Design of Keys and Splines

Why it matters

Keys and splines are essential components in mechanical systems, used to connect rotating elements such as gears, pulleys, and couplings to shafts. They ensure the transmission of torque and motion, which is crucial for the efficient functioning of machinery. Understanding their design helps in preventing mechanical failures and optimizing performance.

Key ideas

• Keys: These are machine elements used to connect a rotating machine element to a shaft. They prevent relative rotation and may enable torque transmission.
  • Types of Keys: Sunk keys, saddle keys, tangent keys, and round keys.
  • Sunk Keys: Most common type, fitted into keyways in both the shaft and the hub.
• Splines: These are multiple keys formed integrally with the shaft, transmitting torque through multiple teeth; axial sliding is possible only when the fit and assembly are designed for it.
  • Types of Splines: Straight splines, involute splines.
• Design Considerations: Material selection, key dimensions, stress concentration, and manufacturing tolerances.

Formulas

• Torque transmitted by a key: T = F·r where:
  • T = Torque (N·m)
  • F = Force acting on the key (N)
  • r = Radius of the shaft (m)
• Shear stress in the key: τ = F / (b·L) where:
  • τ = Shear stress (Pa)
  • F = Force acting on the key (N)
  • b = Width of the key (m)
  • L = Length of the key (m)
• Crushing stress in the key: σ_c = F / ((t/2)·L) where:
  • σ_c = Crushing stress (Pa)
  • t = Thickness of the key (m)

Worked example

Given: A shaft of diameter 50 mm transmits 200 N·m of torque using a rectangular sunk key of width 10 mm, total thickness 10 mm and effective length 50 mm. Assume half the thickness bears in the hub and half in the shaft, with uniform load distribution. Determine the shear and crushing stresses in the key.

1. Calculate the force acting on the key: T = F·r F = T / r r = d / 2 = 50 mm / 2 = 0.025 m F = 200 N·m / 0.025 m = 8000 N

2. Calculate the shear stress in the key: τ = F / (b·L) τ = 8000 N / (0.01 m · 0.05 m) = 16000000 Pa = 16 MPa

3. Calculate the crushing stress in the key: σ_c = F / ((t/2)·L) σ_c = 8000 N / (0.005 m · 0.05 m) = 32000000 Pa = 32 MPa

Final Answer: Shear stress = 16 MPa, Crushing stress = 32 MPa

For unequal embedment depths, replace t/2 with the actual projected bearing height. For splines do not assume all teeth share load perfectly; use the specified effective tooth participation and contact dimensions.

Common mistakes

• Confusing the dimensions of the key (width, thickness, length) leading to incorrect stress calculations.
• Ignoring the effects of stress concentration at the keyway corners.
• Using incorrect units or failing to convert units properly.

For GATE ME

Questions typically involve calculating the stresses in keys and splines, determining the appropriate dimensions for a given load, and understanding the failure modes. Practice problems involving torque transmission and stress analysis.

Quick check

1. What is the primary function of a key in a mechanical system?
2. How does a spline differ from a key?
3. What are the two main types of stresses considered in key design?

Answers: 1. To connect rotating elements to a shaft and transmit torque. 2. A spline uses multiple integral teeth, while a separate key is a single element; axial movement depends on the fit. 3. Shear stress and crushing stress.