Design of Machine Elements – Comprehensive Bullet-Point Notes

Unit 1 – Introduction to Machine Design

• Definition: Use of scientific principles, technical info & imagination to design machines for specific functions with max economy & efficiency.
• Knowledge required: $\text{Maths}$, physics, statics & dynamics, thermodynamics, heat transfer, vibrations, fluid dynamics, materials & standard components (from PSG, CMTI, Westermann).

Phases of Machine Design

1. Need recognition ⇢ problem statement.

2. Data/specification collection (dimensions, capacity, operating parameters, standards).

3. Feasibility study (technical + economical).

4. Mechanism selection.

5. Force analysis.

6. Material selection (performance, life, reliability, cost).

7. Component dimensioning (loads, stresses, failure theories, $\text{F.S.}$).

8. Production drawings (views, dimensions, tolerances, finish, HT).

9. Prototype & testing.

10. Final product & feedback loop.

Aesthetic Design

• Appearance reflects function, quality, cost & environment.
• Guidelines: aerodynamic usefulness, reflect speed/strength, economical material use, harmony with environment.
• 12 aspects: Form, Symmetry, Colour (Morgan code), Continuity, Variety, Proportion, Contrast, Impression, Style, Material/Finish, Tolerance, Noise.

Ergonomics

• Man–machine–environment study aiming to fit machine to user.
• Areas: Communication (displays & controls), Working env., Anatomy/posture, Energy expenditure.

Displays

• Qualitative vs quantitative; circular, straight, coloured, digital.
• Design tips: clear scale, $\text{Height} \ge \dfrac{\text{distance}}{200}$, linear divisions, numbering direction, pointer knife-edge w/mirror, control below/right.

Controls

• Types: handwheels, cranks, knobs, push-buttons, toggles, joysticks, foot pedals.
• Ergo rules: accessible, minimal motion, shape matches anatomy, colour coding (red danger etc.).

Loads & Stresses

• Loads: Static (gradual, constant), Dynamic (magnitude/direction varies).
• Stresses: $\sigma<em>t,\sigma</em>c, \tau$ plus crushing $\sigma<em>{cr}$ and bearing $\sigma</em>b$.
• Eccentric loading introduces bending + direct.

Stress–Strain Diagram (ductile)

• Proportional limit $A$, elastic limit $B$, upper/lower yield $C,D$, ultimate $E$, breaking $F$, proof stress (0.2% offset).

Fatigue & Endurance

• Cyclic/reversed stresses lead to failure below yield.
• Endurance limit $\sigma_e$: max reversed stress for infinite life (S-N curve).

Failure Theories (ductile vs brittle)

• Max principal stress, max shear stress (Tresca), distortion energy (von Mises).
• ASME factors: $k<em>m,k</em>t$ for shock & fatigue.

Factor of Safety

$\text{F.S.}=\dfrac{\sigma<em>{\text{max}}}{\sigma</em>{\text{working}}}$.
Consider reliability of material, loads, consequences of failure etc.

Stress Concentration

• Caused by abrupt section change, holes, keyways, threads.
• Factor $K<em>t=\sigma</em>{max}/\sigma_{nom}$.
• Remedies: fillets, relief holes, under-cut threads, notches.

Unit 2 – Design of Joints & Offset Links

Direct Stress Components

• Pure tension/compression $\sigma=P/A$.
• Combined bending $\sigma_b=M/Z$.

C-Clamp Design (combined tension + bending)

$\sigma_{total}=\dfrac{P}{bt}+\dfrac{6Pe}{b^2t}$.
Solve for thickness $t$ (b=2t). Example gives $t\approx40\,\text{mm}$.

Offset Link

Similar; eccentricity $e=b/2$, $b=3t$.

Cotter Joint (Socket & Spigot)

• Parameters: $d,d<em>1,d</em>2,d<em>3,d</em>4,t,l,c,a$.
• Check modes: rod tension $Pd/4=\sigma<em>t$; spigot tearing, cotter shear $P=2bt\tau$, crushing $P=bd\sigma</em>c$, socket failure, collars etc.
• Empirical: $t\approx0.25d_2,\;l\approx4d$.

Knuckle Joint

• Parts: eye, fork, pin.
• Proportions: $d<em>1=d,\;d</em>2=2d,\;b=1.25d,\;t_1=0.75d$.
• Check rod tension, pin double shear, crushing at eye/fork.

Turn-Buckle

Opposite threads for tensioning rods.
Design for combined shear/tension in rods; nut shear length $l=\dfrac{P}{\pi d_c \tau}$, diameters via bearing & shear.

Lever Design

• Safety-valve lever: forces via moments about fulcrum; size pins (double shear + bearing $P=dp\,l\,p_b$); lever cross-section rectangular $b!\approx3t$; bending $\sigma=M/Z$.
• Bell-crank lever ((90^\circ)): resolve loads, reaction at fulcrum, design three pins & arms.

Unit 3 – Shafts & Couplings

Shafts

• Solid vs hollow.
• Torsion $T=\dfrac{\pi}{16}\tau d^3$ (solid) ; $T=\dfrac{\pi}{16}\tau (d<em>o^4-d</em>i^4)/d<em>o$ (hollow). • Bending $M=\dfrac{\pi}{32}\sigma</em>b d^3$.
• Combined: $\tau<em>{max}=\sqrt{(\tau)^2+(\sigma</em>b/2)^2}$; ASME eq. $T<em>e=\sqrt{(k</em>tT)^2+(k_mM)^2}$.

