ME-503-B Dynamics of Machine - Nov 2022 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
   aWhat do you mean by dynamically equivalent system?
   How to answer

   • Define dynamically equivalent system as two-mass system replacing rigid body
   • State three conditions: same mass, same CG, same mass moment of inertia
   • Give equations m1+m2=m, m1*l1=m2*l2, I=m1*l1^2+m2*l2^2
   • Mention application to connecting rod and condition for exact equivalence
2. 7 Marks
   bThe lengths of crank and connecting rod of a horizontal reciprocating engine are $210\,mm$ and $1.0\,m$ respectively. The crank is rotating at $420\,r.p.m.$ When the crank has turned $30^{\circ}$ from the inner dead centre, the difference of pressure between the cover end and piston end is $0.4\,N/mm^{2}$. If the mass of the reciprocating parts is $100\,kg$ and cylinder bore is $0.4\,m$, then calculate:

   1. i)Inertia force
   2. ii)Force on piston
   3. iii)Piston effort
   4. iv)Thrust on the sides of cylinder walls
   5. v)Thrust in the connecting rod
   6. vi)Crank-effort and Neglect the effect of piston rod diameter and frictional resistance.
   How to answer

   • Calculate angular velocity and n = l/r and acceleration of piston
   • Calculate inertia force F = m*a and net piston force from pressure difference
   • Resolve piston effort, side thrust and connecting rod thrust using sin/cos phi
   • Calculate crank-effort / crank torque T = F_piston_effort * r factor
   • Neglect piston rod diameter and friction as stated
3. 7 Marks
   aDefine and explain the following terms relating to governors:

   1. i)Stability
   2. ii)Sensitiveness
   3. iii)Isochronism
   4. iv)Hunting
   How to answer

   • Define stability: equilibrium speed maintained with one sleeve position
   • Define sensitiveness: ratio of speed range to mean speed
   • Define isochronism: same speed at all radii, sensitiveness infinite
   • Define hunting: fluctuation due to over-sensitiveness
4. 7 Marks
   bProve that the sensitiveness of a Proell governor is greater than that of a Porter governor.
   How to answer

   • Write equilibrium equations for Porter and Proell governors
   • Show sensitiveness expression with ball extension effect
   • Compare denominators showing additional moment in Proell
   • Conclude sensitiveness of Proell > Porter for same parameters
5. 7 Marks
   aWrite short note on 'coefficient of insensitiveness' of governors.
   How to answer

   • Define coefficient of insensitiveness due to friction
   • Give formula (N2-N1)/N in terms of friction force
   • Explain effect on sleeve movement and speed range
   • Note methods to reduce it
6. 7 Marks
   bExplain why only a part of the unbalanced force due to reciprocating masses is balanced by revolving mass.
   How to answer

   • Write primary unbalanced force m*r*omega^2*cos theta
   • Explain balancing by revolving mass gives cos and sin components
   • Show perpendicular sin component causes hammer blow / swaying if fully balanced
   • Conclude only fraction c balanced to limit unbalanced effects
7. 14 Marks
   A Proell governor has arms of $300\,mm$ length. The upper arms are hinged on the axis of rotation, whereas the lower arms are pivoted at a distance of $35\,mm$ from the axis of rotation. The extension of lower arms to which the balls are attached are $100\,mm$ long. The mass of each ball is $8\,kg$ and the mass on the sleeve is $60\,kg$. At the minimum radius of rotation of $200\,mm$, the extensions are parallel to the governor axis. Determine the equilibrium speed of the governor for the given configuration. What will be the equilibrium speed for the maximum radius of $250\,mm$?
   How to answer

   • Draw Proell geometry with arm lengths and offsets
   • Apply moment equilibrium about upper hinge for min radius 200 mm
   • Solve for equilibrium speed N1 using tan alpha relation
   • Repeat for max radius 250 mm to get N2
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 theory p*r = constant
   • Calculate mean radius and axial force relation W = 2*pi*C*(R-r)
   • Find C then p_max at inner radius and p_min at outer radius
   • Calculate average pressure W / pi*(R^2-r^2)
9. 7 Marks
   aDescribe with sketches one form of torsion dynamometer and explain with detail the calculations involved in finding the power transmitted.
   How to answer

   • Sketch torsion dynamometer (e.g., Siemens / epicyclic) arrangement
   • Explain twist measurement over shaft length
   • Derive T = G*theta*J / L and P = 2*pi*N*T/60
   • Show calculation steps for power transmitted
10. 7 Marks
    bA single cylinder two stroke vertical engine a bore of $30\,cm$ and a stroke of $40\,cm$ with a connecting rod of $80\,cm$ long. The mass of the reciprocating parts is $120\,kg$. When the piston is at quarter stroke and moving down, the pressure on it is $70\,N/cm^{2}$. If the speed of the engine crank shaft is $250\,rpm$ clockwise find the turning moment on the crank shaft. Neglect the mass and inertia effects on connecting rods and crank.
    How to answer

    • Calculate piston area and net load from 70 N/cm2 pressure
    • Find crank angle at quarter stroke using r, l geometry
    • Resolve thrust and tangential effort at crank pin
    • Compute turning moment T = tangential force * crank radius, neglect rod/crank inertia
11. 14 Marks
    The following data refer to two-cylinder locomotive with crank $90^{\circ}$. Reciprocating mass per cylinder $= 300\,kg$, Crank radius $= 0.3\,m$, Driving wheel dia. $= 1.8\,m$ Dist. between cylinder centre lines $= 0.65\,m$ Dist. between the driving wheel $= 1.55\,m$. Determine:

    1. i)The fraction of the reciprocating masses to be balanced, if the hammer blow is not to exceed $46 \times 10^{3}\,N$ at $96.5\,km/hr$.
    2. ii)The variation in tractive effort.
    3. iii)The maximum swaying couple.
    How to answer

    • Compute angular speed of wheel from vehicle speed and hammer blow formula
    • Solve for balanced fraction c from B = c*m*r*omega^2
    • Calculate variation in tractive effort +/- sqrt2*c*m*r*omega^2
    • Calculate max swaying couple with cylinder spacing and wheel spacing
12. 14 Marks
    A cam consists of a circular disc of diameter $75\,mm$ with its centre displaced $25\,mm$ from the camshaft axis. The follower has a flat surface (horizontal) in contact with the cam and the line of action of the follower is vertical and passes through the shaft axis as shown in Figure 1. The mass of the follower is $2.3\,kg$ and is pressed downwards by a spring which has a stiffness of $3.5\,N/mm$. In the lowest position the spring force is $45\,N$.

    1. i)Derive an expression for the acceleration of the follower in terms of the angle of rotation from the beginning of the lift.
    2. ii)As the cam shaft speed is gradually increased, a value is reached at which the follower begins to lift from the cam surface. Determine the camshaft speed for this condition.

    How to answer

    • Write displacement x = e*(1-cos theta)+... for eccentric circular cam with flat follower
    • Differentiate twice to get velocity and acceleration vs theta
    • Set contact force = spring force + weight - m*a = 0 for lift-off
    • Solve for camshaft speed N at max negative acceleration