Questions
5 MCQs per paper
Difficulty
Medium
Importance
High yield for HPCL/NTPC
Overview
Machine Design is a cornerstone subject for mechanical engineering PSUs, focusing on the sizing and selection of components under static and dynamic loading. Mastery of this topic requires balancing theoretical stress analysis with empirical design equations, which form the basis for most technical questions in competitive exams.
Design of Shafts and Keys
Shafts are primarily designed based on strength (stress) and rigidity (stiffness). In PSUs, questions often require applying the Maximum Shear Stress theory or Maximum Principal Stress theory for combined bending and torsion scenarios.
- ASME code equation: d^3 = 16/pi*sqrt((Kb*M)^2 + (Kt*T)^2)/tau_allowable
- Torsional rigidity: theta = TL/GJ
- Key design: shear and crushing failure are the primary modes
- For square keys, width = thickness = d/4
- Shaft subjected to pure torsion: T = pi/16 * tau * d^3
Bearings: Rolling and Sliding
Bearings are categorized into hydrodynamically lubricated sliding contact bearings and rolling contact (antifriction) bearings. Exam focus is heavily weighted toward the life expectancy of ball bearings and the Petroff's equation for sliding bearings.
- Bearing life relation: L10 = (C/P)^n where n=3 for ball, n=10/3 for roller
- Petroff's Equation: mu = 2*pi^2 * (mu*N/P) * (r/c)
- Sommerfeld number S = (mu*N/P) * (r/c)^2 * (L/D)
- Stribeck equation for friction
- Hydrodynamic lubrication requires wedge-shaped film and relative motion
Fatigue Design
Fatigue failure is critical for components under fluctuating loads. Understanding the Endurance Limit and the modification factors applied to it is a favorite area for PSU examiners.
- S-N curve describes the stress-life relationship
- Endurance limit Se = ka*kb*kc*kd*ke*kf*Se'
- Goodman criteria: 1/FoS = sigma_m/Sut + sigma_a/Se
- Soderberg criteria: 1/FoS = sigma_m/Syt + sigma_a/Se
- Gerber parabola: 1/FoS = sigma_m/Sut + (sigma_a/Se)^2
Springs and Couplings
Helical springs are analyzed as torsional members, while couplings are designed to transmit torque without shear failure of bolts or keys. Candidates must know the spring index and its effect on stress concentration.
- Spring index C = D/d
- Wahl's Factor K = (4C-1)/(4C-4) + 0.615/C
- Deflection delta = 8*P*D^3*n / (G*d^4)
- Stiffness k = G*d^4 / (8*D^3*n)
- Coupling bolt load: P = 2*T / (D*n)
Formula Sheet
d^3 = 16/pi*tau*sqrt(M^2 + T^2)
L10 = (C/P)^3
k = G*d^4/(8*D^3*n)
1/FoS = sigma_m/Sut + sigma_a/Se (Goodman)
1/FoS = sigma_m/Syt + sigma_a/Se (Soderberg)
S = (mu*N/P)*(r/c)^2
Exam Tip
Always memorize the difference between Soderberg (safe/conservative) and Goodman (closer to experimental data) lines, as this is a frequently tested conceptual differentiator.
Common Mistakes
- Confusing the exponent in bearing life (3 for ball, 3.33 for roller) during rapid calculations.
- Neglecting the stress concentration factor (Wahl's factor) when calculating spring shear stress.
- Using Soderberg instead of Goodman criteria for brittle vs ductile materials or vice versa.
More Revision Notes
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