Rigidity

$\theta=\dfrac{TL}{JG}\le \theta_{allow}$.

Design Examples

Detailed worked problems: power, overhang pulleys, line shafts etc.

Keys

Rectangular: $w=0.25d,\;t=0.167d$.
Shear $P=wtl\tau$, crushing $P=\dfrac{t}{2}wl\sigma<em>c$. For equal strength $\sigma</em>c=2\tau$.

Couplings

Muff (sleeve): $D=2d+15,\;L=3.5d$.

Check sleeve shear $T=\tau_m\dfrac{\pi}{2}(D^2-d^2)L$.

Flange: hub $D=2d,\;L=1.5d$; bolts on pitch $D_1\approx3d$.

Equate $T=\sum n P<em>b D</em>1/2$ with bolt shear/bearing.

Flexible (bushed-pin): bush bearing $W=\dfrac{P}{n} = p<em>b l d</em>2$; pin bending cantilever; combine $\sigma,\tau$.

Unit 4 – Fasteners

Eccentric Bolted Brackets

• Direct shear $W<em>s=W/n$. • Moment about tilting edge: $\sum W</em>i L<em>i = W L$ ⇒ load distribution $W</em>i=w L<em>i$. • Max bolt load $W</em>{max}=W<em>s+w L</em>{max}$.
• Check tension $\sigma=W/A<em>c$ & combined $P</em>e=\sqrt{W<em>t^2+W</em>s^2}$.

Welded Joints

• Fillet weld throat $t=0.707s$.
• Strength – single transverse $P=0.707 s l \sigma_t$; double parallel $P=1.41 s l \tau$; combined.

Unit 5 – Power Screws

Thread Forms

Square, Acme, Buttress (one-way thrust).
Helix angle $\alpha = \tan^{-1}\dfrac{p}{\pi d_m}$.

Torque to Raise Load

$P=\dfrac{W( \tan\alpha+\mu)}{1-\mu\tan\alpha}$ ; $T=P\dfrac{d<em>m}{2}+\mu</em>1WR$ (collar).
Lowering: denominator $1+\mu\tan\alpha$.

Efficiency $\eta=\dfrac{\tan\alpha}{\tan\alpha+\mu}$.

Self-locking when \mu>\tan\alpha.

Stresses

Axial $\sigma=W/A<em>c$ ; torsional $\tau=16T/\pi d</em>c^3$ ; max shear $\tau<em>{max}=\sqrt{\tau^2+(\sigma/2)^2}$; shear of threads $W/(\pi d</em>c n t)$ ; bearing $W/(\pi d_m n t)$.

Screw Jack Design

Steps: core dia from compression; choose standard $p$; compute $T,\;P<em>{handle}=T/L</em>h$; check $\tau,\sigma$; nut height $n\ge \dfrac{C<em>0 W}{\pi d</em>c t p_b}$; collar; body dimensions.

Unit 6 – Springs

Helical Compression Spring (circular wire)

• Mean dia $D$, wire $d$, index $C=D/d$.
• Wahl factor $K=\dfrac{4C-1}{4C-4}+\dfrac{0.615}{C}$.
• Shear $\tau=K\dfrac{8WD}{\pi d^3}$.
• Deflection $\delta=\dfrac{8WD^3 n}{G d^4}$.
• Rate $k=W/\delta=\dfrac{G d^4}{8 D^3 n}$.

Leaf (Semi-elliptic)

• Bending $\sigma=\dfrac{6WL}{n b t^2}$; deflection $\delta=\dfrac{3WL^3}{8 E n b t^3}$.
• Initial nip $C=\delta<em>G-\delta</em>F$ ; leaf lengths progression $l_i=L-\tfrac{i-1}{n-1}(L-l)$.

Unit 7 – Rolling Bearings

Types

• Ball: deep groove, angular contact, double row, self-aligning, thrust.
• Roller: cylindrical, spherical, needle, tapered.

Basic Numbering (ISO)

XYZ..
– Last two digits ×5 → bore $d$ (00=10 mm, 01=12 mm, 02=15 mm, 03=17 mm).
– Third digit = diameter series; prefix digit/letters = type (6 = deep-groove etc.).
Suffix letters: sealing (ZZ, 2RS), clearance (C3), etc.

Ratings

• Static $C<em>0$: load giving $0.0001d$ permanent deformation. Safety $s</em>0=C<em>0/P</em>0$.
• Dynamic $C$: gives life $L<em>{10}=\left(\dfrac{C}{P}\right)^p!10^6$ rev (p = 3 balls, 10/3 rollers). Hours $L</em>{10h}=\dfrac{L_{10}}{60n}$.

Equivalent Loads

$P=X F<em>r+Y F</em>a$ (tables for factors).
Select bearing with $C\ge P L_{10}^{1/p}$.

Mounting

Cold press for d<80 mm; thermal induction heater to $120\,^{\circ}!\text C$; never hammer via balls.

Failure Causes

Poor lubrication, mis-alignment, overload, contamination, vibration Brinelling, high temperature, material defects.

Mounting Do’s/Don’ts

Use fitting sleeves, clean, protect from dust, apply uniform force, heat inner ring only, avoid current passage etc.