6.2 Mechanical Components

6.2 Mechanical Components

1. Gears, Belts, Pulleys

Gears

1. Function: Transmit power and motion between shafts.

2. Types:

   • Spur Gears: Teeth parallel to axis, simplest, transmit power between parallel shafts.

   • Helical Gears: Teeth at helix angle, smoother/quieter than spur, can transmit between parallel/crossed shafts.

   • Bevel Gears: Conical shape, transmit between intersecting shafts (usually 90°).

   • Worm Gears: Screw-like worm meshes with gear, high reduction ratio, non-reversible.

   • Rack and Pinion: Converts rotary to linear motion.

3. Key Terms:

   • Module/Pitch: Size of teeth.

   • Gear Ratio: $GR = \frac{N_{driver}}{N_{driven}} = \frac{\omega_{driven}}{\omega_{driver}}$

   • Velocity Ratio: $VR = \frac{\omega_1}{\omega_2} = \frac{d_2}{d_1} = \frac{N_2}{N_1}$

Belts and Pulleys

1. Belt Types:

   • Flat Belts: Simple, for high-speed/low-power.

   • V-Belts: Wedge-shaped, higher friction, most common.

   • Timing/Synchronous Belts: Have teeth, prevent slippage, precise speed ratio.

   • Round Belts: Small power transmission.

2. Pulley/Sheave: Wheel that carries belt.

3. Advantages:

   • Absorb shock/vibration.

   • Allow large center distances.

   • Simple and inexpensive.

4. Speed Ratio: $\frac{N_1}{N_2} = \frac{d_2}{d_1}$ (ignoring slip).

2. Couplings and Bearings

Couplings

1. Function: Connect two shafts to transmit power.

2. Types:

   • Rigid Couplings: For aligned shafts (sleeve, flange).

   • Flexible Couplings: Accommodate misalignment (jaw, gear, disc, universal joint).

   • Fluid Couplings: Use hydraulic fluid for smooth start (torque converters).

3. Selection Factors: Torque, speed, misalignment, shock loads, space.

Bearings

1. Function: Support rotating shafts, reduce friction.

2. Types:

   • Rolling Contact Bearings:

     • Ball Bearings: Handle radial+axial loads, high-speed.

     • Roller Bearings: Higher load capacity (cylindrical, tapered, spherical).

   • Plain/Sleeve Bearings: Sliding contact, simpler, quieter.

   • Thrust Bearings: Designed for axial loads.

3. Bearing Life (L10): Life where 90% of bearings survive under given load.

4. Lubrication: Essential for reducing wear and cooling.

3. Bolts, Springs, Dampers

Bolts and Fasteners

1. Types: Bolts, screws, nuts, washers, rivets.

2. Thread Types: Metric/Unified, coarse/fine pitch.

3. Preload: Tension in bolt from tightening, critical for joint integrity.

4. Failure Modes: Tensile failure, shear failure, thread stripping, fatigue.

5. Torque-Tension Relationship: $T = K \cdot D \cdot F$ where K = torque coefficient.

Springs

1. Function: Store energy, absorb shock, maintain force.

2. Types:

   • Helical Compression: Most common, resist compression.

   • Helical Tension: Resist pulling force.

   • Torsion Springs: Resist twisting/rotational force.

   • Leaf Springs: Used in vehicle suspensions.

   • Belleville Washers: Disc springs for high load in small space.

3. Spring Rate/Stiffness (k): $k = \frac{F}{x}$ (force per deflection).

4. Spring Materials: Music wire, stainless steel, phosphor bronze.

Dampers (Shock Absorbers)

1. Function: Dissipate energy, control oscillations.

2. Types:

   • Viscous Dampers: Fluid forced through orifices.

   • Friction Dampers: Dry friction surfaces.

   • Magnetic Dampers: Eddy current damping.

3. Damping Coefficient (c): $F_{damping} = c \cdot v$ (linear viscous damping).

4. Brakes, Clutches, Shafts

Brakes

1. Function: Convert kinetic energy to heat, slow/stop motion.

2. Types:

   • Mechanical Brakes:

     • Disc Brakes: Pads clamp rotating disc.

     • Drum Brakes: Shoes press against rotating drum.

   • Hydraulic/Pneumatic Brakes: Use fluid/pressure for actuation.

   • Electromagnetic Brakes: Use magnetic force (eddy current, magnetic particle).

3. Braking Torque: $T = \mu \cdot F_n \cdot r$ where μ = friction coefficient.

Clutches

1. Function: Engage/disengage power transmission.

2. Types:

   • Friction Clutches: Most common (single/multi-plate, cone).

   • Electromagnetic Clutches: Engage via electromagnet.

   • Fluid Couplings: Hydraulic connection.

   • Centrifugal Clutches: Engage automatically at certain RPM.

3. Torque Capacity: $T = n \cdot \mu \cdot F \cdot r_m$ where n = number of friction surfaces.

Shafts

1. Function: Transmit torque and rotation.

2. Types:

   • Line Shafts: Transmit power long distances.

   • Counter Shafts/Jackshafts: Intermediate shafts.

   • Stub Shafts: Short shafts (e.g., motor output).

   • Flexible Shafts: Transmit power around corners.

3. Design Considerations:

   • Torque Transmission: $T = \frac{\pi}{16} \cdot \tau \cdot d^3$ for solid shaft.

   • Strength: Resist bending and torsional stresses.

   • Stiffness: Limit deflection under load.

   • Critical Speed: Avoid natural frequency resonance.

4. Keys and Keyways: Prevent relative rotation between shaft and hub.

5. Shaft Materials: Usually medium-carbon steel, heat-treated.