Introduction
Bolts are commonplace in various mechanical applications. If a system is designed for use in a cryogenic environment, additional measures need to be provided to maintain the pre-load applied by a bolt during cooldown.
Example
Aluminum is often used for the manufacturing of custom components, as it has a good stiffness to density ratio, good thermal conductivity properties, and is easy to machine. In many constructions, aluminum parts are connected using stainless steel bolts. The relative dimensional change of aluminum during a cooldown is much larger than that of stainless steel. During the cooldown, pre-load in the bolt can therefore be lost, as aluminum shrinks at a higher rate than stainless steel.
Structural design
Thermal shrinkage in bolted connections can also happen for different combinations of materials. The following method can be applied to compensate for this effect: A spacer is introduced, as illustrated below. The material and the length of the spacer are chosen such that the average relative dimensional change of the spacer and the clamped part matches that of the bolt at the target temperature.
Relative dimensional change
In the example of aluminum parts clamped together with stainless steel bolts, a titanium spacer is designed. The relative dimensional change of these materials is shown in the first graph. The target temperature is set at 77 K. The values from the graph at this temperature are summarized in the table. To ensure that there is no difference in dimensional change at the target temperature, the following must hold:
$$\frac{L_C\cdot r_C+L_S\cdot r_S}{L_C+L_S}=r_B$$
$$L_S=L_C\frac{r_B-r_C}{r_S-r_B}$$
| Material | Symbol | Value | Unit |
|---|---|---|---|
| Alu-6061 | $r_C$ | -3.89e-3 | [-] |
| S-304 | $r_B$ | -2.80e-3 | [-] |
| Ti-6Al-4V | $r_S$ | -1.62e-3 | [-] |
Verification of the design
Based on the parameters listed in the table, a ratio $L_C: L_S$ of 1:0.93 is obtained. To verify this design, it needs to be ensured that enough pre-load is maintained in the bolted connection during cooldown. The graph below shows the percentual deviation of the average relative dimensional change of the spacer and the clamped part with respect to the bolt. The deviation is 0% at the target temperature of 77 K. While cooling down, the clamped part and the spacer together shrink at a slightly faster rate than the bolt. This means some pre-load is lost. The loss in pre-load is no more than 3% during cooldown. Note that if the construction is cooled below 77 K, the bolt will shrink at a higher rate than the clamped part and the spacer. This means that the pre-load is increased. To ensure that the construction can withstand these temperatures, it must be verified that the bolt does not break due to the increase of stress.
