A satellite component is in the shape of a cube with 10cm edges, has an evenly distributed mass of 2 kg and one bolt hole at each of four corners. If the maximum predicted random vibration environment is 10 Grms, what bolt size would be a good choice for restraint? What other factors might drive bolt size besides force/stress?

Explanation:

We have the following data:

Mass = 2 kg

R.V = 10 Grms

g = 9.8 m/s^2

edge of cube = 10 cm = 0.1 m

Assume that the force is divided between the four bolts, the restraint force will be:

Total Restraint Force = 196.2

Force on each bolt:

Assume the bolt material as metric class 4.6 with:

Proof strength = 225 MPa

Tensile strength = 400 MPa

Yield strength = 240 MPa

The load can be either horizontal or vertical, thus we check for tension and shear.

Tenison:

Assume that the load is on the bolts.

Maximum and Minimum bolt load is =

Stress:

(where stress concentration factor = 2.2)

Mean stress:

Stress amplitude:

Fatigue Strength:

The rotating beam fatigue strength is:

Assume machined thread, the surface condition factor will be:

Size factor:

Loading factor:

Temperature factor:

Reliability factor:

Fatigue strength for infinite cycles:

Using modified Goodman relation with assumed factor of safety:

Shear Failure:

Axial load of the bolt is 49.05 N.

Principal stress are:

We know,

Using endurance strength values:

The bolt is safe in shear.

We will need to check:

1. Natural frequency of supporting system

2. Range of excitation frequencies