Machine Design
Comprehensive guide to the principles and practices of designing mechanical components and systems.
Shaft Design
Shafts are rotating machine elements, usually circular in cross-section, used to transmit power and rotational motion. The design of a shaft is based on strength, rigidity, and critical speed:
d³ = (16/πτₐₗₗ) × √(M² + T²)
Where:
- d = shaft diameter (m)
- τₐₗₗ = allowable shear stress (Pa)
- M = maximum bending moment (N·m)
- T = maximum torque (N·m)
Gear Design
Gears are used to transmit motion and power between rotating shafts. Key parameters in gear design include:
Gear Ratio = N₂/N₁ = D₂/D₁
Module = D/N
Where:
- N₁, N₂ = number of teeth on driving and driven gears
- D₁, D₂ = pitch diameters of driving and driven gears (m)
- Module = ratio of the pitch diameter to the number of teeth (m)
The Lewis equation is commonly used for calculating the bending stress in gear teeth:
σ = F/(b × m × Y)
Where:
- σ = bending stress (Pa)
- F = tangential force (N)
- b = face width (m)
- m = module (m)
- Y = Lewis form factor (dimensionless)
Bearing Selection
Bearings are used to support rotating shafts and reduce friction. The basic rating life of a bearing is given by:
L₁₀ = (C/P)ᵏ × 10⁶ / (60 × n)
Where:
- L₁₀ = basic rating life (hours)
- C = dynamic load capacity (N)
- P = equivalent dynamic bearing load (N)
- k = exponent (3 for ball bearings, 10/3 for roller bearings)
- n = rotational speed (rpm)
The equivalent dynamic bearing load is calculated as:
P = X × F_r + Y × F_a
Where:
- F_r = radial load (N)
- F_a = axial load (N)
- X = radial load factor
- Y = axial load factor