Embedding loss in a bolted joint occurs due to the plastic deformation of asperities on the contact surfaces, leading to a reduction in bolt preload. This can happen during the tightening process or when the joint experiences an external load.
The formula to calculate the embedding loss is:
\[ \text{Embedding Loss (mm)} = \text{Number of Interfaces} \times \text{Surface Roughness (microns)} \times 0.001 \]
The preload loss can be calculated using the stiffness values:
\[ \text{Preload Loss (N)} = \text{Embedding Loss (mm)} \times \left( \frac{\text{Bolt Stiffness} \times \text{Joint Stiffness}}{\text{Bolt Stiffness} + \text{Joint Stiffness}} \right) \]
Consider a bolted joint with the following details:
Using the formula:
\[ \text{Embedding Loss} = 4 \times 5 \times 0.001 = 0.02 \text{ mm} \]
\[ \text{Preload Loss} = 0.02 \times \left( \frac{200 \times 300}{200 + 300} \right) = 0.02 \times 120 = 2.4 \text{ N} \]
This means the estimated preload loss due to embedding is 2.4 N.