposite to the crank at a radius of $150\ mm$ to balance the whole of the revolving mass and two-thirds of the reciprocating mass. Determine the magnitude of the balancing mass and the resultant residual unbalance force when the crank has turned $30^{\circ}$ from the inner dead centre, neglect the obliquity of the connecting rod.
   How to answer

   • Calculate balancing mass from $m_b r_b = m_{rev}r + (2/3)m_{rec}r$.
   • Resolve primary unbalanced forces along and perpendicular to stroke at theta=30 deg.
   • Combine revolving residual and reciprocating residual to get resultant.
   • Neglect connecting rod obliquity as stated.
7. 14 Marks
   A conical pivot supports a load of $20\ kN$, the cone angle is $120^{\circ}$ and the intensity of normal pressure is not to exceed $0.3\ N/mm^2$. The external diameter is twice the internal diameter. Find the outer and inner radii of the bearing surface. If the shaft rotates at $200\ r.p.m.$ and the coefficient of friction is $0.1$, find the power absorbed in friction. Assume uniform pressure.
   How to answer

   • Use uniform pressure relation $W = \pi p (R^2+r^2?) $ corrected for cone: $W = \pi p (R^2 - r^2)$ with $D=2d$.
   • Solve for outer and inner radii with $p_{max}=0.3 N/mm^2$ and cone angle 120 deg.
   • Compute frictional torque $T = (2/3)\mu W (R^3-r^3)/(R^2-r^2) cosec(alpha)$.
   • Find power $P = T\omega$ at 200 r.p.m.
8. 14 Marks
   Determine the maximum, minimum and average pressure in plate clutch when the axial force is $4\ kN$. The inside radius of the contact surface is $50\ mm$ and the outside radius is $100\ mm$. Assume uniform wear.
   How to answer

   • State uniform wear condition $p\cdot r = C$ for plate clutch.
   • Derive $p_{max}$ at inner radius, $p_{min}$ at outer radius, $p_{avg}=W/\pi(R^2-r^2)$.
   • Substitute $W=4 kN, r=50 mm, R=100 mm$.
   • Report max, min and average pressures.
9. 14 Marks
   The layout and dimensions of a double shoe brake is shown in Fig. 1. The diameter of the brake drum is $300\ mm$ and the contact angle for each shoe is $90^{\circ}$. If the coefficient of friction for the brake lining and the drum is $0.4$, find the spring force necessary to transmit a torque of $30\ N\text{-}m$. Also determine the width of the brake shoes, if the bearing pressure on the lining material is not to exceed $0.28\ N/mm^2$.

   

   How to answer

   • Draw free-body of double shoe brake using Fig.1 dimensions 250 mm and 225 mm.
   • Apply moment equilibrium for leading and trailing shoes with $\mu=0.4$ and drum $D=300 mm$.
   • Solve for spring force S to transmit $30 N\text{-}m$ torque.
   • Find shoe width from $p_{max}=0.28 N/mm^2$ with $90^{\circ}$ contact angle.
10. 4 Marks
    aWhat is the function of a flywheel? How does it differ from that of a governor?
    How to answer

    • Define flywheel function: store kinetic energy and reduce fluctuation.
    • Contrast with governor: regulates mean speed by fuel control vs energy storage.
    • Give examples of use.
11. 5 Marks
    bWhat is the difference between absorption and transmission dynamometers? What are torsion dynamometers?
    How to answer

    • Define absorption dynamometer: absorbs and dissipates power as heat/friction.
    • Define transmission dynamometer: transmits power while measuring torque.
    • Explain torsion dynamometers measuring twist of shaft to get torque/power.
12. 5 Marks
    cWhat are in-line engines? How are they balanced? It is possible to balance them completely.
    How to answer

    • Define in-line engine: cylinders in single row along crankshaft.
    • Explain primary/secondary force and couple balancing by crank arrangement.
    • Discuss possibility of complete balance and residual couples.