ME-602 Machine Component Design - May 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
   aWhat is meant by stress concentration? How do you like it into consideration in case of a component subjected to dynamic loading?
   How to answer

   • Define stress concentration and stress concentration factor
   • Causes: geometric discontinuities, holes, notches, keyways
   • Effect under dynamic loading: fatigue strength reduction, notch sensitivity
   • Consideration via fatigue stress concentration factor Kf and design charts
2. 7 Marks
   bA cold drawn steel rod of circular cross-section is subjected to a variable bending moment $565\, \text{N-m}$ to $1130\, \text{N-m}$ as the axial load varies from $4500\, \text{N}$ to $13500\, \text{N}$. The maximum bending moment occurs at the same instant that the axial load is maximum. Determine the required diameter of the rod for a factor of safety $2$. Neglect any stress concentration and column effect. Assume the following values: Ultimate strength $= 550\, \text{MPa}$ Yield strength $= 470\, \text{MPa}$ Size factor $= 0.85$ Surface finish factor $= 0.39$ Correction factors $= 1.0$ for bending $= 0.7$ for axial load The endurance limit in reversed bending may be taken as one-half the ultimate strengths.
   How to answer

   • Calculate mean and variable bending moment and axial load
   • Calculate mean and alternating bending and direct stresses in terms of diameter
   • Determine endurance limit with size, surface and correction factors
   • Apply Soderberg/Goodman criterion with factor of safety 2 to solve for diameter
3. 7 Marks
   aDefine equivalent twisting moment and equivalent bending moment. State when the two terms are used in design of shafts?
   How to answer

   • Define equivalent twisting moment $T_e = \sqrt{M^2+T^2}$
   • Define equivalent bending moment $M_e = (M+T_e)/2$
   • State use for shaft design under combined bending and torsion
   • Mention maximum shear stress and maximum normal stress theories
4. 7 Marks
   bA $45\, \text{mm}$ diameter shaft is made of steel with a yield strength of $400\, \text{MPa}$. A parallel key of size $14\, \text{mm}$ wide and $9\, \text{mm}$ thick made of steel with a steel with a yield strength of $340\, \text{MPa}$ is to be used. Find the required length of key, if shaft is loaded to transmit the maximum permissible torque. Use maximum shear stress theory and assume a factor of safety of $2$.
   How to answer

   • Find allowable shear stress of shaft and key from yield with FOS 2 via max shear theory
   • Find maximum permissible torque from shaft strength
   • Check key against shear and crushing to find required length
   • Select larger length as required key length
5. 7 Marks
   aDesign a spring for a balance to measure $0$ to $1000\, \text{N}$ over a scale of length $80\, \text{mm}$. The spring is to be enclosed in a casing of $25\, \text{mm}$ diameter. The approximate number of turns is $30$. The modules of rigidity is $85\, \text{kN/mm}^2$. Also calculate the maximum shear stress induced.
   How to answer

   • Find wire diameter from spring index and casing constraint
   • Use deflection formula $\delta = 8WD^3n/Gd^4$ for $1000\,N$
   • Check Wahl correction factor for maximum shear stress
   • Select standard wire size and verify strength
6. 7 Marks
   bAnswer the following:

   1. i)What do you understand by overhauling of screw?
   2. ii)What is self locking property of threads and where it is necessary?
   How to answer

   • Define overhauling: screw unwinds under axial load when friction angle < helix angle
   • Condition for overhauling and its implication
   • Define self-locking: friction angle > helix angle, torque to lower required
   • State necessity in jacks, clamps to hold load without brake
7. 7 Marks
   aWrite a short note on uniform wear theory and uniform pressure theory and give the expression for mean radius in both the cases.
   How to answer

   • State assumptions of uniform wear vs uniform pressure theories
   • Derive frictional torque and mean radius for each
   • Give $R_m = (R+r)/2$ for uniform wear and $R_m = 2(R^3-r^3)/3(R^2-r^2)$ for uniform pressure
   • State applicability to new vs worn clutches
8. 7 Marks
   bA single plate clutch, effective on both sides, is required to transmit $25\, \text{kW}$ at $3000\, \text{r.p.m.}$ Determine the outer and inner diameters of frictional surface if the coefficient of friction $0.255$ ratio of diameters is $1.25$ and the maximum pressure is not to exceed $0.1\, \text{N/mm}^2$. Also determine the axial thrust to be provided by springs. Assume the theory of uniform wear.
   How to answer

   • Calculate torque from power and speed
   • Apply uniform wear theory $T = n\mu W R_m$ with $D/d=1.25$ and $p_{max}$ limit
   • Solve for outer and inner diameters
   • Calculate required axial thrust $W$
9. 7 Marks
   aWhat is Self-energizing brake? When brake become self locking?
   How to answer

   • Define self-energizing: frictional moment assists application
   • Explain pivot and shoe arrangement causing energizing
   • State self-locking condition when braking moment exceeds applied moment
   • Mention danger of grabbing and need for manual release
10. 7 Marks
    bIn a band and block brake, the band is lined with $14$ blocks, each of which subtends an angle of $20^\circ$ at the drum centre. One end of the hand is attached to the fulcrum of the brake lever and the other to a pin $150\, \text{mm}$ from the fulcrum. Find the force required at the end of the lever $1\, \text{metre}$ long from the fulcrum give a tongue of $4\, \text{kN-m}$. The diameter of the brake drum is $1\, \text{metre}$ and the coefficient of friction between the blocks and the drum is $0.25$.
    How to answer

    • Calculate tension ratio with $n$ blocks using $T_n/T_0 = [(1+\mu\tan\theta)/(1-\mu\tan\theta)]^n$
    • Apply moment equilibrium of lever and drum torque $4\,kN-m$
    • Solve for tight and loose side tensions
    • Find effort at 1 m lever with 150 mm pin arm
11. 7 Marks
    aList the important physical characteristics of a good bearing material. And also explain what is bearing characteristic number?
    How to answer

    • List low friction, high compressive strength, conformability, embeddability
    • Mention thermal conductivity, corrosion resistance, compatibility
    • Define bearing characteristic number $ZN/p$
    • Explain its use in Sommerfeld number and lubrication regime
12. 7 Marks
    bA footstep bearing supports a shaft of $150\, \text{mm}$ diameter which is counter bored at the end with a hole diameter of $50\, \text{mm}$. If the bearing pressure is limited to $0.8\, \text{N/mm}^2$ and the speed is $100\, \text{r.p.m.}$ Find:

    1. i)The load to be supported
    2. ii)The power lost in friction
    How to answer

    • Calculate load $W = p \cdot \pi(R^2-r^2)$ with uniform pressure
    • Calculate frictional moment and power loss $P = 2\pi NT/60$
    • Use mean radius for flat pivot with counterbore
    • Substitute $D=150\,mm$, $d=50\,mm$, $p=0.8\,N/mm^2$, $N=100\,rpm$
13. 7 Marks
    aWhat are rolling contact bearings? Discuss their advantages over sliding contact bearings. And write a brief note on factors effecting the life of a bearing.
    How to answer

    • Define rolling contact bearings with rolling elements
    • List advantages: low starting friction, compact, easy replacement
    • Compare with sliding bearings on friction, load, maintenance
    • Note factors affecting life: load, speed, lubrication, temperature
14. 7 Marks
    bA ball bearing subjected to a radial load of $5\, \text{kN}$ is expected to have a life of $8000$ hours at $1450\, \text{r.p.m.}$ with a reliability of $99\%$. Calculate the dynamic load capacity of the bearing so that it can be selected from the manufacturer's catalogue based on a reliability of $90\%$.
    How to answer

    • Calculate life in millions of revolutions $L = 60NL_h/10^6$
    • Adjust for reliability 99% vs 90% using $L_a = a_1 L$
    • Use $L = (C/P)^k$ with $k=3$ for ball bearing to find $C$
    • Select catalogue $C$ for 90% reliability
15. 14 Marks
    Write a brief note on any two of following:

    1. i)Soderbergs equation and state its application to different types of loadings.
    2. ii)Describe with the help of neat sketch, the types of various shaft couplings mentioning the use of each type.
    3. iii)Why are square threads preferable to V-threads for power transmission?
    4. iv)Show that the efficiency of self locking screw is less than 50 percent.
    How to answer

    • For Soderberg: state line diagram and equation with applications
    • For couplings: sketch muff, flange, Oldham etc. with uses
    • For threads: explain friction, efficiency, strength comparison
    • For self-locking: prove $\eta < 50\%$ from $\tan\alpha < \mu$